M Bianchini

N Brisset

F Fauth

F Weill

E Suard

L Croguennec

C Masquelier

Li-Rich Li

E Elkaim

J.-M Ateba Mba

P Dagault

E Bogdan

D Carlier

Spinel Electrode Materials: An Operando Neutron Diffraction Study during

Li-ion batteries are the devices that allowed the "wireless revolution". In the last 30 years they brought smartphones in our pockets and laptops in our backpacks by experiencing an amazing improvement in performances. However much work still needs to be done to make this technology competitive for other applications, such as automotive and energy storage for the grid. Other next-generation battery systems are also being developed, as the Na-ion one, a technology analogous to Li-ion but based on a cheaper and more abundant element. The heart of Li-and Na-ion batteries is constituted by the electrodes, materials able to exchange Li + /Na + cations. Their development depends on the discovery of new electrode materials and on a better understanding of the existing ones. This last point in particular is of key importance as it unlocks the full exploitation of an electrode material's capabilities, i.e. obtaining the full theoretical energy density, at sufficiently fast cycling rate and with a long cycle life.

A real comprehension of electrode materials requires a combination of different characterization techniques. Moreover, to understand how they function inside a battery they must be studied in situ, or, going a step further, operando: that is, the material needs to be studied as the battery functions too. Charge and discharge are in fact processes that can induce profound transformations in the electrodes, since Li + /Na + is extracted and inserted and transition metals are oxidized and reduced. Such transformations often happen out of the equilibrium, in dynamical conditions, this being the reason for the necessity of operando studies. In this thesis we mainly make use of diffraction techniques to unravel the crystallographic transformations occurring in electrode materials as they are lithiated and delithiated (or sodiated and desodiated) inside Li-ion and Na-ion batteries. To obtain comprehensive information we combine several probes, sensitive to different atoms in the materials. Neutrons were used extensively because of their peculiar scattering characteristics; this leads to different advantages, the most important of which is that they can shed light on light elements as lithium and oxygen. X-Rays are also much employed as they are cheaper and easier to have at hand, while giving anyway a whole lot of valuable information, for example about transition metals and unit cell parameters. Finally, synchrotron radiation is used in focused studies where high angular, intensity and time resolution are required.

For each one of these probes, we managed to carry out ex situ, in situ and operando studies. To do so, beside electrochemical cells for in situ studies using X-Rays and synchrotron radiation that were available in our group, a new cell for in situ studies using neutrons was developed. Manufactured with a "neutron-transparent" (Ti,Zr) alloy, and coupled with the use of deuterated electrolytes, the cell combines good electrochemical performances with the ability to obtain neutron powder diffraction patterns of great quality to succeed in Rietveld structural refinements. Thus the whole range of diffraction techniques in real time could be applied. This is a great added value of our approach, as we are able to observe new features revealed upon cycling by several different electrode materials for Li-and Na-ion batteries.

The analyzed families of materials range through spinels (Li 1+x Mn 2-x O 4 (x = 0, 0.05, 0.10) and LiNi 0.4 Mn 1.6 O 4 ), olivines (LiFePO 4 ), tavorites (LiVPO 4 O) and fluorophosphates for Na-ion batteries (Na 3 V 2 (PO 4 ) 2 F 3 ). Among the salient facts that we reported, we mention the phase diagram upon cycling of Li 1+x Mn 2-x O 4 , strongly impacted by the presence of the extra lithium in the site of Mn, and the fact that thanks to neutrons we could follow lithium's behavior inside the spinel framework. Sensitive information could be recovered, as site occupancy factors and thermal displacement parameters, giving valuable insight on the long and short range behavior of the atoms in the material (of which LiNi 0.4 Mn 1.6 O 4 is a meaningful example). On the other hand, thanks to synchrotron radiation we were able to answer the tricky question about the nature of Li 0.5 Mn 2 O 4 , a long-debated composition found halfway through charge of LiMn 2 O 4 and that we showed to possess a combined transition metal charge ordering and lithium/vacancy ordering. LiVPO 4 O was instead mainly studied with X-Rays, with only complementary help from neutrons and synchrotron radiation. We revealed the impact of particles' size on the material's electrochemical behavior, as well as its phase diagram built by several phase transitions and intermediate phases of previously unknown structure. We were in fact able to describe for the first time the lithiated phases in Li x VPO 4 O (x = 1.5, 1.75, 2). Finally Na 3 V 2 (PO 4 ) 2 F 3 , an extremely promising material for the Na-ion technology, was revisited concerning its crystal structure and phase diagram: thanks to synchrotron radiation it was indexed in the new orthorhombic space group Amam and, with the contribution of neutron diffraction, it was assigned an improved crystal structure with redefined position of sodium ions. This allowed a detailed operando study of Na + extraction until composition NaV 2 (PO 4 ) 2 F 3 , a process rich in several phase transitions induced by sodium and transition metal orderings, that we were able to evidence for the first time. This thesis is therefore an effort to adopt a com-prehensive approach to the use of diffraction techniques, ex situ, in situ and operando, to unravel the crystal structure modifications occurring in electrode materials for Li-ion and Na-ion batteries upon cycling. The obtained insights reveal the interconnections between crystal structures and electrochemical performances in electrode materials, this having key importance to understand and improve them for the next generation of batteries.

Chapter 1

Introductory concepts and methods

Background and context

The world's population and energy consumption are steadily increasing. We are an estimated 7.2 billion people, which consumed 104407 TWh of energy in 2012 [START_REF] Michael | Efficient hybrid solar cells based on meso-superstructured organometal halide perovskites[END_REF] . This is nearly twice the consumption of 1973 (54326 TWh), when there were almost 4 billion people. It is clear that a society with such a steady and rapid growth should worry about being energy self-sufficient, i.e. it should be able to produce enough electricity to sustain itself without depleting finite resources. However this is not the case. Figure 1.1 shows the world's electricity generation and it is clear that, although increasing, 22668 TWh is quite far from the amount of energy we consume. The biggest difference between the two consists in the oil depleted every year. In 2012 oil still represented more than 40% of the world's energy consumption, clearly showing how our society is heavily dependent on it. However oil is a non-renewable resource, as is coal (still widely used in thermoelectric plants), and at some point (most probably in the next century) they will not suffice anymore. Not to mention the well-known issues of huge CO 2 production and consequent earth-warming and climate changes that oil and coal carry with them. For this reason research has been trying to provide alternatives that are as renewable and "green" as possible. Hydroelectric energy production is one such alternative, exploited for a long time but whose contribution is not likely to increase. Nuclear production is another possible choice but it is not renewable, it [START_REF] Michael | Efficient hybrid solar cells based on meso-superstructured organometal halide perovskites[END_REF] Data taken from the 2014 Key World Energy Statistics published by the IEA (International Energy Agency). creates hardly-disposable nuclear wastes and it is badly perceived by the population after the incidents of Chernobyl and, more recently, Fukushima. We have reached a point where it is common knowledge that truly renewable sources such as wind and solar energy must be the answer to these issues. Photovoltaics, in particular, is experiencing a new era since the introduction of perovskite-based solar cells, reaching efficiencies already exceeding 20%, a remarkable result for such a young technology [START_REF] Michael | Efficient hybrid solar cells based on meso-superstructured organometal halide perovskites[END_REF]2] . However, in 2012 only 5% of the energy produced worldwide came from these sources (actually including also geothermal energy).

The biggest limitation to solar and wind energy production is their unsteady nature, meaning that it is highly dependent on the atmospheric conditions and the moment of the day (Figure 1.2). Reprinted from [3] .

For this reason a reliable energy storage device is required to complement these systems.

Such a device must be able to accumulate energy during peak production hours and to 2 release it when required (at night for example). Being the most advanced electrochemical system available on the market, the Li-ion battery is believed to be the ideal solution to provide these storage capabilities. This battery technology is commercially available since the early 90s, when it started powering the "wireless revolution". By 2002, cell phones, and with them, Li-ion, were everywhere. Thanks to their unprecedented energy and power density (about twice of NiCd and 30% more than NiMH), they allowed electronic devices to be carried around without the need for spare replacement batteries. Besides they have a long cycle life (> 1000 cycles) enabling them to last for years and to dominate the battery market with millions of cells sold every year (Figure 1.3). In 2002 The Economist anointed lithium-ion batteries the "foot-soldiers of the digital revolution". For these reasons the Figure 1.3: Li-ion batteries sold from 2000 to 2015. Reprinted from [START_REF] Scrosati | Lithium batteries: Status, prospects and future[END_REF] . applications of Li-ion batteries, initially limited to portable electronics, are now spreading to two major fields: grid-storage and electric vehicles. The former would mean a significant increase in the use of wind and solar power generation, not only at the industrial scale but mostly at the individual one. An important step in this direction was made in 2015 by Tesla Motors, who started commercializing the Tesla Powerwall, a Li-ion-based device to be installed at home (possibly coupled to photovoltaic panels) to turn positive its energy balance (i.e. to sell energy to the grid instead of consuming it). The latter instead has been considered by carmakers since 1990, when General Motors introduced the first allelectric car, the EV1 "impact". However at this time political and economical issues 2 contributed to the failure of the first electric vehicle (technologically immature to rival with traditional cars). Increased awareness of the environmental impact of CO 2 emissions and the ever-increasing price of oil renewed and boosted the interest in electric cars. Real answers were given by Toyota which commercialized the first hybrid vehicles (the Prius, which sold more than 3 million units by 2013). With some delay all carmakers joined the run for better and more performing electric cars, and nowadays they all offer at least one of such vehicles (hybrids, plug-in hybrids or fully-electric). The Nissan Leaf and the Tesla Model S, in particular, are in 2015 the two world's highest selling all-electric vehicles of all times (180000 and 75000 units, respectively). The road to a society dependent on renewable sources only is quite long, but the first important steps have been made and Li-ion batteries (or similar more evolved battery technologies) are going to play a primary role in this evolution. A battery is a device able to convert chemical into electrical energy. It is made by one or more electrochemical cells, which are its fundamental building units. Each of these cells (shown in Figure 1.4) functions exploiting a reduction/oxidation reaction (named "redox") occurring between two main parts called electrodes. Namely, an electron exchange is made at a given potential in each electrode, normally paired with an ion exchange. The third main component of the electrochemical cell is an ionic conductor called electrolyte (usually but not always a liquid). This is in contact with the electrodes, allowing ionic conduction but preventing direct electron exchange. Electrons in fact must flow through an external circuit, so that the electrical energy can be extracted. Figure 1.4 shows a scheme of a generic electrochemical cell. The electromotive force of the cell V cell (defined at open circuit as V cathode -V anode ) is governed by the redox reactions involved in the electrodes and it is connected to the thermodynamic difference in Gibbs free energy (J) of the electrodes as:

What is a battery?

∆G 0 = ∆x • F • V cell (1.1)
where F is Faraday's constant (96485 C/mole or 26801 mAh/mole) and ∆x is the stoichiometric number of moles of electrons liberated in the reaction. Essentially, the free energy variation during discharge of a battery is given by the work done by the flow of ∆xF electron charges at the potential V cell .

Development of primary batteries

An important distinction should be made when discussing batteries: most of them are built in the charged state and they can provide a single discharge, mainly because the electrodes or the electrolyte are consumed by the reaction. These are called primary batteries.

Rechargeable batteries, on the other hand, are called secondary batteries and, obviously, can provide several charge/discharge cycles. The first working (primary) battery continuously powering a circuit was built in 1799 by Alessandro Volta, who invented an electrochemical cell constituted by copper and zinc metals at the electrodes, and brine as the electrolyte. It exploited the oxidation of zinc (Zn → Zn 2+ + 2e -) and the reduction of brine (2H

3 O + + 2e -→ H 2 + 2H 2 O
), to give a potential of 0.76 V, corresponding to the zinc redox potential vs. the standard hydrogen electrode (SHE). Volta's invention built on Luigi Galvani's 1780s discovery of how a circuit of two metals and a frog's leg can cause the frog's leg to respond. For this reason electrochemical cells are also called galvanic cells, while the first battery made by Volta is called voltaic pile. These discoveries opened the way to the invention of several battery systems. The first was an improved version of voltaic pile, called Daniell pile. It still used zinc and copper, but soaked in acid electrolyte solutions of ZnSO 4 and CuSO 4 . This way the same oxidation reaction happens, while copper becomes the reduced element (Cu 2+ + 2e -→ Cu). The potential of the pile is now the difference of the two redox potentials, i.e. 0.76 V -(-0.34 V) = 1.10 V. In 1866 Georges Leclanché invented the zinc-carbon battery, an example of dry cell (in the sense that the electrolyte is a paste and not a liquid), an evolution that made batteries more practical and safe. It works on the redox reactions of zinc and manganese oxide MnO 2 , providing 1.5 V, the same potential used also in the alkaline battery. This is an invention by Waldemar Jungner in 1899, and, working independently, Thomas Edison in 1901. These battery systems spread and powered electrical devices throughout the whole 20th century. Lithium-based primary batteries are also available; different chemistries exist for the positive electrode, but they all have in common the use of metallic lithium for the negative one. The most commonly found electrodes are MnO 2 -Li, working at a nominal voltage of 3 V, twice that of alkaline batteries, and having a capacity of 280 Wh/kg.

Secondary (rechargeable) batteries

In 1859 Gaston Planté invented the lead-acid battery, a first example of rechargeable battery of extreme importance and still widely used nowadays (notably in the starter for cars). It exploits the overall reaction Pb + PbO 2 + 2H 2 SO 4 ↔ 2PbSO 4 + 2H 2 O (from left to right upon discharge, and vice versa upon charge). Other important rechargeable systems are nickel-cadmium batteries (NiCd, 1898), recently replaced by nickel-metal hydride ones (NiMH, 1967, available for the consumer market since 1989). But the real revolution in rechargeable batteries was made by another technology which saw the light in the same years, the Li-ion battery.

Li-ion batteries

Li-ion batteries are nowadays the most advanced and diffused rechargeable batteries available. The first example of such batteries was introduced by S. Whittingham in the mid '70s [6] . It was based on the idea of Li + cations shuttling through the electrodes, constituted by metallic lithium and TiS 2 (an insertion compound). The term "intercalation" is also very used in the literature; it implies a special case where "insertion" occurs into a host matrix retaining its structural integrity during the intercalation process. These batteries were announced to be commercialized by Exxon. However, the use of metallic and a graphite negative electrode. Reprinted from [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF] .

lithium for a secondary battery posed several safety issues upon reiterate cycles. It can in fact create dendrites growing on lithium's surface and possibly penetrating the separator and short-circuiting the cell, posing a serious hazard. The commercialization of safe

Li-based batteries had to wait for another technology, the Li-ion battery. This was made possible by the work of Mizushima et al. [7] and it was successfully developed by SONY R .

John B. Goodenough, with Yoshio Nishi, Rachid Yazami and Akira Yoshino received the 2014 Charles Stark Draper Prize for being the rechargeable battery pioneers who laid the groundwork for today's lithium ion battery.

A simplified scheme of the battery is shown in Figure 1.5. This technology eliminates the dangerous lithium metal while still exploiting Li + ions which are present in the positive electrode material and as a salt in the electrolyte. In fact, intercalation materials are used in both electrodes: LiCoO 2 at the positive and graphite or amorphous carbon at the negative. Both have layered structures, allowing to accommodate lithium between sheets of CoO 6 octahedra or graphite, respectively. The two are separated by a porous medium called separator, soaked in an electrolyte containing Li salt (usually LiPF 6 ) in organic solvents (ethylene carbonate, dimethyl carbonate and/or propylene carbonate).

The reactions involved are the following: Upon charge:

Cathode : LiCo III O 2 → Co IV O 2 + Li + + e - (1.2)
Anode : 6C + Li + + e -→ LiC 6 (1.3)

It is thus clear that two parallel reactions take place: in the cathode, lithium deintercalation and cobalt oxidation; in the anode, lithium intercalation and carbon reduction. Li + cations travel from LiCoO 2 through the electrolyte in the separator until they reach the carbon sheets. As the electrolyte is a poor electronic conductor, electrons flow outside the cell, through a wire closing the circuit. The reactions described above are not spontaneous; they require a power supply to be carried out and thus to store energy in the battery.

Once it is fully charged, i.e. when all lithium "travelled" from the positive to the negative electrode, the battery is ready to be used. The arrows in equation 1.2 and 1.3 are reversed upon discharge, as are the involved reactions. Power is now generated from the battery, supplying a spontaneous electrons flow to the external load.

Battery conventions and definitions

Note that in the previous section the terms cathode and anode were used. This might be confusing since a rechargeable battery is both an active (during discharge) and passive (during charge) electric component. In the battery community, a convention is to use the term cathode for the positive electrode and anode for the negative one. The convention was thus chosen to match the case of Li-ion battery discharge, as the cathode is usually defined as the electrode where a positive current departs or a negative one enters. The the Co 4+ /Co 3+ redox couple for LixCoO2, and the Co 3+ /Co 2+ redox couple for LixCoPO4. Reprinted from [START_REF] Goodenough | Challenges for Rechargeable Li Batteries[END_REF] .

relationship between Gibbs free energy and external voltage of a battery has been already described (equation 1.1). It can be well-visualized in Figure 1. 6, where the relative position in energy of the electrons density of states (DOS) determines the potential of the cell.

Another key quantity to evaluate battery performance is the theoretical capacity C th . This is the amount of electric charge that can be delivered by the electrode material, per unit of mass. It is then defined as:

C th = ∆x • F M w (1.4)
where M w represents the molecular weight of the material. Faraday's constant value is 96485 C/mole, but in the battery community it is more common to discuss capacity in terms of milliAmpere-hour/g; for this the value of F = 26801 mAh/mole is often used, where the difference is a factor 1000/3600. Once the potential V cell and the capacity C th of an electrochemical cell are known, the gravimetric energy density can be simply calculated as:

Energy[W h/kg] = C th • V cell (1.5)
Or, introducing the density ρ [kg/l], the volumetric energy density as:

Energy[W h/l] = C th • V cell • ρ (1.6)
The quantities described above do not depend on the charging rate of the battery, i.e.

they do not account for the time required for electrons to be delivered. However charging/discharging rate capabilities are extremely important factors in evaluating batteries' performance. In a classic galvanostatic experiment, a fixed current I is imposed to the battery for the time t required to complete a charge or discharge. A convention is used for the current rate: the charge/discharge is said to happen at C/n rate when 1 mole of e -(and of Li + ions) is exchanged in n hours. C/2 will then be charge/discharge in 2 hours, while 2C in 30 minutes. The cycling rate relates to the available capacity to give the current I following:

I = C th [mAh/g] • mass[g] n[hours] (1.7)
I is then the current delivered through an electrode of mass m during a galvanostatic experiment carried out at C/n rate. Another common way to charge or discharge a battery is a potentiostatic experiment, where instead of providing a fixed current I and recording the evolution of the voltage V cell , the contrary is done. Galvanostatic Intermittent Titration Technique (GITT) is another widely used protocol: it consists at alternating galvanostatic current steps with relaxation times of fixed length (imposing a condition on the duration of the relaxation time or on the value of dV/dt). The technique is useful because it allows to determine the equilibrium potential relaxed after every charging step and the shape of the relaxation curve can also give information on lithium's diffusion. Finally, the fixed-voltage counterpart of GITT is called PITT (Potentiostatic Intermittent Titration Technique) and it works analogously.

Positive electrode materials

In a Li-ion battery the positive electrode is not simply constituted by the electrochemically active material (AM), as for example LiCoO 2 . In most cases the electrode's electronic conductivity needs to be improved to provide facile electrons transport to the current collectors. Carbon is therefore added to the AM and the two are intimately mixed. Moreover, during battery operation the electrode must face important volume changes due to lithium insertion and extraction; for this reason a polymeric binder (polyvinylidene fluoride, PVDF or polytetrafluoroethylene, PTFE) is added to the mixture, providing elasticity to the electrode so that good particle connectivity is retained after many cycles. Although

LiCoO 2 has been a successful positive electrode material, it still leaves room for significant improvements. Therefore the scientific community started looking for better AMs for positive electrodes. The most important families of materials have been reviewed in the literature [START_REF] Whittingham | Lithium batteries and cathode materials[END_REF][START_REF] Masquelier | Polyanionic (Phosphates, Silicates, Sulfates) Frameworks as Electrode Materials for Rechargeable Li (or Na) Batteries[END_REF][START_REF] Whittingham | Ultimate limits to intercalation reactions for lithium batteries[END_REF][START_REF] Croguennec | Recent achievements on inorganic electrode materials for lithium-ion batteries[END_REF] and they are briefly described in the following, classified according to their framework structure (Figure 1.7).

Layered materials

Layered materials have been the first explored compositions, starting from LiCoO 2 [7] , developed by analogy with the previously used TiS 2 . They crystallize in the R 3m space group and their structure is clearly suitable for lithium insertion/extraction, as this is stacked into layers of close-packed transition metal (TM) octahedra. This arrangement allows bidimensional Li + transport pathways. They have also the advantage of being rather light, resulting in a high energy density that can reach ≈1.1 kWh/kg (theoretical) at 4 V. On the other hand, LiCoO 2 has drawbacks that pushed researchers to find suitable alternatives.

Firstly, Co is toxic and expensive. Secondly, LiCoO 2 suffers from thermal instability and O 2 loss when more than half lithium is extracted from the framework, limiting the practical capacity to half of the theoretical value [START_REF] Reimers | Electrochemical and insitu x-ray-diffraction studies of lithium intercalation in lixcoo2[END_REF] (although nowadays modifying the electrode's surface LiCoO 2 can be cycled on 0.7 Li + [START_REF] Kyu Tae Lee | Roles of surface chemistry on safety and electrochemistry in lithium ion batteries[END_REF] ). A number of substitutions of Co (or of Ni in the isostructural LiNiO 2 ) with one or more transition metal elements has been proposed, trying to minimize the amount of cobalt and to improve the available capacity. Among this, important compositions are LiNi 1-y-z Co y Al z O 2 [START_REF] Guilmard | Structural and electrochemical properties of LiNi 0.70 Co 0.15 Al 0.15 O 2[END_REF][START_REF] Guilmard | Effects of aluminum on the structural and electrochemical properties of LiNiO 2[END_REF] and LiNi 1/3 Co 1/3 Mn 1/3 O 2 [START_REF] Ohzuku | Layered lithium insertion material of LiCo 1/3 Ni 1/3 Mn 1/3 O 2 for lithium ion batteries[END_REF] , that have reached commercial exploitation. Another route has been to overlithiate manganeserich layered oxides (Li 1+x (TM) 1-x O 2 , TM being one or several transition metals), resulting in materials exhibiting high reversible capacity (> 200 mAh/g) after an activation process during 1 st charge at potential > 4.5 V [18,[START_REF] Lu | x/3)[END_REF] . However in this case redox processes involve both the transition metal ions and the oxygen anions. Irreversible structural modifications (TM reorganization and oxygen loss) occur inducing a continuous decrease in discharge voltage and energy, making these Li-rich materials still not mature for applications.

Spinel materials

Spinel materials have been the second family of heavily studied oxides for Li-ion batteries. They are briefly introduced here, since they will be thoroughly discussed in Chapter 3. The spinel framework is cubic, belonging to the Fd 3m space group. The basic stoichiometry is LiMn 2 O 4 (Figure 1.7), introduced as a positive electrode for Li-ion batteries by M.M. Thackeray in 1983 [START_REF] Thackeray | Lithium insertion into manganese spinels[END_REF][START_REF] Thackeray | Electrochemical extraction of lithium from LiMn 2 O 4[END_REF][22] . The material offers a capacity of ≈150 mAh/g at a very high potential (4.1 V for the Mn III /Mn IV redox couple). Moreover the framework, built by lithium in tetrahedral coordination and Mn in close-packed octahedra, favours tridimensional lithium transport, making it especially suitable for high-rate applications.

As LiMn 2 O 4 suffers of capacity fading upon cycling, over-lithiated (Li 1+x Mn 2-x O 4 ) and cation-defective (Li 1-x Mn 2-2x O 4 ) compositions were proposed to improve the cycling life of the material [23] . Although these compositions are nowadays commercialized, research is still done to improve the energy density by substituting Mn with other TMs. Nickel in particular allows to reach high operating potentials (4.7 V for LiNi 0.5 Mn 1.5 O 4 ) [START_REF] Yuan Gao | Valence band of LiNi 0.5 Mn 1.5 O 4 and its effects on the voltage profiles of LiNi 0.5 Mn 1.5 O 4 /li electrochemical cells[END_REF][START_REF] Amine | A new three-volt spinel Li 1+x Mn 1.5 Ni 0.5 O 4 for secondary lithium batteries[END_REF] , but the lack of stable electrolytes in this window has been the limiting factor for this technology's exploitation.

Polyanionic materials

Polyanionic materials contain more complicated anionic components than the simple O 2- present in oxides. These groups (XO 4 ) n-make materials heavier, which is a limiting factor for electrode materials as it decreases their gravimetric energy density (the so-called "weight penalty"). But they also offer several advantages [START_REF] Masquelier | Polyanionic (Phosphates, Silicates, Sulfates) Frameworks as Electrode Materials for Rechargeable Li (or Na) Batteries[END_REF] :

• Stable frameworks providing structural stability (mainly due to the strong covalent bonds in the (XO 4 ) n-), essential for cycling stability and safety.

• The inductive effect, described by Manthiram et al. [START_REF] Manthiram | Lithium insertion into Fe 2 (MO 4 ) 3 frameworks: Comparison of M = W with M = Mo[END_REF][START_REF] Manthiram | Lithium insertion into Fe 2 (SO 4 ) 3 frameworks[END_REF] , allowing to tune the potential of the materials across a wide range (Figure 1.8) depending on the choice of the counter-anion for a given metal.

• The great amount of possible elements combination and anionic/cationic substitutions, giving these materials unprecedented versatility. redox couples in LixM2(PO4)3. Reprinted from [START_REF] Goodenough | Challenges for Rechargeable Li Batteries[END_REF] .

The interest in polyanionic compositions sparked in 1997, with the discovery of the electrochemical activity of the olivine LiFePO 4 by Padhi et al. [START_REF] Padhi | Phospho-olivines as positive-electrode materials for rechargeable lithium batteries[END_REF][START_REF] Padhi | Effect of Structure on the Fe 3+ /Fe 2+ Redox Couple in Iron Phosphates[END_REF] (Figure 1.7). Once the issue of its low electronic conductivity is properly addressed (by carbon coating, nanostructuration or other means) the material shows a constant (i.e. flat) electrochemical voltagecomposition profile at 3.45 V, for a high capacity reaching 170 mAh/g (theoretical) and 160 mAh/g (actual) [START_REF] Yonemura | Comparative kinetic study of olivine Li x MPO 4 (M = Fe, Mn)[END_REF] . This capacity was shown to be retained for thousands of cycles, even at high rates [START_REF] Yamada | Optimized LiFePO 4 for lithium battery cathodes[END_REF][START_REF] Kang | Battery materials for ultrafast charging and discharging[END_REF] . Moreover, the material is stable at high-temperatures, environmentally benign and safe. LiFePO 4 is also an extremely interesting material for the physics involved in its phase transformation upon delithiation, as it shows a phase diagram dependent upon cycling rate, temperature and particle size [START_REF] Delacourt | The existence of a temperature-driven solid solution in Li x FePO 4 for 0 ≤ x ≤ 1[END_REF][START_REF] Yamada | Room-temperature miscibility gap in Li x FePO 4[END_REF][START_REF] Malik | A critical review of the li insertion mechanisms in LiFePO 4 electrodes[END_REF][START_REF] Liu | Capturing metastable structures during high-rate cycling of LiFePO 4 nanoparticle electrodes[END_REF] . All these factors contribute to explain why the publications on LiFePO 4 can today be counted in thousands (the original paper by Padhi was cited more than 4000 times 3 ). After LiFePO 4 , several compositions were explored as suitable polyanions with good electrochemical properties. Among these, one should mention other olivines Li(TM)PO 4 (TM = Co, Mn...), NASICON structures

3 Data from Web of Knowledge (A x (TM)(TM')(XO 4 ) 3 , actually among the first open-framework structures investigated by Goodenough et al. [START_REF] Goodenough | Fast Na + -ion transport in skeleton structures[END_REF] , Figure 1.8) and more exotic structures such as silicates, borates, alluaudites, diphosphates and hydrated phosphates...which have recently been thoroughly reviewed [START_REF] Masquelier | Polyanionic (Phosphates, Silicates, Sulfates) Frameworks as Electrode Materials for Rechargeable Li (or Na) Batteries[END_REF][START_REF] Gong | Recent advances in the research of polyanion-type cathode materials for li-ion batteries[END_REF] . A class of polyanionic materials of special interest in this thesis is the Tavorite A(TM)XO 4 Y, a promising composition which is the object of Chapter 4.

Li-ion: achievements and limitations

Li-ion batteries have been the main tool that allowed the "wireless revolution". Compared to previous battery technologies, they have a much higher gravimetric energy density, which is the key parameter required to power a portable device. Figure 1.9 compares the Li-ion technology with common commercial alternatives. One quickly notices that Li-ion is superior in terms of gravimetric and volumetric energy density, and in terms of power.

Figure 1.9: Comparison of different battery technologies. Left: in terms of gravimetric and volumetric energy density, taken from [START_REF] Tarascon | Issues and challenges facing rechargeable lithium batteries[END_REF] . Right: in terms of gravimetric energy and power density, from [START_REF] Wagner | Current research trends and prospects among the various materials and designs used in lithium-based batteries[END_REF] .

The origin of this superiority is twofold:

• lithium is the third lightest element on earth (M w = 6.94 g/mol).

• the redox couple Li 0 /Li + has the highest oxidation potential (-3.04 V vs. SHE), meaning that lithium is the element with the strongest tendency to oxidize and release one electron.

Besides energy and power density, Li-ion batteries also have a good cycling life (up to 10000 cycles), adequate safety and cost to power a wide range of applications. Portable electronics has been the first technology to benefit from them, mainly using layered materials as positive electrodes. The advances brought by pouch-cell casings and by the use of polymers Automotive targets for 2025 are also shown. Reprinted from [41] .

as electrolytes (either to make standard electrolytes in the form of gels (LiPo) or using actual ionic-conducting polymers (PLiON)) have been the key to pack more energy in smaller and more customizable batteries. The ability to produce them in almost any desired shape further contributed to make Li-ion batteries unrivalled to power portable devices of any kind. As discussed in section 1.1, recently research and industry have been converging on the common goal of extending the use of high energy density technologies to massive transport and storage applications [3,42] , even though important challenges have to be overcome. The development of spinels and olivine materials helped speeding up this process and they strongly broadened Li-ion's applications range. Although all major car manufacturers already propose at least one fully electric vehicle and different hybrid possibilities, it is in the automotive market that the Li-ion technology shows its limitation.

In fact, it can reach energy densities as high as 170 Wh/kg, but this just falls short when compared to the energy density of gasoline (1700 Wh/kg). Note that the actual energy density of a commercial battery can be as low as 15% of the theoretical value (see Figure 1.10 or simply compare 170 Wh/kg with the theoretical 1.1 kWh/kg of LiCoO 2 ). An interesting automotive perspective on the future of positive electrodes is offered by Andre et al. [41] .

Strong improvements are required to bring electric vehicles' range from the actual ≈150-200 km to > 500 km, competitive with the range of standard combustion engines.

Li-ion: perspectives and future developments

It is possible to envisage several improvements for the current generation of Li-ion batteries. Most efforts are done in the search of better positive electrodes. It is not the goal of this thesis to describe the countless materials that have been synthesized and that show promising properties. Many review papers are available to get a comprehensive view of all investigated materials [START_REF] Goodenough | Challenges for Rechargeable Li Batteries[END_REF][START_REF] Whittingham | Lithium batteries and cathode materials[END_REF][START_REF] Whittingham | Ultimate limits to intercalation reactions for lithium batteries[END_REF][START_REF] Croguennec | Recent achievements on inorganic electrode materials for lithium-ion batteries[END_REF][START_REF] Goodenough | Cathode materials: A personal perspective[END_REF][START_REF] Ellis | Positive Electrode Materials for Li-Ion and Li-Batteries[END_REF][START_REF] Fergus | Recent developments in cathode materials for lithium ion batteries[END_REF] . Among the well-known ones described above, only marginal improvements have been done in recent years since they already became as performing as they can possibly be. It is possible that better battery designs will allow to achieve higher energy densities and improve the situation depicted in Figure 1.10, but these will probably be minimal advancements. Research has now evolved towards attempts to achieve two-electron transfer at a single metal redox center, which would improve the capacity twofold. This implies the transfer of 2 Li + during every charge and discharge, with the consequently augmented volume change. Many materials are known to be able to accomplish the 2 Li + /2 e -reaction (0 ≤ x ≤ 2 in Li x (TM) y Mn 2-y O 4 , Li x VPO 4 O and LiVPO 4 F...) but the challenge of achieving long cycle life with such a significant volume expansion (and through a very wide voltage range) has not been satisfactorily solved yet [START_REF] Whittingham | Ultimate limits to intercalation reactions for lithium batteries[END_REF] .

The improvement of negative electrodes should not be neglected as well, and the same is true for electrolytes stable in a wider range of potentials and temperatures [START_REF] Goodenough | Challenges for Rechargeable Li Batteries[END_REF] . At the negative electrode side, especially, the ideal configuration would be to use lithium metal, which has virtually infinite capacity and the lowest available potential. However every attempt to safely use lithium metal with liquid electrolytes failed because of its high reactivity and the tendency to grow dendrites, especially at high cycling rate, that can cross the separator and short-circuit the battery, resulting is potentially severe hazards [START_REF] Bhattacharyya | In situ nmr observation of the formation of metallic lithium microstructures in lithium batteries[END_REF][START_REF] Harry | Detection of subsurface structures underneath dendrites formed on cycled lithium metal electrodes[END_REF] . The use of carbon at the negative electrode already reduces the available potential by about 0.3 V, and it limits high-rate applications. Other solutions for negative electrodes are under study (Si, Ge, Sn, SnSb, LiTi 4 O 12 ...), often involving conversion-type reactions, and they have been described elsewhere [START_REF] Tarascon | Issues and challenges facing rechargeable lithium batteries[END_REF][START_REF] Cabana | Beyond intercalation-based li-ion batteries: The state of the art and challenges of electrode materials reacting through conversion reactions[END_REF] .

Beyond Li-ion

Although Li-ion will surely be the leading storage technology for many years to come, longer timescale concerns have been raised about the future availability of lithium resources, located in remote and politically sensitive areas [START_REF] Tarascon | Is lithium the new gold?[END_REF][START_REF] Bl Ellis | A multifunctional 3.5 v iron-based phosphate cathode for rechargeable batteries[END_REF] and about the extent to which Li-ion technology is economically sound [START_REF] Wadia | Resource constraints on the battery energy storage potential for grid and transportation applications[END_REF] .

Given the limitations discussed above, a great effort is done to improve the Li-ion technology, but also to go beyond it. For this reason much research has been addressed to lithium's alternatives such as Na-based batteries [START_REF] Palomares | Update on na-based battery materials. a growing research path[END_REF] and more specifically to the Naion technology [START_REF] Palomares | Na-ion batteries, recent advances and present challenges to become low cost energy storage systems[END_REF] . Sodium has been the obvious material to replace lithium since it is abundant and cheap while possessing the same external electronic structure (valence shell).

Nevertheless a few drawbacks (Table 1.1) are present: (i) a standard reduction potential of -2. 71 Volts for the Na + aq /Na redox couple, less negative than that of Li + aq /Li (-3.04 Volts); (ii) a larger ionic radius (1.20 Å instead of 0.7 Å); (iii) a bigger molecular weight, implying a lower energy density. This last point in particular is the reason for which the Na-ion technology is more promising for storage-grid applications than for portable or automotive ones. Yet materials for Na-ion batteries could develop rapidly because of the essential similarity between Li + and Na + intercalation chemistry [START_REF] Komaba | Electrochemical intercalation activity of layered NaCrO 2 vs. LiCrO 2[END_REF] , which made possible to build a sodium counterpart for many positive electrode materials of interest for Li-ion batteries (NaCoO 2 [START_REF] Braconnier | Electrochemical behavior of the phases Na x CoO 2[END_REF][START_REF] Berthelot | Electrochemical investigation of the P2-Na x CoO 2 phase diagram[END_REF] , NaFePO 4 [START_REF] Moreau | Structure and stability of sodium intercalated phases in olivine FePO 4[END_REF][START_REF] Casas-Cabanas | Crystal chemistry of na insertion/deinsertion in FePO 4 -NaFePO 4[END_REF][START_REF] Gaubicher | Abnormal operando structural behavior of sodium battery material: Influence of dynamic on phase diagram of Na x FePO 4[END_REF] , NaVPO 4 F [START_REF] Barker | A sodium-ion cell based on the fluorophosphate compound NaVPO 4 F[END_REF][START_REF] Barker | A comparative investigation of the li insertion properties of the novel fluorophosphate phases, NaVPO 4 F and LiVPO 4 F[END_REF][START_REF] Zhao | A novel sol-gel synthesis route to NaVPO 4 F as cathode material for hybrid lithium ion batteries[END_REF] , Na 3 V 2 (PO 4 ) 3 [START_REF] Jian | Carbon coated Na 3 V 2 (PO 4 ) 3 as novel electrode material for sodium ion batteries[END_REF][START_REF] Uebou | Electrochemical sodium insertion into the 3D-framework of Na 3 M 2 (PO 4 ) 3 (M= Fe, V). Reports of Institute of Advanced Material Study[END_REF][START_REF] Saravanan | The first report on excellent cycling stability and superior rate capability of Na 3 V 2 (PO 4 ) 3 for sodium ion batteries[END_REF] ) while candidates for negative electrodes are more scarce [67][START_REF] Senguttuvan | Na 2 Ti 3 O 7 : Lowest voltage ever reported oxide insertion electrode for sodium ion batteries[END_REF][START_REF] Senguttuvan | Low-Potential Sodium Insertion in a NASICON-Type Structure through the Ti(III)/Ti(II) Redox Couple[END_REF] (Figure 1.11).

A significant fraction of recently proposed electrodes are phosphate-based polyanionic materials [START_REF] Masquelier | Polyanionic (Phosphates, Silicates, Sulfates) Frameworks as Electrode Materials for Rechargeable Li (or Na) Batteries[END_REF] . Among them, vanadium-based fluorophosphates [START_REF] Ellis | Crystal structure and electrochemical properties of A 2 MPO 4 F Fluo-rophosphates (A= Na[END_REF] are of particular interest, as they exploit the (PO 4 ) 3-polyanion and vanadium's chemical versatility, as for example in the Na 3 V 2 O 2δ (PO 4 ) 2 F 3-2δ (0 ≤ δ ≤ 1) family of compositions [START_REF] Serras | High voltage cathode materials for Na-ion batteries of general formula Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x[END_REF][START_REF] Serras | Electrochemical performance of mixed valence Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x /C as cathode for sodium-ion batteries[END_REF][START_REF] Park | Tailoring a fluorophosphate as a novel 4 v cathode for lithium-ion batteries[END_REF][START_REF] Park | A new highenergy cathode for a na-ion battery with ultrahigh stability[END_REF][START_REF] Ponrouch | Towards high energy density sodium ion batteries through electrolyte optimization[END_REF] . Depending on δ, the oxidation state of vanadium varies between 3+ and 4+ with a concomitant modification Na-ion batteries. Reprinted from [START_REF] Ellis | Sodium and sodium-ion energy storage batteries[END_REF] .

of the physical properties and of the electrochemical signature of the material. The end member Na 3 V III 2 (PO 4 ) 2 F 3 (δ = 0) is the object of Chapter 5 and will be carefully described there. Besides Na-ion, other recent technologies are waiting for the leap that will make them suitable for commercial exploitation. Sticking to intercalation reactions, batteries based on multivalent cations are given great attention (Figure 1.12) [START_REF] Muldoon | Quest for nonaqueous multivalent secondary batteries: Magnesium and beyond[END_REF] . Despite the difficulties at developing suitable stable electrolytes, Mg 2+ and Ca 2+ seem promising alternatives as they exchange two electrons for a single metal center (avoiding the problem of excessive volume expansion generated by a 2 Li + intercalation). However, the higher charge density poses solid state diffusion challenges. Denser multivalent cations such as aluminum and zinc have also been reported to be able to cycle, but the potentials involved are much lower than those of Li-ion batteries [START_REF] Li | Advanced zinc-air batteries based on high-performance hybrid electrocatalysts[END_REF][START_REF] Lin | An ultrafast rechargeable aluminium-ion battery[END_REF] . Among completely different chemistries that could replace Li-ion, one should mention rechargeable lithium-sulfur (Li-S) [START_REF] Manthiram | Rechargeable lithium-sulfur batteries[END_REF] and lithium-air (Li-air) batteries [START_REF] Luntz | Nonaqueous Li-Air batteries: A status report[END_REF] , both promising especially in terms of the huge capacity they can provide.

Figure 1.12: Energy density of current and future battery technologies. Reprinted from [START_REF] Van Noorden | A better battery[END_REF] .

Electrochemical (de)lithiation/(de)sodiation mechanisms

As previously mentioned, intercalation materials are compounds where insertion (of alkali cations in our case) into the material's framework occurs leaving its host structure untouched. This is a simplified view, since on the atomic scale Li + (or Na + ) insertion can happen in different ways, significantly impacting the material's physical properties and electrochemical performances. Two main processes can usually be observed, a monophasic or a biphasic reaction (Figure 1. • A monophasic reaction, also called solid solution, is a second-order process characterized by a complete miscibility of the lithiated A and delithiated B phases. Therefore, during such a transition only one phase A 1-y B y is present in all particles of the material. As an example, Li x FePO 4 at high temperature shows a complete solid solution (0 ≤ x ≤ 1) between LiFePO 4 and FePO 4 [START_REF] Delacourt | The existence of a temperature-driven solid solution in Li x FePO 4 for 0 ≤ x ≤ 1[END_REF] . During the transformation, the composition x continuously changes and so do the cell parameters (and possibly all other structural parameters) to allow the volume change induced by Li + (de)intercalation.

• A biphasic reaction is a first-order process where the lithiated A and delithiated B phases are not miscible. Therefore during delithiation, for example, the Li-poor phase has to nucleate, overcoming an energy barrier required to create the interface. Once it does so, the phase front propagates and the whole particle has composition (1-y)A + yB while transforming from Li-rich to Li-poor. Again mentioning micrometer-sized LiFePO 4 , at T amb and under slow cycling conditions, the material is an example of perfect biphasic reaction between LiFePO 4 and FePO 4 . During the transformation from one end-member to the other, the two in principle have constant composition (therefore the crystal structures of A and B do not change, although the two do not have to be the same) and only the relative weight % y is modified (linearly).

Different theories exist to model this behaviour, as core-shell models [START_REF] Srinivasan | Existence of path-dependence in the LiFePO 4 electrode[END_REF] or dominocascade ones [START_REF] Delmas | Lithium deintercalation in LiFePO 4 nanoparticles via a domino-cascade model[END_REF] . Their domain of application strongly depends on the considered material, on the morphology of its particles determining phase front's stability, on the thermodynamic (or not) equilibrium situation, etc. This is an interesting domain, which fully showed its complexity in the case of the phase diagram of LiFePO 4 [START_REF] Malik | A critical review of the li insertion mechanisms in LiFePO 4 electrodes[END_REF][START_REF] Meethong | Strain accommodation during phase transformations in olivine-based cathodes as a materials selection criterion for high-power rechargeable batteries[END_REF] .

The existence of a monophasic "solid solution" reaction or of a biphasic one directly impacts the electrochemical behaviour of an electrode material. Indeed, Gibbs phase rule states that:

F = C -P + 2 (1.8)
where F is the number of the thermodynamic system's degrees of freedom, C the number of components and P the number of phases in equilibrium with each other. The rule comes from the fact that the equilibrium condition imposes a constraint on the number of intensive variables. This is relevant to Li-ion batteries because during (de)intercalation the system is composed of 2 components (the Li-rich and the Li-poor) and as we discussed P can be either 1 or 2. In the first case (the solid solution) F = 3. Since temperature and pressure are already supposed to be constant, one degree of freedom is left for the voltage. Upon cycling, the voltage-composition curve of a material showing a single-phase reaction will then be sloping. On the other hand, if the reaction is biphasic P = 2 and thus F = 2 too.

The two degrees of freedom are taken by temperature and pressure, and therefore the value of the voltage must be fixed. During a two-phase reaction the voltage-composition curve will then be flat or, using the French word, a "plateau". Reprinted from [START_REF] Delmas | Lithium batteries: a new tool in solid state chemistry[END_REF] .

Note that the two reaction mechanisms described above are not exclusive; a certain material can react in a given composition range through a monophasic reaction and in another through a biphasic one; this actually happens most of the time and several examples will be discussed in this thesis. Distinguishing the two mechanisms is sometimes easy from the voltage-composition curve of a galvanostatic experiment V = f(x) (flat vs. sloping), while sometimes it can be hard. A valuable tool in this case is the inverse derivative curve (dV/dx) -1 of the voltage-composition one. As can be seen in Figure 1.14, this representation shows intense narrow peaks for biphasic reactions, at the voltage typical of the considered redox reaction. In contrast, when the (de)intercalation mechanism is a solid solution, it shows broader and weaker peaks.

Characterization techniques

Several characterization techniques are employed in this thesis to get insight on the behaviour of electrode materials for Li-ion and Na-ion batteries. Besides electrochemical characterizations (mainly galvanostatic cycling and GITT) which have already been described, diffraction is the main technique that we used, thus deserving a detailed discussion.

Powder Diffraction

Diffraction is a phenomenon occurring when a wave (whatever its nature) interact with an obstacle. Among several possible interactions, diffraction dominates when the typical length of the obstacle (for example the dimension of a hole or the distance between two objects) is comparable to the wavelength. The discovery of X-Rays by Röntgen (1895)

was the first step that allowed Bragg (father W.H. and son W.L.) to lay the basis for the modern science of crystallography [START_REF] Meurig | Centenary: The birth of x-ray crystallography[END_REF] . In fact X-Ray tubes produce radiation having a wavelength of the order of 1 Å, the same of typical inter-atomic distances in crystals.

Therefore shining X-Rays on a NaCl crystal allowed the Braggs to observe the first X-Ray diffraction (XRD) pattern in 1913, which earned them the Nobel Prize in 1915. The most basic comprehension of X-Ray diffraction is provided by Bragg's law. When considering an X-Ray beam of wavelength λ incident on a crystal with angle θ with respect to a given set of crystallographic planes (labelled by the Miller indices hkl), the elastic diffraction condition is given by:

2d hkl sinθ = nλ (1.9)
that essentially imposes constructive interference between the reflected beams. Here d hkl indicates the distance between successive (hkl) crystallographic planes and n the order of diffraction. The same law can be stated in a more general way using Van Laue's vectorial formulation:

Q = G = n2π d hkl (1.10)
Here Q represents the difference of incoming and scattered wavevector (in the common case of elastic scattering Q = 4πsin(θ)/λ) and G is a vector of the reciprocal lattice. Hence equation 1.10 states that to have diffracted intensity the momentum transfer from the wave to the crystal lattice must equal a vector of the reciprocal lattice. Every time this condition is matched a so-called Bragg peak appears. The intensity of every one of these peaks depends on the scattering power of the atoms in a given crystallographic plane (hkl) (N.B. X-Rays are scattered by the electrons orbiting the nucleus, so heavier atoms are those who scatter the most). Such intensity can be shown to be proportional to the so-called structure factor F hkl following:

I hkl ∝ |F hkl | 2 = n j=1
O j f j e i2π(hx j +ky j +lz j ) (

where x j , y j and z j represent the atomic positions of the j th atom, f j its atomic scattering factor and O j the fraction of sites (x j , y j , z j ) occupied by the atom.

X-Ray diffraction is the basic tool of crystallography, and it is worth mentioning that we just celebrated 2014 as the international year dedicated to this science. Several techniques have been developed during the last century to carry out more and more advanced X-Ray diffraction experiments. It is not worth discussing this in too many details here, as several textbooks already did [START_REF] Scrosati | Lithium batteries: Status, prospects and future[END_REF] . It is only important to mention that, after the first experiments carried out on single crystals (the so-called single crystal XRD), new techniques dealing with polycrystalline samples and powders have been developed. A powder is a polycrystalline sample where all crystallites have perfectly random orientation. This is of special importance as many materials synthesized by a variety of chemical methods are in the form of powders, and therefore X-Ray Powder Diffraction (XRPD) was established as the technique of choice to characterize the crystal structure of new synthesized materials.

Although equation 1.9 only shows one angular dependence, in a monochromatic single crystal XRD experiment one finds Bragg reflections distributed all over the surface of a sphere to account for all possible planar orientations in the crystal (Figure 1.15). Thus two angular coordinates (θ,φ) are required to determine the position of a Bragg spot (once a detector is set at a given distance). Instead, shining monochromatic X-Rays on a powder sample is the same as making an integration over one angular direction, leaving only one (θ) free variable. Then one observes cones diffracting from the sample (instead of spots), drawing characteristic circles on a flat-plate detector. Every circle appears at an angle θ

given by Bragg's law (equation 1.9) which relates to the crystallographic planes distance and ultimately to the material's space group and unit cell parameters, while the integrated intensity of every circle is given by the position of the atoms inside the unit cell. Note that X-Rays were the first probe to allow diffraction from crystals, but they are definitely not the only ones. Nowadays diffraction experiments can also be carried out using electrons, synchrotron radiation and neutrons. The diffraction of these probes is similar to X-Rays' one (Bragg's law holds) but each probe has specific properties dependent on the different radiation-matter interaction mechanism (in equation 1.11, f j has a different behaviour for every probe). As a conclusive remark, one should note that the golden age of crystal structures did not start until 1969, when the Rietveld method became available [START_REF] Rietveld | A profile refinement method for nuclear and magnetic structures[END_REF] .

This is a refinement procedure, developed by Hugo Rietveld, that allows precise determination of a crystal structure starting from an XRPD pattern, provided that an initial model sufficiently close to the actual one is known. The basic idea is that a certain quantity estimating the difference between the calculated and experimental diffraction pattern is minimized, providing a final model closer to reality than the initial one. Reiteration of the process until convergence usually provides the true crystal structure.

Neutrons

Neutrons are one of the fundamental particles that constitute our universe, since they are among the building blocks of atomic nuclei. Neutrons were discovered in 1932 by James Chadwick, who was bombarding beryllium with α particles ( 4 He 2+ ) and he observed the reaction:

9 Be + α → 12 C + 1 n + 5.7M eV (1.12)
Because of mass and energy conservation, Chadwick understood that the neutron exists and that it has approximately the same mass of the proton. He won the Nobel prize in Physics for his achievement in 1935.

Nowadays the properties of neutrons are well-known: they are spin 1/2 particles, without electric charge (this was actually measured at ILL in 1987, finding a charge of -0.2(8) • 10 -21 e) and with a lifetime of 880(1) s (or, more precisely, with a half-life of 611(1) s). Being electrically neutral, neutrons interact weakly with matter; however they still experience gravity, weak nuclear force and strong nuclear force. Since they have a nuclear magnetic moment, they also respond to magnetic fields. These interactions allow the use of neutrons for several important applications, both industrial and scientific. The first use of neutrons is due to Enrico Fermi, who understood the principles of nuclear fission. Neutrons are fundamental to it because they are the key to achieve a chain reaction. In fact, in a nuclear reactor uranium is hit by neutrons and as a consequence it is split in lighter elements, releasing energy. The extra neutrons freed in the process allow the reaction to sustain itself.

While industrial reactors are designed to safely sustain a fission chain reaction to exploit energy in the form of heat, the scientific use of neutrons relies mainly on reactors specifically designed for their extraction. The Institut Laue-Langevin is one example of such reactors, where different tubes exit the reactor's nucleus to bring neutrons to the instruments. Another possible way to produce neutrons is called spallation, which is based on the bombardment of a heavy element target (e.g. Hg) by highly accelerated protons; the impact destabilizes the heavy element and it induces the release of many particles, among which several neutrons that can be collimated for subsequent use.

The interaction of neutrons with matter is a complicated subject, properly described in many works [START_REF] Schober | An introduction to the theory of nuclear neutron scattering in condensed matter[END_REF][START_REF] Bacon | Neutron Diffraction[END_REF] . Related to this thesis, three main isotope-dependent processes are relevant and should be noted here: elastic coherent scattering, elastic incoherent scattering and neutron absorption. In the first case, neutrons are scattered coherently between different atoms, meaning that one can probe correlations among them (such mechanism for example is at the origin of Bragg peaks in diffraction). In the second case, elastic incoherent scattering cause neutrons to be randomly scattered, originating a strong featureless background; this is due to the isotopic distribution of a given element (namely in most cases there is no control on the actual isotope present in the sample, but elements with "natural abundance" are used). Finally, few elements are also strong neutrons absorbers, as for example lithium, boron or cadmium (i.e. they have at least one isotope which is a strong neutron absorber).

Neutrons' scattering length is the key property when considering the diffraction of neutrons. In fact, these are particles but also waves (as clear from the De Broglie principle) and therefore they can diffract. But a strong difference is present with respect to other probes as for example X-rays. Neutrons used for diffraction are in most cases thermal neutrons, i.e. they have an energy of approximately 25 meV. At this energy, their wavelength has an order of magnitude of 1 Å because of their heavy mass. However, neutrons do not interact with the electrons surrounding the nucleus, but with the nucleus itself, which has a typical dimension of 10 -5 Å. Thus the potential they experience, called the Fermi potential, is a point-like one of the form:

V ( r, R 0 ) = 2πh 2 M bδ( r -R 0 ) (1.13)
where δ( r -R 0 ) is a Dirac delta and M is the neutron's mass. In this description, b is called scattering length and it defines the intensity of the potential felt by a neutron when it interacts with a nucleus. Related to powder diffraction, when neutrons are the probe eq.1.11 for the intensity still holds but with the form factor f j replaced by the scattering length b j of the j th atom. Note that, although f j is always positive, b j can be negative for a few elements. This is due to the fact that the interaction is not always repulsive but, in a few cases, it can be attractive. Neutron scattering lengths and their importance for the study of Li-ion batteries are further discussed in the next chapter (2).

Powder diffraction and electrode materials

In the field of Li-ion batteries, powder diffraction has classically been used to characterize pristine synthesized materials in terms of structure and purity. The study of compositions formed upon electrochemical cycling is also extremely important, as these are usually unstable in air and cannot be synthesized by standard chemical techniques. These measurements can be done rather easily ex situ, i.e. out of the electrochemical cell. This means that a certain composition is prepared via lithium extraction or insertion in the cell, which is subsequently opened in an argon-filled glove-box in order to recover the material, properly wash it and/or grind it, and perform a powder diffraction experiment. This approach, albeit valuable, is very limited because the composition under study might be metastable and evolve once the material is extracted from the cell. Moreover, once this is done the risk of contamination or oxidation from atmospheric agents (O 2 , H 2 O...) or tools used in the process is significant. Hence it is hard to be sure that the material studied in the diffraction experiment is exactly the same that was prepared upon electrochemical cycling.

In situ/operando studies applied to Li-ion batteries

To overcome the limitations of ex situ studies, in situ and operando approaches have been developed. A distinction is made since in situ means "in place" (i.e. in the battery in our case), while operando means "during operation". In both cases the electrochemically prepared material is studied directly inside the battery. This has the advantage of avoiding exposure to the atmosphere outside it; but an in situ (not operando) experiment still requires that the battery cycling is stopped, put in relaxation (open circuit voltage OCV)

and mounted in the diffractometer (or other experimental setup) to perform the measurement. In an operando approach, instead, the battery is in the diffractometer as it is operating, namely the diffraction measurement is done in real time as the battery charges and discharges. The advantage is that metastable phases can be captured, and the real out-of-the-equilibrium battery's behaviour is observed. Note that an operando experiment is necessarily in situ, while the vice versa is not true.

In situ & operando techniques started developing right after the invention of the first Liion batteries, and they proved to be exceptionally useful tools to understand the electrodes behavior in Li-ion batteries [START_REF] Dahn | In situ x-ray diffraction experiments on lithium intercalation compounds[END_REF] ; these are dynamical in nature and their understanding is limited if they are only looked at through a series of snapshots, such as those we can get from ex situ studies. X-ray powder diffraction (XRPD), in particular, has been the leading technique thanks to the possibility to exploit laboratory diffractometers [START_REF] Dahn | In situ x-ray diffraction experiments on lithium intercalation compounds[END_REF][91][START_REF] Gustafsson | The polymer battery as an environment for in situ x-ray diffraction studies of solid-state electrochemical processes[END_REF][START_REF] Andersson | Lithium extraction/insertion in LiFePO 4 : an x-ray diffraction and mossbauer spectroscopy study[END_REF][START_REF] Morcrette | In situ x-ray diffraction techniques as a powerful tool to study battery electrode materials[END_REF][START_REF] Bianchini | Multiple phases in the -VPO 4 O -LiVPO 4 O-Li 2 VPO 4 O system: a combined solid state electrochemistry and diffraction structural study[END_REF] , as well as more powerful synchrotron sources [START_REF] Liu | Capturing metastable structures during high-rate cycling of LiFePO 4 nanoparticle electrodes[END_REF][START_REF] Albertini | In situ studies of electrodic materials in li-ion cells upon cycling performed by very-high-energy x-ray diffraction[END_REF][START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF][START_REF] Ouvrard | Heterogeneous behaviour of the lithium battery composite electrode LiFePO 4[END_REF][START_REF] Ravnsbaek | Extended solid solutions and coherent transformations in nanoscale olivine cathodes[END_REF][START_REF] Zhang | Rate-induced solubility and suppression of the first-order phase transition in olivine LiFePO 4[END_REF] . Many studies have been published and their importance is noteworthy. The in situ approach to study Li-ion batteries has been applied to almost any other technique, such as Raman spectroscopy [START_REF] Huang | In situ raman spectroscopic studies of electrochemical intercalation in Li x Mn 2 O 4 -based cathodes[END_REF] XANES (and EX-AFS) [START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF][START_REF] Orikasa | Transient phase change in two phase reaction between LiFePO 4 and FePO 4 under battery operation[END_REF][START_REF] Borkiewicz | The ampix electrochemical cell: a versatile apparatus for in situ x-ray scattering and spectroscopic measurements[END_REF][START_REF] Koga | Operando x-ray absorption study of the redox processes involved upon cycling of the li-rich layered oxide Li 1.20 Mn 0.54 Co 0.13 Ni 0.13 O 2 in li ion batteries[END_REF] , NMR [START_REF] Letellier | In situ 7li nmr during lithium electrochemical insertion into graphite and a carbon/carbon composite[END_REF][START_REF] Key | Real-Time NMR Investigations of Structural Changes in Silicon Electrodes for Lithium-Ion Batteries[END_REF] , Mössbauer [START_REF] Ionica-Bousquet | In situ 119Sn Mossbauer Effect Study of Li-CoSn 2 electrochemical system[END_REF][START_REF] Jumas | Combined operando studies of new electrode materials for li-ion batteries[END_REF][START_REF] Perea | Operando Fe-57 Mossbauer and XRD investigation of Li x Mn y Fe 1-y PO 4 /C composites (y=0; 0.25)[END_REF][START_REF] Perea | Operando Fe-57 Mossbauer and XRD investigation of Li x Mn y Fe 1-y PO 4 /C composites (y=0.50; 0.75)[END_REF][START_REF] Dunlap | Application of in situ mossbauer effect methods for the study of electrochemical reactions in lithium-ion battery electrode materials[END_REF] , Transmission X-Ray microscopy (TXM-STXM) [START_REF] Wang | In operando tracking phase transformation evolution of lithium iron phosphate with hard x-ray microscopy[END_REF][START_REF] Ohmer | Phase evolution in singlecrystalline LiFePO 4 followed by in situ scanning x-ray microscopy of a micrometresized battery[END_REF] , TEM [START_REF] Huang | In situ observation of the electrochemical lithiation of a single SnO 2 nanowire electrode[END_REF][START_REF] Niu | In situ observation of random solid solution zone in LiFePO 4 electrode[END_REF] , Neutron reflectometry [START_REF] Jerliu | Neutron reflectometry studies on the lithiation of amorphous silicon electrodes in lithium-ion batteries[END_REF] and X-Ray tomography [START_REF] Ebner | Visualization and quantification of electrochemical and mechanical degradation in li ion batteries[END_REF] , resulting in a great amount of different perspectives to look at electrochemical reactions in real time. A comprehensive review was recently published by Harks et al. [START_REF] Harks | In situ methods for Liion battery research: A review of recent developments[END_REF] .

Electrochemical cells for in situ XRPD

Whatever the probe, the first step to carry out in situ studies is the development of custom setups to combine the electrochemical needs of the battery with those of the characterization technique of choice. In the field of diffraction studies, setups for laboratory XRPD are common nowadays, while those for Synchrotron Radiation facilities have been developed by several groups (ours included) and have become more readily available [START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF][START_REF] Borkiewicz | The ampix electrochemical cell: a versatile apparatus for in situ x-ray scattering and spectroscopic measurements[END_REF] . The design of an electrochemical cell for operando neutron diffraction is a more complicated task, and our own prototype, along with its advantages and drawbacks, is described in the next chapter of this thesis (2).

Figure 1.16: Electrochemical cell for operando measurements, from [START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF] . (a) Photo and (b) detailed view of the cell with incoming and outcoming beam paths in transmission geometry.

Here we show the cell for operando experiments developed at LRCS in recent years [START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF] and used in the following for many of the described XRPD measurements. It is reported in Figure 1.16. The design allows for measurements both in reflection (Bragg-Brentano) and transmission geometry. The former is used on the Bruker D8 Advance in-house diffractometer in Amiens (equipped with Cu Kα 1,2 radiation), while the latter is used for experiments

Neutron instruments and synchrotron beamlines

The most used instruments and beamlines used in this thesis for neutron powder diffraction and synchrotron X-Ray powder diffraction experiments are described in this section. The neutron diffractometers used in this work are mainly D2B and D20 at the Institut Laue-Langevin (ILL, Grenoble) (Figure 1.18), both chosen because of their complementary features. D2B is a very high-resolution diffractometer designed to achieve optimal resolution (∆d/d = 5•10 -4 ). We used such an instrument for all standard neutron powder diffraction measurements. The setup of choice involved a Germanium monochromator at reflection (335), resulting in the optimal wavelength for the instrument of λ = 1.594 Å. In this configuration, a neutron flux of about 10 6 cm -1 s -1 is obtained. Beam size at sample position is 2x5 cm 2 , usually further collimated by slits. The angular range is very wide, measuring 5 • < 2θ < 165 • . A typical room-temperature experiment on the D2B diffractometer is made by filling a vanadium cylindrical container (cans of diameter 6.5 mm or higher) with the powder to be measured. For air-sensitive samples, the containers are filled in an argon-filled glove-box and sealed with an indium wire.

On the other hand, D20 is a very high-intensity diffractometer, especially well-suited for in situ measurements due to the ability to collect NPD patterns in short times. The instrument is also very flexible, with different take-off angles and monochromator combinations available to tune intensity and resolution. Neutron flux can thus range between 10 7 cm -1 s -1 and 10 8 cm -1 s -1 . In our in situ/operando experiments, we privileged a compromise between the best available flux and resolution, choosing a take-off angle of 90 • with a Germanium monochromator either on the (115) reflection (λ = 1.54 Å) or on the (113) one (λ = 2.4 Å), depending on the sample. In principle, a wide angular range of 153.6 • is available.

MSPD at ALBA

Most of synchrotron radiation XRPD measurements in this thesis were carried out in collaboration with François Fauth at the Materials Science Powder Diffraction (MSPD) beamline at ALBA synchrotron facility [START_REF] Fauth | The new material science powder diffraction beamline at alba synchrotron[END_REF] in Cerdanyola del Valles, Barcelona. Two main setups of the beamline were interesting in our case:

• A high-angular mode of the station (13 channels Si111 multi-analyzer setup) where data are collected in Debye-Scherrer geometry in the 2 • -50 • 2θ angular range. A very high angular resolution (up to ∆d/d = 2•10 -4 ) can be reached in this operating mode.

The energy can be chosen in a wide range (8-50 KeV); in our case we selected the rather short wavelength of 0.620 Å to avoid absorption issues. Samples were enclosed in 0.7-1 mm diameter borosilicate capillaries and measured at ambient temperature.

In case of high temperature measurements, capillaries were heated using a FMB Oxford hot air blower, while for low temperature ones we used a Cryostream Plus nitrogen blower from Oxford Cryosytems.

• A high acquisition-rate mode (but with lower angular resolution). In this case powder diffraction patterns were collected using the one dimensional silicon based position sensitive detector MYTHEN in the 2 • -50 • angular 2θ range (d-range: 1.12 -40 Å).

Since MYTHEN detector spans a ≈ 40 • angular 2θ range, this setup allows fast data acquisition with extremely high statistics and good angular resolution (but lower than the one of a multi-analyzer setup). This mode of the instrument was mainly used for operando experiments. In this case batteries were prepared using the cell described in section 1.6.5. Transmission geometry was used, with the beam going through all the layers of the cell. Throughout all the experiments, the operating wavelength was λ = 0.953 Å. The longer wavelength was specifically chosen in order to minimize peak overlap and in particular to better resolve Bragg reflections. The quality of the data collected in these operando conditions allows Rietveld structural refinements of all the identified phases with goodness comparable to refinements performed using the highest angular resolution mode.

CRISTAL at SOLEIL

Synchrotron radiation XRPD experiments were also carried out at room temperature at the CRISTAL beamline of the SOLEIL synchrotron in Saint-Aubin (Paris). CRISTAL is an undulator-based diffraction beamline, dedicated to single crystals and powders between 4 and 30 keV. In our experiments, data were collected using a 2-circle diffractometer at λ = 0.669 Å in the 5 • -50 • 2θ angular range (energy resolution ∆E/E ≈ 10 -4 ). The measurements were performed in Debye-Scherrer geometry, with the powder sealed in a 0.7 mm capillary and the acquisition done with a multi-analyzer (21 Silicon (111) crystals).

Aim of the thesis

This thesis is the result of the collaboration of three work of Jean-Marcel Ateba Mba in our group [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF] . They are able to both intercalate and deintercalate lithium; we studied both domains of both materials, looking at the relation between electrochemical and structural properties. We made combined use of XRPD, synchrotron XRPD and NPD techniques, in situ/operando and ex situ, to shade light on the complex phase transformations encountered in these promising compounds. Chapter characterization techniques are effective for the materials' study. We focused our interest on the polyanionic compound Na 3 V 2 (PO 4 ) 2 F 3 as one of the most promising positive electrode materials for a future generation of Na-ion batteries. During our studies we realized that for this compound the most suitable probe is synchrotron radiation, given the small orthorhombic distortion present in the unit cell and the subtle transformations that we could show to happen during Na + extraction and insertion. However, neutrons were still used as a complement for structural determinations. This thesis is therefore an attempt at combining the most advanced diffraction techniques available, using or developing whenever possible an operando approach, to shed light on the structural transformations that electrode materials undergo in Li-ion and Na-ion batteries. We chose here a number of materials that we thought are of special interest. However the techniques employed and the tools developed are completely general and can be applied to the study of any of these challenging materials, in the hope to obtain an ever-better comprehension of their working mechanisms and that this will reflect on the betterment of future batteries.

Chapter 2

An electrochemical cell for in situ/operando neutron powder diffraction

Introduction

In the last decade the quest to ameliorate Li-ion and Na-ion batteries followed a great number of different paths, some of which were briefly discussed in the introduction of this thesis. However, the improvement of a given battery technology does not depend solely on the discovery of new chemistries, new materials or new electrode formulations but it also relies on better characterization techniques, allowing to probe chemical reactions in more and more details, until a full comprehension of the mechanisms involved is achieved. In this respect, in situ techniques are extremely valuable and their use has been described in the previous chapter. Here we will show how neutrons can be an important probe to study battery materials and how they can be used to carry out in situ and operando studies.

Neutrons and Li-ion batteries

Until about 15 years ago, neutron powder diffraction (NPD) was not considered for in situ studies on lithium/Li-ion batteries because of the intrinsic difficulties it held, although its advantages should not be neglected. Electrode materials often contain light elements such as lithium and oxygen, almost transparent to X-Rays and lithium in particular is the element whose position, amount and dynamics must be known. These properties can be probed using neutrons [START_REF] Aatiq | On the structure of Li 3 Ti 2 (PO 4 ) 3[END_REF] because, although lithium's scattering length is small, it is negative and generates a significant contrast with other elements (most of which have positive scattering lengths, see Figure 2.1). 6 Li, 7 Li and naturally occurring 6. [START_REF] Morcrette | In situ x-ray diffraction techniques as a powerful tool to study battery electrode materials[END_REF] Li, obtained from [START_REF] Dianoux | Neutron Data Booklet[END_REF] . Columns: nuclide, relative amount, nuclear spin state I. Scattering lengths in fm: bound coherent scattering length (bc), spin-dependent scattering length for I + 1/2 (b+), spin-dependent scattering length for I -1/2 (b-). Cross sections in barns: coherent cross-section σ coh , incoherent cross-section σinc, total cross-section σscatt, and absorption cross-section σ abs . Another advantage of neutrons comes from the fact that many electrode materials contain more than one transition metal element (Mn, Fe, Co, Ni, ...), poorly distinguished using X-Rays diffraction because of their similar scattering powers. Neutrons' scattering lengths, on the other hand, do not vary continuously throughout the periodic table (Figure 2.1): a much higher contrast between such elements may be attained using NPD [START_REF] Croguennec | Structural and electrochemical characterization of the LiNi 1-y Ti y O 2 electrode materials obtained by direct solid-state reactions[END_REF] .

Also, neutrons are in general superior to X-Rays and other characterization techniques in terms of their high penetrating power (due to their weak interaction with matter), allowing to probe simultaneously a whole electrode or even a whole battery, depending on the chosen geometry. Finally, another advantage comes from the physics of neutron scattering: X-rays are diffracted by electrons distributed around the nucleus, generating a form factor that decays with Q (the scattering vector Q = 4πsin(θ)/λ). Neutrons, on the other hand, interact directly with the nucleus and this point-like potential leads to Q-independent scattering lengths. Therefore, in a NPD experiment one can observe significant intensities at high Q values, leading to important structural information about atomic parameters as site occupancies and Debye-Waller factors. These advantages, which have been the engine to push the development of in situ NPD, will be fully illustrated in this thesis. Nevertheless, some obvious drawbacks of neutrons have to be recalled here: first of all, a neutron source is less easy to have at hand. Secondly, Li-batteries include many problematic components such as hydrogen-rich electrolytes that create a strong continuous background, such as natural lithium that absorbs neutrons and such as various other battery parts (aluminum/copper current collectors, steel protective case etc...) that give rise to very intense Bragg peaks. For these reasons in situ NPD took more time to be developed. Neutron scattering facilities, worldwide, that can provide the necessary flux and resolution for this kind of investigations are still rare.

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 -6 -4 -2 0 2 4 6 8 1 0 1 2 1 4 U B G d D y C d N i F e S c Z r C M n V T i L i 1 H b c o h ( f m ) Z 2 D Figure 2.

Development of electrochemical cells for in situ NPD

The fabrication of custom-made electrochemical cells able to satisfy both the needs of a battery and those of NPD is a mandatory requirement to carry out successful in situ experiments and first interesting attempts were reported around 2000 by different researchers in Uppsala, Sweden [START_REF] Bergstom | A neutron diffraction cell for studying lithium-insertion processes in electrode materials[END_REF][START_REF] Berg | Neutron diffraction study of electrochemically delithiated LiMn 2 O 4 spinel[END_REF][START_REF] Berg | The LiMn 2 O 4 to lambda-MnO 2 phase transition studied by in situ neutron diffraction[END_REF] (Figure 2.2a). The challenge that such cells had to face consisted in combining a good electrochemistry with sufficient statistics for neutron diffraction, knowing that the two requirements often conflict. A big amount of powder for the positive electrode is required for NPD, while this is usually problematic for a homogeneous electrochemical reaction. At that time, the results did not match expectations and improved cell designs were reported by the group of P. Novak at PSI (Switzerland) [START_REF] Rosciano | A novel electrochemical cell for in situ neutron diffraction studies of electrode materials for lithium-ion batteries[END_REF][START_REF] Colin | In situ neutron diffraction study of li insertion in Li 4 Ti 5 O 12[END_REF] Although these first experiments were important, the results they led to in terms of structural information were quite poor. Qualitative information about the evolution of Bragg reflections was usually found, while the quantitative information was limited to cell parameters and relative amount of crystalline phases, obtained in just a few points (< 10 compositions) during charge. For this reason such early experiments cannot really be regarded as operando, in the sense that the resolution in electrode composition (∆x) was not sufficient to follow closely lithium's (de)intercalation reaction. More recently it became clear that even commercially available lithium batteries could be studied with in situ NPD [START_REF] Rodriguez | Quantitative analysis of li contents in Li x CoO 2 cathodes via rietveld refinement[END_REF][START_REF] Rodriguez | Simultaneous in situ neutron diffraction studies of the anode and cathode in a lithium-ion cell[END_REF][START_REF] Rodriguez | In situ analysis of LiFePO 4 batteries: Signal extraction by multivariate analysis[END_REF][131][START_REF] Sharma | In situ neutron powder diffraction studies of lithiumion batteries[END_REF][START_REF] Senyshyn | Inoperando neutron scattering studies on Li-ion batteries[END_REF][START_REF] Wang | Visualizing the chemistry and structure dynamics in lithium-ion batteries by in-situ neutron diffraction[END_REF][START_REF] Dolotko | Fatigue process in li-ion cells: An in situ combined neutron diffraction and elec-trochemical study[END_REF][START_REF] Cai | In-situ observation of inhomogeneous degradation in large format li-ion cells by neutron diffraction[END_REF][START_REF] Cai | In-situ observation of inhomogeneous degradation in large format li-ion cells by neutron diffraction[END_REF][START_REF] Sharma | Current-dependent electrode lattice fluctuations and anode phase evolution in a lithium-ion battery investigated by in situ neutron diffraction[END_REF][START_REF] Sharma | Overcharging a lithium-ion battery: Effect on the Li x C 6 negative electrode determined by in situ neutron diffraction[END_REF][START_REF] Senyshyn | Lithium intercalation into graphitic carbons revisited: Experimental evidence for twisted bilayer behavior[END_REF] giving interesting information on their overall behavior and showing that their diffraction patterns are not worse than those of early custom-made cells. Indeed, a commercial battery possesses quite a significant amount of electrode material (a few grams) illuminated by the beam giving a strong signal and allowing for fast detec- tion. The drawback is the presence of at least 5-6 crystalline phases diffracting and once again detailed Rietveld analysis would be extremely challenging. Still, the application to commercial batteries strongly increased the interest of the battery community towards in situ neutron diffraction and led to a rather straightforward evolution: the idea to produce custom-made laboratory batteries in a classic roll-over battery design (18650-like) or in a simple but effective pouch-cell design. This approach was undertaken by different groups, as for example by Peterson and Sharma [START_REF] Sharma | In-situ neutron diffraction study of the MoS 2 anode using a custom-built Li-ion battery[END_REF][START_REF] Sharma | Time-Dependent in-Situ Neutron Diffraction Investigation of a Li(Co 0.16 Mn 1.84 )O 4 Cathode[END_REF][START_REF] Du | Brdoped Li 4 Ti 5 O 12 and Composite TiO 2 anodes for li-ion batteries: Synchrotron x-ray and in situ neutron diffraction studies[END_REF][START_REF] Sharma | Direct evidence of concurrent solid-solution and two-phase reactions and the nonequilibrium structural evolution of LiFePO 4[END_REF][START_REF] Sharma | Non-equilibrium Structural Evolution of the Lithium-Rich Li 1+y Mn 2 O 4 Cathode within a Battery[END_REF] , Gustaffson and Edstrom [START_REF] Roberts | Design of a new lithium ion battery test cell for in-situ neutron diffraction measurements[END_REF] and several others [START_REF] Liu | In-situ neutron diffraction study of the xLi 2 MnO 3 • (1-x)LiMO 2 (x = 0, 0.5; M = Ni, Mn, Co) layered oxide compounds during electrochemical cycling[END_REF] . Two of these designs are reported in Figure 2.2c-d. These have the advantage of simplicity, customizability and extremely good electrochemical properties, but still possess all the disadvantages of having a whole battery in the neutron beam. Very recently, another improved cell was designed (Figure 2.3a) by the group of Novak (PSI Switzerland) in such a way to combine most of the required aspects for in situ NPD [START_REF] Godbole | Circular in situ neutron powder diffraction cell for study of reaction mechanism in electrode materials for li-ion batteries[END_REF] : adequate geometry for diffraction and reliable electrochemistry, able to match most of the expectations. But the design looks over-complicated with respect to what is necessary, and the use of aluminum or titanium metals as current collectors generates strong additional diffraction peaks. After we proposed our own in situ electrochemical cell in 2013 [START_REF] Bianchini | A new null matrix electrochemical cell for rietveld refinements of in-situ or operando neutron powder diffraction data[END_REF] , discussed in detail in the following, other groups kept pushing cells development. Another complicated design was proposed by Vadlamani et al. [START_REF] Vadlamani | An in-situ electrochemical cell for neutron diffraction studies of phase transitions in small volume electrodes of li-ion batteries[END_REF] (Figure 2.3b), who used silicon (110) single-crystal sheets for the cell casing, giving a very weak background and very few diffraction peaks. Another idea is the use of modified pouch-cells [START_REF] Kong Pang | Lithium migration in Li 4 Ti 5 O 12 studied using in situ neutron powder diffraction[END_REF][START_REF] Kong | A custom battery for operando neutron powder diffraction studies of electrode structure[END_REF] (Figure 2.3c), which can be quite effective as they are simple and allow to place a big amount of electrode material in the neutron beam (but again, the whole battery pack is diffracting and not just one electrode). Table 2.2 gathers all in situ NPD experiments published at present in the literature, while Figure 2.4 represents the evolution of the publications per year on the subject. In spite of all efforts spent up to now and to the best of our knowledge, all the in situ NPD data reported until 2012 still suffered from poor reliability of the attempted Rietveld refinements, due to the presence of high background (caused by the electrolyte) and many additional diffraction peaks besides those of the studied electrode material, arising from the cell itself (current collectors, casing, graphite, ...). In such cases, we think that it is almost impossible to perform a good quality multi-phase pattern refinement. For this reason in early 2013 we made a few different design choices for our custom-made setup, which will be described in the next paragraph.

Table 2.2: Summary of all batteries used for in situ neutron powder diffraction studies of Li-ion batteries, adapted from [START_REF] Kong | A custom battery for operando neutron powder diffraction studies of electrode structure[END_REF] .

Year

Reference Material studied Cell Battery Type Bergstom et al. [START_REF] Bergstom | A neutron diffraction cell for studying lithium-insertion processes in electrode materials[END_REF] LixMn 2 O 4 Half Pyrex tube-like Berg et al. [START_REF] Berg | The LiMn 2 O 4 to lambda-MnO 2 phase transition studied by in situ neutron diffraction[END_REF] LiMn 2 O 4 Half Pyrex tube-like Rodriguez et al. [START_REF] Rodriguez | Simultaneous in situ neutron diffraction studies of the anode and cathode in a lithium-ion cell[END_REF] LiCoO 2 , graphite Full Commercial 18650-type Rosciano et al. [START_REF] Rosciano | A novel electrochemical cell for in situ neutron diffraction studies of electrode materials for lithium-ion batteries[END_REF] LiNiO 2 Half Polyetherketone large coin-type Colin et al. [START_REF] Colin | In situ neutron diffraction study of li insertion in Li 4 Ti 5 O 12[END_REF] Li 4 Ti 5 O 12 Half Polyetherketone large coin-type Rodriguez et al. [START_REF] Rodriguez | In situ analysis of LiFePO 4 batteries: Signal extraction by multivariate analysis[END_REF] LiFePO 4 , graphite Full Commercial 18650-type Sharma et al. [131] LiCoO 2 , graphite Full Commercial 18650-type Du et al. [START_REF] Du | Brdoped Li 4 Ti 5 O 12 and Composite TiO 2 anodes for li-ion batteries: Synchrotron x-ray and in situ neutron diffraction studies[END_REF] Li 4 Ti 5 O 12 , TiO 2 Half Roll-over cylindrical vanadium Sharma, Du et al. [START_REF] Sharma | In-situ neutron diffraction study of the MoS 2 anode using a custom-built Li-ion battery[END_REF] MoS 2 Half Roll-over cylindrical vanadium Sharma, Reddy et al. [START_REF] Sharma | Time-Dependent in-Situ Neutron Diffraction Investigation of a Li(Co 0.16 Mn 1.84 )O 4 Cathode[END_REF] LiCo 0.16 Mn 1.84 O 4 Half Roll-over cylindrical vanadium Dolotko et al. [START_REF] Dolotko | Fatigue process in li-ion cells: An in situ combined neutron diffraction and elec-trochemical study[END_REF] LiCoO 2 , graphite Full Commercial 18650-type Senyshin et al. [START_REF] Senyshyn | Inoperando neutron scattering studies on Li-ion batteries[END_REF] LiCoO 2 , graphite Full Commercial 18650-type Sharma et al. [START_REF] Sharma | Direct evidence of concurrent solid-solution and two-phase reactions and the nonequilibrium structural evolution of LiFePO 4[END_REF] LiFePO 4 Half Roll-over cylindrical vanadium Sharma, Peterson [START_REF] Sharma | In situ neutron powder diffraction studies of lithiumion batteries[END_REF] LiCoO 2 , LiFePO 4 , LiMn 2 O 4 , Half Roll-over cylindrical vanadium graphite, YFe(CN) 6 , FeFe(CN) 6 Wang et al. [START_REF] Wang | Visualizing the chemistry and structure dynamics in lithium-ion batteries by in-situ neutron diffraction[END_REF] graphite Full Commercial 18650-type Bianchini et al. [START_REF] Bianchini | A new null matrix electrochemical cell for rietveld refinements of in-situ or operando neutron powder diffraction data[END_REF] LiFePO 4 and Li 1.1 Mn 1.9 O 4 Half (Ti,Zr) alloy large cylindrical Cai, An et al. [START_REF] Cai | In-situ observation of inhomogeneous degradation in large format li-ion cells by neutron diffraction[END_REF] LiMn 2 O 4 , graphite Full Commercial pouch-type Godbole et al. [START_REF] Godbole | Circular in situ neutron powder diffraction cell for study of reaction mechanism in electrode materials for li-ion batteries[END_REF] LiFePO 4 , Li 4 Ti 5 O 12 , graphite Half Al or Ti alloy large coin cell Li 1.1 (Ni 1/3 Co 1/3 Mn 1/3 ) 0.9 O 2 Hu et al. [START_REF] Hu | Real-time investigation of the structural evolution of electrodes in a commercial lithium-ion battery containing a V-added LiFePO 4 cathode using in-situ neutron powder diffraction[END_REF] V-doped LiFePO 4 Full Commercial pouch-type Liu et al. [START_REF] Liu | In-situ neutron diffraction study of the xLi 2 MnO 3 • (1-x)LiMO 2 (x = 0, 0.5; M = Ni, Mn, Co) layered oxide compounds during electrochemical cycling[END_REF] xLi 2 MnO 3 •(1-x)LiMO 2 Full Commercial pouch-type x=0, 0.5. M = Ni,Mn,Co Roberts et al. [START_REF] Roberts | Design of a new lithium ion battery test cell for in-situ neutron diffraction measurements[END_REF] LiFePO 4

Half Roll-over cylindrical Swagelock-type Senyshin et al. [START_REF] Senyshyn | Lithium intercalation into graphitic carbons revisited: Experimental evidence for twisted bilayer behavior[END_REF] Graphite Full Commercial 18650-type Sharma et Peterson [START_REF] Sharma | Current-dependent electrode lattice fluctuations and anode phase evolution in a lithium-ion battery investigated by in situ neutron diffraction[END_REF][START_REF] Sharma | Overcharging a lithium-ion battery: Effect on the Li x C 6 negative electrode determined by in situ neutron diffraction[END_REF] Graphite Full Commercial 18650-type Sharma et al. [START_REF] Sharma | Non-equilibrium Structural Evolution of the Lithium-Rich Li 1+y Mn 2 O 4 Cathode within a Battery[END_REF] Li 1+y Mn 2 O 4 Full Pouch-type Alam et al. [START_REF] Alam | Comparison of the so-called cgr and ncr cathodes in commercial lithium-ion batteries using in situ neutron powder diffraction[END_REF][START_REF] Kong Pang | Structural evolution of electrodes in the NCR and CGR cathode-containing commercial lithiumion batteries cycled between 3.0 and 4.5 V: An operando neutron powder-diffraction study[END_REF] LiNi 1/3 Co 1/3 Mn 1/3 O 2 and Full Commercial 18650-type Al-doped LiNi 1/2 Co 1/2 O 2 Bianchini et al. [START_REF] Bianchini | Li-Rich Li 1+x Mn 2-x O 4 Spinel Electrode Materials: An Operando Neutron Diffraction Study during Li+ Extraction/Insertion[END_REF] Li 1+x Mn 2-x O 4 (x = 0, 0.05, 0.10) Half (Ti,Zr) alloy large cylindrical Biendicho et al. [START_REF] Jordi | New in-situ neutron diffraction cell for electrode materials[END_REF] Ni-MH (Li-ion possible) -Large coin type Bobrikov et al. [START_REF] Bobrikov | Structural evolution in LiFePO 4 -based battery materials: In-situ and ex-situ time-of-flight neutron diffraction study[END_REF] LiFePO 4 Full Commercial pouch-type Brant et al. [START_REF] Brant | In situ neutron powder diffraction using custom-made lithium-ion batteries[END_REF] Li 0.18 Sr 0.66 Ti 0.5 Nb 0.5 O 3 Half Roll-over cylindrical Vanadium Dolotko et al. [START_REF] Dolotko | Understanding structural changes in NMC Li-ion cells by in situ neutron diffraction[END_REF] LiNi 1/3 Co 1/3 Mn 1/3 O 2 Full Commercial 18650-type Pang, Peterson et al. [START_REF] Kong Pang | Lithium migration in Li 4 Ti 5 O 12 studied using in situ neutron powder diffraction[END_REF][START_REF] Kong Pang | Structure of the Li 4 Ti 5 O 12 anode during charge-discharge cycling[END_REF] Li 4 Ti 5 O 12 Full Pouch-type Pang, Sharma et al. [START_REF] Kong Pang | In-situ neutron diffraction study of the simultaneous structural evolution of a LiNi 0.5 Mn 1.5 O 4 cathode and a Li 4 Ti 5 O 12 anode in a LiNi 0.5 Mn 1.5 O 4 -Li 4 Ti 5 O 12 full cell[END_REF] LiNi 0.5 Mn 1.5 O 4 and Li 4 Ti 5 O 12 Full Pouch-type Pang, Kalluri et al. [START_REF] Kong Pang | Electrochemistry and structure of the cobalt-free Li 1+x MO 2 (M = Li, Ni, Mn, Fe) composite cathode[END_REF] LiNi 1/3 Fe 1/3 Mn 1/3 O 2 Full Pouch-type Senyshyn et al. [START_REF] Senyshyn | Spatially resolved in operando neutron scattering studies on li-ion batteries[END_REF] LiCoO 2 , graphite Full Commercial 18650-type Vadlamani et al. [START_REF] Vadlamani | An in-situ electrochemical cell for neutron diffraction studies of phase transitions in small volume electrodes of li-ion batteries[END_REF] LiCoO 2 , LiMn 2 O 4 , graphite Full Planar stacking-type with Si case Zinth et al. [START_REF] Zinth | Lithium plating in lithium-ion batteries at sub-ambient temperatures investigated by in situ neutron diffraction[END_REF] Graphite Full Commercial 18650-type Pang et al. [START_REF] Kong | A custom battery for operando neutron powder diffraction studies of electrode structure[END_REF] review Full Pouch-type Senyshyn et al. [START_REF] Senyshyn | Low-temperature performance of li-ion batteries: The behavior of lithiated graphite[END_REF] graphite Full Commercial 18650-type 2.4 Design of a (Ti,Zr) electrochemical cell at the Institut

Laue-Langevin

The design of our custom-made electrochemical cell for in situ and operando neutron powder diffraction experiments was made combining the experience developed by the scientific community (especially the battery one) during the first 15 years of in situ NPD with the knowledge of neutron scattering present at ILL. The cell that we had to develop had to respond to some specific requirements:

• being able to cycle electrochemically for tens of cycles and for loadings of electrode materials comprised between 10 mg and 300 mg,

• at the highest loadings, being able to cycle at rates up to C/5,

• being easy to use, wash and re-use for potential users in large scale facilities,

• provide good quality neutron powder diffraction patterns in 30 min or less with no contributions besides those of the electrode material under study.

Moreover:

• minimize the quantity of battery components probed by the beam,

• focus on one of the battery electrodes only, trying to maximize its contribution to the neutron diffraction pattern.

The idea behind such choices is not to probe the whole battery, which as discussed above, results in many Bragg peaks in the diffraction pattern, but to probe a single electrode instead. This significantly distinguishes our cell design from others present in the literature.

The goal is to isolate the electrode from the rest of the electrochemical system, resulting in a maximum of Bragg reflections to succeed in reliable Rietveld structural analysis. The scheme and a picture of the battery designed at ILL (with the participation of Jean-Luc Laborier and Ludovic Gendrin (ILL) and Jean-Bernard Leriche (LRCS)) are reported in Figure 2.5. In the following we will address every battery component and discuss the choices we made.

Cell protective case and positive current collector

Every battery needs a protective case to keep it airtight i.e to isolate it from the external environment. This is problematic since cases are usually made of steel or aluminum, both generating intense Bragg reflections. To get rid of this problem the battery protective case, that in our design acts as the positive current collector as well, was fabricated using a (Ti,Zr) Null-Matrix alloy [START_REF] Dobromyslov | Structure studies of quenched and tempered ZrTi alloys[END_REF][START_REF] Murray | The Ti-Zr (Titanium-Zirconium) system[END_REF][START_REF] Doi | Study of Nb-Zr-Ti phase diagram[END_REF][START_REF] Sidhu | Neutron diffraction study of titaniumâzirconium system[END_REF][170] . This special material, developed for the last 50 years at neutron scattering facilities and well-known at ILL, is neutron "transparent": its coherent contribution to the scattering of neutrons is very weak and in general negligible (on the other hand, incoherent scattering from this material is still present, resulting in a featureless diffused background). Titanium and Zirconium have scattering lengths opposite in sign and in a ≈1:2 ratio (b T i = -3.37 fm and b Zr = 7.16 fm) and their alloy, prepared with the corresponding necessary stoichiometric amounts of the two elements, has zero overall scattering intensity, thus being a perfect container material for NPD experiments.

Calculating the required Ti/Zr ratio is rather trivial, knowing that titanium and zirconium in their pure metallic forms have the same crystal structure, belonging to the hexagonal space group P6 3 /mmc, and that their alloy does not differ from this. Thus Ti and Zr are both placed in a 2c Wyckoff site of fractional atomic coordinates x/a = 1/3, y/b = 2/3, z/c = 1/4, with a random site occupancy factor respecting the constraint of a full site

O T i + O Zr = 1.
Starting from a simple expression for the structure factor for the diffraction of neutrons:

F = n j=1 O j b j exp -i2π(hx+ky+lz) = T i,Zn O j b j exp -i2π(hx+ky+lz) = (-3.37O T i + 7.16O Zr )exp -i2π(hx+ky+lz) (2.1)
Which leads to zero structure factors (for any set of h,k,l, thus for any Bragg reflection) when:

-3.37O T i + 7.16O Zr = 0 ⇒    O T i /O Zr = 2.1 O T i + O Zr = 1 (2.2)
This results in a formula unit for the null scattering alloy of Ti 0.68 Zr 0.32 (≈ Ti 2.1 Zr).

As Titanium and Zirconium have atomic weight of 47.867 g/mol and 91.224 g/mol, respectively, the alloy with null coherent scattering length contains 52.2 wt% Ti and 47.8 wt% Zr. These results were already proved in 1956 by Sidhu et al. [START_REF] Sidhu | Neutron diffraction study of titaniumâzirconium system[END_REF] , who measured NPD patterns from metallic Ti, Zr and from an alloy close to the Null-Matrix composition (Ti 0.6 Zr 0.4 ). Their results are shown in Figure 2.6. The fact of being neutron-transparent is not the only requirement needed for a good material acting as current collector and protective case. Such a material must also be a good current conductor, mechanically resistant and should not be easily oxidized, making the cell resistant mechanically and chemically.

The Null-matrix (Ti,Zr) alloy used at ILL respond to all these requirements, making it the Reprinted from [START_REF] Sidhu | Neutron diffraction study of titaniumâzirconium system[END_REF] .

material of choice for our cell [170] . The volume of the cylindrical container we designed is

approximately 9 cm 3 (h • π • R 2 ≈ 3 • π • 1 2 ).
When placed in this container, 200 mg of the powder electrode to be investigated occupy ≈ 1 mm in height, to be exposed to the neutron beam.

The Positive Electrode

The positive electrode is usually the battery component under study. It is mainly composed by an electrochemically active material (AM), often having poor electronic conductivity, and by an amorphous carbon, to improve it. In this thesis the positive electrode has always been prepared with commercial Carbon Super P (Csp, unless specified otherwise), intimately mixed with the AM using a mortar. Their relative ratio depends on the specific conductivity of the material, but in general it ranges between 90% AM -10% Csp (in weight, noted as 90:10 wt%) for good conductors to 80:20 wt% for poorer electronic conductors.

The amount used will be specified for every experiment. The contribution of Csp to a NPD experiment can be described as an augmented background that can be observed in Figure 2.7. In this case, LiFePO 4 is compared to a mixture of LiFePO 4 and Csp in weight ratio 85:15. Csp is amorphous and it does not present any Bragg peak (contrary to graphite for example). However its interaction with neutrons is mainly coherent (σ coh = 5.551(2) barns vs. σ inc = 0.001(4) barns) [START_REF] Dianoux | Neutron Data Booklet[END_REF] implying that the scattered intensity does not give a completely flat background, but it rather results in a slowly undulated background, typical of amorphous structures. The maxima of such undulations can be seen around 25 • and 80 • at λ = 1.594 Å (1.76 and 5.28 Å-1 ). The background increase is in general not significant, except for the regions of the maxima. Since this undulating contribution is not straightforward to take into account, the amount of carbon present in the electrode is minimized whenever possible. It is also true, however, that its contribution to the background is poor when compared to other parasitic contributions, particularly the electrolyte's one discussed in the following. For this reason carbon's signal during data analysis is just carefully included in the background, not affecting Bragg peaks' intensities of the material of interest.

After the first studies made with the electrode formulation discussed above, we realized that, due to the big amount of powder used in the electrode, the obtained capacity was good but not optimal (see the studies on spinel materials in the next chapter). A part of the electrode, probably on the sides, did not fully react. Therefore, in the following studies, we adopted an improved formulation for the electrode by adding a binder. This is a polymeric material that, when added to the active material plus carbon mixture, gives as a result a paste (instead of a simple powder). The binder is electrochemically inert, while ensuring a better mechanical strength of the electrode and, more importantly, a better homogeneity.

In our case the choice of the binder was relatively easy, since among those used in the battery community only one was completely hydrogen-free, this being a strong advantage in neutron diffraction (see the next paragraph for a discussion on hydrogen's contribution to neutron diffraction). We hence chose polytetrafluoroethylene C 2 F 4 (PTFE, or Teflon R ) for our electrode formulation. It was mixed in a mortar with active material and Csp, in a variable amount around 6-10% in weight, which will be specified in the following when needed.

Electrolyte and Separator

In a Li-ion battery the separator is a porous medium used to keep the positive and negative electrodes physically separated (avoiding short-circuits) while insuring ionic conductivity between them, thanks to the electrolyte that wets the whole system. This means that there is no way to avoid that the bottom part of the separator and of the electrolyte are exposed to the neutron beam. A wise choice of both components is thus required to minimize their (hydrogen-rich) contribution to the diffracted pattern. Hydrogen is in fact a very strong incoherent scatterer (σ coh = 1.75 barns vs. σ inc = 80.27 barns) [START_REF] Dianoux | Neutron Data Booklet[END_REF] , meaning that in a diffraction experiment it barely affects Bragg peaks, while creating a very intense background, featureless in the whole angular range, hence reducing the available signal to noise ratio. For the separator material, the most common choices are glass-fiber, PVDF is a strong neutron absorber because its isotope 10 B has a high neutron absorption crosssection (3835 barns, resulting in 767 barns for natural boron) [START_REF] Dianoux | Neutron Data Booklet[END_REF] . This could represent a significant problem because of the consequent signal attenuation. However, the amount of boron in glass-fiber separators is just around 3%, thus inducing only a small reduction of the neutrons diffracted. We could readily observe that in fact such material's contribution to the NPD pattern is poor and therefore we retained it as best choice for our studies.

(polyvinylidene difluoride, [C 2 H 2 F 2 ] n ) or Celgard (polypropylene, [C 3 H 6 ] n ).
Recently, Pang and Peterson [START_REF] Kong | A custom battery for operando neutron powder diffraction studies of electrode structure[END_REF] measured Celgard, PVDF and glass-fiber separators in a NPD experiment, showing indeed that glass-fiber is the best choice.

Regarding the non-aqueous electrolyte, this is an extremely hydrogen-rich system. barns, significantly reduced with respect to hydrogen's one of 80.27(6) barns [START_REF] Dianoux | Neutron Data Booklet[END_REF] . This solves the electrolyte problem, while significantly increasing the cost of any in situ NPD experiment because of the high cost for purchasing deuterated solvents (for example, 20 mL of d-dimethyl carbonate cost about 900 euros, while the normal version costs 43 euros for 100 mL; 5 g of d-ethylene carbonate cost about 1950 euros, while 100 g of the normal version cost 32 euros). One recent attempt of performing in situ NPD experiments using standard hydrogenated solvents was carried out by Godbole et al. [START_REF] Godbole | Circular in situ neutron powder diffraction cell for study of reaction mechanism in electrode materials for li-ion batteries[END_REF] . Their results clearly show that the qualitative evolution of Bragg peaks position and intensity can be followed, provided that an extremely high neutron flux is available, but they also show that data quality is not sufficient for any quantitative analysis. Considering that our main goal was to succeed in Rietveld refinement of data collected operando, the use of hydrogenated solvents was not satisfactory and we decided to utilize deuterated solvents. The selected electrolyte composition used throughout all in situ NPD experiments in this thesis is 1M LiPF 6 (Sigma Aldrich) in EC:DMC (1:4 wt%, both from Armar Chemicals). The reason of such proportion choice is both historical (other groups chose this composition in the past, showing that it could properly work [START_REF] Roberts | Design of a new lithium ion battery test cell for in-situ neutron diffraction measurements[END_REF] ) and practical, the price of EC being about four times the one of DMC. Very recently a work by Petibon et al. [START_REF] Petibon | The use of deuterated ethyl acetate in highly concentrated electrolyte as a lowcost solvent for in situ neutron diffraction measurements of li-ion battery electrodes[END_REF] showed a new possible electrolyte formulation, based on deuterated ethyl acetate, able to give comparable performances at a much lower price.

Other battery components

After the sandwich of positive electrode plus electrolyte-wetted separator, the battery stack is completed by the negative electrode: a lithium foil (Sigma Aldrich) which is put below a negative current collector (this is a 1 mm-thick disk made in Ti 2. 1 Zr to insure that it would not interact with the neutron beam). A spring generates pressure on the whole stack, a plunger closes the cell with a plastic gasket and a screw completes the cell (see again Figure 2.5). It is important to note that a mylar film covers the internal part of the in situ cell and together with the gasket assures the electrical insulation between the positive and the negative electrodes and makes the cell air-tight. Once closed, the cell can be mounted (vertically) in the diffractometer as illustrated in Figure 2.8 thanks to a plastic screw entering the top of the plunger, and aligned with slits so that the beam irradiates only the bottom part of the cell where the electrode powder is located.

Mounting of the cell on the D20 diffractometer

The geometry of an in situ/operando experiment is shown in However, due to the dimension of our cell and to our experimental geometry during in situ experiments, only 120 • out of 156 • were fully exploited.

Cell Validation and testing

The performances of our electrochemical cell were tested with commercially available positive electrode materials. In particular, we report here the data we acquired on an olivinetype phase, LiFePO 4 [START_REF] Padhi | Phospho-olivines as positive-electrode materials for rechargeable lithium batteries[END_REF] . 18 years after its discovery, this material has now reached industrial exploitation and, although its basic crystal structure is well-known [START_REF] Rousse | Magnetic structures of the triphylite LiFePO 4 and of its delithiated form FePO 4[END_REF][START_REF] Andersson | The source of first-cycle capacity loss in LiFePO4[END_REF] , it keeps attracting much attention due to the versatility of its electrochemical properties depending for instance on temperature, particle size, carbon coating, etc. [START_REF] Delacourt | The existence of a temperature-driven solid solution in Li x FePO 4 for 0 ≤ x ≤ 1[END_REF][START_REF] Yamada | Room-temperature miscibility gap in Li x FePO 4[END_REF][START_REF] Orikasa | Transient phase change in two phase reaction between LiFePO 4 and FePO 4 under battery operation[END_REF][START_REF] Gibot | Room-temperature single-phase Li insertion/extraction in nanoscale Li x FePO 4[END_REF][START_REF] Delacourt | Crystal chemistry of the olivine-type Li x FePO 4 system (0 ≤ x ≤ 1) between 25 and 370 degrees c[END_REF] , some of which were already discussed in the introduction. It is worth mentioning that we also tested the cell with a commercial over-stoichiometric spinel-type phase Li 1.10 Mn 1.90 O 4 [23] , but the results are not shown here since spinel compositions are treated in more detailed studies in the next chapter.

The validation of our cell followed three main steps: first, we conducted electrochemical galvanostatic cycling using different electrolytes and at different rates. Second, we measured LiFePO 4 as pure powder in a standard NPD experiment, subsequently comparing the obtained patterns to those recorded in a "full-battery configuration", i.e. with the active material mixed with Csp, mounted in the in situ cell with all battery components (electrolyte, lithium, etc.). We then compared the accuracy of the parameters we could obtain from Rietveld refinement in the two cases. Finally, we validated the possibility to conduct a real operando experiment measuring NPD patterns upon charge of LiFePO 4 and obtaining reliable structural information from Rietveld analysis of the data.

Electrochemical testing

Batteries were assembled in the in situ cell described above. Only the first cycles are depicted here but subsequent prolonged cycling with good coulombic efficiency was achieved under these conditions. The observed polarization of the cell is quite satisfactory as it does not increase significantly when the mass of the electrode exceeds 100 mg. The voltage plateau observed around 3.45 V vs. Li + /Li reveals as expected a classical two-phase electrochemical reaction between Li 1-δ FePO 4 and Li FePO 4 [START_REF] Yamada | Phase change in Li x FePO 4[END_REF] . These data show, additionally, that the deuterated electrolyte we used possessed similar properties than a standard EC:DMC-based one (LP30) at cycling rates as high as C/10. Although it presents slightly lower kinetics, this does not represent a problem for operando NPD because of the counting times which are rather long (≥ 10 min/scan). Additionally, only small capacity loss was observed (at slower regime) for higher electrode loadings (≈ 105 mg). The electrochemical cell designed to obtain in situ or operando neutron diffraction data was thus shown to deliver electrochemical performances comparable to those obtained in classical electrochemical cells, with an active mass that can be rather large and a cycling rate that can be rather fast. All the diffraction patterns were refined by the Rietveld method [START_REF] Rietveld | A profile refinement method for nuclear and magnetic structures[END_REF] , i.e. with the determination of cell parameters, atomic positions, occupancy factors and Debye-Waller factors, thanks to the FullProf suite [START_REF] Rodriguez-Carvajal | Recent advances in magnetic-structure determination by neutron powder diffraction[END_REF] . The similar wavelengths are helpful for a straight comparison of peaks intensities of the collected NPD patterns since they are approximately at the same angular position. The in situ pattern shows a large bump in the low-angle region (15-30 • ) due to the scattering from the deuterated electrolyte (and not from the glass fiber separator) that was taken into account by a point by point background definition. As pre- For this first operando experiment, a lithium battery within our (Ti,Zr) cell was prepared using LiFePO [START_REF] Yamada | Room-temperature miscibility gap in Li x FePO 4[END_REF] for nano-sized LiFePO 4 .

For each of the two end members, 15 parameters have been refined: the scale factor, 3 cell parameters and 11 fractional atomic coordinates. Zero shift and wavelength had been previously refined thanks to an internal standard and have been fixed afterwards. Isotropic thermal displacement parameters were instead kept fixed to the values obtained for the pattern measured on D2B for LiFePO 4 . Besides, the absorption coefficient µR had to be considered due to the presence of lithium. It had thus its maximum value for LiFePO 4 (about 0.43) and it was negligible for FePO 4 . In the case of the three intermediate twophase compositions, the refined parameters were still 15 for each phase, making a total of 30 for each pattern. The coefficient µR was then reduced according to the weight percent of LiFePO 4 remaining in the structure. The main structural results coming from this analysis are reported in Table 2.5, where the good quality of the refinement can be seen from R Bragg parameters, never exceeding 10.6%, and bond length distances in agreement for a given phase between the different compositions. Refined values are slightly inaccurate only when the crystalline weight of the considered phase is around 25% or less. Moreover, bond length distances for LiFePO 4 and FePO 4 can be compared to those reported in literature [START_REF] Delmas | Lithium deintercalation in LiFePO 4 nanoparticles via a domino-cascade model[END_REF] showing a good agreement. A sequential refinement of the operando diffraction patterns was also performed, involving all the recorded patterns. In this case the structural parameters were fixed and only scale factors were permitted to vary. This allowed determining weight fractions for LiFePO 4 and FePO 4 , within the crystalline part of all the compositions studied. Indeed, as shown by the results given in Figure 2.15, FePO 4 is not detected at the very beginning of the charge, as happens to LiFePO 4 at the end of the charge. Note that it does not mean that these minority phases are effectively not present, but their crystalline domains could be small and not extended enough to diffract efficiently. Then, the distribution between LiFePO 4 and FePO 4 does not follow exactly the theoretical line, although a linear variation is expected for a two-phase reaction. This is well explained by: i) a quantification that is in fact only semi-quantitative due to the absence of an internal standard with a known fraction (versus LiFePO 4 ) in our positive electrode and thus to the impossibility to take into account the possible presence of non-crystalline phases [START_REF] Orlhac | Determination of the crystallized fractions of a largely amorphous multiphase material by the rietveld method[END_REF] and ii) the strong absorption of Li which is present in one phase, LiFePO 4 , and not in the other one, FePO 4 , affecting thus also slightly the ratio between the two weight fractions. Such a deviation from the theoretical behavior had also been observed before by Andersson and Thomas [START_REF] Andersson | The source of first-cycle capacity loss in LiFePO4[END_REF] . Despite of that, the change in the weight fractions between LiFePO 4 and FePO 4 is still close to a linear behavior, as additional proof of the quality of the analysis of these in situ NPD data.

6 2θ (°)
∆ = 1/N i (di -d / d ) 2 .
100 % LiFePO 4 0 % FePO 4 a = 10.320(1) Å; b = 6.004(1) Å; c = 4.6907(7) Å; -V = 290.68(7) Å3 ; R B = 6.51% -

Interatomic distances ( Å) / Distortion Interatomic distances ( Å) / Distortion

Fe-O1=2. 19(3)

P-O1 = 1.57(3) Li-O1(x2) = 2.16(2) Fe-O2 = 2.10(3) P-O2= 1.52(3) Li-O2(x2) = 2.09(2) Fe-O3(x2) = 2.05(2) P-O3(x2) = 1.56(2) Li-O3(x2) = 2.20(2) - - - Fe-O3(x2) = 2.25(2) - - ∆ = 16.1E-04 ∆ = 1.3E-04 ∆ = 4.2E-04 75

Interatomic distances ( Å) / Distortion Interatomic distances ( Å) / Distortion

Fe-O1=2.18(4)

P-O1 = 1.56(4) Li-O1(x2) = 2.16(2) Fe-O1=2.0(1) P-O1 = 1.7(2) Fe-O2 = 2.09(4) P-O2= 1.54(5) Li-O2(x2) = 2.11(2) Fe-O2 = 2.0(1) P-O2= 1.3(2) Fe-O3(x2) = 2.08(2) P-O3(x2) = 1.55(3) Li-O3(x2) = 2.20(2) Fe-O3(x2) = 1.8(1) P-O3(x2) = 1.7(1) - Fe-O3(x2) = 2.21(3) - - Fe-O3(x2) = 2.3(1) - ∆ = 7.3E-04 ∆ = 0.2E-04 ∆ = 2.8E-04 ∆ = 134.2E-04 ∆ = 155.1E-04 50

Interatomic distances ( Å) / Distortion Interatomic distances ( Å) / Distortion

Fe-O1 = 2.2(1)

P-O1 = 1.6(2) Li-O1(x2) = 2.2(1) Fe-O1=1.91(3) P-O1 = 1.54(4) Fe-O2 = 2.2(2) P-O2= 1.2(2) Li-O2(x2) = 2.1(1) Fe-O2 = 1.97(3) P-O2= 1.45(4) Fe-O3(x2) = 1.92(9) P-O3(x2) = 1.6(1) Li-O3(x2) = 2.28(9) Fe-O3(x2) = 2.01(2) P-O3(x2) = 1.58(3) - Fe-O3(x2) = 2.5(1) - - Fe-O3(x2) = 2.16 (3)

Conclusions and perspectives

This chapter recalls the important parameters that have been taken into consideration to successfully develop an electrochemical cell for in situ and operando neutron powder diffraction. We showed that it could properly function electrochemically, while leading at the same time to NPD patterns of high quality for Rietveld structural refinements. Important choices have been in particular the use of a neutron-transparent material such as the (Ti,Zr) alloy, the use of a deuterated electrolyte and the high neutron flux available on the D20 diffractometer. We showed the satisfactory electrochemical curves obtained for a representative material, LiFePO 4 . Subsequently, in situ NPD measurements were conducted upon charge. For the first time a single-and multi-phase Rietveld refinement could be successfully performed on in situ and operando patterns, leading to reliable and accurate structural parameters. For these reasons, such a cell can be an extremely useful tool to study new materials of interest for Li-ion and Na-ion batteries, where the understanding of phase transition mechanisms is essential for further improvements and development. The use of our cell to study different classes of materials is described in the following of this thesis. Here it is important to note that in situ/operando NPD for the study of electrode materials has kept developing ever more rapidly in 2014 and 2015. New cell designs have been proposed [START_REF] Vadlamani | An in-situ electrochemical cell for neutron diffraction studies of phase transitions in small volume electrodes of li-ion batteries[END_REF][START_REF] Kong | A custom battery for operando neutron powder diffraction studies of electrode structure[END_REF][START_REF] Jordi | New in-situ neutron diffraction cell for electrode materials[END_REF] and several new studies undertaken [START_REF] Kong Pang | Structural evolution of electrodes in the NCR and CGR cathode-containing commercial lithiumion batteries cycled between 3.0 and 4.5 V: An operando neutron powder-diffraction study[END_REF][START_REF] Bobrikov | Structural evolution in LiFePO 4 -based battery materials: In-situ and ex-situ time-of-flight neutron diffraction study[END_REF][START_REF] Dolotko | Understanding structural changes in NMC Li-ion cells by in situ neutron diffraction[END_REF][START_REF] Kong Pang | In-situ neutron diffraction study of the simultaneous structural evolution of a LiNi 0.5 Mn 1.5 O 4 cathode and a Li 4 Ti 5 O 12 anode in a LiNi 0.5 Mn 1.5 O 4 -Li 4 Ti 5 O 12 full cell[END_REF][START_REF] Zinth | Lithium plating in lithium-ion batteries at sub-ambient temperatures investigated by in situ neutron diffraction[END_REF] , making this an extremely rich, challenging and competitive field, as already proved by 2.4. On our side, future developments mainly regard: i) the use of cheaper deuterated electrolytes, as recently reported [START_REF] Petibon | The use of deuterated ethyl acetate in highly concentrated electrolyte as a lowcost solvent for in situ neutron diffraction measurements of li-ion battery electrodes[END_REF] , ii) the operando study of more challenging materials, especially among polyanionic compositions, and iii) the development of similar electrochemical cells for operando studies on all-solid-state lithium batteries (i.e. cells able to operate at high temperatures).

Chapter 3

Operando neutron powder diffraction studies of spinel materials for Li-ion batteries 3.1 Introduction

The spinel family

Spinels are a class of minerals of general formulation A 2+ B 3+ 2 X 2- 4 , crystallizing in the cubic crystal system. They have a close-packed lattice of anions, being in most cases oxygen O 2-, while A and B occupy tetrahedral and octahedral sites in the structure [START_REF] Walter | Crystal structures[END_REF] , respectively. If the anion is not oxygen but another chalcogenide element, the structure is named thiospinel. Although the prototypical spinel MgAl 2 O 4 contains elements A and B in oxidation states 2+ and 3+, respectively, many other combinations are possible, including monovalent and quadrivalent cations as well. This is of special interest in this thesis, since lithium is monovalent and it is normally the A element in the structure, giving rise to a higher oxidation state for the B element (3.5+). Several minerals in nature are found to crystallize in the spinel crystal structure. "The" Spinel is MgAl 2 O 4 , named in 1779 by Jean Demeste from the latin "spinella", little thorn, alluding to its sharp octahedral crystals [180] . This can be a precious stone, depending on the impurities it may contain.

The most abundant member of the spinel family is magnetite Fe 3 O 4 , where A and B are Fe 2+ and Fe 3+ cations, respectively. These two materials, MgAl 2 O 4 and Fe 3 O 4 , were used to unravel the general crystal structure of spinels by the co-father of X-Ray diffraction himself, H. W. Bragg, in parallel with S. Nishikawa, in 1915 [START_REF] Bragg | The structure of magnetite and the spinels[END_REF][START_REF] Bragg | The structure of the spinel group of crystals[END_REF][183] . Their first discoveries were sustained and complemented by successive works, leading to a good knowledge of the spinels' crystal structure (Figure 3.1) [START_REF] Barth | Spinel structures with and without variate atom equipoints[END_REF] . A very clear description of such structures was given a few years later by M.M. Thackeray, who was working on the composition LiMn 2 O 4 . In his words: "The cubic spinel possesses prototypic symmetry Fd 3m (O 7 h ) and has a general structural formula A[B 2 ]X 4 . The anions X form a cubic-close-packed array occupying the 32e sites of the space group; the B cations occupy half the octahedral sites, the 16d sites, and the A cations occupy one-eighth of the tetrahedral sites, 8a. The interstitial octahedral sites 16c are interconnected in 3D by sharing common edges with six like near neighbors exactly as the 16d sites, but shifted by half a lattice parameter in space. Each 16c site shares two common faces, on opposite sides, with occupied 8a sites; the other faces are shared with empty, interstitial tetrahedral sites, 48f. The final empty tetrahedral sites, 8b, shares faces with four, occupied 16d octahedral sites; it would require a large energy to insert cations into the 8b sites" [START_REF] Thackeray | Lithium insertion into manganese spinels[END_REF] . This structure properly describes "normal" spinels. In this picture, tetrahedral sites are in general smaller that octahedral ones, determining a preference based on cation size for the elements that will better fit in these spaces. In fact, it is also possible to observe a spinel inversion [START_REF] Barth | Spinel structures with and without variate atom equipoints[END_REF][START_REF] Verwey | Physical properties and cation arrangement of oxides with spinel structures i. cation arrangement in spinels[END_REF] : a total inversion happens when all the A cations occupy octahedral sites, inducing a displacement of half of the B cations to tetrahedral ones. This is the case of magnetite, for example. The inversion can also be incomplete, resulting in a crystal

structure of the form [A 1-x B x ] T d [A x/2 B 1-x/2 ] Oh 2 O 4
, where x denotes the degree of inversion. x = 0 represents the normal spinel, x = 1 the inverse one. If A and B are close in the periodic table and thus their scattering powers for X-Rays are similar, it can be difficult to distinguish a normal from an inverse spinel, as it is the case for MgAl 2 O 4 . In such cases, neutron diffraction can usually lift the doubt [START_REF] Bacon | A neutron-diffraction study of magnesium aluminium oxide[END_REF] . The occurrence of inverse spinels has been widely studied; surprisingly, the relative size of s and p atomic orbitals of the two types of atom A and B has been shown to be the leading factor to determine site preference and thus the favourable type of spinel, while the type/size of d orbitals involved only play a secondary role [START_REF] Burdett | Role of the crystal-field theory in determining the structures of spinels[END_REF] . Goodenough in Oxford, UK, who had already a wide knowledge of the spinel family due to early works [START_REF] Goodenough | Theory of ionic ordering, crystal distortion, and magnetic exchange due to covalent forces in spinels[END_REF] . The first spinel structure Thackeray looked at was magnetite, showing with other iron oxides an interesting electrochemical activity [START_REF] Thackeray | A preliminary investigation of the electrochemical performance of α-Fe 2 O 3 and Fe 3 O 4 cathodes in high-temperature cells[END_REF][START_REF] Thackeray | Structural characterization of the lithiated iron oxides Li x Fe 3 O 4 and Li x Fe 2 O 3 (0leqxleq2)[END_REF] . As a consequence of these first studies, he began investigating LiMn 2 O 4 both in terms of lithium insertion and extraction [START_REF] Thackeray | Lithium insertion into manganese spinels[END_REF][START_REF] Thackeray | Electrochemical extraction of lithium from LiMn 2 O 4[END_REF][22] . It is worth mentioning that lithium being placed in the tetrahedral site 8a, as described above, was not an obvious conclusion. It was understood because (220) and ( 422) reflections, usually present in spinels and therefore allowed by symmetry, are actually extremely weak (almost extinct) in LiMn 2 O 4 (Figure 3.3). The intensities of these two reflections are chiefly dependent upon the atomic scattering factors of the ions occupying tetrahedral sites. Therefore, the light lithium atoms (Z = 3) with their low scattering power for X-rays were deduced to be the occupants of the tetrahedral sites in the structure of LiMn 2 O 4 [START_REF] Barth | Spinel structures with and without variate atom equipoints[END_REF][START_REF] Wickham | Crystallographic and magnetic properties of several spinels containing trivalent manganese[END_REF] . The structure of pristine LiMn 2 O 4 was already well-known at the beginning of such studies [START_REF] Goodenough | Theory of ionic ordering, crystal distortion, and magnetic exchange due to covalent forces in spinels[END_REF][START_REF] Wickham | Crystallographic and magnetic properties of several spinels containing trivalent manganese[END_REF] , so that the investigation could focus on the role of lithium upon intercalation and deintercalation. Figure 3.4 summarizes the electrochemistry of the material in both reactions. Upon Li + insertion (Li 1+x Mn 2 O 4 ), it was found that the cubic symmetry (of cell parameter a = 8.248 Å) is disrupted as a consequence of cooperative Jahn-Teller effect [START_REF] Thackeray | Lithium insertion into manganese spinels[END_REF] ,

LiMn 2 O 4 for Li-ion batteries

inducing a tetragonal distortion when lithium content exceeds 1.2 Li/f.u. and thus the ratio of Mn 3+ /Mn 4+ increases above ≈3/2. The phase transition between LiMn 2 O 4 and Li 2 Mn 2 O 4 is first-order and a two-phase region is observed for 0.1 < x < 0.8 [START_REF] Thackeray | Lithium insertion into manganese spinels[END_REF][START_REF] Ohzuku | Electrochemistry of manganese-dioxide in lithium nonaqueous cell. x-ray diffractional study on the reduction of spinel-related manganese-dioxide[END_REF] . This means that, electrochemically, a flat voltage-composition curve is observed at a potential close to 3.0 V vs. Li + /Li. The newly inserted Li + ions occupy the interstitial 16c sites.

These share faces with the 8a tetrahedra, thus electrostatic interactions between the lithium ions on these two sets of sites cause an immediate displacement of the tetrahedral-site lithium ions into neighboring, vacant 16c octahedra. Therefore in the rock salt Li 2 Mn 2 O 4 most of the lithium ions are in 16c sites, although a non-zero occupation of the 8a ones has been demonstrated using neutron diffraction [START_REF] David | Structure refinement of the spinel-related phases Li 2 Mn 2 O 4 and Li 0.2 Mn 2 O 4[END_REF] . The actual tetragonal space group becomes F4 1 /ddm with a bigger unit cell volume caused by lithium insertion (however, the Jahn-Teller effect causes a to decrease and c to increase, a = 7.994(l) Å, c = 9.329 (1)

Å) [START_REF] Thackeray | Lithium insertion into manganese spinels[END_REF]22] .

Figure 3.4:

The electrochemical profile (voltage-composition galvanostatic curve) of a LiMn2O4//Li half cell. Both the high-voltage Li deintercalation domain and low-voltage Li intercalation one are displayed. Reprinted from [23] .

Upon lithium extraction (Li 1-x Mn 2 O 4 ), the cubic structure described in space group Fd 3m is maintained. The completely delithiated end member is λ-MnO 2 , a rocksalt compound whose cell parameter is a = 8.03 Å [194] , significantly decreased with respect to that of LiMn 2 O 4 [START_REF] Thackeray | Electrochemical extraction of lithium from LiMn 2 O 4[END_REF]22,[START_REF] David | Structure refinement of the spinel-related phases Li 2 Mn 2 O 4 and Li 0.2 Mn 2 O 4[END_REF] . The process involves manganese oxidation until 100% Mn 4+ is obtained. This is electrochemically observed as a sequence of two plateaus in the voltage-composition curve, around 4.05 V and 4.15 V vs. Li + /Li [START_REF] Thackeray | Electrochemical extraction of lithium from LiMn 2 O 4[END_REF][START_REF] Ohzuku | Electrochemistry of manganese-dioxide in lithium nonaqueous cell. x-ray diffractional study on the reduction of spinel-related manganese-dioxide[END_REF][START_REF] Thackeray | Spinel electrodes from the Li-Mn-O system for rechargeable lithium battery applications[END_REF] (see Figure 3.5 for instance). The ex-istence of an intermediate phase of composition Li 0.5 Mn 2 O 4 has been proposed (although not demonstrated) to explain this feature [START_REF] Liu | Mechanism of the electrochemical insertion of lithium into LiMn 2 O 4 spinels[END_REF][START_REF] Baehtz | Design and performance of an electrochemical in-situ cell for high resolution full-pattern xray powder diffraction[END_REF][START_REF] Van Der Ven | Phase transformations and volume changes in spinel Li x Mn 2 O 4[END_REF] and it will be further discussed in the next paragraphs of this chapter. Such a phase was observed in more recent studies, but it did not seem to involve any change in the crystal structure, i.e. spinel-spinel biphasic transitions were observed [START_REF] Bianchini | Li-Rich Li 1+x Mn 2-x O 4 Spinel Electrode Materials: An Operando Neutron Diffraction Study during Li+ Extraction/Insertion[END_REF][START_REF] Baehtz | Design and performance of an electrochemical in-situ cell for high resolution full-pattern xray powder diffraction[END_REF] .

LiMn 2 O 4 has been one of the most widely studied materials in the last 30 years, with thousands of publications reporting synthesis routes and relative electrochemical properties [START_REF] Thackeray | Spinel electrodes from the Li-Mn-O system for rechargeable lithium battery applications[END_REF][START_REF] Tarascon | Li metal-free rechargeable batteries based on Li 1+x Mn 2 O 4 cathodes (0 ≤ x ≤ 1) and carbon anodes[END_REF][START_REF] Tarascon | The spinel phase of LiMn 2 O 4 as a cathode in secondary lithium cells[END_REF][START_REF] Guyomard | High-voltage-stable electrolytes for Li 1+x Mn 2 O 4 /carbon secondary batteries[END_REF][START_REF] Tarascon | The Li 1+x Mn 2 O 4 /C rocking-chair system: a review[END_REF][START_REF] Tarascon | Synthesis conditions and oxygen stoichiometry effects on li insertion into the spinel LiMn 2 O 4[END_REF][START_REF] Guyomard | The carbon/Li 1+x Mn 2 O 4 system[END_REF][START_REF] Tarascon | The Li 1+x Mn 2 O 4 /C system materials and electrochemical aspects[END_REF][START_REF] Gao | Synthesis and characterization of Li 1+x Mn 2-x O 4 for Li-Ion Battery Applications[END_REF][START_REF] Liu | Synthesis and electrochemical studies of spinel phase LiMn 2 O 4 cathode materials prepared by the pechini process[END_REF][START_REF] Xia | An investigation of lithium ion insertion into spinel structure li-mn-o compounds[END_REF] , phase diagram and phase transition as a function of several external parameters [23,[START_REF] Liu | Mechanism of the electrochemical insertion of lithium into LiMn 2 O 4 spinels[END_REF][START_REF] Rousse | X-ray study of the spinel LiMn 2 O 4 at low temperatures[END_REF][START_REF] Rousse | Cubic orthorhombic transition in the stoichiometric spinel LiMn 2 O 4[END_REF][START_REF] Rodriguez-Carvajal | Electronic crystallization in a lithium battery material: Columnar ordering of electrons and holes in the spinel LiMn 2 O 4[END_REF][START_REF] Mukerjee | Structural evolution of Li x Mn 2 O 4 in lithium-ion battery cells mea-sured in situ using synchrotron X-ray diffraction techniques[END_REF][START_REF] Thurston | Synchrotron x-ray diffraction studies of the structural properties of electrode materials in operating battery cells[END_REF][START_REF] Kanno | The relationships between phases and structures of lithium manganese spinels[END_REF][START_REF] Yonemura | Synthesis, structure, and phase relationship in lithium manganese oxide spinel[END_REF] , nano-fabrications and nano-structurations [START_REF] Kim | Spinel LiMn 2 O 4 nanorods as lithium ion battery cathodes[END_REF][START_REF] Hosono | Synthesis of single crystalline spinel LiMn 2 O 4 nanowires for a lithium ion battery with high power density[END_REF] ... until finally it led to concrete industrial applications, for example as the positive electrode in the Nissan Leaf vehicle, commercialized from 2010-2011 [218] . The interest in the manganese spinel class of materials does not only lie in its industrial potential; it also lies in the fact that it possesses an extremely rich set of physical and chemical properties, at the origin of many debates and doubts in the scientific community, not all clarified yet. Typical examples include the presence of two electrochemical features at 3.3 V and 4.6 V vs. Li + /Li [START_REF] Palacin | On the origin of the 3.3 and 4.5 v steps observed in LiMn 2 O 4 -based spinels[END_REF][START_REF] Mr Palacin | On the role of defects in decreasing the extra 3.3/3.95 and 4.5 v redox steps in li-mn-o spinels[END_REF][START_REF] Dupont | Tem studies: The key for understanding the origin of the 3.3 v and 4.5 v steps observed in LiMn 2 O 4 -based spinels[END_REF] , or the role played by a possible oxygen under-stoichiometry [START_REF] Kanno | The relationships between phases and structures of lithium manganese spinels[END_REF][START_REF] Yonemura | Synthesis, structure, and phase relationship in lithium manganese oxide spinel[END_REF][START_REF] Masquelier | Chemical and magnetic characterization of spinel materials in the LiMn 2 O 4 -Li 2 Mn 4 O 9 -Li 4 Mn 5 O 12 system[END_REF][START_REF] Yamada | Synthesis and structural aspects of LiMn 2 O 4+-δ as a cathode for rechargeable lithium batteries[END_REF][START_REF] Xia | Correlating capacity fading and structural changes in Li 1+y Mn 2-2y O 4-δ spinel cathode materials: A systematic study on the effects of li/mn ratio and oxygen deficiency[END_REF] . In addition, the crystal chemistry of lithium manganese spinels is extremely varied, with phase transitions at various temperatures [START_REF] Rousse | X-ray study of the spinel LiMn 2 O 4 at low temperatures[END_REF] and for different composition ranges [START_REF] Thackeray | Lithium insertion into manganese spinels[END_REF] . Note, however, that the material used for applications is not "stoichiometric" LiMn 2 O 4 . This material was shown to suffer from capacity retention issues [START_REF] Thackeray | Lithium insertion into manganese spinels[END_REF][START_REF] Thackeray | Electrochemical extraction of lithium from LiMn 2 O 4[END_REF][22][23][START_REF] Tarascon | The Li 1+x Mn 2 O 4 /C rocking-chair system: a review[END_REF][START_REF] Tarascon | The Li 1+x Mn 2 O 4 /C system materials and electrochemical aspects[END_REF][START_REF] Xia | Correlating capacity fading and structural changes in Li 1+y Mn 2-2y O 4-δ spinel cathode materials: A systematic study on the effects of li/mn ratio and oxygen deficiency[END_REF][START_REF] Jang | Dissolution of spinel oxides and capacity losses in 4V Li/Li x Mn 2 O 4 coils[END_REF][START_REF] Xia | Capacity fading on cycling of 4 V Li/LiMn 2 O 4 cells[END_REF] , mainly caused by the presence of a significant amount of Mn 3+ (which is at the origin of cooperative Jahn-Teller distortion and/or disproportionation to yield soluble Mn 2+ species [START_REF] Gummow | Improved capacity retention in rechargeable 4v lithium/lithium manganese oxide (spinel) cells[END_REF][START_REF] Cho | Structural changes of LiMn 2 O 4 spinel electrodes during electrochemical cycling[END_REF][START_REF] Amatucci | Failure mechanism and improvement of the elevated temperature cycling of LiMn 2 O 4 compounds through the use of the LiAl x Mn 2-x O 4-z F z solid solution[END_REF][START_REF] Kim | Significance of the Tetrahedral A Site on the Electrochemical Performance of Substituted Li 1[END_REF] ). Thorough control of the synthesis conditions of these apparently simple oxides revealed to be extremely important. Typically, a slight departure from the original oxidation state of manganese (+3.5) towards the value +4 led to better capacity retention, at the expense of the theoretical capacity [START_REF] Tarascon | The Li 1+x Mn 2 O 4 /C rocking-chair system: a review[END_REF][START_REF] Tarascon | Synthesis conditions and oxygen stoichiometry effects on li insertion into the spinel LiMn 2 O 4[END_REF][START_REF] Xia | Capacity fading on cycling of 4 V Li/LiMn 2 O 4 cells[END_REF] .

Several routes are possible to solve this problem by reducing the amount of Mn 3+ . Some of them, rather successful, were already proposed by Thackeray himself and involve the use of lithium in excess or defect to change the properties of LiMn 2 O 4 . Two mains series of compositions were proposed by Thackeray [23,[START_REF] Gummow | Improved capacity retention in rechargeable 4v lithium/lithium manganese oxide (spinel) cells[END_REF] and others [START_REF] Tarascon | The Li 1+x Mn 2 O 4 /C rocking-chair system: a review[END_REF][START_REF] Tarascon | The Li 1+x Mn 2 O 4 /C system materials and electrochemical aspects[END_REF][START_REF] Kanno | The relationships between phases and structures of lithium manganese spinels[END_REF][START_REF] Masquelier | Chemical and magnetic characterization of spinel materials in the LiMn 2 O 4 -Li 2 Mn 4 O 9 -Li 4 Mn 5 O 12 system[END_REF] : Li-rich stoichiometric spinels Li 1+x Mn 2-x O 4 (0 ≤ x ≤ 0.33) and defect spinels Li 1-x Mn 2-2x O 4 (0 ≤

x ≤ 0.11). The first ones change the Li/Mn ratio by adding extra-lithium in the site of manganese, and are described in detail in the next paragraph, as the samples used for our operando NPD studies belong to this family. The second ones preserve the Li/Mn = 1/2 ratio, but they are cation-deficient in the sense that vacancies are introduced in the lithium and manganese sublattices in order to increase the average Mn oxidation state.

Research has also evolved towards the substitution of part of the manganese with other transition metal elements (Ti, Fe, Cr, Ni etc...) [START_REF] Amine | A new three-volt spinel Li 1+x Mn 1.5 Ni 0.5 O 4 for secondary lithium batteries[END_REF][START_REF] Kim | Significance of the Tetrahedral A Site on the Electrochemical Performance of Substituted Li 1[END_REF][START_REF] Sigala | Positive electrode materials with high operating voltage for lithium batteries: LiCr y Mn 2-y O 4 (0 ≤ y ≤ 1)[END_REF][START_REF] Amine | Preparation and electrochemical investigation of LiMn 2-x Me x O 4 (Me: Ni, Fe, and x = 0.5, 1) cathode materials for secondary lithium batteries[END_REF][START_REF] Zhong | Synthesis and electrochemistry of LiNi x Mn 2-x O 4[END_REF][START_REF] Wu | Improvement of electrochemical properties of LiNi 0.5 Mn 1.5 O 4 spinel[END_REF][START_REF] Liu | The electrochemical properties of LiNi 0.5 Mn 1.2 Ti 0.3 O 4 compound[END_REF][START_REF] Hyoung Oh | Structural and electrochemical investigations on the LiNi 0.5-x Mn 1.5-y M x+y O 4 (M = Cr, Al, Zr) compound for 5 V cathode material[END_REF][START_REF] Patoux | High voltage nickel manganese spinel oxides for li-ion batteries[END_REF][START_REF] Patoux | High voltage spinel oxides for li-ion batteries: From the material research to the application[END_REF][START_REF] Wang | A comparative study of Fd 3m and P4 3 32 LiNi 0.5 Mn 1.5 O 4[END_REF][START_REF] Mikhailova | Structural changes in the LiCrMnO 4 Cathode Material during Electrochemical Li extraction and insertion[END_REF][START_REF] Duncan | Relationships between Mn3+ Content, Structural Ordering, Phase Transformation, and Kinetic Properties in LiNi x Mn 2-x O 4 cathode materials[END_REF][START_REF] Murat Yavuz | Influence of iron on the structural evolution of LiNi 0.4 Fe 0.2 Mn 1.4 O 4 during electrochemical cycling investigated by in situ powder diffraction and spectroscopic methods[END_REF][START_REF] Saravanan | A study of room-temperature Li x Mn 1.5 Ni 0.5 O 4 solid solutions[END_REF] . This leads to extremely promising electrode materials because other redox couples than Mn 2+ /Mn 3+ /Mn 4+ are exploited, mostly resulting in much higher electrochemical potentials when used in Li-ion batteries.

This could mean a drastic energy increase, once electrolytes stable at such high potentials are fully developed [START_REF] Scrosati | Lithium batteries: Status, prospects and future[END_REF][START_REF] Goodenough | Challenges for Rechargeable Li Batteries[END_REF][START_REF] Tarascon | Issues and challenges facing rechargeable lithium batteries[END_REF] . LiNi x Mn 2-x O 4 (0 ≤ x ≤ 1/2) is one of the most promising high-voltage electrode materials, relying mainly on the Ni 2+ /Ni 3+ /Ni 4+ redox couples and operating at a voltage as high as 4.7 V vs. Li + /Li. More details about these compositions are given in section 3. 4, where an operando NPD study of LiNi 0.4 Mn 1.6 O 4 [START_REF] Patoux | High voltage nickel manganese spinel oxides for li-ion batteries[END_REF][START_REF] Patoux | High voltage spinel oxides for li-ion batteries: From the material research to the application[END_REF][START_REF] Dedryvere | Electrode/electrolyte interface reactivity in high-voltage spinel LiMn 1.6 Ni 0.4 O 4 /Li 4 Ti 5 O 12 lithium-ion battery[END_REF][START_REF] Wang | CMC as a binder in LiNi 0.4 Mn 1.6 O 4 5 V cathodes and their electrochemical performance for Li-ion batteries[END_REF] is reported.

Operando NPD studies of spinel materials

We decided to exploit our custom-made (Ti,Zr)-alloy cell for in situ and operando NPD measurements (described in the previous chapter) to get valuable insight into the lithium extraction mechanisms from Li-rich spinels of compositions Li 1+x Mn 2-x O 4 (0 ≤ x ≤ 0.10).

In this x range, manganese oxidation state can be increased from 3.5+ to 3.63+ by substituting part of the manganese in the 16d crystallographic sites with lithium. This reduces the usable capacity, but also eliminates significantly capacity fading upon cycling thanks to the lower amount of Mn 3+ (which as discussed above is at the origin of capacity fading issues). Only few studies have addressed the mechanism of Li + extraction from these compositions by means of ex situ and in situ X-ray diffraction [START_REF] Ohzuku | Electrochemistry of manganese-dioxide in lithium nonaqueous cell. x-ray diffractional study on the reduction of spinel-related manganese-dioxide[END_REF][START_REF] Liu | Mechanism of the electrochemical insertion of lithium into LiMn 2 O 4 spinels[END_REF][START_REF] Baehtz | Design and performance of an electrochemical in-situ cell for high resolution full-pattern xray powder diffraction[END_REF][START_REF] Mukerjee | Structural evolution of Li x Mn 2 O 4 in lithium-ion battery cells mea-sured in situ using synchrotron X-ray diffraction techniques[END_REF] , none of them in a systematic way and for comparison purposes for different Li/Mn ratios. We therefore

decided

Experimental

Three samples of the spinel positive electrode material Li 1+x Mn 2-x O 4 were prepared for x = 0 (Sample S1), x = 0.05 (Sample S2) and x = 0.10 (Sample S3). To this end, as described in [START_REF] Masquelier | Chemical and magnetic characterization of spinel materials in the LiMn 2 O 4 -Li 2 Mn 4 O 9 -Li 4 Mn 5 O 12 system[END_REF] , stoichiometric amounts of (1+x)/2•Li 2 CO 3 and (2-x)•MnOOH were carefully mixed, heated at 400 • C for 2 hours, cooled and mixed at RT prior to being heated for 20 hours at 800 • C in air and rapidly cooled (≤10 • C/min) down to RT. For electrochemical testing, the active materials were mixed with Carbon Super P in 90:10 wt% ratios and ground in a mortar. For these first experiments, no binder was added to the mixture.

Swagelok-type cells were used to prepare lithium half cells. Glass fiber separators (Whatman) and LP30 electrolyte (Aldrich) were used. The half cells were cycled at C/20 rate between 3.2 V and 4.5 V vs. Li + /Li, using small amounts of powders (≤ 20-25 mg) as positive electrodes. Diffraction experiments were initially performed using X-Rays produced within a Bruker D8 diffractometer (Cu Kα 1,2 wavelength, Bragg-Brentano geometry). NPD was subsequently carried out on the D2B high-resolution neutron diffractometer at the Institut Laue-Langevin. Powder samples were put in cylindrical vanadium cans and measured in transmission geometry at λ = 1.5944 Å (calibrated using Na 2 Ca 3 Al 2 F 14 as a reference).

In situ (operando) experiments were performed on the D20 high-flux neutron diffractometer at ILL. For each of the three samples, a battery was prepared in our in situ cell [START_REF] Bianchini | A new null matrix electrochemical cell for rietveld refinements of in-situ or operando neutron powder diffraction data[END_REF] .

The electrode preparation followed the procedure described above, but with high loadings of about 200 mg. Standard electrolytes were replaced by a deuterated version, prepared with 1 M LiPF 6 in d-EC:d-DMC (1:4 wt%), which had also been previously tested [START_REF] Bianchini | A new null matrix electrochemical cell for rietveld refinements of in-situ or operando neutron powder diffraction data[END_REF] . No lithium enrichment was performed, i.e. lithium with (nominal) natural isotope abundance was used for all battery components. The batteries were measured operando continuously on the D20 diffractometer (λ = 1.5471 Å) in transmission geometry. Every pattern was acquired for 30 minutes while charging the battery at C/20 rate up to 4.5 V vs. Li + /Li (4.6 V for the sample x = 0), corresponding to a variation of 0.025 Li/pattern. Data treatment and Rietveld refinements were performed using the FullProf Suite [START_REF] Rodriguez-Carvajal | Recent advances in magnetic-structure determination by neutron powder diffraction[END_REF] . It is worth emphasizing that for every sample, each operando diffraction pattern has been independently treated (i.e. no sequential refinements possible) due to the fact that lithium extraction results both in a decrease of the sample's absorption (lithium is a neutron absorber) and in an increase of the background due to organic components of the battery (deuterated electrolyte) and other scattering elements (separator, carbon). Note that the variable absorption has been dealt with by using a decreasing µR coefficient, starting from about 0.5 for the pristine samples and de-creasing by 0.0125/pattern to reach a value between 0.1 and 0.2 at the end of charge, depending on the sample.

For sample S1 (LiMn 2 O 4 , Table 3.1), which generates different phases upon electro- chemical cycling, Debye-Waller factors (B iso ) were refined for the pristine, final and intermediate compositions and then kept constant within the different domains during charge.

For samples S2 (Li 1.05 Mn 1.95 O 4 ) and S3 (Li 1.10 Mn 1.90 O 4 ), which react through significant solid solution regions, a fixed B iso could not take into account the modifications occurring in these domains and thus B iso were refined for every pattern (we used a B overall factor, the same B iso for all atoms). For S2 we observed a decrease of B overall from 1.46 to 0.50, while for S3 from 1.26 to 0.53. One should note that although considering thermal agitation is necessary to account for the data, it is detrimental for the value of the error bars obtained from refinement. This is particularly true for site occupancy factors (SOFs) since the parameters can be correlated. Moreover, lithium and manganese have poor contrast for neutrons (they have both negative scattering lengths, b Li = -1.90 fm and b M n = -3.75 fm) which explains why error bars for SOFs are far more important than for every other parameter. For this reason such error bars will often be reported with two digits.

Analysis of pristine materials

The three samples were initially characterized in their pristine forms. The neutron powder diffraction patterns collected using the D2B high-resolution neutron diffractometer at ILL are gathered in Figure 3.5. The obtained cell parameters are reported in Table 3.1, in remarkable agreement with those found in the literature [23,[START_REF] Kanno | The relationships between phases and structures of lithium manganese spinels[END_REF][START_REF] Masquelier | Chemical and magnetic characterization of spinel materials in the LiMn 2 O 4 -Li 2 Mn 4 O 9 -Li 4 Mn 5 O 12 system[END_REF] when lithium substitutes part of manganese with concomitant oxidation of the remaining Mn: from X-Ray diffraction we obtain a = 8.2484(2) Å for LiMn 2 O 4 (Sample S1), a = 8.2307(4) Å for Li (S2) and a = 8.2188(3) Å for Li 1.10 Mn 1.90 O 4 (S3). It should be kept in mind that since the oxidation state of manganese increases with increasing x in Li 1+x Mn 2-x O 4 , the total amount of lithium that can be extracted from the spinel structure decreases accordingly.

More precisely, simple calculations show that the total amount of extractable lithium decreases as 1-3x (0 ≤ x ≤ 0.33), and therefore the amount of lithium that remains in the structure at the end of charge increases as 4x (i.e. reaching the fully oxidized Mn IV compositions Li 0 Mn 2 O 4 for sample S1, Li 0.2 Mn 1.95 O 4 for S2 and Li 0.4 Mn 1.90 O 4 for S3). The values we observed experimentally from galvanostatic electrochemical Li + extraction agree with these considerations and are reported in Table 3.1. The decrease of cell parameters and of Mn-O distances (Figure 3.5) are also in good agreement with an increase in the manganese oxidation state. Rietveld refinements of the crystal structures of the three pristine samples were performed from the NPD data, using the structures reported in literature as initial models (ICSD 40485 and ICSD 166746 [START_REF] Mosbah | Phases Li x MnO 2 -λ rattachees au type spinelle[END_REF][START_REF] Blasse | The structure of some new mixed metal oxides containing lithium[END_REF] ). As expected, Li 0 Mn 2 O 4 crystallizes in the Fd 3m space group, with Mn in octahedral 16d sites and oxygen in close-packed 32e sites, building a framework of MnO 6 edge-sharing octahedra. Lithium is confirmed to be in 8a tetrahedral position. The substitution of Li for Mn in Li 1+x Mn 2-x O 4 occurs on the 16d site, therefore generating Li + in octahedral oxygen environment [23] , written as Li 8a [Li x Mn 2-x ] 16d O 4 . Our Rietveld refinements confirmed that the oxygen's fractional atomic coordinates are close to x = y = z = 0.2368(2) for all the samples. Debye-Waller factors and, more importantly, lithium-manganese exchange ratios on the 16d site were also refined. Table 3.1 reports the obtained values, in excellent agreement with nominal compositions. For sample S1 (LiMn 2 O 4 ) we also tried to refine oxygen's site occupancy factors (SOF) together with Li-Mn exchange but this did not result in any significant deviation from the full occupancy of the 32e site, confirming the stoichiometry of the sample.

To further prove this, we verified that S1 undergoes a structural transition from cubic to orthorhombic symmetry below 285 K. It was in fact previously demonstrated [START_REF] Rousse | X-ray study of the spinel LiMn 2 O 4 at low temperatures[END_REF][START_REF] Rousse | Cubic orthorhombic transition in the stoichiometric spinel LiMn 2 O 4[END_REF][START_REF] Rodriguez-Carvajal | Electronic crystallization in a lithium battery material: Columnar ordering of electrons and holes in the spinel LiMn 2 O 4[END_REF] that such a transition is due to charge ordering and it thus happens only for the exact stoichiometry of LiMn 2 O 4 (Figure 3.6). I n t e n s i t y ( a r b . u n i t s )

2 θ ( °) , C u K α O r t h o r h o m b i c d i s t o r t i o n o f L i M n 2 O 4 b e l o w R T R e f i n e m e n t a t 2 3 0 K 2 3 0 K 3 5 0 K I n t e n s i t y ( a r b . u n i t s ) 2 θ ( °) , C u K α Figure 3.6:
LiMn2O4 after cooling at 230 K. Rietveld refinement is performed using the model published in [START_REF] Rodriguez-Carvajal | Electronic crystallization in a lithium battery material: Columnar ordering of electrons and holes in the spinel LiMn 2 O 4[END_REF] to account for the observed orthorhombic distortion. The inset shows a comparison with the room-temperature data.

Contrary to what was reported by Berg-Thomas and Sharma [START_REF] Sharma | Non-equilibrium Structural Evolution of the Lithium-Rich Li 1+y Mn 2 O 4 Cathode within a Battery[END_REF][START_REF] Berg | Neutron diffraction study of stoichiometric spinel Li 1+x Mn 2-x O 4 showing octahedral 16c-site li-occupation[END_REF] , we did not find any occupation of the 16c site by Li + . In the case of Sharma et al. in particular, an in situ NPD study is reported but comparison with our data is difficult since they provide no information on the sample in its pristine form, received as deintercalated and characterized as [Li 0.11(6) ] 8a [Li 0.23 (11) ] 16c Mn 2 O 4 . Inspection of reported cubic cell parameter reveals that upon cycling it never exceeds a = 8.218 Å which is typical of non-stoichiometric spinels as discussed above (Li-Mn exchange for example). The non-stoichiometry of the sample of Sharma et al. could also explain the fact that they observe the (dis)charge as a solid solution, while on the contrary we observe biphasic domains for the stoichiometric sample S1 (Li/Mn = 1/2). The galvanostatic electrochemical data, gathered in Figure 3 fractional atomic coordinate was also refined, revealing a weak dependence on the state of charge. Indeed, it only increased from 0.2362(6) to 0.2370 (5). This will remain in general true for all other samples. As previously discussed, there are two kinds of lithium in the structure: octahedral Li 16d that partly substitutes for Mn (0.1 Li 16d /formula unit here)

and tetrahedral Li 8a . One can then write Li ) with the constraint that Li 8a +Li 16d shall equal the amount of lithium/f.u. deduced from the electrochemical data. This only resulted in a small variation in the value of Li 16d SOF from 0.1 to 0.18 (15). Because of the large error bar this increase is not significant; moreover, it is meaningless both because this would force manganese to quit its site and because it is contrary to what is expected for lithium extraction. We hence did not refine the Li 16d occupancy, keeping it constant at 0.1 and ). Very interestingly, and revealed for the first time thanks to operando neutron powder diffraction, the delithiation does not proceed at "uniform speed".

The refinement of Li 8a SOF reveals a sharper Li occupancy variation for maximal values of (dV/dy) -1 , as plotted in Figure 3.11d. This suggests that, although the unit cell shrinkage proceeds at uniform rate, lithium deintercalation does not follow the same linear behavior.

We estimate a rate of delithiation of 0.02 Li/(formula unit•hour) in the "slow" regions and of 0.08 Li/(formula unit•hour) in the "fast" regions, i.e. lithium extraction is about 4 times faster on the derivative peaks. This finding relates to an observation recently done on a similar sample by in situ Li NMR [START_REF] Zhou | Paramagnetic electrodes and bulk magnetic susceptibility effects in the in situ NMR studies of batteries: Application to Li 1.08 Mn 1.92 O 4 spinels[END_REF] : during charge, the broad Li 8a -related signal at 570 ppm not only shifts, but progressively disappears during charge. However such vanishing was found to be not continuous: it shows a local maximum in the intermediate region of charge (i.e. between the derivative peaks), possibly related to the relaxation time T2 and therefore to lithium's mobility [START_REF] Zhou | Paramagnetic electrodes and bulk magnetic susceptibility effects in the in situ NMR studies of batteries: Application to Li 1.08 Mn 1.92 O 4 spinels[END_REF] . This relates well with our finding of a slower delithiation in the voltage region between the two derivative peaks. Such observations suggest that the intermediate composition formed could present subtle lithium/vacancy charge ordering slowing down ionic mobility. diminishes from the initial value a 1 = 8.2358(4) Å to a 1 = 8.1424(4) Å i.e. with a unit-cell volume shrinkage of 3.4% from 558.6 Å3 to 539.8 Å3 . Within the solid solution domain, the lithium's Li 8a SOF decreases from 1 to 0.59 (21), in a similar fashion as for sample S3, namely a fast delithiation on top of the first derivative peak. When the second electro-chemical feature at 4.15 V vs. Li + /Li is reached, the diffraction peaks of the initial phase start to vanish, while a new phase appears characterized by a cubic unit cell parameter a 2 = 8.097(3) Å and a Li 8a SOF of 0.25 (25). In a matter of about 3 patterns, i.e. 1.5 hours, this new phase overcomes the initial one and in another 3 patterns the initial one has almost completely disappeared (as shown in Figure 3.10, the observed miscibility gap is ∆x ≈ 0.25, which becomes ∆x ≈ 0.3 when correcting for the inactive phase). We noticed, interestingly, that during this transformation and until the end of charge, the cell parameter a 2 decreases continuously. This result is not expected from thermodynamic equilibrium, but its occurrence has recently been reported by several authors and for several materials in non-equilibrium conditions. In general it can be caused by strains in the phase front during the biphasic transformation [START_REF] Wagemaker | A kinetic two-phase and equilibrium solid solution in spinel Li 4+x Ti 5 O 12[END_REF] . It should also be noted that the biphasic reaction observed here involves a volume change from 539. 84 For stoichiometric LiMn 2 O 4 (x = 0) the average oxidation state of Mn is +3.5 and, theoretically, all the lithium ions can be extracted from the tetrahedral position to yield the fully delithiated Li 0 Mn 2 O 4 composition, referred to as λ-MnO 2 in the literature [START_REF] Hunter | Preparation of a new crystal form of manganese dioxide lambda MnO 2[END_REF] . Previous studies have demonstrated the difficulty of reaching full delithiation (both chemically and electrochemically) [START_REF] Berg | Neutron diffraction study of electrochemically delithiated LiMn 2 O 4 spinel[END_REF][START_REF] Berg | The LiMn 2 O 4 to lambda-MnO 2 phase transition studied by in situ neutron diffraction[END_REF][START_REF] Baehtz | Design and performance of an electrochemical in-situ cell for high resolution full-pattern xray powder diffraction[END_REF] . In our case, from this operando NPD experiment (using high This reaction happens quickly and is over in a matter of 5 patterns (i.e. 2.5 hours, ∆x ≈ 0.10-0.12 as reported in Figure 3.10): this has often been treated as a solid solution domain in the literature [START_REF] Liu | Mechanism of the electrochemical insertion of lithium into LiMn 2 O 4 spinels[END_REF] , until Baehtz et al. [START_REF] Baehtz | Design and performance of an electrochemical in-situ cell for high resolution full-pattern xray powder diffraction[END_REF] showed it to be biphasic thanks to in situ synchrotron radiation powder diffraction. We also confirmed this in our own in situ synchrotron XRPD study reported in section 3.3. [22,[START_REF] Van Der Ven | Phase transformations and volume changes in spinel Li x Mn 2 O 4[END_REF] . However, that phase has not been observed yet and its existence was put in doubt by Liu et al. [START_REF] Liu | Mechanism of the electrochemical insertion of lithium into LiMn 2 O 4 spinels[END_REF] thanks to ex situ NPD that did not reveal any superstructure peak related to Li + ordering. This was confirmed later on by Baehtz et al. [START_REF] Baehtz | Design and performance of an electrochemical in-situ cell for high resolution full-pattern xray powder diffraction[END_REF] . However NPD is not the most suited technique to observe superstructure peaks of extremely weak intensity, especially if, as we will discuss was reported to be cubic with a = 8.03 Å [194] ). For this sample the volume change in the second biphasic reaction is significant, namely from 542.54(5) Å3 to 526.73(5) Å3 (∆V/V = 2.9% for ∆x ≈ 0.34 -0.4, approximately twice the one of sample S2). It should be noted that the a 3 value at the end of charge (a 3 = 8.0442(3) Å) is very close to a = 8.03 Å expected for λ-MnO 2 ; besides, the fact that such value is not exactly reached confirms the presence of some residual lithium in tetrahedral sites, as obtained by Rietveld refinements.

Mechanism of Li

The refinement of the final phase is shown in Figure 3.12c. As we clearly showed there that our electrodes made only with AM + Csp leave a small but significant unreacting part, in this electrode preparation we added PTFE as binder to insure better homogeneity. This allowed us to confirm the results previously obtained upon charge, in the absence this time of the pristine-like phase. A qualitative view of the experiment can be seen in Figure 3.14. Three observations are striking when looking at the full cycle:

Complementing NPD by operando synchrotron XRPD

• The phase diagram in terms of position and duration of the biphasic domains presents differences between charge and discharge.

• At the end of discharge all Bragg reflections significantly lose intensity with respect to their initial value. As we will show in the following, this is due to the peaks becoming more lorentzian, but in this operando experiment the background is too important to deduce such a behaviour.

• Great difficulty is found while trying to use Rietveld refinement to fit these data of charge+discharge, especially in terms of peaks' shape.

This last point, in particular, prevented us from completing a meaningful quantitative analysis of the full-cycle data.

LiMn 2 O 4 studied by operando synchrotron XRPD

Intrigued by the questions left unanswered during our full-cycle operando NPD study, we decided to reinvestigate the same system using the high angular resolution offered by operando synchrotron X-Ray powder diffraction at MSPD (ALBA) [START_REF] Fauth | The new material science powder diffraction beamline at alba synchrotron[END_REF] . The same electrode formulation was used, including the PTFE binder. The battery was mounted in our in situ cell for experiments at synchrotron radiation facilities, which was described in the introduction [START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF] . Galvanostatic cycling was performed at C/6 rate in the extended voltage range between 3 V and 4.8 V vs. Li + /Li, while measuring XRPD patterns (in transmission) every 5 minutes continuously. The results of this operando experiment are shown in 1 st cycle irreversibility Figure 3.17 compares the Bragg peaks in the pristine state with their counterpart after one and two in situ cycles had been carried out. One immediately notices a strong peaks' shape evolution upon the first cycle, while almost no evolution is observed between the 1 st one and the 2 nd one: the shapes of diffracted peaks become significantly more Lorentzian

1 1 . 3 1 1 . 5 1
2 θ ( °) 2 θ ( °)
Figure 3.17: (111), (311) and (400) Bragg reflections of LiMn2O4 in the pristine state and after the 1 st and 2 nd electrochemical cycle from operando synchrotron XRPD data. The curve after 1 cycle (red) shows a shoulder on the right side of the (311) peak, due to a reflection of the experimental setup of variable intensity (also seen in Figure 3. 15). Note that the cell rotates on its axis during the measure to obtain a better powder averaging.

and a careful observation of the diffraction scans reveals a continuous broadening, starting from the very first scans. Therefore the phenomenon is not related to some reaction happening at high voltage, but it proceeds continuously throughout charge and discharge.

The broadening we observe here, created during the first cycle, is not a simple increase in peak's FWHM. On the contrary, while the FWHM is rather constant, the peak shape after the first electrochemical cycle tends towards a pure Lorentzian function. It is clearly evidenced in Figure 3.17 by the occurrence of extended tails at the base of Bragg reflections and the effect is so significant that the observed peaks can no longer be modelled using a single mathematical function. They have to be described as so-called super-Lorentzian shaped, i.e. two Lorentzian peaks, one narrow and one very broad, centered at the same angular position [START_REF] Young | Bimodal distributions of profile-broadening effects in rietveld refinement[END_REF] (Figure 3.18). From the physical point of view this means that we suggest the presence of several "phases", very close in composition (and cell parameters, etc) but with a bimodal distribution of coherent domain sizes. The two Lorentzian peaks will then give the two most representative domain sizes. A slight asymmetry is also observed in Figure 3.17. This indicates that, as a secondary effect, such domains different in size might also have a slightly different composition than the nominal one (of course with a preference for being under-lithiated, since upon cycling Li + is extracted and then almost completely reinserted). Note that we say this effect is secondary because it cannot in any way contribute at creating the tails present on the left side of the Bragg peaks, because a different composition in this case would mean that we reached Li x Mn 2 O 4 with x>1, in contrast with our electrochemical data. For these reasons (and because it proved very hard to be included in the data analysis due to limitations in the stability of the Rietveld refinement) this asymmetry was not taken into account.

From a practical point of view, the "two phases" we used in the Rietveld refinements only differ by their isotropic size parameter. One finds that in the pristine state there is essentially no broadening due to size effects (obtained particle size > 100 nm), while after 1 cycle the extremes of the domain size distribution are well identified: one is pristine-like (not broadened) and a second one, from the very broad peaks' tails, corresponds to an apparent domain size of 9.2(1) nm. The "two phases" appear to be in a ≈2:1 ratio and we can conclude that at the end of the 1 st cycle about 66% of LiMn 2 O 4 maintains the same crystallinity, while the other 34% has a significantly reduced coherent domain size, decreasing down to 9.2(1) nm. If the same refinement is performed in the middle of the first cycle, i.e. at the end of charge, one similarly finds that the fraction with reduced domain size is already of 20%, for a domain size which is similar, i.e. 9.9(1) nm. Whether this effect is due to the creation of several small domains within the particles or at the interfacial region is an issue that cannot be addressed by XRPD, but will be further investigated using TEM. Note also the limits of our analysis in this case, since the complicated peak shapes, combined with peaks asymmetry and additional spurious peaks coming from the setup, made Rietveld refinement only partially satisfactory (Figure 3.18c). A more detailed knowledge of the causes of the peaks becoming Lorentzian will help finding a more suitable model to explain this behaviour.

Li + and charge ordering in Li 0.5 Mn 2 O 4 • The (111) diffracted peak is the most intense one for spinels, due to the high packing density of Mn cations in this family of planes. It shows the same behaviour already observed for (311) and (400) in Figure 3.15, i.e. only partial reversibility.

• The (220) reflection is interesting as it is strongly correlated in spinels with the scattering power of the atom in the tetrahedral site 8a [START_REF] Barth | Spinel structures with and without variate atom equipoints[END_REF] . In this case this atom is lithium, meaning that the reflection is already very weak in the pristine state and that it totally loses its intensity while approaching the λ-MnO 2 phase, to partially regain it afterwards when lithium is reinserted in the site.

• The most important observation here is the presence of two reflections, ( 110) and (200), in the middle of charge and discharge, i.e. around the composition Li 0.5 Mn 2 O 4 .

Fig. 11 Li 0.5 Mn 2 O 4

• Disordered Mn 3+ /Mn 4+ cations • lithium in 8a position, SOF = ½

• Ordered 1:3 Mn 3+ /Mn 4+ (Mn 3.75+ )

• lithium in 8a position, SOF = ½

• Ordered 1:3 Mn 3+ /Mn 4+ (Mn 3.75+ )

• lithium in fully occupied 4a position These reflections are forbidden in the Fd 3m space group of the pristine spinel. They are observed here for the first time and they are extremely important because they hold the key to reveal and understand the symmetry/ordering within Li 0.5 Mn 2 O 4 .

The presence of the (110) reflection can be understood by using an analogy with another spinel-based material, LiNi 2+ 0.5 Mn 4+ 1.5 O 4 . In this composition, a classical cation-disordered structure can turn into an ordered one where the 1 Ni 2+ : 3 Mn 4+ ratio leads to a reduction in space group symmetry, from Fd 3m to P4 3 32 , hence allowing the presence of the (110) reflection [START_REF] Wang | A comparative study of Fd 3m and P4 3 32 LiNi 0.5 Mn 1.5 O 4[END_REF][START_REF] Kim | Comparative study of LiNi 0.5 Mn 1.5 O 4 -delta and LiNi 0.5 Mn 1.5 O 4 cathodes having two crystallographic structures: Fd 3m p4 3 32[END_REF][START_REF] Amdouni | Structure and insertion properties of disordered and ordered LiMn 1.5 Ni 0.5 O 4 spinels prepared by wet chemistry[END_REF] . It is interesting to notice that Li 0.5 Mn 2 O 4 can indeed be written as Li 0.5 Mn 3+ 0.5 Mn 4+ 1.5 O 4 , showing the same cation ratio (1:3) as in LiNi 0.5 Mn 1.5 O 4 . We applied this space group reduction of LiNi 0.5 Mn 1.5 O 4 (ICSD 70045 [START_REF] Gryffroy | A neutron diffraction study of some spinel compounds containing octahedral ni and mn at a 1:3 ratio[END_REF] ) to Li 0.5 Mn 2 O 4 . The results of the structural Rietveld refinements displayed in Figure 3.20 show how the (110) reflection is nicely fitted taking into account the space group P4 3 32, enlightening for the first time an ordering between Mn 3+ and Mn 4+ cations in Li 0.5 Mn 3+ 0.5 Mn 4+ 1.5 O 4 during charge and discharge of LiMn 2 O 4 , whenever they reach a ratio of 1:3. While these refinements perfectly account for the existence of the (110) Bragg peak, they still maintain the (200) one as forbidden. We hence envisaged possible Li/vacancy ordering at the composition Li 0.5 Mn 3+ 0.5 Mn 4+ 1.5 O 4 using a further space group symmetry reduction. In fact, in P4 3 32 all lithium ions are placed in the same 8a site which must therefore be only half occupied to respect the stoichiometry. Among the cubic subgroups of P4 3 32, P2 1 3 allows to maintain the 1:3 cations ratio, while reducing the multiplicity of the tetrahedral lithium site to 4 in such a way that that newly defined lithium site (4a) is full whereas that corresponding to the vacancies is obviously empty. In the P2 1 3 space group, systematic conditions for extinctions allow the presence of both the (110) and (200) reflections, as illustrated in As already well documented in the literature, the oxygen ccp-based spinel structure can be described as a stacking of two types of cations layers, referred to as [Oh] 3 (Mn-rich, with 3 octahedral (Oh) sites occupied and 1 Oh empty) and [Td] 2 [Oh] (Li-rich, with 2 tetrahedral (Td) sites occupied, 1 Oh occupied and 3 Oh vacant), perpendicular to the [111] cubic direction. Importantly, Mn 3+ and Mn 4+ are present in the two types of layers (in an ordered fashion respecting in both cases the 1:3 ratio) and are also ordered along the [111] direction. The red circles in Figure 3.21 show how layers are stacked: a Mn 3+ cation in the Li-rich layer is always on top of 3 Mn 4+ cations in the Mn-rich layer. Even though the obtained values of Mn-O bond lengths gathered in Table 3.3 (for P2 1 3) show significant error bars, the environments around Mn(2) (Mn 4+ , with most Mn-O bonds in the range 1.90 -1.94 Å) and Mn(1) (Mn 3+ , with longer Mn-O bonds in the range 1.94 -2.01 Å) clearly enlighten the presence of two Mn environments, further supported by bond valence sum calculations (Figure 3.22). It is noteworthy that this bonds' distribution around Mn(1) (3+3) is not compatible with a "classical" Jahn-Teller distortion of the Mn 3+ cation (4+2), that one could expect. First-principles calculations (applied to Li 2 Mn 2 O 4 ) [START_REF] Van Der Ven | Phase transformations and volume changes in spinel Li x Mn 2 O 4[END_REF] indicated that a compression of the Mn 3+ -O bond can lead to a favorable low-spin configuration, where the eg electron is instead placed as the 4th electron in the t 2g energy levels (crystal field energy lower than exchange energy). This could be the case here because of the constraints applied by surrounding Mn 4+ cations on a central Mn 3+ one, possibly explaining the missing Jahn-Teller distortion. An analogous effect had been for instance observed for Ni 3+ (3d 7 ) cations in LiNi 3+ 0.3 Co 3+ 0.7 O 2 [START_REF] Mansour | A unique structure of Ni(III) in LiNi 0.3 Co 0.7 O 2 Without Jahn-Teller Distortion[END_REF] . As previously mentioned, the P2 1 3 space group is well-suited to support lithium/vacancy ordering. Lithium is located in the 8a site in Fd 3m and P4 3 32 space groups, while it is located in the 4a one in P2 1 3. This site, once filled, represents only half of those partially occupied within the previous space groups, and it satisfies the stoichiometry of Li 0.5 Mn 2 O 4 .

This ordering scheme is the same one that was predicted by Van der Ven et al. through computational methods [START_REF] Van Der Ven | Phase transformations and volume changes in spinel Li x Mn 2 O 4[END_REF] , with lithium and vacancies alternated along the [110] was first synthesized and recognized for its electrochemical and crystallographic properties around 1996 [START_REF] Yuan Gao | Valence band of LiNi 0.5 Mn 1.5 O 4 and its effects on the voltage profiles of LiNi 0.5 Mn 1.5 O 4 /li electrochemical cells[END_REF][START_REF] Amine | A new three-volt spinel Li 1+x Mn 1.5 Ni 0.5 O 4 for secondary lithium batteries[END_REF][START_REF] Amine | Preparation and electrochemical investigation of LiMn 2-x Me x O 4 (Me: Ni, Fe, and x = 0.5, 1) cathode materials for secondary lithium batteries[END_REF] . Manganese is found to be completely oxidized (Mn 4+ ) and the electrochemical activity is thus only brought by the nickel cations, exploiting oxidation states from Ni 2+ to Ni 4+ . This gives a gravimetric capacity of 147 mAh/g for LiNi 0.5 Mn 1.5 O 4 at ≈ 5 V potential vs. Li + /Li, thus delivering a high energy density [START_REF] Yuan Gao | Valence band of LiNi 0.5 Mn 1.5 O 4 and its effects on the voltage profiles of LiNi 0.5 Mn 1.5 O 4 /li electrochemical cells[END_REF][START_REF] Amine | A new three-volt spinel Li 1+x Mn 1.5 Ni 0.5 O 4 for secondary lithium batteries[END_REF][START_REF] Amine | Preparation and electrochemical investigation of LiMn 2-x Me x O 4 (Me: Ni, Fe, and x = 0.5, 1) cathode materials for secondary lithium batteries[END_REF][START_REF] Zhong | Synthesis and electrochemistry of LiNi x Mn 2-x O 4[END_REF] (Figure 3.23).

Also, the fact of avoiding the presence of any Mn 3+ is an advantage, as previously dis- Reprinted from [START_REF] Patoux | High voltage nickel manganese spinel oxides for li-ion batteries[END_REF] .

cussed in the case of LiMn 2 O 4 . In principle it is also possible to intercalate a second Li ion, resulting in Li 2 Ni 0.5 Mn 1.5 O 4 through a reaction at 3 V vs. Li + /Li, but in this case Mn 3+ is involved. Several studies were published in recent years, dealing with the many aspects of the optimization and understanding of such a material [START_REF] Patoux | High voltage nickel manganese spinel oxides for li-ion batteries[END_REF][START_REF] Duncan | Relationships between Mn3+ Content, Structural Ordering, Phase Transformation, and Kinetic Properties in LiNi x Mn 2-x O 4 cathode materials[END_REF][START_REF] Kunduraci | Synthesis and characterization of nanostructured 4.7V Li x Mn 1.5 Ni 0.5 O 4 spinels for high-power lithium-ion batteries[END_REF][START_REF] Kunduraci | The effect of particle size and morphology on the rate capability of 4.7V Li x Mn 1.5+δ Ni 0.5-δ O 4 spinel lithium-ion battery cathodes[END_REF][START_REF] Lee | Revealing the coupled cation interactions behind the electrochemical profile of Li x Ni 0.5 Mn 1.5 O 4[END_REF] . From the crystallographic point of view LiNi 0.5 Mn 1.5 O 4 is analogous to LiMn 2 O 4 , crystallizing in the Fd 3m space group and thus having Ni and Mn randomly distributed in the 16d crystallographic site. For certain synthesis conditions, the Ni/Mn ratio of 1:3 can lead to a reduction in symmetry to the cubic P4 3 32 space group, due to cations charge ordering [START_REF] Gryffroy | A neutron diffraction study of some spinel compounds containing octahedral ni and mn at a 1:3 ratio[END_REF] . This phase has however poorer transport properties than the cation-disordered Fd 3m one [START_REF] Wang | A comparative study of Fd 3m and P4 3 32 LiNi 0.5 Mn 1.5 O 4[END_REF][START_REF] Duncan | Relationships between Mn3+ Content, Structural Ordering, Phase Transformation, and Kinetic Properties in LiNi x Mn 2-x O 4 cathode materials[END_REF][START_REF] Kim | Comparative study of LiNi 0.5 Mn 1.5 O 4 -delta and LiNi 0.5 Mn 1.5 O 4 cathodes having two crystallographic structures: Fd 3m p4 3 32[END_REF][START_REF] Amdouni | Structure and insertion properties of disordered and ordered LiMn 1.5 Ni 0.5 O 4 spinels prepared by wet chemistry[END_REF][START_REF] Gryffroy | A neutron diffraction study of some spinel compounds containing octahedral ni and mn at a 1:3 ratio[END_REF] thus showing poorer electrochemical properties and not being interesting for applications (Figure 3.23). Regarding the lithium (de)intercalation reaction at 4.7 V, most studies reported on the presence of two topotactic two-phase transitions involving three cubic phases in the ordered spinels (P4 3 32). In the disordered one, the first of the two biphasic reaction is still present, but on a narrower miscibility gap, revealing a clear influence of the cations distributions on the phase diagram and electrochemical properties of the material [START_REF] Duncan | Relationships between Mn3+ Content, Structural Ordering, Phase Transformation, and Kinetic Properties in LiNi x Mn 2-x O 4 cathode materials[END_REF] . Note that the ordered spinel LiNi 0.5 Mn 1.5 O 4 therefore possesses a stable intermediate phase in the middle of (dis)charge, at composition Li 0.5 Ni 0.5 Mn 1.5 O 4 .

This can be seen in the light of the ordering scheme that we showed in paragraph 3. Compositions within the solid solution LiNi x Mn 2-x O 4 exhibit an increasing voltage upon lithium extraction when x increases, while the gravimetric capacity is reduced as Ni is heavier than Mn. A good trade-off is found for x = 0.4, i.e. for LiNi 0.4 Mn 1.6 O 4 (i.e.

LiNi 2+

0.4 Mn 3+ 0.2 Mn 4+ 1.4 O 4 ) now widely studied as a next-generation positive electrode material for Li-ion batteries [START_REF] Patoux | High voltage nickel manganese spinel oxides for li-ion batteries[END_REF][START_REF] Patoux | High voltage spinel oxides for li-ion batteries: From the material research to the application[END_REF][START_REF] Dedryvere | Electrode/electrolyte interface reactivity in high-voltage spinel LiMn 1.6 Ni 0.4 O 4 /Li 4 Ti 5 O 12 lithium-ion battery[END_REF][START_REF] Wang | CMC as a binder in LiNi 0.4 Mn 1.6 O 4 5 V cathodes and their electrochemical performance for Li-ion batteries[END_REF] . The capacity originates for 20% from the Mn 3+ /Mn 4+ redox couple (around 4.2 V vs. Li + /Li), while the remaining 80% is provided by the Ni 2+ /Ni 3+ and Ni 3+ /Ni 4+ ones in equal amount at 4.7 V vs. Li + /Li [START_REF] Patoux | High voltage nickel manganese spinel oxides for li-ion batteries[END_REF][START_REF] Saravanan | A study of room-temperature Li x Mn 1.5 Ni 0.5 O 4 solid solutions[END_REF][START_REF] Arai | Phase transition kinetics of LiNi0.5Mn1.5O4 electrodes studied by in situ x-ray absorption near-edge structure and x-ray diffraction analysis[END_REF] (Figure 3.24). LiNi 0.4 Mn 1.6 O 4 exhibits low capacity fading upon cycling, high energy density and good rate capabilities, making it a more interesting choice than other compositions in the LiNi x Mn 2-x O 4 solid solution [START_REF] Croguennec | Recent achievements on inorganic electrode materials for lithium-ion batteries[END_REF] . The mechanism of Li + deintercalation from LiNi 0.4 Mn 1.6 O 4 is described as a solid solution, followed by a biphasic reaction corresponding to the Ni 3+ /Ni 4+ redox couple. Namely it behaves as a cation-disordered LiNi 0.5 Mn 1.5 O 4 spinel where the first biphasic reaction has been completely suppressed [START_REF] Duncan | Relationships between Mn3+ Content, Structural Ordering, Phase Transformation, and Kinetic Properties in LiNi x Mn 2-x O 4 cathode materials[END_REF] .

To understand the mechanism behind such phase diagram and to get insight into the deintercalation reaction, we decided to observe it in real time using operando NPD. We studied a sample prepared at CEA-Liten (Grenoble) and our (Ti,Zr) electrochemical cell was used to cycle the material (a first charge followed by a discharge at C/20 rate) versus a lithium metal negative electrode, while NPD patterns were continuously acquired for 30 minutes each. Charging the material up to 5 V was challenging: normal electrolytes already tend to decompose/oxidize at such high potentials, and this is even clearer for our deuterated electrolyte which is not optimized for this purpose. The electrochemical data obtained during our experiment is showed in Figure 3 served through the full electrochemical cycle, summarized as follows:

• We confirm the existence of a solid solution region followed by a biphasic reaction upon • Lithium's SOF is observed to decrease. In the Li-rich solid solution it decreases down to 0.42(14) Li/f.u.. The Li-poor phase contains instead 0.12(12) Li/f.u. at the end of charge. About 10% of lithium seems thus to remain in the structure, consistent with the fact that 91% of the theoretical capacity is measured to be obtained from the electrochemical cycling. Thanks to the use of a PTFE binder in the electrode formulation the whole amount of spinel is electrochemically active (no residue of the pristine material is observed). Note thus that the unexploited capacity is simply due to the already encountered [START_REF] Baehtz | Design and performance of an electrochemical in-situ cell for high resolution full-pattern xray powder diffraction[END_REF][START_REF] Martinez | Chemical vs. electrochemical extraction of lithium from the Li-excess Li 1.10 Mn 1.90 O 4 spinel followed by NMR and DRX techniques[END_REF] difficulty in extracting the whole amount of lithium from spinels. An interesting behaviour was observed upon close inspection of the Debye-Waller thermal parameters. In a first step, we considered B iso to be the same for all atoms (refining B overall in FullProf) to reduce the amount of free parameters. We observed that it remained almost constant during the electrochemical reaction of the Mn 3+ /Mn 4+ redox couple while a substantial and somehow unexpected increase (more than 50%) of B overall was found upon oxidation of Ni 2+ into Ni 3+ . During the Ni 3+ /Ni 4+ reaction, which is biphasic, B overall recovers a value that is for both phases similar but slightly lower than the initial one. 9)) the refinement led to B iso (O) = 1.5(1) while B iso (Ni/Mn) = 0.2(2) and B iso (Li) = 0.9(5) (Figure 3.28). Ni 3+ is a 4s 0 3d 7 cation prone to Jahn-Teller distortion (low spin state t 6 2g e 1 g ) but too diluted by Mn in this sample to create a cooperative effect and cause a cubic-to-tetragonal transition. The distortion of the Ni 3+ O 6 octahedra occurs nonetheless at the local scale, with two long and four short Ni-O bonds (typically around 2.09 Å and 1.91 Å as observed in LiNiO 2 and in LiNi 1/2 Mn 1/2 O 2 , vs. 1.90 Å for the six Mn-O bonds in Mn 4+ O 6 [START_REF] Rougier | Non-cooperative Jahn-Teller effect in LiNiO 2 : An EXAFS study[END_REF]263] ). As Ni and Mn occupy the same crystallographic site and are sitting at the centre of a regular octahedral MO 6 environment (as imposed by the cell description), the oxygen's B iso hence provides an alternative to describe how the M-O distances are distributed at the local scale. Upon further lithium deintercalation from LiNi 0.4 Mn 1.6 O 4 the most oxidized composition is formed with all the transition metal ions at the Ni 4+ or Mn 4+ states and, as expected, with the smaller value observed for oxygen's B iso . Indeed, Ni 4+ and Mn 4+ are 4s 0 3d 6 and 4s 0 3d 3 cations stable in regular

Conclusions and perspectives

In this chapter we described how we used operando neutron powder diffraction (combined with synchrotron XRPD) to elucidate the deintercalation mechanism occurring in manganese spinels. We mainly dealt with Li plemented this operando NPD study using operando synchrotron XRPD, aiming for new insights brought by high-intensity and high-resolution measurements. We found indeed a 1 st cycle irreversibility present upon the cycling of LiMn 2 O 4 , further showing its inadequacy for industrial applications. On the other hand it is an extremely interesting material from the crystallographic point of view, and we reported for the first time the structure of the phase Li 0.5 Mn 2 O 4 . This composition observed in the middle of charge and discharge has been thought to possess lithium/vacancy ordering, responsible for the 0.1 V jump in the electrochemical curve of the material. However no proof of this had been found yet.

We demonstrate here that Li 0.5 Mn 2 O 4 is more correctly written as Li 0.5 Mn 3+ 0.5 Mn 4+ 1.5 O 4 because a charge ordering of Mn cations is present, as well as the Li/vacancy one. The cations ratio of 1:3 Mn 3+ :Mn 4+ leads to a first symmetry reduction from Fd 3m to P4 3 32.

Li/vacancy ordering along the [110] direction gives the final representation in the P2 1 3 space group, allowing to explain all weak Bragg reflections observed at this composition only. These observations open the door to a number of interesting questions, as to indentify the magnetic behaviour of Mn 3+ (HS or LS?) or, importantly, to detail using SEM and TEM the irreversibility observed upon the 1 st electrochemical cycle. Finally, we studied one example among high-voltage spinels, namely the nickel-substituted LiNi 0.4 Mn 1.6 O 4 . A full cycle was observed by operando NPD, giving insightful information about lithium extraction/reinsertion process, bond-lengths variations and, unexpectedly, Ni 3+ Jahn-Teller distortion that could be observed because it correlates to the Debye-Waller factor of oxygen in the structure. This study is further proof that NPD allows us to be sensitive to all structural parameters of interest for electrode materials, and that it can be effective not only on the long (crystallographic) range, but on the local scale as well. The careful (and often tricky) analysis of SOFs and B iso is a powerful tool, distinguishing neutrons from other techniques, and it will certainly be the key for future studies of electrode materials using operando NPD. One could imagine also other applications, as measuring the materials in situ (but not operando) in order to make longer acquisition with better statistics and then analyze the anisotropic Debye-Waller factors B aniso . An electrochemical cell for NPD experiments at high temperature is also under development, as we envisage pushing forward our studies on thermal parameters, but also because we hope to extend our studies to all-solid-state lithium batteries, which cycle above 100 • C.

Introduction

Polyanionic materials were already mentioned in the general introduction of this thesis as important positive electrodes for Li-ion batteries. The reasons that lead many researchers to investigate them despite their "weight penalty" have been already detailed. Within this wide family, some compositions are more promising than others : not only they offer very good energy densities during the exchange of 1 Li + /f.u. (thus one electron/f.u., Figure 4.1), but they also pledge the exchange of a second Li + /f.u. [START_REF] Masquelier | Polyanionic (Phosphates, Silicates, Sulfates) Frameworks as Electrode Materials for Rechargeable Li (or Na) Batteries[END_REF][START_REF] Whittingham | Ultimate limits to intercalation reactions for lithium batteries[END_REF] . This would double the theoretical capacity and energy density, making a revolutionary material for the Li-ion battery technology. Several challenges must be faced to electrochemically cycle a material on 2 Li + cations per transition metal but the result would fully repay the effort. Compositions like LiVPO 4 O and LiVPO 4 F belong to these promising materials, and for this reason they have been studied at ICMCB and LRCS since 2011 (PhD thesis of J.M. Ateba Mba [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF] ). They are homeotypic, namely they belong to the same structural family, the Tavorite one, described in the next section. This chapter aims at reviewing most of Ateba Mba's work on the subject, to subsequently introduce the ex situ, in situ and operando X-Ray powder diffrac-tion (XRPD) and neutron powder diffraction (NPD) studies we undertook to unravel the phase diagram of these fascinating materials. We used these techniques, often combined, to better understand lithium's (de)intercalation, hoping that this could lead in the near future to the possibility of exploiting the full potentialities of LiVPO 4 F and LiVPO 4 O.

Tavorite compositions among polyanionic materials

The name Tavorite was introduced 67 years ago by Dr. Elysiário Távora Filho who first discovered it as a mineral [START_REF] Filho | Estudos brasileiros de geologia[END_REF] . The first study of the Tavorite mineral was performed by M.L. Lindberg et al. [START_REF] Lindberg | Tavorite and barbozalite, 2 new phostate minerals from minas-gerais, brazil[END_REF] who proposed the chemical formula of LiFePO 4 OH, similar to the already known Montebrasite LiAlPO 4 OH [START_REF] Cloizeaux | On a new locality of amblygonite and on montebrasite, a new hydrated aluminium and lithium phosphate[END_REF] . Note that the description of the Tavorite structure (LiFePO 4 OH) is exactly the same as that of the Amblygonite structure, of chemical formula LiAlPO 4 F. Amblygonite and Tavorite are therefore isostructural and both differ from the Montebrasite structure. Indeed the latter crystallizes in the monoclinic system with the space group of C2/c, while the Tavorite structure crystallizes in the triclinic system with the space group P 1.

The general chemical formula of the Tavorite family is AMXO 4 Y with A as the alkaline ion, M as a transition metal or earth-alkaline metal, X as phosphorus or sulfur and Y as halide, hydroxide, oxygen, or a mixed halide/hydroxide (Figure 4.2). V.I. Simonov and N.V. Belov [START_REF] Simonov | The crystal structure of amblygonite[END_REF] first described the Tavorite's crystal structure, built on MO 4 Y 2 octahe- Adapted from [START_REF] Marx | The structure of tavorite LiFePO 4 (OH) from diffraction and gga plus u studies and its preliminary electrochemical characterization[END_REF] .

dra and XO 4 tetrahedra connected to each other through their corners by oxygen atoms.

The octahedral MO 4 Y 2 units are connected through the ligand Y along -YO 4 MY-YO 4 MYchains connected to each other through XO 4 tetrahedra by oxygen atoms. Two crystallographic sites were observed for the transition metal M (both at special Wyckoff positions) and one crystallographic site for X. Although sulphate tavorite materials are interesting because of the possibility to exploit the Fe 2+ /Fe 3+ redox couple at 3.6 V [START_REF] Rousse | Sulfate-based polyanionic compounds for li-ion batteries: Synthesis, crystal chemistry, and electrochemistry aspects[END_REF] , they are also chemically unstable in air. Hence in the following we will mainly focus on phosphate structures, where X = P. The Tavorite structure generates 3 tunnels (in three directions), two of which containing the A atom. The number of Li/Na sites and their precise localization were hypothetical in the work of Simonov et al. [START_REF] Simonov | The crystal structure of amblygonite[END_REF] : through their studies of the LiAlPO 4 (F x OH 1-x ) series, they reported a large and extremely anisotropic displacement parameter for the Li atom and suggested that the site was split into two fractionally occupied positions. Later, during the study of the same series (performed using single crystals), L.A. Groat et al. [START_REF] Lee | The amblygonite (LiAlPO 4 F)montebrasite (LiAlPO 4 OH) solid solution: A combined powder and single-crystal neutron diffraction and solid-state 6Li MAS, CP MAS[END_REF] confirmed the distribution of Li between two sites, highly dependent on the amount of fluorine in the sample. In the following we will stress how such considerations are better addressed using neutron diffraction. Note, as a final remark, that four models of triclinic unit cells describing the Tavorite structure are reported in literature.

As this can be quite confusing, they can be found in [START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] where the relationship between different descriptions is discussed.

In this chapter we limit our study to LiVPO 4 Y (Y = F, O). However, the Tavorite family is a large one, born from the combination of several alkali, anions and transition metals. Figure 4.3 gathers some significant fluorophosphate compositions. Note the great amount of different redox potentials vs Li + /Li that these materials can attain when used as battery electrodes, which can in principle be tuned to match a specific requirement.

Vanadium, in particular, is the only transition metal able to exploit 3 redox couples, from V 2+ to V 5+ , making it extremely versatile. It is then easy to understand the reason for the great attention given to Tavorite materials in the battery community, and to vanadium phosphates in particular in our group.

V V PO 4 O 3.95 V LiV III PO 4 F Li 2 V II PO 4 F 1.80 V V IV PO 4 F 4.26 V 1.5 V

Synthesis

The synthesis of LiVPO 4 O and LiVPO 4 F has been thoroughly described by Ateba Mba et al. in [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF][START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] . Here we summarize the most important steps. LiVPO 4 F was first synthesized by Barker et al. [START_REF] Barker | Lithium metal fluorophosphate materials and preparation thereof[END_REF][START_REF] Barker | Electrochemical insertion properties of the novel lithium vanadium fluorophosphate, LiVPO 4 Fâ[END_REF] using a two-step ceramic method. It is based on the formation of the intermediate phase VPO 4 , prepared by carbothermal reduction (CTR), which subsequently reacts to form LiVPO 4 F. The synthesis procedure has been improved during Ateba Mba's

PhD work [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF] , constituting a precious know-how for ICMCB and LRCS. The materials used in this thesis were in fact sinthesized by Ateba Mba and Philippe Dagault (ICMCB). In more details, the involved reactions are: is mixed with lithium fluoride LiF. The mixture is pressed as a pellet, put in a gold tube sealed inside an argon-filled glovebox and heated at 750 • C for 1h. Alternatively, for high purity the pellet can be put in a gold boat and heated in the oven under argon flow. Then the pellet is quenched in liquid nitrogen. This process can possibly leave impurities in the product (α-Li 3 V 2 (PO 4 ) 3 for example), but these were found to be soluble in water and could thus be eliminated by stirring in water, filtering and drying. Regarding the synthesis of LiVPO 4 O, it follows a simpler one-step ceramic route procedure. This uses V 2 O 3 as a vanadium precursor, together with NH 4 H 2 PO 4 and Li 3 PO 4 . The detailed reaction is:

V 2 O 5 + 2N H 4 H 2 P O 4 + 2C sp → 2V P O 4 + 2N H 3 + 3H 2 O + 2CO ( 4
1 2 V 2 O 3 + 1 3 Li 3 P O 4 + 2 3 N H 4 H 2 P O 4 + 1 2 O 2 → LiV P O 4 O + 2 3 N H 3 + H 2 O (4.3)
Instead of Li 3 PO 4 , LiF can also be used. The procedure is as follows: the precursors are mixed in a planetary ball milling machine (or SPEX, conditions??) and then pressed as a pellet. A first thermal treatment at 300 • C for 5 hours is followed by grinding, making a new pellet and then a second thermal treatment at 800 • C for 10 h under argon flow.

The pellet is then quenched and the powder recovered. It is worth mentioning that we do not put any prefix before LiVPO 4 O, for homogeneity with LiVPO 4 F. However the product we obtain is one among different polymorphs. Here the material we synthesize is the Tavorite composition crystallizing in the P 1 space group, sometimes referred to as α-LiVPO 4 O [START_REF] Allen | Synthesis, structure and electrochemistry of lithium vanadium phosphate cathode materials[END_REF][START_REF] Harrison | Chemical and electrochemical lithiation of LiVOPO 4 cathodes for lithium-ion batteries[END_REF][START_REF] Ling | Phase stability and its impact on the electrochemical performance of VOPO 4 and LiVOPO 4[END_REF] . Other polymorphs are tetragonal α 1 -LiVPO 4 O (P4/nmm [START_REF] Hameed | Synthesis and electrochemical studies of layer-structured metastable α I -LiVOPO 4[END_REF] ) and orthorhombic β-LiVPO 4 O (Pnma [START_REF] Gaubicher | Li/β-VOPO 4 : A New 4 V System for Lithium Batteries[END_REF] ), not considered in this thesis.

Crystal Structures

Phase pure LiVPO 4 O and LiVPO 4 F can be reproducibly obtained using the procedure described above. As already discussed, they both crystallize in the Tavorite crystal structure.

Typical XRPD diffraction patterns of the two materials are reported in Figure 4.4. Bragg positions are calculated in the P 1 space group, with the reported cell parameters [START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] . One notices that, although the two materials are homeotypic, the unit cell of LiVPO and cell parameters. Reprinted from [START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] .

LiVPO 4 F

Knowing that LiVPO 4 F belongs to the Tavorite family, a complete structural determination aims at precisely refining the various atomic coordinates (which are already approximately known) and most importantly at localizing Li + cations within the tunnels of the structure.

Simonov et al. [START_REF] Simonov | The crystal structure of amblygonite[END_REF] had previously published the crystal structure of LiAlPO 4 F where two sites of lithium were proposed, each site being occupied at 50% and separated from the other by a distance of 0.5 Å. Based on this work, Ellis et al. [START_REF] Ellis | Structure and electrochemistry of two-electron redox couples in lithium metal fluorophosphates based on the tavorite structure[END_REF] carried out a structural determination using synchrotron XRPD. Their proposed model confirms the presence of two lithium sites, although X-Rays are not an effective probe for light elements such as lithium. A more insightful approach was undertaken by Ateba Mba et al. [START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] , who made combined used of XRPD (high-angular resolution Cu Kα 1 ) and neutron powder diffraction (NPD)

to characterize the structure and the position of lithium sites (thanks to Fourier difference maps). Interestingly, only one lithium site was found, whose fractional coordinates are at the barycentre of the two Li sites proposed for LiAlPO 4 F. The crystal structure of LiVPO 4 F is shown in Figure 4.5, while detailed atomic parameters are reported in [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF][START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] . Briefly, the structure is built on VO 4 F 2 octahedra which share common fluorine atoms so as to form Regarding LiVPO 4 O, the only structural determination published until 2012 was that of Lavrov et al. [START_REF] Lavrov | Synthesis and crystal-structure of mixed vanadyl and lithium ortho-phosphate, LiVOPO 4[END_REF] . Ateba Mba et al. [START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] recently carried out a new structural study, taking Adapted from [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF] .

-F-V-F-V-infinite
advantage of XRPD (again Cu Kα 1 ) and NPD, to verify the older one and to further address the similarity with LiVPO 4 F. Detailed atomic parameters are reported in [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF][START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] .

The 3D structure of LiVPO 4 O is shown in sites with a wide range of V-O distances: 1.62-2.17 Å for V(1) and of 1.71-2.21 Å for V(2), as a typical example of alternate short and long distances in vanadyl-containing compounds [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF][START_REF] Bianchini | Multiple phases in the -VPO 4 O -LiVPO 4 O-Li 2 VPO 4 O system: a combined solid state electrochemistry and diffraction structural study[END_REF][START_REF] Schindler | Crystal chemical aspects of vanadium: Polyhedral geometries, characteristic bond valences, and polymerization of (von) polyhedra[END_REF] . The short and long V-O distances in VO 4 O 2 octahedral chains are alternated along the [010] P 1 direction. The lithium ions are distributed over two fully occupied distinct crystallographic sites, Li(1) and Li(2), due to the doubling of the unitcell, at a distance of 3.44 Å from each other. They lie in two distorted pentahedral sites.

Electrochemistry

The electrochemical response of LiVPO 4 Y (Y = F, O) towards Li + insertion / extraction has been well studied by Ateba Mba in his PhD thesis [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF] , following the pioneering work of Barker [START_REF] Barker | Electrochemical insertion properties of the novel lithium vanadium fluorophosphate, LiVPO 4 Fâ[END_REF][START_REF] Barker | Structural and electrochemical properties of lithium vanadium fluorophosphate, LiVPO 4[END_REF] . We report here the salient results, stressing the similarities and most importantly the differences between the two materials. Li metal. Detailed battery preparation procedures can be found in [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF] . Here we recall that the electrodes, in the form of a cast film, are composed by active material (> 73 wt.%), Adapted from [START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] .

carbon Csp (12-15 wt.%) and PVdF binder (12 wt.%). In the case of LiVPO [START_REF] Azmi | Cathodic performance of LiVOPO 4 prepared by impregnation method for li ion secondary battery[END_REF][START_REF] Bustam M Azmi | LiVOPO 4 as a new cathode materials for li-ion rechargeable battery[END_REF] . The triclinic Tavorite form of LiVPO 4 O has been thought to possess poor electrochemical properties instead, mainly attributed to the fact that it is a wide bandgap semiconductor with low intrinsic electrical conductivity [START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF][START_REF] Azmi | Cathodic performance of LiVOPO 4 prepared by impregnation method for li ion secondary battery[END_REF][START_REF] Yang | Towards the understanding of poor electrochemical activity of triclinic LiVOPO 4 : Experimental characterization and theoretical investigations[END_REF] . In the low voltage domain, the electrochemical behavior of LiVPO 4 O is extremely interesting and complicated, in contrast with the simplicity of LiVPO 4 F's plateau. The insertion of lithium into LiVPO 4 O was first reported by Allen et al. [START_REF] Allen | Synthesis, structure and electrochemistry of lithium vanadium phosphate cathode materials[END_REF] , who reported on both the tavorite and the orthorhombic (β-LiVPO 4 O) polymorphs. They reached compositions Li Regarding the electrochemical response, it is important to note that it strongly depends on the particle size of LiVPO 4 O. As reported in [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF][START_REF] Bianchini | Multiple phases in the -VPO 4 O -LiVPO 4 O-Li 2 VPO 4 O system: a combined solid state electrochemistry and diffraction structural study[END_REF][START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] , the synthesis procedure leads to the formation of 1-2 µm particles, highly agglomerated (5-6 µm). We performed SPEX ballmilling to decrease the particle size and, as illustrated in Figure 4.8 (for similar electrode masses (≈4 mg)), the longer the grinding process, the higher the electrochemical reactivity. This significant improvement is achieved thanks to the smaller size of the obtained particles, which also reflects on the broadening of the X-Ray diffraction peaks (Figure 4.8, insets).

Therefore, for a sample milled for a long time (30 minutes here), a discharge capacity close to the theoretical one can be achieved together with good reversibility, while for shorter milling times the capacity decreases and a strong irreversibility is observed, probably due to limited diffusion within the large particles. As we will discuss in the following, this is also a hint to understand the limited reactivity of LiVPO 4 O at high potential.

Phase diagram of LiVPO

4 F (0 ≤ x ≤ 2)
In this section the phase diagram and the crystal structures observed by Ateba Mba [START_REF] Mba | New Transition Metal Fluorophosphates as Positive Electrode Materials for Li-ion Batteries[END_REF][START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF][START_REF] Mba | Lithium insertion or extraction from/into tavorite-type LiVPO 4 F: An in situ X-ray diffraction study[END_REF] upon lithium insertion and extraction into/from LiVPO 4 F are briefly reviewed.

Lithium extraction from LiVPO 4 F -High voltage domain

Li + extraction from LiVPO 4 F proceeds through 2 voltage-composition plateaus at 4.24 V and 4.28 V vs. Li + /Li. This observation (Figure 4.7) was verified for the first time by Ateba Mba et al. using in situ XRPD [START_REF] Mba | Lithium insertion or extraction from/into tavorite-type LiVPO 4 F: An in situ X-ray diffraction study[END_REF] . Upon charge a sequence of two first-order transitions was discovered, the first one between LiVPO 4 F and Li 0.67 VPO 4 F, the second one between Li 0.67 VPO 4 F and VPO 4 F. The two reactions are clearly correlated with the two electrochemical plateaus. The structure of the end member VPO 4 F was previously reported by Ellis et al. [START_REF] Ellis | Structure and electrochemistry of two-electron redox couples in lithium metal fluorophosphates based on the tavorite structure[END_REF] In good agreement with this, Ateba Mba reported a monoclinic unit cell of a = 7.164(4) Å, b = 7.119(7) Å, c = 7.121(5) Å, β = 118.09(7) • and a volume V = 320.46(4) Å3 (Table 4.1). This corresponds to a volume change ∆V/V of more than 8% when all lithium is extracted from LiVPO 4 F (Figure 4.9). Thus it is not entirely surprising that an intermediate phase forms upon charge, in order to avoid such an important volume change, which would induce significant stress in the material [START_REF] Casas-Cabanas | Crystal chemistry of na insertion/deinsertion in FePO 4 -NaFePO 4[END_REF] . The intermediate phase is observed to form around the composition Li 0.67 VPO 4 F. This particular stoichiometry immediately suggests lithium/vacancy and/or charge ordering, since it can be written as Li 2/3 V 3+ 2/3 V 4+ 1/3 PO 4 F. The exact nature of this phase, however, has not been determined yet. Its unit cell parameters were reported in triclinic P 1 setting, being a = 5.171( 9 be energetically favourable, a remarkable fact is that the composition Li 0.67 VPO 4 F is not stabilized reversibly upon charge and discharge: during the latter no intermediate phase was observed [START_REF] Mba | Lithium insertion or extraction from/into tavorite-type LiVPO 4 F: An in situ X-ray diffraction study[END_REF] . Further studies are required to fully understand the structure of this interesting phenomenon. involving successive two-phase reactions. Reprinted from [START_REF] Mba | Lithium insertion or extraction from/into tavorite-type LiVPO 4 F: An in situ X-ray diffraction study[END_REF] .

( Å) c ( Å) α ( • ) β ( • ) γ ( • ) Vol. ( Å3 ) V/Z ( Å3 ) VPO4F C2/c

2% 6% 8%

Lithium insertion into LiVPO 4 F -Low voltage domain

As we observed from the electrochemical GITT profile presented in Figure 4.7, the lithium insertion into LiVPO 4 F proceeds through an extremely flat voltage-composition plateau at exactly 1.81 V vs. Li + /Li. This is usually the signature of a first order transition. Ateba Mba verified this by means of in situ XRPD [START_REF] Mba | Lithium insertion or extraction from/into tavorite-type LiVPO 4 F: An in situ X-ray diffraction study[END_REF] : he indeed observed a biphasic reaction where LiVPO 4 F gradually disappeared while the end member phase Li 2 VPO 4 F forms. This composition was already reported by Ellis et al. [START_REF] Ellis | Structure and electrochemistry of two-electron redox couples in lithium metal fluorophosphates based on the tavorite structure[END_REF] , crystallizing in the monoclinic C2/c space group.

Phase diagram of LiVPO

4 O (0 ≤ x ≤ 2)
In this section the study of lithium extraction and insertion from/into LiVPO 4 O is described in details, with special attention to the crystallographic transitions involved and to the new structures determined.

Experimental

Electrodes were prepared by ball-milling (SPEX, 30 minutes) LiVPO 4 O with Carbon Super P (85:15 wt% when not specified otherwise). For batteries cycled in coin cells, PVdF was added as a binder (12 wt%) according to the Bellcore protocol (described in [START_REF] Larcher | Effect of particle size on lithium intercalation into α-Fe 2 O 3[END_REF] ), while in situ measurements were carried out using directly a mixture of LiVPO 4 O and Carbon Super P. 1M LiPF 6 in EC:DMC (1:1) was used as the electrolyte (LP30). In situ measurements were performed using a Bruker D8 diffractometer with Cu-Kα 1,2 wavelengths or a PANalytical Empyrean diffractometer with a Cu-Kα 1 setting. In the first case, lithium batteries were prepared in our in situ cell [START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF][START_REF] Ouvrard | Heterogeneous behaviour of the lithium battery composite electrode LiFePO 4[END_REF] , able to perform both in reflection and transmission geometry. Reflection was used in this case. The same geometry but with a custom modified in situ cell was used in the second case. Both cells were described in section 1. at Institut Laue-Langevin. Data analysis and structural refinements through the Rietveld method [START_REF] Rietveld | A profile refinement method for nuclear and magnetic structures[END_REF] were performed thanks to the FullProf suite [START_REF] Rodriguez-Carvajal | Recent advances in magnetic-structure determination by neutron powder diffraction[END_REF] . As part of a collaboration with Dany Carlier and Elena Bogdan (ICMCB), we calculated the total energies with the GGA (PBE) [START_REF] John P Perdew | Generalized gradient approximation made simple[END_REF] and GGA + U method, using the Projector Augmented Wave (PAW) method [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmentedwave method[END_REF] as implemented in the Vienna Ab Initio Simulation Package (VASP, [START_REF] Kresse | Efficient iterative schemes for ab initio totalenergy calculations using a plane-wave basis set[END_REF] ). The DFT+U method (LDA+U or GGA+U) allows to treat more accurately strongly correlated systems, such as transition metals or rare earth-based materials [START_REF] Vladimir I Anisimov | Band theory and mott insulators: Hubbard u instead of stoner i[END_REF][START_REF] Ai Liechtenstein | Density-functional theory and strong interactions: Orbital ordering in mott-hubbard insulators[END_REF] . In our study, the Dudarev's approach was used to perform the GGA + U. The effective on site Coulomb (U) and exchange (J) parameters were not input separately as only the difference U ef f = (U-J) is meaningful. Here U ef f values of 0, 3, 4 and 4.5 eV were used. A plane wave cutoff energy of 600 eV and a 6x6x6 k-point grid were used to let the total energies converge by less than 5 meV/unit cell. not fully contribute to the electrochemical reaction but also shows that the kinetics can be significantly improved. Such an improvement in electrochemical properties agrees with our previous observations of an increased capacity of LiVPO 4 O in the low-voltage region when ball milled (also observed for orthorhombic β-LiVPO 4 O [START_REF] Bustam M Azmi | LiVOPO 4 as a new cathode materials for li-ion rechargeable battery[END_REF] ).

4.4.3

The crystal structure of -VPO 4 O [START_REF] Calvo | Crystal structure of βVPO 5[END_REF] ) Orthorhombic Pnma 1.56 2.59 α I -VPO 4 O (ICSD 108983 [START_REF] Tachez | A structural explanation for the polymorphism of the α form of anhydrous vanadyl phosphate[END_REF] ) Tetragonal P4/n 1.63 2.48

α II -VPO 4 O (ICSD 2889 [START_REF] Jordan | Crystal structure of α-vpo 5[END_REF] ) Tetragonal P4/n 1.58 2.86

The study of the end reaction member VPO 4 O has also been carried out, since it is a material with a rich crystal chemistry as witnessed by the existence of many different polymorphs reported in the literature (Table 4.2). Among these, the preparation of VPO 4 O from LiVPO 4 O, both chemically and electrochemically, results in the monoclinic -VPO 4 O phase. Interestingly, a recent study by Ling et al. [START_REF] Ling | Phase stability and its impact on the electrochemical performance of VOPO 4 and LiVOPO 4[END_REF] showed that, energetically, the structures. Indeed, the -VPO 4 O polymorph had first been indexed in the monoclinic P2 1 /n space group and its structure determined [START_REF] Kerr | Highly reversible Li Insertion at 4 V in -VOPO 4 /α-LiVOPO 4 Cathodes[END_REF][START_REF] Song | -VOPO 4 : Electrochemical synthesis and enhanced cathode behavior[END_REF] . More recently, a second indexation was performed in the Cc space group [START_REF] Girgsdies | The crystal structure of -VOPO 4[END_REF] and the two structures were compared, demonstrating a less distorted Cc structure. For this reason we performed careful X-Ray diffraction experiments on a VPO 4 O powder, chemically obtained from the oxidation of LiVPO 4 O and sealed in a capillary. The measured XRPD pattern is shown in Figure 4.12.

β
: XRD measurement and Rietveld refinement of a VPO O powder sealed The possible space groups found from the automatic indexation of XRPD data are Cc, C2/c and P2 1 /n. In order to investigate theoretically the phase stability of the different structural hypotheses we compared the total energies resulting from DFT calculations using GGA and GGA+U methods. For VPO 4 O with the P2 1 /n and Cc space groups, we used as initial structures those reported in [START_REF] Girgsdies | The crystal structure of -VOPO 4[END_REF][START_REF] Kerr | Highly reversible Li Insertion at 4 V in -VOPO 4 /α-LiVOPO 4 Cathodes[END_REF] . For VPO 4 O with the C2/c space group, we used as initial structure the one of VPO 4 F [START_REF] Ellis | Structure and electrochemistry of two-electron redox couples in lithium metal fluorophosphates based on the tavorite structure[END_REF] replacing F by O. We also considered a cell with a P 1 space group using the cell of LiVPO V 5+ ions are located in the center of the VO 6 octahedra with similar V-O distances along the chains as observed in VPO 4 • H 2 O [START_REF] Vaughey | Synthesis, structure, and properties of two new vanadium (iii) phosphates: Vpo 4 •h 2 o and v1. 23 (po4)(oh) 0.69 (h2o) 0.31. cntdot. 0.33 h2o[END_REF] , where the oxidation state is 3+, or in VPO 4 F, where it is 4+ [START_REF] Ellis | Structure and electrochemistry of two-electron redox couples in lithium metal fluorophosphates based on the tavorite structure[END_REF] . This indicates that the formation of short V=O (vanadyl type) and long V-O bonds along the chains, as it is the case for the three other structural hypotheses, strongly stabilizes the structure. Based on our theoretical study, the structure was refined (Figure 4.12) thanks to the Rietveld method in the space groups Cc or P2 1 /n, leading to better results for the parameters refined using the Cc crystal structure (Table 4. 4) Å, in agreement with the structure reported by Girgsdies et al. [START_REF] Girgsdies | The crystal structure of -VOPO 4[END_REF] ). More recently, this result was confirmed by Chen et al. [START_REF] Chen | Electrochemical behavior of nanostructured -VOPO 4 over two redox plateaus[END_REF] , further supporting the description of -VPO 4 O in the monoclinic Cc space group.

Lithium insertion into LiVPO 4 O -Low voltage domain

We introduced in section 4.2.3 the complex behaviour of LiVPO 4 O during lithium insertion.

A sequence of three reactions is observed: Allen et al. [START_REF] Allen | Synthesis, structure and electrochemistry of lithium vanadium phosphate cathode materials[END_REF] . On the other hand, those reported by Harrison et al. [START_REF] Harrison | Chemical and electrochemical lithiation of LiVOPO 4 cathodes for lithium-ion batteries[END_REF] and it is more likely to result in defects (their unit cell volume differs from ours by 1.2 Å3 ). The cell parameters obtained are plotted in Figure 4.17 and those determined for patterns #1, #14, #21, and #27 are reported in Table 4.6. The lattice parameters variation obtained considering the single-phase model is not fully convincing, since it is not smooth but rather step-like. This suggests the presence of a major phase that dominates the behavior and of a minor one that is almost unseen. Also, the evolution of χ 2 factors (bottom part of Figure 4.17

LiV 4+ P O 4 O + 1 2 Li + + 1 2 e -⇔
a ( Å) b ( Å) c ( Å) α ( • ) β ( • ) γ ( • ) V ( Å3 )
LiVPO 4 O ref. [START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] 6.7320( 1 We therefore decided to carry on the investigation and to refine the patterns #14, #21 and #27 as single phases, while all intermediate compositions were refined with two phases for which the cell parameters were allowed to vary (the zero shift was always fixed thanks to a Beryllium diffraction peak used as reference). The result is shown in Figure 4.18.

Despite the presence of two triclinic phases, it is remarkable that the cell parameters do not vary significantly. This is particularly true for a, b and c, while a certain variation of the angles is observed. Two main reasons can be adduced to justify this behavior.

The first one is of experimental nature. Indeed, we cannot expect a perfect accuracy from the proposed Le Bail fit, since there are many Bragg positions composing every apparent peak. As an example, the doublet in the [27.5 • -28.5 • ] region (pattern #14, red in Figure 4.15) is actually composed of 6 different Bragg positions. When the subsequent patterns are considered and two phases are present, the number of Bragg positions in the same peak becomes 12. The second reason is physical and it deals with the fact that the experimental observation of an evolution of the cell parameters in a two phase reaction is not impossible, and has been recently reported for several systems (NaFePO 4 [START_REF] Gaubicher | Abnormal operando structural behavior of sodium battery material: Influence of dynamic on phase diagram of Na x FePO 4[END_REF] ,

LiFePO 4 [START_REF] Liu | Capturing metastable structures during high-rate cycling of LiFePO 4 nanoparticle electrodes[END_REF] , LiMn y Fe 1-y PO 4 [START_REF] Ravnsbaek | Extended solid solutions and coherent transformations in nanoscale olivine cathodes[END_REF] , Li 1+x Mn 2-x O 4 [START_REF] Bianchini | Li-Rich Li 1+x Mn 2-x O 4 Spinel Electrode Materials: An Operando Neutron Diffraction Study during Li+ Extraction/Insertion[END_REF] ...). This can have different causes, like the presence of nanosized particles or important strains at the interface between the transforming phases. Once again, a look at the evolution of the χ 2 factor is relevant, not because of the lower obtained values which are somehow expected having doubled the amount of free parameters, but for the lack of a structure in the χ 2 distribution for the different patterns, which is approximately flat and satisfactory for all of them. Besides, (almost 2% for 0.25 lithium atoms) and they thus take place with significant strain in the material, determining a small but observable variation in the cell parameters.

The crystal structures of Li

x VPO 4 O (x = 2, 1.75, 1.5) x = 2
To the best of our knowledge, no detailed description of the crystal structure of Li 2 VPO 4 O has been reported in the literature so far, besides the values of the cell parameters [START_REF] Stanley Whittingham | Some transition metal (oxy) phosphates and vanadium oxides for lithium batteries[END_REF] . We not in good agreement with the previous report [START_REF] Stanley Whittingham | Some transition metal (oxy) phosphates and vanadium oxides for lithium batteries[END_REF] , but they are remarkably similar to those obtained from the end member of the in situ XRPD experiment described in the previous section (Table 4.6). were subsequently located thanks to the FOX software [START_REF] Cerny | Fox: A friendly tool to solve nonmolecular structures from powder diffraction[END_REF] and the XRPD and NPD patterns refined by the Rietveld method. [START_REF] Schindler | Crystal chemical aspects of vanadium: Polyhedral geometries, characteristic bond valences, and polymerization of (von) polyhedra[END_REF] . Indeed, the 3+ oxidation state in vanadium-centered octahedra is reported to result in an average bond length of 2.01 Å, with a maximum occurrence supports XANES observations made by other groups [START_REF] Allen | Synthesis, structure and electrochemistry of lithium vanadium phosphate cathode materials[END_REF][START_REF] Harrison | Chemical and electrochemical lithiation of LiVOPO 4 cathodes for lithium-ion batteries[END_REF] , showing that lithiation of LiVPO 4 O progressively eliminates the shortest V=O bond.

x = 1.5 and x = 1.75

We determined the crystal structures of all the end members Li x VPO 4 O (x = 0, 1, 2), but the intermediate phases x = 1.5, 1.75 still remained unknown, except for the cell parameters that we retrieved from our in situ XRPD experiment (Table 4.6). Initial attempts to establish these two structures failed because of the difficulty at preparing samples for ex situ studies as was done for Li 2 VPO 4 O. We then decided to use in situ synchrotron XRPD to observe them in real time while crystallizing. We carried out our experiment at the MSPD beamline in ALBA, Barcelona. A battery was prepared with LiVPO 4 O as positive electrode (mixed with 18% Csp and 11% PTFE), in our custom setup for synchrotron XRPD measurements in transmission geometry [START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF] . The battery was then discharged slowly at C/32 rate. Due to the limited available beamtime, we did not follow the whole reaction operando, but we only put the battery in the beam when the key compositions (x = 1, 1.5, 1.75, 2) were almost formed. This way we were able to capture several 5-minutes diffraction scans of the pure intermediate phases. The obtained cell parameters are reported in Table 4.9 and Table 4.10. To be consistent with LiVPO 4 O and Li 2 VPO 4 O, all unit cells are set so that the vanadium octahedral chains run along the b axis. Given the good agreement with the cell parameters of Table 4.6, we pursued a structural determination. However, one should note that this is only a partial determination since, as previously mentioned, the triclinic unit cell contains several oxygen and lithium positions and thus the accuracy resulting from synchrotron XRPD measurements is limited. Thanks to the use of the FOX software and to subsequent Rietveld and V(2) 3.2(3)+ suggests an alternation of V 4+ and V 3+ environments along the chains.

In Li 1.75 VPO 4 O V(1) still shows a slightly higher oxidation state than V(2): 3.4(3)+ vs.

3.1(3)+, giving on average exactly the expected 3.25+. The V-O bond-lengths along the chains offer less clear indications because of the significant error bars on oxygen positions; however one can observe that, in Li 1.5 VPO 4 O, V(1) possesses alternated long-short bonds, as is the case for V 4+ , while V(2) has more homogeneous bonds, as for V 3+ . This agrees issues when the experiment is applied to a material with triclinic crystal structure.

Conclusions and perspectives

This chapter presented the electrochemical properties and structural modifications upon cycling of two vanadium phosphates of great interest for Li-ion batteries: LiVPO An insightful operando XRPD experiment was carried out using Cu Kα 1 radiation to take advantage of the best available angular resolution and well distinguish the Bragg reflections of the triclinic phases involved. It showed how the volume change between the end members is a key parameter to determine the nature of the biphasic reaction observed: crystallographic phase transitions which involve small volume changes give rise to perfect biphasic reactions, while significant volume changes induce stress at the phases interface and a consequent variation of the cell parameters in the process.

The crystal structures of the above-mentioned phases were also determined for the first time: Li 2 VPO 4 O's structure was completely described in the P 1 space group thanks to a combined ex situ XRPD-NPD approach; interestingly, we noticed how vanadium's oxidation state in the real engine promoting the transformation of the octahedral chains:

long-short alternated bonds were present along the chain in -VPO 4 O, but as vanadium is reduced from 5+ to 4+ and then 3+, such V-O bonds become more regular and the octahedra less distorted. For the intermediate phases Li revealed to be more difficult to prepare for ex situ studies, in situ synchrotron XRPD was used to determine the structures, although the contribution of neutrons will still be needed in forthcoming studies to completely describe lithium's features. Further perspective work include the optimisation of LiVPO 4 O's particle size, since as discussed above this parameter is crucial to obtain full capacity both at high and low potential (in fact, long ball milling time are necessary at the moment). In the longer term, the goal is to achieve the functioning of Li x VPO 4 O in the full range 0 ≤ x ≤ 2 while reducing the volume changes that would limit the use of this material on the two-cations intercalation reaction in real batteries. Finally, note that the tavorite crystal structure can accommodate several compositions, and among these several different polymorphs, possibly showing various degrees of electrochemical activity; therefore the research activity on materials belonging to this family will continue searching for new compositions with improved energy density and, possibly, able to exchange more than one Li + /f.u..

Chapter 5

Na 3 V 2 (PO 4 ) 2 F 3 : a fluorophosphate for Na-ion batteries

Introduction

In the Introduction of this thesis it was discussed how Na-ion is one of the most promising candidates to replace Li-ion when looking for a lower-cost and abundant elements-based battery technology for storage grid applications. In this chapter we investigate a polyanionic material, Na 3 V 2 (PO 4 ) 2 F 3 , showing performances among the best ever achieved for a positive electrode for Na-ion batteries. This fluorophosphate also has an incredibly rich crystal chemistry, that we analyzed in details at different temperatures and different compositions upon Na + deintercalation, to provide a comprehensive phase diagram and understand its crystallographic transformations. Na 3 V III 2 (PO 4 ) 2 F 3 was first proposed by Barker et al. [START_REF] Barker | Hybrid-ion: A lithium-ion cell based on a sodium insertion material[END_REF][START_REF] Gover | The electrochemical insertion properties of sodium vanadium fluorophosphate, Na 3 V 2 (PO 4 ) 2 F 3[END_REF] as a positive electrode for Li-ion batteries vs. lithium or graphite to substitute the Na + cations for Li + . It showed promising properties from the beginning, with a theoretical capacity of 128 mAh/g that could be experimentally obtained at an average potential of 3.95 V vs. Na + /Na. More precisely, the extraction of 2 Na + ions has been demonstrated (Figure 5.1) following two main voltage-composition plateaus at about 3.7 V and 4.2 V vs. Na + /Na, delivering ≈507 Wh/kg [START_REF] Barker | Hybrid-ion: A lithium-ion cell based on a sodium insertion material[END_REF][START_REF] Gover | The electrochemical insertion properties of sodium vanadium fluorophosphate, Na 3 V 2 (PO 4 ) 2 F 3[END_REF][START_REF] Barker | Li 4/3 Ti 5/3 O 4 parallel to Na 3 V 2 (PO 4 ) 2 F3: An example of a hybrid-ion cell using a non-graphitic anode[END_REF] . This value is comparable to commercial positive electrodes developed for Li-ion batteries such as LiFePO 4 (580 Wh/kg) and LiMn 2 O 4 (480 Wh/kg). However this only includes the extraction/reinsertion of two sodium ions per formula unit. The extraction of the third one could increase the theoretical capacity up to a maximum value of 192.4 mAh/g, although this has not been proved to be possible in a Na-ion cell yet [START_REF] Ponrouch | Towards high energy density sodium ion batteries through electrolyte optimization[END_REF][START_REF] Chihara | Cathode properties of Na 3 M 2 (PO 4 ) 2 F 3 (M = Ti, Fe, V) for sodium-ion batteries[END_REF] . The deintercalation of the third sodium around 5 [START_REF] Barker | Hybrid-ion: A lithium-ion cell based on a sodium insertion material[END_REF] .

V could lead to a huge energy density (> 800 Wh/kg), but this goal could not be easily achieved because of the high voltage involved, lying outside the stability window of available electrolytes [START_REF] Ponrouch | Towards high energy density sodium ion batteries through electrolyte optimization[END_REF] . The group of J.B. Goodenough [START_REF] Xu | Theoretical and experimental study of vanadium-based fluorophosphate cathodes for rechargeable batteries[END_REF] recently reported theoretical calculations showing that such a high voltage is due to the strong Coulombic attraction between Na + and the structure's anions. It was suggested that swapping the O and F anions to the less-electronegative Cl and Br ones could facilitate the extraction. It is worth mentioning again that Na 3 V 2 (PO 4 ) 2 F 3 belongs to a family of compositions that can be written as Na 3 V 2 O 2δ (PO 4 ) 2 F 3-2δ (0 ≤ δ ≤ 1) [START_REF] Serras | High voltage cathode materials for Na-ion batteries of general formula Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x[END_REF][START_REF] Park | Tailoring a fluorophosphate as a novel 4 v cathode for lithium-ion batteries[END_REF][START_REF] Ponrouch | Towards high energy density sodium ion batteries through electrolyte optimization[END_REF][START_REF] Serras | Electrochemical Na Extraction/Insertion of Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x[END_REF] . Here, depending on δ, the oxidation state of vanadium varies between 3+ and 4+ with a concomitant modification of the physical properties and of the electrochemical signature of the material. In this family, Na 3 V III 2 (PO 4 ) 2 F 3 (δ = 0) is one of the end members and it is the most interesting composition in terms of energy density. The crystal structure of Na 3 V 2 (PO 4 ) 2 F 3 has been described in 1999 by Le Meins et al. [START_REF] Le Meins | Phase Transitions in the Na 3 M 2 (PO 4 ) 2 F 3 Family (M=Al3+, V3+, Cr3+, Fe3+, Ga3+): Synthesis, Thermal, Structural, and Magnetic Studies[END_REF] , belonging to the tetragonal P4 2 /mnm space group. However this structure is in contrast with our recent observations [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: A high-resolution diffraction study[END_REF] , and in the next section we will thoroughly describe our new structural determination.

The fact that we found a new crystal structure for Na 3 V 2 (PO 4 ) 2 F 3 is not completely surprising. In fact, despite recent published studies [START_REF] Chihara | Cathode properties of Na 3 M 2 (PO 4 ) 2 F 3 (M = Ti, Fe, V) for sodium-ion batteries[END_REF][START_REF] Ra Shakoor | A combined first principles and experimental study on Na 3 V 2 (PO 4 ) 2 F 3 for rechargeable na batteries[END_REF] , some of the properties of Na 3 V 2 (PO 4 ) 2 F 3 have not been observed in sufficient details yet: for instance, a close look at the literature reveals quite strong discrepancies [START_REF] Gong Zhengliang | In situ XRD and solid state NMR characterization of Na 3 V 2 (PO 4 ) 2 F 3 as cathode material for lithium-ion batteries[END_REF] between the structural unit cell parameters of "Na 3 V 2 (PO 4 ) 2 F 3 ", as gathered in Table 5.1. The reason for this is the versatility of vanadium towards oxidation/reduction and the concomitant existence of possible F/O mixing and substitution in the Na 3 V 2 O 2δ (PO 4 ) 2 F 3-2δ framework. Moreover, these stoichiometry issues may have profound impact on the electrochemical signature of these compositions, when used as positive electrodes in Na batteries, involving the V 3+ /V 4+ Gover [START_REF] Gover | The electrochemical insertion properties of sodium vanadium fluorophosphate, Na 3 V 2 (PO 4 ) 2 F 3[END_REF] P42/mnm 9.0378(3) 9.0378(3) 10.7482(4) 877.94( 6) Na3V2(PO4)2F3

Chihara [START_REF] Chihara | Cathode properties of Na 3 M 2 (PO 4 ) 2 F 3 (M = Ti, Fe, V) for sodium-ion batteries[END_REF] P42/mnm 9.04 9.04 10.74 877.69 Na3V2(PO4)2F3

Liu [START_REF] Liu | Local structure and dynamics in the na ion battery positive electrode material Na 3 V 2 (PO 4 ) 2 F 3[END_REF] P42/mnm 9.04 9.04 10.735 877.5 Na3V2(PO4)2F3

Shakoor [START_REF] Ra Shakoor | A combined first principles and experimental study on Na 3 V 2 (PO 4 ) 2 F 3 for rechargeable na batteries[END_REF] XRD P42/mnm Le Meins [START_REF] Le Meins | Phase Transitions in the Na 3 M 2 (PO 4 ) 2 F 3 Family (M=Al3+, V3+, Cr3+, Fe3+, Ga3+): Synthesis, Thermal, Structural, and Magnetic Studies[END_REF] P42/mnm 9.047(2) 9.047(2) 10.705(2) 876.2(3) Na3V2(PO4)2F3

Song [START_REF] Song | Multifunctional dual Na 3 V 2 (PO 4 ) 2 F 3 cathode for both lithium-ion and sodium-ion batteries[END_REF] P42/mnm 9.05 9.05 10.679 874.64 Na3V2(PO4)2F3

Barker [START_REF] Barker | Hybrid-ion: A lithium-ion cell based on a sodium insertion material[END_REF] P42/mnm 9.0304(5) 9.0304(5) 10.6891( 9) 871.68 Na3V2(PO4)2F3

Serras [START_REF] Serras | High voltage cathode materials for Na-ion batteries of general formula Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x[END_REF] P42/mnm 9.04258 9.04258 10.62738 869.0

Na3V III 0.4 (V IV O)1.6 (PO4)2F3
Tsirlin [START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na 1.5 VOPO 4 F 0.5[END_REF] P42/mnm and/or the V 4+ /V 5+ redox couples. Contrary to the two (∆V = 0.5 V, Figure 5.1) or even three voltage domains previously reported upon Na + extraction [START_REF] Chihara | Cathode properties of Na 3 M 2 (PO 4 ) 2 F 3 (M = Ti, Fe, V) for sodium-ion batteries[END_REF][START_REF] Liu | Local structure and dynamics in the na ion battery positive electrode material Na 3 V 2 (PO 4 ) 2 F 3[END_REF][START_REF] Ra Shakoor | A combined first principles and experimental study on Na 3 V 2 (PO 4 ) 2 F 3 for rechargeable na batteries[END_REF][START_REF] Song | Multifunctional dual Na 3 V 2 (PO 4 ) 2 F 3 cathode for both lithium-ion and sodium-ion batteries[END_REF] , we found indeed that Na + extraction from stoichiometric Na 3 V III 2 (PO 4 ) 2 F 3 towards Na 1 V IV 2 (PO 4 ) 2 F 3 proceeded reversibly through four oxidation potential steps, as displayed in Figure 5.2 and as already reported by some of us in [START_REF] Ponrouch | Towards high energy density sodium ion batteries through electrolyte optimization[END_REF] . The relation between these features and the crystal structure of Na 3 V 2 (PO 4 ) 2 F 3 will be discussed in the following: indeed, the precise mechanism associated with such a complex electrochemistry is described in section 5.3, where we investigate this by in situ / operando Synchrotron X-Ray powder diffraction. cell was charged and discharged at a current rate equivalent to C/50, meaning in the case of Na 3 V 2 (PO 4 ) 2 F 3 the extraction/insertion of each Na + ion within 50 hours. Diffraction data were collected on a number of instruments: laboratory X-Ray diffraction was performed on a PANalytical Empyrean diffractometer using Cu Kα 1,2 , the powder being sealed in a 0.3 mm capillary used in Debye-Scherrer geometry. Synchrotron radiation XRPD data at room temperature were collected at the CRISTAL diffractometer of the SOLEIL synchrotron facility, at 0.6687 Å in the 5 • -50 • 2θ angular range. High and low temperature measurements were performed at the MSPD beamline of the ALBA synchrotron facility (λ = 0.6198 Å and 0.6200 Å, respectively) [START_REF] Fauth | The new material science powder diffraction beamline at alba synchrotron[END_REF] . Neutron diffraction data were acquired at the D2B high-resolution powder diffractometer of the ILL, at the wavelength of 1.594 Å, calibrated with a Na 2 Ca 3 Al 2 F 14 (NACALF) reference. For more experimental information about the beamlines, see the Introduction. Diffraction data treatment and Rietveld refinements were performed using the FullProf Suite [START_REF] Rodriguez-Carvajal | Recent advances in magnetic-structure determination by neutron powder diffraction[END_REF] .

Operando synchrotron XRPD experiments

Electrodes were prepared by mixing Na 3 V 2 (PO 4 ) 2 F 3 with Carbon Super P (Csp) as a conductive additive and Polyvinylidene fluoride (PVDF) as a binder (84:10:6 wt.%) and grinding them in a mortar until an homogeneous paste was obtained. Small pellets of ≈5 mm diameter and ≈300 µm thickness were used in our in situ cell for transmission experiments at synchrotron facilities [START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF] . The use of a binder is fundamental because it allows overcoming the problem of spatially-inhomogeneous electrodes observed while cycling in the in situ cell [START_REF] Ouvrard | Heterogeneous behaviour of the lithium battery composite electrode LiFePO 4[END_REF] . The active part of the cell is composed of layers of positive electrode, glass fiber separators (Whatman) wet with 1M NaPF 6 in EC:PC (1:1) electrolyte and sodium metal as a counter electrode. The stack is inserted between two Beryllium windows, acting as X-Ray-transparent current collectors. The internal pressure within the cell is applied through a spring to ensure optimal electrical contact.

Two batteries were prepared in two separate in situ cells. The first voltage-composition plateau was measured using a GITT (Galvanostatic Intermittent Titration Technique) protocol, for which steps of 5 minutes of charge and 5 minutes of relaxation are alternated.

During charging steps, the current rate was set to be C/5 (extraction of 1 Na + ion in 5 hours in this case). Upon cycling, 5 minutes diffraction scans were continuously recorded during the 5' charge -5' relaxation sequence. For the observation of the second voltage-composition plateau, the second cell was cycled off-line through the first voltage-composition plateau and kept at the composition Na 2 V 2 (PO 4 ) 2 F 3 until we could mount it on the instrument.

Since in the first experiment we did not observe any significant evolution between subsequent scans recorded upon charge and relaxation, a continuous electrochemical cycling at C/5 rate was used (with 10 minutes relaxation times every 0.25 Na + exchange), while recording again diffraction scans continuously every 5 minutes.

Operando synchrotron radiation diffraction measurements were performed at the MSPD beamline [START_REF] Fauth | The new material science powder diffraction beamline at alba synchrotron[END_REF] of the ALBA synchrotron. The experiment was carried out as described in the Introduction, in transmission geometry, at the operating wavelength of λ = 0.9535(1) Å as refined using a NIST standard silicon sample (NIST SI640D). Powder diffraction patterns were collected using the MYTHEN detector. The full width at half maximum (FWHM) for representative peaks of the pristine phase is 0.022 • at 2θ = 17.15 • (increasing to 0.04 • towards the highest angles) and the signal-to-noise ratio for the most intense peak is ≈36. Table 5.5 (section 5.3) compares refinements outputs of the pristine phase from data collected in capillaries with actual results obtained using the in situ cell setup. Note that the use of the in situ cell only slightly increases the error bars, allowing refinements of all atomic parameters, including isotropic thermal factors B iso (constraint to be equal for the same type of atoms) and site occupancy factors (SOFs) for sodium. However when performing Rietveld refinements on data collected using the in situ cell a few precautions have to be taken:

• The beam is going through all the layers stacked in the battery, generating Bragg peaks from sodium (often textured) and Beryllium (two windows displaced one with respect to the other). Detailed knowledge of the pristine phase allows eliminating the (narrow) 2θ regions where these peaks appear. In the following, Figure 5.3 shows the full measured 2θ range, indicating the position of the extra-Bragg peaks.

• Each layer suffers differently from X-Ray absorption. Beryllium is a light element and its absorption (0.24 cm -1 ) can be neglected at this energy. Sodium metal is heavier but the absorption (24.9 cm -1 ) can still be neglected as sodium is crossed before the sample. The absorption from the sample itself is important and it is taken into account using the correction factor for flat-plate samples in transmission geometry implemented in the Fullprof suite (approximately mt = 1, where m = 36.7 cm -1 is the absorption and t = 300 µm is the sample's thickness).

• Because the sample is enclosed in the in situ cell, hence not visible, it is impossible to precisely position the sample in the center of the goniometer by standard optical alignment means. To correctly refine the data, both a zero-shift and a systematic shift (sinθ dependence) correction are hence needed to compensate a possible misalignment of the sample. As a first step we thus used the pristine Na 3 V 2 (PO 4 ) 2 F 3 , whose unit cell parameters are well known, to determine zero-shift and systematic shift. As a second step we fixed these two parameters throughout all the subsequent refinements.

Again, data treatment and Rietveld refinements [START_REF] Rietveld | A profile refinement method for nuclear and magnetic structures[END_REF] were performed using the Fullprof Suite [START_REF] Rodriguez-Carvajal | Recent advances in magnetic-structure determination by neutron powder diffraction[END_REF] .

Figure S1: Whole angular range obtained from synchrotron radiation diffraction measurement of Na 3 V 2 (PO 4 ) 2 F 3 (top) and Na 2 V 2 (PO 4 ) 2 F 3 (bottom) in situ in our electrochemical cell. Extra Bragg reflections (from sodium and beryllium) are marked with an *.

Bianchini et al., fig. S1

Na 3 V 2 (PO 4 ) 2 F 3 A sample of nominal composition Na 2 V 2 (PO 4 ) 2 F 3 was also prepared ex situ by chemically oxidizing Na 3 V 2 (PO 4 ) 2 F 3 with nitronium tetrafluoroborate (NO 2 BF 4 ) in acetonitrile media. The resulting powder was washed, sealed in a 0.5 mm diameter capillary and then measured under the same experimental conditions.

Synthesis of Na

3 V 2 (PO 4 ) 2 F 3
The synthesis of Na 3 V 2 (PO 4 ) 2 F 3 was performed by Nicolas Brisset, Philippe Dagault and Gwenaël Lepage (ICMCB). It consists of two steps, following a procedure similar to the one patented by Barker et al. [START_REF] Barker | Lithium metal fluorophosphate materials and preparation thereof[END_REF] , where VPO 4 was used as an intermediate phase.

1 2 V 2 O 5 + (N H 4 ) 2 HP O 4 + C sp → 3 2 H 2 O + 2N H 3 + CO + c * V P O 4 (5.1) 2c * V P O 4 + 3N aF → N a 3 V 2 (P O 4 ) 2 F 3 (5.
2)

The presence of Csp in reaction (1) (in the form of highly-divided soot) is necessary to allow for the carbothermal reduction of vanadium from 5+ to 3+. For reaction 5.1, the precursors V 2 O 5 , (NH 4 ) 2 HPO 4 and Csp were mixed in a planetary grinder FRISTSCH Mono Mill for 12 hours at 400 rpm. The mixture was then pressed in a pellet and heated for 5 hours at 300 • C in an alumina crucible to evaporate possible ammonia residues. For homogenization the obtained product was milled again for 4 hours at the same speed and a pellet remade. This was finally heated at 800 • C for 5 hours to allow the carbothermal reduction and the formation of carbon coated VPO 4 (c-VPO 4 ). Na/P=1.60 and V/P=1.03 were found, which agree rather well with the expected stoichiometry (1.50, 1.50 and 1.00, respectively). To further confirm the value found for the vanadium oxidation state we performed magnetic susceptibility measurements. Figure 5.4 reports the resulting 1/χ M versus temperature, showing a typical behavior of the Curie-Weiss law for paramagnetic materials. A linear fit of the data in the 100 -300 K region leads to a value for the Curie constant of C = 0.944 (9), in remarkable agreement with the previous report of Le Meins et al. [START_REF] Le Meins | Phase Transitions in the Na 3 M 2 (PO 4 ) 2 F 3 Family (M=Al3+, V3+, Cr3+, Fe3+, Ga3+): Synthesis, Thermal, Structural, and Magnetic Studies[END_REF] and with the approximate theoretical value of C = 1, obtained as χT=1/8 n(n+2), where n is the number of unpaired electrons, i.e. n=2 for V 3+ which has 4s 0 3d 2 electronic configuration. The antiferromagnetic behavior of the material is also described by a Néel temperature θ N = 74 K.

It is worth mentioning that numerous other synthesis techniques can be used to prepare Na 3 V 2 (PO 4 ) 2 F 3 , as recently reported by different groups. Liu et al. [START_REF] Liu | Local structure and dynamics in the na ion battery positive electrode material Na 3 V 2 (PO 4 ) 2 F 3[END_REF] propose a two step process with intermediate c-VPO 4 , but with different precursors in the first step: in particular, they use citric acid as both a chelating species and a carbon source. Song et al. [START_REF] Song | Multifunctional dual Na 3 V 2 (PO 4 ) 2 F 3 cathode for both lithium-ion and sodium-ion batteries[END_REF] instead, make use of a single-step process based on CTR. Finally, Zhao et al. [START_REF] Zhao | A phase-transfer assisted solvo-thermal strategy for low-temperature synthesis of Na 3 (VO 1-x PO 4 ) 2 F 1+2x cathodes for sodium-ion batteries[END_REF] propose a phase-transfer assisted solvothermal strategy to achieve low-temperature synthesis of Na 3 V 2 (PO 4 ) 2 F 3 . Based on single-crystal and powder X-Ray diffraction experiments, the crystal structure of Na 3 V 2 (PO 4 ) 2 F 3 (Figure 5.5) was thought to be well-established since 1999. Le Meins et al. [START_REF] Le Meins | Phase Transitions in the Na 3 M 2 (PO 4 ) 2 F 3 Family (M=Al3+, V3+, Cr3+, Fe3+, Ga3+): Synthesis, Thermal, Structural, and Magnetic Studies[END_REF] initially described it using the tetragonal space group P4 2 /mnm, with a distribution of Na + ions over 2 crystallographic sites: a first one, Na1 P , fully occupied and a second one, Na2 P , half-occupied only (here the subscript helps identifying the space group used, since several ones will be encountered in the following). The crystal structure of Na 3 V 2 (PO 4 ) 2 F 3 highlights pairs of V 3+ ions localized in bi-octahedral environments and surrounded by four oxygen and two fluorine each, these fluorine being along the axis of the bi-octahedra. These V 2 O 8 F 3 have regular V-O and V-F bond lengths close to 2 Å and they are bridged by PO 4 tetrahedra, building a 3D framework with large tunnels along the [110] and [1-10] directions, where sodium ions are placed. This grants them a significant mobility and confers to Na 3 V 2 (PO 4 ) 2 F 3 the ability to (de)intercalate sodium ions.

The same space group is used to describe the other members of the "solid solution"

Na 3 V 2 O 2δ (PO 4 ) 2 F 3-2δ . V 2 O 8 F 3 bi-octahedra become V 2 O 8+2δ F 3-2δ with 2δ vanadium
ions present as vanadyl (VO) 2+ and the others (2-2δ) as V 3+ . The V=O vanadyl type bonds are much shorter (≈1.6 Å) than V-F ones (≈2.1 Å). The end member δ =1,

Na 3 V IV 2 O 2 (PO 4
) 2 F (sometimes written as Na 1.5 V IV OPO 4 F 0.5 ), can deliver a theoretical capacity of 156 mAh/g through two voltage-composition plateaus at 3.6 V and 4 V vs.

Na + /Na [START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na 1.5 VOPO 4 F 0.5[END_REF][START_REF] Massa | Crystal structure of a new sodium vanadyl(IV) fluoride phosphate Na 3 V 2 O 2 F(PO 4 ) 2[END_REF][START_REF] Sauvage | Crystal structure and electrochemical properties vs. Na+ of the sodium fluorophosphate Na 1.5 VOPO 4 F 0.5[END_REF] . The crystal chemistry of this material was thoroughly studied by Tsirlin et al. [START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na 1.5 VOPO 4 F 0.5[END_REF] , who proposed the existence of three different polymorphs with different space groups depending on the short, medium or long range ordering of sodium ions within the framework. The high temperature Na-disordered form (α phase) is described in the highly symmetric space group I4/mmm. At lower temperatures, Na becomes partially ordered in the β phase (298 K, space group P4 2 /mnm) and almost completely ordered (γ phase) below 235 K (P4 2 /mbc space group).

Room temperature crystal structure

As we just discussed, the work of Le Meins et al. [START_REF] Le Meins | Phase Transitions in the Na 3 M 2 (PO 4 ) 2 F 3 Family (M=Al3+, V3+, Cr3+, Fe3+, Ga3+): Synthesis, Thermal, Structural, and Magnetic Studies[END_REF] assigned the tetragonal space group P4 2 /mnm to Na 3 V 2 (PO 4 ) 2 F 3 , used until now to describe the structure. However, close inspection of the published atomic coordinates points towards a very high (meaningless) value of the thermal parameter B iso (Debye-Waller) on the Na(2) site (8.3 Å2 ), occupied at 50%. The structure refinements of both neutron and laboratory X-Ray diffraction data, using the published structure of Na 3 V 2 (PO 4 ) 2 F 3 [START_REF] Le Meins | Phase Transitions in the Na 3 M 2 (PO 4 ) 2 F 3 Family (M=Al3+, V3+, Cr3+, Fe3+, Ga3+): Synthesis, Thermal, Structural, and Magnetic Studies[END_REF] as a starting model are plotted in sites (both in 8i Wyckoff positions) respectively and confirmed, accordingly, an abnormally high thermal parameter value for sodium ions on the Na(2) site: 6.15 Å2 . Note that this site cannot be fully occupied as two equivalent positions generated by the mirror m perpendicular to [110] are too close (1.8 Å).

To gain further insight into the crystal structure of Na 3 V 2 (PO 4 ) 2 F 3 (in particular in the sodium ions distribution within the available crystallographic sites), we performed high angular resolution synchrotron radiation XRPD. Interestingly, we found that the indexation of the crystal structure of our Na 3 V 2 (PO 4 ) 2 F 3 powder sample in the tetragonal space group P4 2 /mnm is not correct. Indeed, as Figure 5.7 shows, in-house X-ray diffraction generates diffraction peaks with rather large FWHMs (> 0.1 • ) from which (h00) tetragonal and (0k0) tetragonal reflections, for example, seem to be merged at the same 2θ angle. For a very subtle orthorhombic distortion, which appears to be the case here, high angular range for the case of our measurement at SOLEIL) was essential for allowing us to refine the unit-cell parameters of Na 3 V 2 (PO 4 ) 2 F 3 . We chose the low-symmetry Pmmm space group to begin with, finding from Le Bail fit cell parameters values of a = 9.02837(3) Å, b = 9.04438(3) Å, c = 10.74643(3) Å, i.e. a b/a ratio of about 1.002 (Figure 5.8). Such a distortion had never been observed before because of a twofold reason. On one side, the synthesis conditions may surely play a role even if it appears to be a "general" property for the series of samples we have studied and obtained through the two-step solid state reaction described above. For instance, whatever the cooling rate (quenching in air, cooling at a controlled temperature rate (< 2 • C/min) or cooling according to the furnace inertia) the orthorhombic distortion was always observed. As completely different synthesis routes are reported in literature (see the synthesis section 5.1.2) we cannot speculate whether they lead to orthorhombic distortion or not. On the other hand, we showed that extremely high angular resolution is required to observe the peaks' splitting. As most of the works recently reported on Na 3 V 2 (PO 4 ) 2 F 3 did not focus on the structure but on syntheses and electrochemical performances, relying thus on laboratory powder X-Ray diffractometers only, these new features could not be observed. Even when synchrotron radiation sources are used, some choices of energy/detector (such as an image plate detector, for example) might not result in a sufficient angular resolution [START_REF] Park | A family of high-performance cathode materials for Na-ion Batteries, Na 3 (VO 1-x PO 4 ) 2 F 1+2x (0 ≤ x ≤ 1): combined first-principles and experimental study[END_REF] . Having found the cell parameters, a suitable space group was searched for, since it was easily observed that Pmmm does not take into account many of the systematic extinctions. First, we observed that the obtained cell parameters are the only possible choice, i.e. none of the other possibilities reported in the literature for similar compounds could fit the data [START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na 1.5 VOPO 4 F 0.5[END_REF] . Indeed, cell parameters bigger by a factor √ 2 (with the cell rotated by 45 • ) would shift the (hh0) reflections, which are not splitted in the orthorhombic group, in the angular position of the (h00) -(0k0), where a splitting is needed to fit the data. Also, a cell smaller by a factor √ 2 (again with 45 • rotation) would be incorrect, since the first peak in angular range (at 5.54 • ) could not be taken into account. Therefore we chose a combined approach using several indexing softwares (Dicvol, MacMaille, Fox), electron diffraction (performed by F. Weill at ICMCB) and crystallographic considerations to select the suitable space groups. We focused on non primitive cells since electron diffraction showed the existence of systematic extinctions in the whole reciprocal space. In particular, as shown in Figure 5.9a, with our choice of cell parameters (and therefore of orthorhombic setting) the only possible translation mode found from indexation is A. It can be observed that general (hkl) diffracted peak positions

Bianchini et al., Figure 7

A centering (T = 300 K) I centering (T > 353K) respected k+l=2n. Moreover, an examination of systematic extinctions in the synchrotron radiation pattern revealed the following conditions for reflections to exist: for (h00), (0k0) and (00l), h = 2n, k = 2n and l = 2n; for (0kl), k+l = 2n; for (h0l) and (hk0), conditions were less clear due to peaks' vicinity, but we finally converged on h,l = 2n and k = 2n, respectively. Thanks to these considerations, the structure was subsequently refined for the best groups, namely Ama2 (n • 40), Amam (n • 63) and A2 1 am (n • 36). The first is in its main setting, while the other two are Cmcm and Cmc2 1 , both in their setting 4. It is crucial to note that Ama2 and A2 1 am are associated with the point group symmetry mm2-m2m-2mm, while Amam belongs to the mmm one, which allows its symmetry elements to be more similar to those obtained for P4 2 /mnm. The structure was solved and the structural parameters refined using the Rietveld method. The results are shown in Figure 5.10, as obtained from combined structural refinements from synchrotron (top) and neutron (bottom) diffraction data with a relative weight of 50% for the two patterns. The refined parameters are reported in Table 5.2, while Table 5.3 reports bond-length distances and structural parameters. It is important to stress that the interatomic distances are in line with the expected values, and similar to those known from the "standard" model. The structural framework looks in fact identical to the one shown in Figure 5.5. For instance, we find tetrahedral distances P-O1 = 1.532( 9) Å and P-O2 = 1.534( 9) Å (Standard model: P1-O1 = 1.537 Å, P2-O2 = 1.533 Å and P2-O3 = 1.528 Å) and octahedral distances V-O1 = 2.006(9) Å, V-O2 = 1.965(9) Å, V-F1 = 1.981(2) Å and V-F2 = 1.968( 6) Å (standard model: (V-O1 = 1.996 Å, V-O2 = 1.971 Å, V-F1 = 2.017 Å and V-F2 = 1.881 Å). The only difference that can be noted is a rather uniform V-F distance in our model, while in the "standard" one there are a shorter (1.881 Å) distance and a longer (2.017 Å) one. This shorter distance might in fact be an indication of the presence of oxygen in the bi-octahedra (δ = 0 in V 2 O 8+2δ F 3-2δ ), leading to shorter vanadyl V=O bonds.

Bianchini et al.,

We confirmed that sodium is present in the unit cell of Na 3 V 2 (PO 4 ) 2 F 3 in the planes at z = 0 and z = 1/2, as proposed by the "standard" model. However, due to the different symmetry elements in our unit cell, the Na ions distribution is modified. We found that sodium is distributed in 3 crystallographic sites, with partial site occupancy factors (SOFs)

for 2 of them. Figure 5.11 shows the sodium distribution in the a-b plane. Na1 A is placed in the center of a capped prism and when its SOF is refined it always leads to a value higher than 0.95, meaning that this site is essentially fully occupied. Na2 A and Na3 A , instead, cannot be simultaneously occupied because of their vicinity (Na2 A -Na3 A = 0.93 Å). In good agreement with this, the independent simultaneous refinement of their SOFs leads to 0.68 and 0.28, meaning that either one or the other is always occupied. With respect to the surrounding environment, Na2 A and Na3 A are not equivalent since the first one occupies a capped prism, while the second one sits in a pyramidal site. However, none of them is in the center of the respective site, but the two positions are precisely divided by the face F(2) 2 O(2) 2 , representing the boundary between the polyhedra describing the two sites (Figure 5.10). The fact that Na2 A is more occupied than Na3 A is explained by the shorter Na3 A -Na3 A distance if compared to the Na2 A -Na2 A (2.87 Å vs. 3.87 Å), responsible for a stronger electrostatic repulsion. Moreover, the triangular-like distribution of sodium

= 1/N i (di -d / d ) 2 ,
bond valences as reported in [255] . cations can be regarded as the cause of the observed orthorhombic distortion, since such arrangement generates different electrostatic repulsion forces between the ions in the a and b directions, while in a square-like distribution as proposed in the standard model there is no reason to imagine such a distortion. Note that in this triangular arrangement the distances Na1 A -Na2 A and Na1 A -Na3 A are 3.04 Å and 3.39 Å respectively.

Na 3 V 2 (PO 4 ) 2 F 3 V P Na (1) Na(2) Na(3)
As a conclusive remark to complete the description of sodium ions distribution, we observed that reflections (hhl) where the contribution of h to dhhl is small with respect to the one of l (i.e. (002), ( 113), ( 006), (115) etc.) showed a marked asymmetry towards higher 2θ angles (insets in Figure 5.10), likely due to the occurrence of defects within the structure along the c axis. These defects can be related to stacking faults (or randomly distributed Na along c) or to a slight amount of vanadyl-type defects. Furthermore, the presence of disorder is supported by the fact that Fourier difference maps at the end of the refinements still show a small residual intensity present in the form of sodium ions rings (the same distribution as in the high-temperature phase). To support our conclusions we verified if other configurations for sodium ions were possible. Indeed we observed that another possibility is to place the sodium atoms rotated by 180 • , while leaving the rest of the structure unchanged. Figure 5.11 (middle) illustrates this distribution. We found that two symmetric distributions of the sodium ions could lead to the same fit of the data, leading to a maximal difference between the two of 50/50000 counts (R bragg 1 = 4.45%, R bragg 2 = 4.39%). However, the two descriptions could not coexist at the same time. In fact, considering two phases, one with the setting 1 and the other with the setting 2 for the sodium ions distribution, did not allow the software to converge because of the excessive similarity of the two phases, while placing all the sodium atoms from the two possible distributions in the structure together (6 crystallographic sites) leaving their occupancy unconstrained resulted in the Rietveld refinement converging towards one of the two single solutions. This is an important sign confirming that the triangular-like shape of the sodium distribution is really the cause for the orthorhombic distortion and that no other arrangement can lead to a good fit of our data. Moreover, we speculate that defects in the stacking along c of unit cells with the two different configurations of sodium are the cause for the asymmetric broadening of the reflections discussed above.

As previously stated, the correlation between the electrochemical data (Figure 5.2) and the sodium arrangement can be determined in details only by means of the in situ characterization we describe later on. Nevertheless, it is interesting to highlight that the separation between the first two voltage plateaus at 3.68 V and 3.7 V vs. Na + /Na takes place at a composition Na x V 2 (PO 4 ) 2 F 3 with x between 2.3 and 2.4, corresponding namely to the deintercalation of about the first 2/3 Na + ions over the 2 expected. Our determination of the crystal structure led us to propose three sodium sites for Na 3 V 2 (PO 4 ) 2 F 3 with the following stoichiometry:

[Na1 A ] 1 [Na2 A ] ≈4/3 [Na3 A ] ≈2/3 . Na1 A , fully occupied and
in the center of the respective pyramidal site, reasonably seems to be the most stable one and it could be the sodium ion that has never been experimentally extracted, as it requires a too high potential. Na2 A and Na3 A might not be as stable, being out of the center of their respective sites and they can thus be deintercalated. It is interesting to point out that the deintercalation of the Na + ions occupying the Na3 A crystallographic site could count for the 2/3 Na + ions deintercalated at 3.68 V. Our hypothesis is thus that the Na3 A site is emptied first. No further hypothesis can be done at this stage, since the electrochemical behavior will strongly depend on a possible sodium rearrangement happening at this intermediate composition, Na ≈7/3 V 2 (PO 4 ) 2 F 3 , after the deintercalation of 2/3 Na + ions, or afterwards at the composition Na 2 V 2 (PO 4 ) 2 F 3 . This discussion will be resumed and completed in section 5.3. Since the Na 3 V 2 O 2 (PO 4 ) 2 F system is reported to undergo an order-disorder transition at ≈500 K [START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na 1.5 VOPO 4 F 0.5[END_REF] , Differential Scanning Calorimetry measurements were performed at 10 • C/min under Ar and show indeed a similar transition for Na 3 V 2 (PO 4 ) 2 F 3 , completed at 395 K (Figure 5.12). The lower transition temperature suggests that Na 3 V 2 (PO 4 ) 2 F 3 is more prone to sodium ions disordering than Na 3 V 2 O 2 (PO 4 ) 2 F. We hence decided to perform synchrotron radiation diffraction at temperatures of 300 K, 350 K and 400 K at the ALBA synchrotron facility. Thanks to these measurements (Figure 5.13) we could observe that the b cell parameter remains almost unchanged upon heating, while the a cell parameter converges to the value of b as the temperature increases, leading to a tetragonal symmetry confirmed also by the disappearance of many diffraction peaks. Furthermore, electron diffraction experiments were carried out (F. Weill, ICMCB) with the specimen stage at 353 K. Note that due to the heating effect of the electron beam, the actual temperature of the sample under investigation is higher. The obtained electron diffraction pattern (Figure 5.9b) can be indexed with a centered cell I. One notes in fact that the weak spots present at room temperature (Figure 5.9a) disappeared. The XRPD reflections of Na 3 V 2 (PO 4 ) 2 F 3 at 400 K were subsequently indexed in the I4/mmm space group and the crystal structure refined with the Rietveld method. The obtained structural parameters are gathered in Table 5.4. The dimension of the unit cell is √ 2 times smaller than the one obtained at 298 K, namely a = b = 6.3927(1) Å and c = 10.756(1) Å (Volume V =

High

I n t e n s i t y ( a . u . ) 2 θ ( °) , λ = 0 . 6 1 9 8 Å T = 3 0 0 K T = 3 5 0 K T = 4 0 0 K ( 0 2 0 ) -( 2 0 0 ) 2 θ ( °)
( 2 1 1 )

( 2 2 0 )

( 1 1 3 ) ( 0 4 0 ) -( 4 0 0 ) 2 θ ( °) 2 θ ( °) 2 θ ( °)
Figure 5.13: Synchrotron radiation XRPD of Na3V2(PO4)2F3 at increasing temperatures from 300 K to 400 K.

439.558(3) Å3

). This is in line with the values observed for the high temperature phase of Na 3 V IV 2 O 2 (PO 4 ) 2 F by Tsirlin et al. [START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na 1.5 VOPO 4 F 0.5[END_REF] (a = b = 6.3956(1) Å, c = 10.6591(2) Å, V = 436.000(1) Å3 ), the only dissimilarity being thus a shorter c axis in that case and hence a smaller unit cell volume. Note that this is expected in a V 4+ -containing compound with respect to a V 3+ -containing one. The general 3D framework is very similar in the two cases, the difference being that the units. This agrees well with the fact that V 3+ in octahedral environment tends to induce homogeneous bond length distances, here close to 1.98 Å [10,95] . We expect therefore to observe a difference with Na 3 V IV 2 O 2 (PO 4 ) 2 F, where the oxidation state 4+ of vanadium is more likely to induce long-short alternated distances for the out-of-plane bonds of the octahedra [START_REF] Schindler | Crystal chemical aspects of vanadium: Polyhedral geometries, characteristic bond valences, and polymerization of (von) polyhedra[END_REF] . As a matter of fact, reported values for Na

Atomic Parameters

V 2 O 10 F bi-octahedra of Na 3 V 2 O 2 (PO 4 ) 2 F are replaced by V 2 O 8 F 3 ones in Na 3 V 2 (PO 4 ) 2 F 3 ,
3 V 2 O 2 (PO 4 ) 2 F are V IV -O(2) = 2.011(1) Å (in-plane), V IV -O(1) = 1.626(3) Å (out-of-plane) and V IV -F = 2.113(1) Å (while the reported P-O distance is 1.530(1) Å). Concerning sodium atoms, as in Na 3 V 2 O 2 (PO 4 ) 2 F
the increase of symmetry at high temperature is due to the loss of ordering between sodium ions in the a-b plane with respect to the room temperature phase, we could expect a similar behavior for Na 3 V 2 (PO 4 ) 2 F 3 . As depicted in Figure 5.14, we observe that sodium ions are in fact disordered at 400 K and distributed in two crystallographic sites, building for symmetry constraints a "circle" around the fluorine atoms F(2) that are the extremes of the bi-octahedra (F(2) is however not in the plane z = 0 of the sodium ions, but above and below, at z = 0.3672 (8)). In good agreement with the reported values for Na 3 V 2 O 2 (PO 4 ) 2 F, we find that the Na1 I and Na2 I sites are approximately half occupied (SOF = 0.45(3)) and 1/8 occupied (SOF = 0.15(2)), with still meaningful isotropic displacement parameters of 2.3(5) Å2 and 2.6(9) Å2 , respectively. To conclude, the two compounds Na 3 V 2 (PO 4 ) 2 F 3 and Na 3 V 2 O 2 (PO 4 ) 2 F differ from the transition temperature between the room and high temperature phases (400 K vs. 500 K) and for their out-of-plane V-O or V-F distances in the octahedra. These are in particular homogeneous (V 3+ ) or alternated long-short (V 4+ ) distances, behavior caused by the different oxidation state of vanadium. On the other hand, the two high temperature phases have a strong similarity in terms of P-O bonds, in-plane V-O bonds and more importantly in the disordered circular arrangement of sodium cations in the a-b plane, which are the key factor driving symmetry changes for this class of materials.

Bianchini et al.,

Low Temperature (T < 300 K) crystal structure

To draw a more complete description of the phase diagram of Na 3 V 2 (PO 4 ) 2 F 3 we carried out similar synchrotron radiation XRPD experiments upon cooling of the material, illustrated in Figure 5.15. We firstly note that the orthorhombic distortion is maintained and amplified. In fact we observe a variation of cell parameters, which tend to become smaller as expected from a temperature decrease. However not all of them change: it is clear from the behavior of Bragg reflections such as (011) or (040) that b and c remain rather constant, while a significantly decreases (see (400) constantly shifting to higher 2θ values). All the reflections present at room temperature are preserved while new ones appear concurrently: the transition begins at T = 200 K and these new reflections gain intensity as T decreases; the pattern at T = 100 K shows the most intense reflections. Such observations clearly suggest the presence of a superstructure due to sodium/vacancy ordering in the a-b plane. A detailed description of this ordering has not been found yet due to the complexity of the large unit cell (V = 2623. 98(3) Å3 ), while electron diffraction did not provide conclusive results because of the material's instability under the beam at low temperature. Note that, as described previously in this chapter, Na 3 (V IV O) 2 (PO 4 ) 2 F also shows phase transformations upon heating and cooling [START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na 1.5 VOPO 4 F 0.5[END_REF] . At high temperature, the same space group (I4/mmm) is applicable to both materials because in both cases sodium ions are disordered. However, at room temperature Na 3 V 2 (PO 4 ) 2 F 3 shows an orthorhombic distortion that has not been reported for Na 3 (V IV O) 2 (PO 4 ) 2 F up to date. The latter also shows a low temperature form, found to belong to the P4 2 /mbc tetragonal space group at NaV 2 (PO 4 ) 2 F 3 (deintercalation of two sodium ions) has been often described as a solid solution based on ex situ and in situ X-Ray diffraction and more recently on ab-initio calculations and NMR experiments [START_REF] Chihara | Cathode properties of Na 3 M 2 (PO 4 ) 2 F 3 (M = Ti, Fe, V) for sodium-ion batteries[END_REF][START_REF] Liu | Local structure and dynamics in the na ion battery positive electrode material Na 3 V 2 (PO 4 ) 2 F 3[END_REF][START_REF] Ra Shakoor | A combined first principles and experimental study on Na 3 V 2 (PO 4 ) 2 F 3 for rechargeable na batteries[END_REF][START_REF] Song | Investigation of the sodium ion pathway and cathode behavior in Na 3 V 2 (PO 4 ) 2 F 3 combined via a first principles calculation[END_REF][START_REF] Song | Exploration of ion migration mechanism and diffusion capability for Na 3 V 2 (PO 4 ) 2 F 3 cathode utilized in rechargeable sodium-ion batteries[END_REF][START_REF] Song | Mechanistic investigation of ion migration in Na 3 V 2 (PO 4 ) 2 F 3 hybrid-ion batteries[END_REF] . In other words, every composition x in Na x V 2 (PO 4 ) 2 F 3 (3 ≤ x ≤ 1) ever observed has been simply described in the P4 2 /mnm space group, the only one known up to now. We stress that here (and in the following) we will be referring to the phases Na x V 2 (PO 4 ) 2 F 3 (1 ≤ x ≤ 3) and not to Na

3 V 2 O 2δ (PO 4 ) 2 F 3-2δ (0 ≤ δ ≤ 1)
. Possible reasons at the origin of these discrepancies are (i) the lack of sufficient angular resolution of diffraction data and (ii) differences in the actual stoichiometry of the pristine samples. In particular the control of the O/F ratio is not straightforward and can result in additional electrochemical features around 3.6 V vs. Na + /Na, related with mixed valence phases of the family Na 3 V 2 O 2δ (PO 4 ) 2 F 3-2δ (the operating voltage decreases as δ increases). Moreover recently published in situ studies showed that for the two compositions δ = 1 and δ = 0.8, which are still supposed to belong to the tetragonal P4 2 /mnm space group, the sodium extraction mechanism is far from being a simple solid solution [START_REF] Park | A new highenergy cathode for a na-ion battery with ultrahigh stability[END_REF][START_REF] Serras | Structural evolution of high energy density V3+/V4+ mixed valent Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x (x = 0.8) sodium vanadium fluorophosphate using in situ synchrotron X-ray powder diffraction[END_REF][START_REF] Sharma | Sodium Distribution and Reaction Mechanisms of a Na 3 V 2 O 2 (PO 4 ) 2 F Electrode during Use in a Sodium-Ion Battery[END_REF] . The δ = 0.8 sample (V 3.8+ ) revealed for the first time a biphasic reaction during the lower voltage-composition plateau, while the biggest part of the charging process was modeled as a solid solution [START_REF] Park | A new highenergy cathode for a na-ion battery with ultrahigh stability[END_REF][START_REF] Serras | Structural evolution of high energy density V3+/V4+ mixed valent Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x (x = 0.8) sodium vanadium fluorophosphate using in situ synchrotron X-ray powder diffraction[END_REF] . The V 4+ extreme member (Na 3 V 2 O 2 (PO 4 ) 2 F, δ = 1) showed instead a sequence of two biphasic reactions upon extraction of the first sodium (hence with observation of an intermediate phase), followed by a long solid solution region and finally another biphasic reaction at the end of charge [START_REF] Sharma | Sodium Distribution and Reaction Mechanisms of a Na 3 V 2 O 2 (PO 4 ) 2 F Electrode during Use in a Sodium-Ion Battery[END_REF] . These observations are actually not surprising since Na-intercalation compounds exhibit a strong tendency to form intermediate phases [START_REF] Berthelot | Electrochemical investigation of the P2-Na x CoO 2 phase diagram[END_REF][START_REF] Meng | An investigation of the sodium patterning in Na x CoO 2 (0.5<x<1) by density functional theory methods[END_REF] . For the reasons described above we decided to study the extraction of sodium from Na 3 V 2 (PO 4 ) 2 F 3 (δ = 0) by means of operando diffraction experiments [START_REF] Bianchini | Comprehensive investigation of the Na 3 V 2 (PO 4 ) 2 F 3 -NaV 2 (PO 4 ) 2 F 3 system by operando high resolution synchrotron x-ray diffraction[END_REF] . Given the complexity of the reactions involved and considering the small orthorhombic distortion of Na 3 V 2 (PO 4 ) 2 F 3 , it appears clearly that high angular resolution (comparable to the one that can be obtained for standard synchrotron measurements in capillaries) is a mandatory requirement for this kind of experiments. We achieved this goal using both the MSPD beamline [START_REF] Fauth | The new material science powder diffraction beamline at alba synchrotron[END_REF] at ALBA synchrotron and the electrochemical cell for in situ XRD and XAS measurements in transmission geometry described in the introduction [START_REF] Leriche | An electrochemical cell for operando study of lithium batteries using synchrotron radiation[END_REF][START_REF] Ouvrard | Heterogeneous behaviour of the lithium battery composite electrode LiFePO 4[END_REF] . The electrochemical extraction of Na + from Na 3 V 2 (PO 4 ) 2 F 3 was fol- lowed in real time and several phase transitions were identified upon cycling, often involving ordering/disordering phenomena within the sodium ions sub-lattice. The extremely good angular resolution and high intensity offered on the MSPD beamline (Figure 5.3) allowed to follow the reaction with unprecedented details, making full structural Rietveld refinements possible (Figure 5.16c) and even a first-time crystal structure determination for the end member NaV 2 (PO 4 ) 2 F 3 directly from in situ (operando) diffraction data.

As previously described (Figure 5.2), sodium ions are extracted from the framework of Na 3 V 2 (PO 4 ) 2 F 3 through two different voltage regions, a lower one around 3.7 V vs.

Na + /Na and a higher one around 4.2 V vs. Na + /Na. Given the incredibly rich phase diagram found and analyzed in this study (Figure 5.17) and for sake of clarity, the two voltage domains are discussed separately. Additionally, each definite Na x V 2 (PO 4 ) 2 F 3 composition will be labeled as Na x VPF in the following.

Na

3 V 2 (PO 4 ) 2 F 3 -Na 2 V 2 (PO 4
) 2 F 3 system (3.7 V vs. Na + /Na) the amount of Na/f.u. (determined from electrochemistry in this case, as described in the Experimental section). These are Na 2.4 V 2 (PO 4 ) 2 F 3 (Na 2.4 VPF), Na 2.2 V 2 (PO 4 ) 2 F 3 (Na 2.2 VPF) and Na 2 V 2 (PO 4 ) 2 F 3 (Na 2 VPF), corresponding to new single phases found in this sub-system and they are discussed in the following. Besides the obvious correlated appearances/disappearances of these phases (Figure 5.18), a peculiar attention was paid to reflections of weaker intensities (Figure 5.18b) which usually act as indicators of the presence/absence of sodium/vacancy ordering within the framework. As described for example for Na 3 VPF in the transition from 298 K (orthorhombic Amam) to 400K (tetragonal I4/mmm) [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: A high-resolution diffraction study[END_REF] ), sodium ions disorder upon heating and adopt a "circular" arrangement above fluorine anions, inducing the material to adopt a more symmetrical space group and thus to lose several weak reflections. The detailed evolution of specific Bragg peaks in the two-phase region Na 3 VPF -Na 2.4 VPF is depicted in Figure 5.19. From the very beginning of the Na + extraction, large "shoulders" appear on the right side of the reflections of Na 3 VPF, progressively revealing an internal structure, where at least three distinct diffraction peaks can be noticed (scan #30). These reflections remain broad, indicating that the reaction crosses different intermediate states (probably metastable) where sodium partially orders on the short-medium range only, until reaching the composition Na 2.4 VPF. A close examination of the data reveals as well the appearance of additional weak-intensity diffraction peaks for Na 2.4 VPF, in particular at a 2θ value of 3 • (d hkl ≈ 18 Å, shown on Figure 5.18b) which suggests a doubling of the unit cell (superstructure) in the a or b directions (or both) due to Na + /vacancy and/or V 3+ /V 4+ possible ordering. Considering that the values of a and b were 9.026 Å and 9.042 Å respectively in the Na 3 VPF pristine phase (Table 5.6), the d-spacing of 18 Å (2 × 9 Å) in Na 2. 4 VPF is consistent with the oxidation of vanadium from V 3+ to "V 3.3+ " (shorter in-plane bonds). However no complete indexation was found for this phase because a simple doubling of any of the unit cell parameters could not explain all observed reflections. We believe this composition is in fact not fully "stabilized" and that it still contains domains which have not reached complete ordering. A complex behavior can be noticed in the structured shape of the peaks ( 200)-( 020) and (220). Other peaks as (211) disappear (effect of sodium disordering), while some are almost unaffected (113). A complex behavior can be noticed in the structured shape of the peaks ( 200)-( 020) and (220). Other peaks as (211) disappear (effect of sodium disordering), while some are almost unaffected (113). ported in Figure 5.22) reveal that both Na1 I and Na2 I sodium positions are occupied, leading to a refined composition of x = 2.3(2), in good agreement with the electrochemical data (x = 2.2). These refinements show, interestingly, that the above mentioned variation of the cell parameter c (between Na 3 VPF and Na 2.2 VPF) is opposite to the shortening of the V-F bond lengths along the F-V-F-V-F chain in the bi-octahedra (Table 5.7): V-F1 decreases from 1.981(2) Å to 1.953(5) Å and V-F2 decreases from 1.968(6) Å to 1.91(1) Å, as expected for the oxidation of vanadium. Considering the model used in ref. [START_REF] Park | A family of high-performance cathode materials for Na-ion Batteries, Na 3 (VO 1-x PO 4 ) 2 F 1+2x (0 ≤ x ≤ 1): combined first-principles and experimental study[END_REF] (c ≈ 2h+d with h = height of an octahedron and d = height of sodium's tunnels, Figure 5.16a), we notice a significant increase in the value of d. In fact, d varies from 2.86(1) Å for the pristine Na 3 VPF phase to 3.06(1) Å for Na 2.2 VPF. The increase in the value of c is mainly due to the increased electrostatic repulsion between subsequent bi-octahedra, caused by a smaller global screening effect of sodium.

The final reaction observed in the 3.7 V vs. Na region is again a biphasic one. The XRPD peaks of Na 2.2 VPF disappear while new peaks belonging to the Na 2 VPF endmember appear (Figure 5.18). A first look at the 24

Composition

Refined Na/f.u. V-F1 ( Å) V-F2 ( Å) V-O1 ( Å) V-O2 ( Å) Na3V2(PO4)2F3 (ref. [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: A high-resolution diffraction study[END_REF] ) 2.9(2) explained assuming that not only sodium ions adopt some sort of ordering, but vanadium cations do the same (V 3+ and V 4+ ) as the average oxidation state of V within Na 2 VPF is V 3.5+ . To verify the reproducibility of our in situ data we prepared Na 2 VPF ex situ (Fig- (parameters reported in Table 5.6 and Table 5.7). Importantly, Fourier difference maps (Figure 5.25) do not show any intensity on the Na2 I site, leaving only the square-like distribution generated by the Na1 I site (its occupancy can be refined to give 2.05(6) Na/f.u., Figure 5.25). This is however only an "average" distribution and several first principle calculations [START_REF] Park | A new highenergy cathode for a na-ion battery with ultrahigh stability[END_REF][START_REF] Xu | Theoretical and experimental study of vanadium-based fluorophosphate cathodes for rechargeable batteries[END_REF][START_REF] Ra Shakoor | A combined first principles and experimental study on Na 3 V 2 (PO 4 ) 2 F 3 for rechargeable na batteries[END_REF][START_REF] Park | A family of high-performance cathode materials for Na-ion Batteries, Na 3 (VO 1-x PO 4 ) 2 F 1+2x (0 ≤ x ≤ 1): combined first-principles and experimental study[END_REF] predicted that instead of 4 half-occupied positions (generated by the same crystallographic site) it is favorable for sodium to arrange in 2 fully occupied positions (trans arrangement), alternated so as to minimize the electrostatic repulsion. The fact that we observe a superstructure is in good agreement with these studies and the actual structure determination of Na 2 VPF will possibly confirm them. We are confident that our observation of a large unit cell combining different types of orderings will stimulate further research especially in terms of DFT and ab-initio calculations, in order to propose an adequate crystal structure for Na 2 VPF.

A close look at the correspondence between the electrochemical and diffraction data reveals a somewhat puzzling behavior. As can be seen in the inverse derivative curve of both upon charge and subsequent discharge, while it is hardly expected from the shape of the voltage-composition electrochemical curve on discharge. This asymmetry phenomenon was tentatively attributed by the authors to different lattice mismatches [START_REF] Moreau | Structure and stability of sodium intercalated phases in olivine FePO 4[END_REF][START_REF] Gaubicher | Abnormal operando structural behavior of sodium battery material: Influence of dynamic on phase diagram of Na x FePO 4[END_REF][START_REF] Boucher | Elucidation of the Na 2/3 FePO 4 and Li 2/3 FePO 4 intermediate superstructure revealing a pseudouniform ordering in 2d[END_REF] . In our case the two compositions Na 2.4 VPF and Na 2.2 VPF are so close to each other in energy that they cannot be differentiated from their electrochemical (voltage) signature, even at extremely relaxed GITT conditions (see Figure 5.26). The Na 2. 4 VPF composition is able to stabilize a long range order (2/3 V 3+ , 1/3 V 4+ for example) suppressed in Na 2.2 VPF, even if local orders might be maintained.

GITT To study the higher voltage domain, i.e. the extraction of sodium from Na 2 VPF to NaVPF, a second electrochemical cell was cycled off-line until the Na 2 VPF composition was reached and then placed in the beam. The evolution of Bragg's reflections when Na + is extracted from Na 2 VPF is shown in Figure 5.27. The diffraction peaks of the pristine phase Na 2 VPF lose intensity right away (red curve), while new ones start growing. Specific compositions and their corresponding XRPD patterns are highlighted again with colored circles indicating the amount of Na/f.u. (determined from XRPD in this case, since from galvanostatic cycling we notice that the theoretical capacity ∆x = 1 is exceeded because of partial electrolyte oxidation). We discuss in the following the new single phases found in this sub-system, which are Na 2 V 2 (PO 4 ) 2 F 3 (Na 2 VPF), Na x V 2 (PO 4 ) 2 F 3 (Na x VPF, 1.8 < x < 1.3) and NaV 2 (PO 4 ) 2 F 3 (NaVPF).

In the early stage of Na + extraction from Na 2 VPF, the weakest diffraction peaks disappear, most likely because of sodium and vanadium cations disordering in the structure (Figure 5.27b). The (dV/dx) -1 shoulder at 4.16 V vs. Na + /Na (Figure 5.2) corresponds to a biphasic first order reaction that could be easily mistaken for a second order one due to the extreme vicinity of the disappearing peaks of Na 2 VPF with those of the growing phase Na ≈1.8 VPF. However a few reflections are lost in the process, leaving no doubt about the reaction mechanism. Interestingly, in the Na 2 VPF -Na 1.8 VPF miscibility gap, the cell parameters of both phases continue to vary (results from Rietveld refinement in Figure 5.28a), although this would be in principle thermodynamically forbidden (in equilibrium conditions a biphasic reaction implies that the two phases, the sodium-rich and the sodium-poor, change in relative weight but not in the amount of sodium in every phase, thus keeping constant cell parameters). This is directly observable in Figure 5.27, where the diffracted reflections from Na 2 VPF (in red) lose intensity but also shift concurrently (although in absolute values the variation of cell parameters during that 2-phase region is only of 0.01 Å to 0.02 Å). Such a behavior has been recently reported for several materials as an effect induced by particle size, strains and high-rate (non-equilibrium) cycling conditions [START_REF] Bianchini | Multiple phases in the -VPO 4 O -LiVPO 4 O-Li 2 VPO 4 O system: a combined solid state electrochemistry and diffraction structural study[END_REF][START_REF] Ravnsbaek | Extended solid solutions and coherent transformations in nanoscale olivine cathodes[END_REF][START_REF] Zhang | Rate-induced solubility and suppression of the first-order phase transition in olivine LiFePO 4[END_REF][START_REF] Liu | Local structure and dynamics in the na ion battery positive electrode material Na 3 V 2 (PO 4 ) 2 F 3[END_REF][START_REF] Galceran | The mechanism of NaFePO 4 (de)sodiation determined by in situ X-ray diffraction[END_REF] . In our case the battery charged rather slowly (C/5 per Na + ) and the volume change from Na 2 VPF to Na 1.8 VPF is only ∆V/V = -0.2%. At present we do not have any obvious hypothesis to explain this puzzling lattice parameters' variation within a biphasic electrochemical process.

The single phase Na 1.8 VPF is sodium-disordered and undergoes a solid solution reaction upon further Na + extraction within the Na x VPF (1.8 < x < 1.3) composition range. All Å for V-F2) as often encountered during vanadium oxidation [START_REF] Masquelier | Polyanionic (Phosphates, Silicates, Sulfates) Frameworks as Electrode Materials for Rechargeable Li (or Na) Batteries[END_REF][START_REF] Bianchini | Multiple phases in the -VPO 4 O -LiVPO 4 O-Li 2 VPO 4 O system: a combined solid state electrochemistry and diffraction structural study[END_REF] , while V-O increases slightly from 1.926(9) Å to 1.942(9) Å (Table 5.7). It is interesting to observe the distortion of vanadium's octahedral environment (Figure 5.28b), which increases by a factor 30 during this solid solution process, mainly due to the continuous shortening of the V-F2 bond.

Figure 12:

Structure of NaVPF (full composition NaV 2 (PO 4 ) 2 F 3 ) in the Cmc2 1 space group. Two different environments for vanadium cations are observed (dark and light blue), suggesting a V 3+ -V 5+ pair (oxidation state from BVS calculations is displayed). Environment of sodium in a capped prism is also reported. Two different environments for vanadium cations are observed (dark and light blue), suggesting a V 3+ -V 5+ pair (oxidation state from BVS calculations is displayed). Environment of sodium in a capped prism is also reported.

The end of charge occurs through a biphasic reaction between Na 1.3 VPF and NaVPF at 4.19 V vs. Na + /Na (Figure 5.2). Extra reflections at low 2θ angles indicate the formation of a new sodium-ordered phase, NaVPF (Figure 5.27b). The reaction between Na 1.3 VPF and NaVPF is peculiar because it shows a delay. NaVPF starts forming promptly, but its crystallization is not evolving linearly. A possible explanation is that this phase nucleates in the form of stable small domains spread in the sample, making it hardly detectable by diffraction. As the process goes on, the domains either grow and/or coalesce until a long range NaVPF crystalline structure is observed. This process can be understood in view of the proposed NaVPF crystal structure as will be discussed with more details at the end of the next paragraph. The diffraction pattern of the obtained NaVPF phase does not correspond to any of those previously encountered. Cell parameters reveal a certain similarity with the pristine phase because of a subtle orthorhombic distortion: a = 8.7822(3) Å, b = 8.7962(3) Å, c = 11.0015(2) Å that can be noticed in the right part of Figure 5.28 (in green, peaks (400) and ( 040)). This indicates an extremely small volume change ∆V/V = 3% along the overall charge of the material (Table 5.6). Systematic extinctions reveal a Ccentered space group for the crystal structure of NaVPF and the space groups showing the best results from profile-matching are Cmcm, Cmc2 1 and C2cm in setting 1. A structural determination in space groups Cmcm and C2cm was attempted without success, while Cmc2 1 (a subgroup of Cmcm) allowed us to obtain a structure related to the pristine one, showing V bi-octahedra and PO 4 tetrahedra. This description requires a shift of the unit cell origin of (1/4, 0, 0) with respect to the pristine one, placing V in two different 4a Wyckoff positions and generating two different V environments (Figure 5.29). Rietveld refinement (reported with relative Fourier maps in Figure 5.30) indeed showed that the two vanadium belonging to the same bi-octahedron have different environments: bond-valence sum calculations clearly differentiates them as a V 3+ -V 5+ -type pair (+4.7(3) for V1 and +3.3(2) for V2) rather than a V 4+ -V 4+ one. More than two oxidation states of vanadium have already been shown to coexist in the same material and vanadium's disproportionation is an occurring reaction (2V 4+ → V 3+ + V 5+ ). As an example, it was found for Li 1+x V 3 O 8 that upon reduction (Li insertion) the signature of V 3+ can coexist with the V 4+ and V 5+ ones [START_REF] Boucher | Study of Li 1+x V 3 O 8 by band structure calculations and spectroscopies[END_REF] . In the same way, the coexistence of V 3+ and V 5+ has also been observed using XANES spectroscopy for NaV

3 V 4.8+ 2 O 1.6 (PO 4 ) 2 F 1.
4 [START_REF] Serras | Electrochemical Na Extraction/Insertion of Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x[END_REF] : the signature of V 3+ is reported to be present with those of V 4+ and V 5+ . The authors proposed that the small amount of V 3+ present in the pristine material would not be involved in the redox processes, but considering our results obtained for NaV IV 2 (PO 4 ) 2 F 3 , it could also be that V 3+ is oxidized to V 4+ and it subsequently undergoes disproportionation. In our case, a 50%-50% V 3+ -V 4+ ordered composition was most likely formed upon Na + extraction towards Na 2 VPF. Upon further oxidation, tetragonal symmetry suggests that only one site of V is present in the solid solution domain.

When the final biphasic reaction takes place, either every vanadium has 3d 1 4s 0 electronic structure (i.e. one unpaired electron) or they are distributed 50%-50% 3d 2 4s 0 and 3d 0 4s 0 (i.e. one vanadium with no unpaired electron and one with a pair). It seems in our case that this charge distribution is energetically favorable, especially in a system where the two vanadium environments share one corner. Na1A which is filled in the structure of Na3VPF (dashed cell), while it is now empty.

Table 5.8 gathers all the structural information related to NaVPF obtained from Rietveld refinement. The V1-O distances are significantly shorter than the V2-O ones and the V1-F3 bond-length is rather short (but already observed for other V 5+ -F containing compounds [START_REF] Benkic | Crystal structure of (Xe 2 F 11 +)(VF 6 )[END_REF] ). Our conclusions on the V 5+ /V 3+ disproportionation in NaVPF are based, noticeably, on structural refinements from in situ XRPD data and will deserve supporting electronic structure calculations and oxidation-sensitive analysis techniques (XAS for example). Regarding sodium ions, we found them placed in a single fully occupied site

From Na

3 V 2 (PO 4 ) 2 F 3 to Ag 3 V 2 (PO 4 ) 2 F 3 : Na + /Ag + ion exchange
Our operando experiment on Na 3 VPF as well as the remarkable properties of this material upon Na + extraction / insertion at high rates [START_REF] Ponrouch | Towards high energy density sodium ion batteries through electrolyte optimization[END_REF] strongly suggest facile ion transport properties of the Na + cations. This opens up several possibilities of ion exchange to prepare new compositions for different purposes and silver-containing compounds can be of interest for a few niche but important applications. The Ag + cation is slightly bigger than Na + (1.29 Å vs. 1.16 Å) but it is also well-known to be more polarisable due to its electronic configuration 5s 0 4d 10 . This fact allows substitution of these cations within similar frameworks [START_REF] Quarez | Crystal structures of new silver ion conductors Ag 7 Fe 3 (X 2 O 7 ) 4 (X = P, As)[END_REF][START_REF] Quarez | Crystal structures and sodium/silver distributions within the ionic conductors Na 5 Ag 2 Fe 3 (As 2 O 7 ) 4 and Na 2 Ag 5 Fe 3 (P 2 O 7 ) 4[END_REF] . The compounds investigated in the literature include open structures of NASICON-type such as Ag 1+x Zr 2-x M x (PO 4 ) 3 (M = Sc, Fe [START_REF] Angenault | Ionic conductivity of solid solutions Ag 1+x Zr 2-x M x (PO 4 ) 3 with MIII = Sc, Fe[END_REF] ), AgTaMP 3 O 12 (M = Al, Ga, In, Cr, Fe and Y) [START_REF] Koteswararao | Preparation, characterization and impedance study of AgTaMPO (M=Al, Ga, In, Cr, Fe and Y)[END_REF] , AgSbMP 3 O 12 (M = Al, Ga, Fe and Cr) [START_REF] Rambabu | Powder x-ray diffraction, infrared and conductivity studies of AgSbMP 3 O 12 (M=Al, Ga, Fe and Cr)[END_REF] and other structural families such as (Ag 1-x Na x ) 2 -FeMn 2 (PO 4 ) 3 [START_REF] Daidouh | Structural and electrical study of the alluaudites (Ag 1-x Na x ) 2 FeMn 2 (PO 4 ) 3 (x = 0, 0.5 and 1)[END_REF] , Ag 2 VP 2 O 8 [START_REF] Daidouh | Structure characterization and ionic conductivity of Ag 2 VP 2 O 8[END_REF] , AgRu 2 (P 2 O 7 ) 2 [341] and Ag 7-x Na x Fe 3 (X 2 O 7 ) 4 (X = P, As) [START_REF] Quarez | Crystal structures of new silver ion conductors Ag 7 Fe 3 (X 2 O 7 ) 4 (X = P, As)[END_REF][START_REF] Quarez | Crystal structures and sodium/silver distributions within the ionic conductors Na 5 Ag 2 Fe 3 (As 2 O 7 ) 4 and Na 2 Ag 5 Fe 3 (P 2 O 7 ) 4[END_REF] . The high ionic conductivity of these ceramics can be exploited in devices such as membranes, fuel cells and gas sensors [START_REF] Meunier | Pulsed laser deposition of superionic ceramic thin films: deposition and applications in electrochemistry[END_REF][START_REF] Collongues | Superionic conducting oxides[END_REF] .

Other potential applications include low thermal expansion materials [START_REF] Alamo | Crystal chemistry of the NaZr 2 (PO 4 ) 3 , NZP or CTP, structure family[END_REF] , hosts for radioactive waste [START_REF] Roy | Nzp, a new radiophase for ceramic nuclear waste forms[END_REF] , catalyst supports [START_REF] Serghini | Decompotion of 2-butanol over nasicon zirconium-copper phosphates[END_REF] , ion exchangers [START_REF] Hirose | Ion-exchange properties of NASICON-type phosphates with the frameworks Ti 2 (PO 4 ) 3 and Ti 1.7 Al 0.3 (PO 4 ) 3[END_REF] and insertion/extraction reactions [START_REF] Kirshenbaum | In situ visualization of Li/Ag 2 VP 2 O 8 batteries revealing rate-dependent discharge mechanism[END_REF] . Here we report on our preliminary study to obtain a new silver fluorophosphate Ag 3 V III 2 (PO 4 ) 2 F 3 prepared through ion exchange from the sodium analogous Na 3 V III 2 (PO 4 ) 2 F 3 (Na 3 VPF). For the preparation, carried out by Fabien Lalère in LRCS, as-synthesized Na 3 VPF powder was stirred during several hours in a saturated solution of AgNO 3 to exchange sodium ions by silver ions. The resulting powder was washed several times with water and then acetone, and dried at 50 • C under vacuum to be characterized and eventually put back into the AgNO 3 solution to carry on the ion exchange as much as needed (to displace the equilibrium) to get the desired Ag 3 V 2 (PO 4 ) 2 F 3 phase. indexation quickly revealed the compatibility of such Bragg positions with the space group Amam of Na 3 VPF [START_REF] Bianchini | Na 3 V 2 (PO 4 ) 2 F 3 revisited: A high-resolution diffraction study[END_REF] . As all peaks are properly indexed, no doubt is left about the presence of a single phase after our ionic exchange. As previously discussed, the parent compound has the peculiarity of an extremely small orthorhombic distortion in the ab plane (Table 5.9). The distortion is found to significantly increase in Ag 3 VPF , where a = Na3 SOF is found slightly negative, thus it is set to 0.

• bond-length distances within the octahedra and tetrahedra are in general poorly affected: P-O distances in PO 4 and V-O ones in VO 4 F 2 are barely modified, while a small difference is found for V-F bonds: V-F1 increases from 1.98 Å to 1.995( 5) Å and V-F2 decreases from 1.97 Å to 1.95(1) Å.

• the angle between the two octahedra, given by V-F1-V, decreases from an almost straight one in Na 3 VPF (179.5(2) • ) to a significantly bent one (173.5(3) • ). The bending completely happens in the (b,c) plane, since x/a is fixed by symmetry to be 1/4 for V and F1. It is interesting to note that such bending does not correlate to a bigger value of the b cell parameters (on the contrary, b slightly decreases), while, on the other hand, a and c increase. The increase of the unit cell can be explained by steric effects of the bigger Ag + ions with respect to Na + . As reviewed by Shannon [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF] , effective ionic radii for 6-coordinated Na + and Ag + are 1.02 Å and 1.15 Å, respectively (If classical crystal ionic radii are used, the two values become 1.16 Å and 1.29 Å, the difference being the choice of the radius of oxygen r(O 2-)). Regardless of the choice, in both cases a difference of 0.13 Å is present, whose effects have been described above. It is important to mention that, although Ag + is bigger and somehow distorts the structure of Na 3 VPF, it is also sufficiently polarisable (due to the high number of electrons, 5s 0 4d 10 ) not to demand a symmetry modification of the structure.

In Na 3 VPF, sodium ions are found in the plane z = 0 and z = 1/2, distributed on a "triangular" arrangement of three crystallographic sites Na1 A , Na2 A and Na3 A . The first one is fully occupied, while Na2 A and Na3 A have partial occupancy, respectively, close to 2/3 and 1/3. We found, surprisingly, that Ag + ions place themselves on the exact same sites of Na + ions in Na 3 VPF. Even relative occupations are similar (Table 5.10). Figure 5.34 also gathers Na + and Ag + distributions in the z = 0 plane with the relative inter-cationic distances. Since from MEB-EDX it is found that the ion exchange is not complete (about 0.38 Na/f.u. remaining) we used this information during Rietveld refinement to localize sodium by constraining the total Na amount to 0.38. We observe that the remaning Na + cations are localized in Na1 A (0.08(1) / f.u.) and Na2 A (0.30(3) / f.u.) sites, but not in the Na3 A one, where the site occupancy factor (SOF) converged to a negligible (slightly negative) value. We can conclude that Ag-Ag distances are very similar to Na-Na ones in Na 3 VPF, except for Ag3-Ag3 which are farther away (Na3-Na3 = 2.84 Å in Na 3 VPF whereas Ag3-Ag3 = 3.50 Å).

Conclusions and perspectives

In this work we showed how the use of high resolution techniques led to new insight on Na 3 V 2 (PO 4 ) 2 F 3 , a material previously thought to be well-known from the crystal structure and electrochemical points of view, but with a significant amount of discrepancies found throughout the literature, which we believe to be the result of a partial substitution of oxygen for fluorine. Since the fully disordered sodium distribution is obtained at lower temperature for Na 3 V 2 (PO 4 ) 2 F 3 than for Na 3 V 2 O 2 (PO 4 ) 2 F (∆T = 100 • C), it is reasonable to expect higher ionic conductivity for the fluorine-rich phase. As a result, it appears that the O/F ratio could be a very critical parameter. Its control will allow getting the optimized composition and thus the material with the most attractive electrochemical properties for Na-ion batteries. For the actual composition Na 3 V 2 (PO 4 ) 2 F 3 (Na 3 VPF), slow galvanostatic cycling showed the presence of four distinct electrochemical features, an original electrochemical signature for Na 3 VPF that we have reported for the first time [START_REF] Ponrouch | Towards high energy density sodium ion batteries through electrolyte optimization[END_REF] .

More importantly, synchrotron radiation powder diffraction data revealed a small but significant orthorhombic distortion in Na 3 VPF (b/a=1.002). This led to an indexation in the Amam space group and to a new structure preserving the framework but strongly impacting the sodium distribution in the planes. This arrangement is the most interesting aspect of Na 3 VPF because it derives from a totally disordered one at high temperature to a par- behavior. Our study proves how even resolving weak Bragg reflections can be a key element because it allows, for example, distinguishing among sodium ordered and sodium disordered structures. This is important as it paves the way to direct observation of fine reaction pathways and thus to a more exact knowledge of electrode materials' properties.

Finally, we began to study the ion exchange of Na + in Na 3 VPF with other cations, exploiting its high ionic conductivity. In particular we report here the exchange with Ag + , since materials for silver intercalation are used for interesting applications. We show how we can obtain almost pure Ag 3 VPF (Ag 2.70 Na 0.38 V 2 (PO 4 ) 2 F 3 ) and how it preserves the crystal structure of Na 3 VPF, although with modified cell parameters. Interestingly, even the positions of Ag + cations are those who were occupied by Na + , producing further evidence of the correctness of our structural determination on Na 3 VPF. Several studies are envisaged to complete those reported here. Firstly, a direct measurement of the ionic conductivity of Na 3 VPF, which could not be completed in time because of technical issues, and the growth of Na 3 VPF single crystals, to confirm our structure and to facilitate ionic conductivity measurements. Secondly, the phase diagram of Na 3 VPF is still far from being totally understood. The superstructures encountered at compositions Na 2.4 VPF and Na 2 VPF still need to be explained. Here the help of electron diffraction will probably be of key importance, once the phases are stabilized under the beam. Moreover, temperature-controlled studies at key compositions such as Na 2 VPF or NaVPF are currently in the making, to get further insights into Na + diffusion into the VPF framework. Finally, note that our study of Na 3 VPF demonstrates the potentialities of operando synchrotron radiation XRPD studies to understand reaction processes in electrode materials. This is complementary to operando NPD and they can be both used, depending on the properties under investigation, to get detailed insights through the Rietveld method. Countless materials could then beneficiate from these advanced characterization techniques, as we plan to do with those we believe to be more significant for the Li-ion and Na-ion technology.

Conclusion

The central idea of this thesis has been the application of the operando methodology to a va- These studies require appropriate setups to be carried out: the electrochemical cells needed must be able to combine good electrochemical properties with the specific requirements of the characterization techniques of choice. Often contrasting, these requirements make setups design quite tricky. In our research groups two of such cells were developed for in situ/operando XRPD and synchrotron XRPD studies, so that they could be extensively used in this thesis. Then, a large part of the PhD project has been the development of a complementary cell for in situ/operando neutron powder diffraction. Given the significant issues that such experiments present, special precautions had to be taken in the design, like the use of "neutron-transparent" (Ti,Zr) alloy for cell manufacture and of deuterated elec- attainable from in situ NPD; the technique will then continue to be exploited to study new interesting materials, both in our group and for the whole scientific community since the (Ti,Zr) in situ cell will remain available at ILL. In our specific case, we also envisage to widen the application range of such experiments: new materials will be studied, mostly among polyanionic phosphates; new cells will be designed, with the goal of allowing also electrochemical cycling at high temperature (for application in all-solid-state batteries);

and new electrolytes will be developed to cut the cost of experiments.

When they are not the main characterization technique used, neutrons can be a valuable tool to support (less expensive) XRPD studies, as in the case of LiVPO 4 O. We reported our study on such a material in Chapter 4, where the phase diagram and phase transformations observed on both lithiation and delithiation are described in detail. This Tavorite compound, already part of the PhD of a previous student in our group, is of great interest as it offers good gravimetric energy density and the ability to exchange 2 Li + /f.u., possibly doubling the available capacity. We combined electrochemical characterizations, revealing the importance of controlling particle size to obtain good cyclability, with structural studies analyzing in-depth the mechanisms of lithium extraction/insertion. Here we showed the strength and richness of the operando diffraction approach, even when laboratory diffractometers are used instead of large-scale instruments. Complex series of phase transition could be followed in real time and the effect of strains induced by the volume change between different phases was highlighted. Neutrons were still used as a complement in this study, specifically to determine detailed crystal structures when significant amounts of light elements are present in the stoichiometry. In the light of the phase transformations thoroughly described in this work, improvement of the electrochemical performances and rate capabilities will possibly be achieved in future studies. To complete the range of large scale instruments represented in this thesis, synchrotron radiation was also used for selected stud- during charge of LiMn 2 O 4 . This material has been studied for 30 years and the two separated electrochemical regions observed during its charge are well-known. However, the cause of such a separation had only been conjectured to be an ordered phase, without any experimental proof. We could finally show that it is due to a cooperative cation charge ordering and lithium/vacancy ordering occurring in Li 0.5 Mn 3+ 0.5 Mn 4+ 1.5 O 4 , reducing the phase symmetry from Fd 3m to P2 1 3. This observation fully validated the precious contribution of high-resolution operando synchrotron radiation to the study of battery materials.

In conclusion, this thesis attempted at exploiting a maximum of diffraction techniques, ex situ, in situ and operando, using X-Rays, synchrotron radiation and neutrons as probes, to obtain in turn a picture as complete as possible on electrode materials as they transform inside a battery. Our approach based on combined use of different techniques revealed to be extremely useful to obtain complementary insights and to reveal the interconnection between crystal structures and electrochemical properties present in these materials. We are hopeful that deeper understanding will be of primary importance to improve their performances or to develop in the future new electrode materials with better electrochemical properties for next-generation battery systems. physical distance, followed each of my steps, giving me strength and always supporting me.

And last but not least, my wife Camilla, for sharing with me this path and sometimes the weight of difficult scientific days. • fonctionner électrochimiquement pour des dizaines de cycles de charge/décharge pour des quantités de matériaux d'électrode comprises entre 10 mg et 300 mg,

• pour de telles électrodes, être capable de cycler à des régimes allant jusqu'à C/5, iv • être facile à utiliser, laver et réutiliser pour les utilisateurs potentiels dans les grands instruments,

• fournir des digrammes de diffraction de neutrons sur poudre de bonne qualité en 30 min ou moins, sans d'autres contributions que celles des matériaux d'électrode à étudier,

• minimiser la quantité de composants de la batterie sondée par le faisceau,

• se concentrer sur l'une des électrodes de la batterie seulement, en essayant de maximiser sa contribution au digramme de diffraction de neutrons.

La tâche a été accomplie grâce la conception d'une cellule électrochimique cylindrique (similaire aux plus classiques cellules swagelok) comportant: (i) un matériau d'alliage en (Ti, Zr) en tant que boîtier et collecteur de courant positif, choisi parce qu'il est transparent aux neutrons, (ii) une version deutérée de l'électrolyte, pour réduire la diffusion incohérente des neutrons par les composants de la batterie riches en hydrogène comme les solvants organiques. Notre travail a permis de mettre au point une cellule électrochimique fiable capable de fonctionner en utilisant des électrodes massives (de l'ordre de 200 mg, massives à l'échelle de la batterie, mais un petit échantillon pour les neutrons) avec de bonnes performances électrochimiques et en mesure de donner des diagrammes de NPD de haute qualité pour l'analyse des données. Nos études ont été menées sur le diffractomètre à haut flux D20 à Institut Laue-Langevin (ILL) de Grenoble, où la faisabilité d'expériences réelles operando en diffraction de neutrons a pu être démontrée en utilisant le matériau commercial LiFePO 4 . La validation de notre cellule a suivi trois étapes principales: premièrement, nous avons mené des cycles galvanostatiques électrochimiques en utilisant différents électrolytes et à des régimes différents. Deuxièmement, nous avons mesuré LiFePO 4 comme poudre pure dans une expérience de NPD standard, comparant ensuite les diagrammes de NPD obtenus à ceux enregistrés dans une "configuration complète de batterie", cet-à-dire avec le matériau actif en mélange avec du carbone Csp, monté dans la dans la cellule in situ avec tous les composants de la batterie (l'électrolyte, le lithium, etc.). Nous avons ensuite comparé la précision des paramètres que nous avons pu obtenir par affinement Rietveld dans les deux cas. Enfin, nous avons validé la possibilité de mener une expérience réelle operando: • Certaines compositions, comme par example Na 2 V 2 (PO 4 ) 2 F 3 , montrent une maille élémentaire plus étendue à cause de la présence d'ordres sodium/lacune et de cations de sodium (V 3.5+ ).

• Certaines autres, comme Na 2.2 V 2 (PO 4 ) 2 F 3 ou comme dans le domaine de composition Na 1.8 V 2 (PO 4 ) 2 F 3 -Na 1.3 V 2 (PO 4 ) 2 F 3 , se stabilisent avec le sodium désordonné dans une structure similaire à Na 3 V 2 (PO 4 ) 2 F 3 à haute température. Ceci est la conséquence d'une délocalisation des ions Na + qui résulte en une distribution "circulaire".

• D'autres encore ont dévoilé des réactions inattendues, comme le membre final NaV 2 (PO 4 ) 2 F 3 , dans lequel le vanadium est à priori au degré d'oxydation V 4+ .

La haute résolution de notre étude structurale operando a été en mesure de révéler un nouveau groupe d'espace, de symétrie inferieure (Cmc2 1 ), résultant en une nouvelle structure que nous avons proposée pour la première fois. Surtout, nous montrons que la cause de ce changement est la présence des paires V 3+ -V 5+ dans les environnements bi-octaédriques de NaV 2 (PO 4 ) 2 F 3 , ce qui a également été confirmé grâce à des mesures de XRPD ex situ .

Enfin, nous avons décidé d'explorer d'autres possibilités offertes par la conductivité ionique élevée de Na 3 V 2 (PO 4 ) 2 F 3 , en effectuant l'échange ionique Na + /Ag + .

Nous avons réussi à obtenir une composition très proche de Ag 3 V 2 (PO 4 ) 2 F 3 dont nous avons déterminé la structure cristalline. Il conserve le groupe d'espace Amam, avec une distorsion orthorhombique plus prononcée mais une structure toute de même très similaire à l'initiale. L'argent occupe également les mêmes positions que le sodium, montrant encore une fois la stabilité de cette charpente polyanionique vis-à-vis de différents échanges ioniques.

Conclusion

Mots-clés

Li-ion, Na-ion, in situ, operando, diffraction, structures crystalline, electrode, neutron xiv

Thesis Summary in English

This work aims at studying electrode materials for Li-ion and Na-ion batteries as they function inside batteries. Diffraction is the mainly used technique, exploiting neutrons, X-Rays and synchrotron radiation (SR), to obtain insights on the structural evolution of such materials as Li + or Na + are inserted/extracted from their framework. We adopted a combined approach of ex situ, in situ and operando measurements to extract a maximum of information from our studies. At first, we designed an electrochemical cell for in situ neutron powder diffraction (NPD) measurements, featuring a "neutron-transparent" (Ti,Zr) alloy; this cell, joined to others previously developed in our group, gave us a complete set of tools to perform our studies. We demonstrated the feasibility of operando

Keywords

Li-ion, Na-ion, in situ, operando, diffraction, crystal structures, electrode, neutron xv

Figure 1 . 1 :

 11 Figure 1.1: World electricity generation (TWh) from 1971 to 2012 by fuel. Data from the International Energy Agency (IEA).

Figure 1 . 2 :

 12 Figure 1.2: Evolution of energy production from wind (left) and solar (right) during several days.

Figure 1 . 4 :

 14 Figure 1.4: Schematic representation of a battery during common use (discharge).

Figure 1 . 5 :

 15 Figure 1.5: Schematic representation of a Li-ion battery, constituted by a LiCoO2 positive electrode

Figure 1 . 6 :

 16 Figure 1.6: Schematic of the energy vs. density of states showing the relative positions of the Fermi energy in an itinerant electron band for LixC6, the Ti 4+ /Ti 3+ redox couple for LixTiS2 and Lix[Ti2]S4,

Figure 1 . 7 :

 17 Figure 1.7: Structural frameworks of the most common positive electrode materials: left) layered LiCoO2, middle) spinel LiMn2O4, right) olivine LiFePO4.

Figure 1 . 8 :

 18 Figure 1.8: (a) Positions of the Fe 3+ /Fe 2+ redox couple relative to the Fermi energy of lithium in the NASICON structure with different polyanion countercations. (b) Positions of some M n /M n+1

Figure 1 . 10 :

 110 Figure 1.10: Specific energy density of Li-ion batteries at the material, electrode, cell and battery level. Automotive targets for 2025 are also shown. Reprinted from [41] .

Figure 1 . 11 :

 111 Figure 1.11: Gravimetric capacity and operating potential of the most promising electrodes for

Figure 1 . 13 :

 113 Figure 1.13: Scheme showing particles reacting through a biphasic reaction (left) and a solid solution (right). Phases are represented as circles: blue ones are the A phase, red ones the B phase and green one the intermediate A1-yBy.

Figure 1 . 14 :

 114 Figure 1.14: Relation of the electrochemical galvanostatic curve V = f(x) (top) with the inverse derivative (dV/dx) -1 (bottom) for the layered material LiNiO2. The three most intense peaks close to R1, R2 and R3 indicate biphasic transitions, while M indicate an extended solid solution region.

Figure 1 .

 1 Figure 1.15: a) Max Von Laue's X-ray diffraction pattern from a zinc-blende (ZnS) single crystal, revealing spots of various shape and intensity. b) X-Ray powder diffraction pattern of a sample of the soil of Mars, collected by the Curiosity rover, revealing the classical cones created by the powder averaging. Pictures taken from the Editorial of Nature Milestones in Crystallography, 2014 (doi:10.1038/nature13348).

Figure 1 . 17 :

 117 Figure 1.17: Cell for in situ/operando XRPD experiments in reflection diffraction on the PANalytical Empirean diffractometer.

Figure 1 .

 1 Figure 1.18: D2B (left) and D20 (right) diffractometers at ILL.

  French institutions: the Institut Laue-Langevin (ILL, Grenoble), the Laboratoire de Réactivité et de Chimie des Solides (LRCS, Amiens) and the Institut de Chimie de la Matière Condensée (ICMCB, Bordeaux). It aims at exploiting the potentialities of real-time diffraction experiments for the analysis of electrode materials for Li-ion batteries. Real-time is meant as a synonym of operando, i.e. experiments carried out during battery operation. At the material scale, this means during Li + extraction or insertion from/into the 3D framework of the intercalation materials constituting the electrodes. We have tried to promote the synergy and take advantage of the complementarities between different probes for diffraction experiments, with a special accent put on neutrons. The first two chapters of this thesis describe in fact the design and development of an electrochemical cell for operando neutron diffraction experiments on electrode materials for Li-ion batteries. After building such a cell, we confirmed that it worked as required and we used it to study challenging materials. In particular we analyzed the detailed structural information that neutrons could provide on spinel compositions (LiMn 2 O 4 , Li 1+x Mn 2-x O 4 , LiNi x Mn 2-x O 4 ), stressing especially the insights that are missed by other characterisation techniques. Chapters 4 and 5 are instead more material-centered and reflect the interest of our research groups on polyanionic compositions. The former deals in fact with the electrochemical transformations of the Tavorite compounds LiVPO 4 O and LiVPO 4 F. These phases were already the object of the thesis

Figure 1 . 19 :

 119 Figure 1.19: Topics treated in this thesis.

  (Figure 2.2b).

Figure 2 . 2 :

 22 Figure 2.2: Electrochemical cells designed for in situ NPD using custom-made geometries (a, b) or traditional roll-over geometries (c, d).

Figure 2 . 3 :

 23 Figure 2.3: Recent electrochemical cells designed for in situ NPD using custom-made geometries (a, b) or pouch-cell geometry (c).

Figure 2 . 4 :

 24 Figure 2.4: Evolution of the amount of publications per year concerning in situ neutron powder diffraction on electrode materials in peer-reviewed journals.

Figure 2 . 5 :

 25 Figure 2.5: Scheme (left) and picture (right) of the electrochemical cell designed for operando NPD at ILL.

Figure 2 . 6 :

 26 Figure 2.6: Neutron powder diffraction patterns of Zr, Ti0.6Zr0.4, and Ti. Neutron wavelength is λ = 1.26 Å. Reprinted from[START_REF] Sidhu | Neutron diffraction study of titaniumâzirconium system[END_REF] .

  Figure 2.7: Comparison between pure LiFePO4 powder and a mixture of LiFePO4 + Csp, as measured on the D2B diffractometer at ILL.

Figure 2. 8 .

 8 It can be observed that the electrochemical cell is mounted in the center of the diffractometer by means of a plastic screw, which electrically isolates it from the rest of the environment. Cables reach the cell from the top and are connected to a potentiostat (Biologic SP-200) for electrochemical charge and discharge of the battery. The neutron beam size is appositely reduced by means of cadmium masks put on the instrument's final collimating guide (called

Figure 2 . 8 :

 28 Figure 2.8: Setup of an operando NPD experiment with our electrochemical (Ti,Zr) cell on the D20 diffractometer at ILL.

Figure 2 . 9 :

 29 Figure 2.9: Electrochemical galvanostatic data obtained within the in situ electrochemical cell with the positive electrode material LiFePO4. Different tests were performed depending on the active mass, the cycling rate and the electrolyte used (LP30 or a deuterated one).

Figure 2 .

 2 Figure 2.9 illustrates the electrochemical data obtained within the in situ electrochemical cell for i) 31 mg of LiFePO 4 cycled at C/10, ii) 33 mg at C/10 and iii) 105 mg at C/24.

2. 5 . 2 •

 52 Figure 2.10.

Figure 2 . 10 :

 210 Figure 2.10: Observed (red dots), calculated (black line) and difference (blue line) plots obtained for the Rietveld refinement of neutron powder diffraction data recorded: (top) on the diffractometer D2B for the pure LiFePO4 powder and (bottom) on the diffractometer D20 for the electrode within the in situ lithium cell, in a complete battery configuration.

Figure 2 . 11 :Figure 2 . 12 :

 211212 Figure 2.11: Crystal structure of the olivine compound LiFePO4 and of its delithiated form FePO4. PO4 tetrahedra are shown in blue, FeO6 octahedra in brown and Li + as green spheres.

4 Figure 2 . 13 :

 4213 Figure 2.13: Tridimensional visualization of the charge of a LiFePO4 electrode. The biphasic reaction between the two end members can be clearly observed.

Figure 2 . 14 :

 214 Figure 2.14: Observed (red dots), calculated (black line) and difference (blue line) plots obtained for the Rietveld refinement of neutron powder diffraction data recorded within the in situ lithium cell during Li + extraction from LiFePO4. Five compositions are given as examples: (a) pristine LiFePO4, (b) 3/4 LiFePO4: 1/4 FePO4, (c) 1/2 LiFePO4: 1/2 FePO4, (d) 1/4 LiFePO4: 3/4 FePO4 and (e) FePO4.

Figure 2 . 15 :

 215 Figure 2.15: Weight fractions for LiFePO4 and FePO4, within the crystalline part of each composition, determined from NPD data recorded operando during Li + deintercalation from LiFePO4.

  % LiFePO 4 (79(3)%) 25 % FePO 4 (21(2)%) a = 10.316(1) Å; b = 6.003(1) Å; c = 4.6922(7) Å; a = 9.823(6) Å; b = 5.796(3) Å; c = 4.781(3) Å; V = 290.58(8) Å3 ; R B = 4.8% V = 272.2(3) Å3 ; R B = 9.28%

Fe 25 %

 25 % LiFePO 4 (50(3)%) 50 % FePO 4 (50(3)%) a = 10.313(3) Å; b = 6.004(2) Å; c = 4.692(1) Å; a = 9.821(2) Å; b = 5.793(1) Å; c = 4.777(1) Å; V = 290.5(1) Å3 ; R B = 7.78% V = 271.8(1) Å3 ; R B = 7.59% Interatomic distances ( Å) / Distortion Interatomic distances ( Å) / Distortion (x2) = 2.05(4) P-O3(x2) = 1.56(5) Li-O3(x2) = 2.22(4) Fe-O3(x2) = 1.93(4) P-O3(x2) = 1.61(LiFePO 4 (18(2)%) 75 % FePO 4 (82(3)%) a = 10.338(7) Å; b = 6.007(4) Å; c = 4.690(3) Å; a = 9.820(1) Å; b = 5.7891(8) Å; c = 4.7786(7) Å; V = 291.3(3) Å3 ; R B = 10.6% V = 271.65(7) Å3 ; R B = 5.89%

  .69(5) Å3 ; R B = 5.30% Interatomic distances ( Å) / Distortion Interatomic distances ( Å) / Distortion Fe-O1=1.92(2) P-O1 = 1.53(3) Fe-O2 = 1.93(2) P-O2= 1.51(3) ---Fe-O3(x2) = 2.02(2) P-O3(x2) = 1.58(2) -Fe-O3(x2) = 2.15(2) -∆ = 20.0E-04 ∆ = 3.7E-04

Figure 3 . 1 :

 31 Figure 3.1: Structure of the spinel MgAl2O4. Small red spheres represent oxygen, blue octahedra represent aluminium and its coordination, yellow spheres 4-coordinated magnesium. One unit cell contains 8 formula units. a) and b) are the two settings reported in the international tables of crystallography, having the origin at -3m and -43m, respectively. b) is obtained from a) via a (1/8, 1/8, 1/8) unit cell translation.

Figure 3 . 2 :

 32 Figure 3.2: Ternary phase diagram of Li-Mn-O at ambient temperature. The highlighted triangle emphasizes the region of highest interest for Li-ion batteries, where Mn 3+ -containing LiMn2O4 is shown. Other important compositions are Mn 3+ -containing LiMnO2 and Mn 4+ -containing λ-MnO2, Li2Mn4O9, Li4Mn5O12 and Li2MnO3.

Figure 3 . 3 :

 33 Figure 3.3: Rietveld refinement of a synchrotron XRPD measurement of LiMn2O4. Observed pattern Yobs in red, calculated Ycalc in black, difference Yobs-Ycalc in blue, Bragg positions as green ticks. In the insets, (220) and (422) reflections are shown, stressing the difference between a model with (black) and without (purple) lithium in the 8a site.

  to perform an operando neutron powder diffraction study during the extraction of lithium from Li 1+x Mn 2-x O 4 spinels, with the goal of giving quantitative information about the different phases involved and with special attention to lithium's site occupancy factors (SOFs). To this end, we synthesized three samples of nominal stoichiometries LiMn 2 O 4 (x = 0), Li 1.05 Mn 1.95 O 4 (x = 0.05) and Li 1.10 Mn 1.90 O 4 (x = 0.10).

Figure 3 . 5 :

 35 Figure 3.5: Top: Rietveld refinement of neutron powder diffraction data recorded using the D2B high-resolution diffractometer at ILL for LiMn2O4 (left), Li1.05Mn1.95O4 (center) and Li1.10Mn1.90O4 (right). Bottom: Respective voltage-composition curves recorded vs. Li + /Li during galvanostatic cycling at C/20 rate (left) and their inverse derivative curves (right), showing the two electrochemical features typical of spinel materials.

  Figure 3.7: Operando neutron diffraction patterns recorded upon charge (Li + extraction at C/20 rate) for LiMn2O4. Red patterns indicate the central region of the two biphasic reactions.

Figure 3 . 8 :

 38 Figure 3.8: Contour plots of neutron powder diffraction patterns recorded operando upon charge (Li + extraction at C/20 rate) for LiMn2O4 (left), Li1.05Mn1.95O4 (middle) and Li1.10Mn1.90O4 (right).Focus on the 90 • -120 • 2θ angular range. Every scan was recorded for 30 minutes; the y axis scale can be read as scan number but also as time (hours), divided by 2.

Figure 3 . 9 :

 39 Figure 3.9: Detailed zoom on the 35.5 • -41.5 • 2θ region in the Rietveld refinement of the endof-charge phase of Sample S3 Li0.33[Mn1.90Li0.10]O4 (Figure 3.11c) showing the contribution of the unreacted part of the electrode.

Figure 3 . 10 :

 310 Figure 3.10: Phase diagram and observed miscibility gaps for LiMn2O4 (top), Li1.05Mn1.95O4 (middle) and Li1.10Mn1.90O4 (bottom). In red is given the y value at the end of the in situ charge. For every sample, two bars are reported to account for the bias given by the unreacting part of the electrode. The top bar represents the observed phase diagram and miscibility gaps, while the bottom one represents those corrected considering the full capacity C theor. of the materials (i.e. every observed composition interval is divided by the ratio C obtained /C theor. , <1 since obtained capacity < theoretical capacity). Arrows show noteworthy compositions studied in detail in the following.

Figure 3 .

 3 Figure 3.11: a) Refined parameters (Rietveld) from neutron powder diffraction data recorded operando during Li + extraction from Li1.10Mn1.90O4. A full solid solution is observed with regular monotonous decrease of the cell parameter a. From top to bottom: electrochemical galvanostatic data, total % in weight of the different phases involved, respective cell parameters, oxygen fractional atomic coordinates and 8a lithium site occupancy factor. Top panel also reports the composition of the Li1.10Mn1.90O4 electrode. Values measured during electrochemical cycling and calculated from the results of Rietveld refinement are compared. b)-c) Rietveld refinements of the intermediate phase Li0.72Mn1.90O4 and of the end-of-charge phase Li0.33Mn1.90O4. The second set of Bragg positions represents the unreacted part of the electrode, corresponding to the pristine material (10-15 wt.%). d) Inverse derivative of the voltage-composition curve, plotted with lithium's site occupancy factors for the different phases. The arrow indicates the phase Li0.72Mn1.90O4. Vertical dotted lines help to notice the variation in 8a lithium's SOF decrease.

Figure 3 .

 3 Figure 3.12: a) Refined parameters (Rietveld) from neutron powder diffraction data recorded operando during Li + extraction from Li1.05Mn1.95O4, where a solid solution followed by a biphasic reaction is observed. From top to bottom: electrochemical galvanostatic data, total % in weight of the different phases involved, respective cell parameters, oxygen fractional atomic coordinates and 8a lithium site occupancy factor. Top panel also reports the composition of the Li1.05Mn1.95O4 electrode. Values measured during electrochemical cycling and calculated from the results of Rietveld refinement are compared. b)-c) Rietveld refinements of the intermediate phase Li0.69[Mn1.95Li0.05]O4 and of the end-of-charge phase Li0.19[Mn1.95Li0.05]O4. The second set of Bragg positions represents the unreacted part of the electrode, corresponding to the pristine material (10-15 wt%). d) Inverse derivative of the voltage-composition curve, plotted with lithium's site occupancy factors for the different phases. The arrow indicates the phase Li0.69[Mn1.95Li0.05]O4.

  Figure 3.13: a): Refined parameters (Rietveld) from neutron powder diffraction data recorded operando during Li + extraction from LiMn2O4, where two biphasic reactions are observed. From top to bottom: Electrochemical galvanostatic data, total % in weight of the different phases involved, respective cell parameters, oxygen fractional atomic coordinates and 8a lithium site occupancy factor. Top panel also reports the composition of the LiMn2O4 electrode. Values measured during electrochemical cycling and calculated from the results of Rietveld refinement are compared. b)-c) Rietveld refinements of the intermediate phase Li0.67Mn2O4 and of the end-of-charge phase Li0.1Mn2O4. The second set of Bragg positions represents the unreacted part of the electrode, corresponding to the pristine material (10-15 wt.%). d) Inverse derivative of the voltage-composition curve, plotted with lithium's site occupancy factors for the different phases. The arrow indicates the phase Li0.67Mn2O4.

  later, they mainly rise from cation charge ordering. Based on our in situ NPD data, we cannot argue with the existing literature on this point. The fact that we observe an intermediate phase at composition Li 0.67 Mn 2 O 4 is largely caused by the inactive part of the electrode. It can be seen in Figure 3.10 that the range where this single-phase intermediate composition is present appears to be 0.68 < x < 0.53, but when this is corrected for the inactive part of the electrode, it becomes 0.62 < x < 0.44, consistent with an intermediate phase around Li = 0.5. The presence of this side phase also reduces the precision in the lithium content determination due to peaks' overlap, possibly leading to an overestimation at Li 0.67 Mn 2 O 4 . A high-angular resolution synchrotron XRPD experiment conducted operando is reported in the next paragraph to lift the doubt on such a long-unanswered question. Lithium deintercalation from LiMn 2 O 4 proceeds finally through a second well-established biphasic reaction, corresponding to the intense peak in the derivative curve at 4.15 V vs. Li + /Li. In this case the reaction is clear and much slower than the previous one, involving a final phase with parameters quite different from the initial ones and a large miscibility gap ∆x ≈ 0.34 (0.4 when corrected for the unreacted part of the electrode, Figure 3.10). Indeed, the third phase (3) appears with a 3 = 8.076(3) Å and Li 8a SOF ≈ 0.2 and it evolves to final values a 3 = 8.0442(3) Å and Li 8a SOF = 0.10(21). The value of the unit-cell parameter of the final member confirms the presence of remaining lithium in the structure (λ-MnO 2

Figure 3 . 14 :

 314 Figure 3.14: 3D representation of a full cycle (charge + discharge) of LiMn2O4 observed by operando NPD. On the right the Bragg peaks' loss of intensity and chenge in shape during the 1 st cycle is shown.

4 l

 4 Figure 3.15: Evolution of (311) and (400) Bragg reflections of LiMn2O4 during a full electrochemical cycle of a LiMn2O4//Li half cell, observed by operando synchrotron XRPD.

Figure 3 . 15 .

 315 Figure 3.15. During charge one clearly notices an initial solid solution region, extending to Li ≈0.6 Mn 2 O 4 , followed by two topotactic biphasic reactions. This allowed us to isolate an intermediate cubic phase of cell parameter a = 8.1529(1) Å (around Li 0.5 Mn 2 O 4 ) and a final one, known as λ-MnO 2 , of cell parameter a = 8.0363(1) Å (shown in Figure 3.16).Upon discharge the process is reversed, but not fully reversible. The lithiation, almost complete, could proceed to composition Li 0.95 Mn 2 O 4 with a = 8.2435(1) Å, a value extremely close to the pristine one (a = 8.2451(1) Å). However, importantly, the solid solution region is now found to be associated with the Li-poor phase λ-MnO 2 and not with the Li-rich one as was during charge (Figure3.15).

Figure 3 . 16 :

 316 Figure 3.16: Rietveld refinements of operando synchrotron XRPD of the end member λ-MnO2 obtained after a full galvanostatic charge of the LiMn2O4//Li half cell. Excluded regions account for reflections coming from the cell, metallic Li, PTFE binder, beryllium windows and their protective aluminum layer.

Figure 3 .

 3 Figure 3.18: Rietveld refinement of synchrotron XRPD data collected operando on LiMn2O4 at the end of the 1 st complete galvanostatic cycle. a) Peak shape modeled as a single pseudo-Voigt function. b) Peak shape modeled as super-Lorentzian, i.e. two pseudo-voigdt centered at the same angular position. In this second case the fit improves, especially on the (111) reflection. c)Rietveld refinement of case b) with the highlighted contribution of the narrow and large peaks of the super-Lorentzian.

Fig. 10

 10 Fig. 10

Figure 3 . 19 :

 319 Figure 3.19: Contour plots of significant Bragg reflections observed upon electrochemical cycling of LiMn2O4 from operando synchrotron XRPD. On the right, the evolution of the most intense peak (111) is reported, together with the (220) one, both always present during the experiment (although (220) almost loses all its intensity in the delithiated phase). On the left, (110) and (200) reflections are observed for the intermediate phase only, both during charge and discharge, implying a symmetry reduction.

FFigure 3 . 20 :

 320 Figure 3.20: Rietveld refinements of operando synchrotron XRPD data for the phase Li0.5Mn2O4 obtained during galvanostatic cycling of LiMn2O4. Top: pristine-like space group Fd 3m. Middle: Cation-ordered P4332. Bottom: Cation-and lithium/vacancy-ordered P213. Respective crystal structures are displayed. Insets focus on 8.8 • -10.0 • and 12.8 • -14.0 • angular ranges. A secondary pristine-LiMn2O4-like phase is added in the refinements (≈3 wt%) because of the dynamic operando conditions.

Figure

  Figure 3.20.

Figure 3 . 21 :

 321 Fig. 12

Figure 3 . 22 :

 322 Figure 3.22: Bond-lengths of Mn 3+ -O and Mn 4+ -O octahedra.

  direction (as can be seen at the bottom of Figure3.20). However, a priori, the distribution of lithium and vacancies could be reversed (translation by 3/4, 1/4, 3/4) and we cannot determine yet any preference for one or the other lithium/vacancy ordering. Additional considerations regarding the possible minimization of electrostatic repulsions fail because for both lithium/vacancy distributions lithium ions have in their vicinity (0 -3.5 Å) 12 manganese cations of which 3 Mn 3+ and 9 Mn 4+ with similar bond-lengths. We left the Li position constant to the value reported in the literature for LiNi 0.5 Mn 1.5 O 4 , knowing that x = y = z = 0.011 in P4 3 32 is very close to x = y = z = 0 in Fd 3m of the classic spinel.3.4 Operando NPD of high-voltage LiNi0.4 Mn 1.6 O 4In the introduction of this chapter it was discussed how the substitution of different transition metals TM for Mn in Li(TM) x Mn 2-x O 4 is an interesting path to synthesize spinel materials operating as high-voltage positive electrodes (often around 5 V). One of the most common and widely studied choices is TM = Ni, leading to a solid solution of composition LiNi x Mn 2-x O 4 in the range 0 ≤ x ≤ 0.5. The end member x = 0.5 (LiNi 0.5 Mn 1.5 O 4 )

Figure 3 . 23 :

 323 Figure 3.23: Potential-composition profiles of ordered and disordered LiNi0.5Mn1.5O4 spinel oxidevs. metallic lithium, obtained in galvanostatic mode at C/5 rate (for each material, the 10th cycle is reported). Reprinted from[START_REF] Patoux | High voltage nickel manganese spinel oxides for li-ion batteries[END_REF] .

3. 1 for composition Li 0. 5

 15 scheme and space group belonging. However, to the best of our knowledge this has not been shown yet.

Figure 3 . 24 :

 324 Figure 3.24: Voltage-composition profiles obtained for LiNi0.4Mn1.6O4. Top figures show an ex situ galvanostatic cycle using commercial LP30 electrolyte. Bottom ones show galvanostatic cycling during the operando experiment. Inverse derivatives are shown on the right.

. 24 .

 24 Upon charge we could obtain 91% of the theoretical capacity but the electrolyte was likely significantly damaged, indeed the voltage-composition profile upon subsequent discharge was badly impacted. The abundance of electrolyte allowed the reaction to proceed nonetheless and we could recover the composition Li 0.8 Ni 0.4 Mn 1.6 O 4 at the end of the next discharge, giving meaningful results on the overall cycle. Figure 3.25 shows a complete representation of the experiment.

Figure 3 . 25 :

 325 Figure 3.25: Left: Contour view on the 1 st cycle of the LiNi0.4Mn1.6O4//Li cell observed by operando NPD in the 80 • -130 • angular range. Wavelength is λ = 1.54 Å. Right: Rietveld refinement of scan #31 during the biphasic reaction leading to Li-poor Li0.08Ni0.4Mn1.6O4.

Figure 3 .

 3 Figure 3.26 gathers the evolution of the main structural parameters and features ob-

Figure 3 . 26 :

 326 Fig. 5

4 ( 4 (

 44 charge. The single-phase reaction proceeds up to the composition Li 0.40 Ni 0.4 Mn 1.6 O Li 0.42(14) Ni 0.4 Mn 1.6 O 4 from Rietveld refinement), corresponding to the full oxidation of Mn 3+ to Mn 4+ and Ni 2+ to Ni 3+ . From this composition, Li + extraction occurs through a two-phase reaction involving the oxidized composition Li 0.08 Ni 0.4 Mn 1.6 O Li 0.12(12) Ni 0.4 Mn 1.6 O 4 from Rietveld refinement). The two processes are reversible upon discharge. • The Mn/Ni-O average bond lengths significantly decrease upon charge, consistent with the TM oxidation. Similarly to the case of Li 1+x Mn 2-x O 4 spinels, this results mainly from the decrease of the unit cell parameter value, while the oxygen fractional atomic coordinate inside the unit cell is poorly affected. The unit cell parameter contracts from 8.1807(7) Å to 8.057(3) Å in the Li-rich phase (∆a/a = 1.5%), and from 8.029(2) Å to 8.0200(3) Å in the Li-poor phase (∆a/a = 0.1%). This induces Mn/Ni -O bonds to decrease from 1.944(4) Å to 1.923(14) Å in the Li-rich phase (∆B/B = 1.0%), and from 1.915(22) Å to 1.908(3) Å in the Li-poor one (∆B/B = 0.3%). Error bars fluctuate significantly, becoming large when phases are in minority (< 20 wt%).

Figure 3 . 27 :

 327 Figure 3.27: Structural parameters obtained from Rietveld refinements upon the charge of LiNi0.4Mn1.6O4, plotted against Voltage and matched with the inverse derivative (dV/dx) -1 of the electrochemical curve.

Figure 3 . 28 :

 328 Figure 3.28: Rietveld refinement of scan #17 corresponding to the maximum value of the refined Biso. Wavelength is λ = 1.54 Å. Composition is Li0.68Ni0.4Mn1.6O4 and the respective structural parameters are in Table 3.4.

Figure 3 .

 3 Figure3.27 shows the correlation between B overall and electrochemistry in this experiment, i.e. with the inverse differential curve (dV/dx) -1 : B overall increases exactly as Ni cations oxidize from 2+ to 3+. To understand the reason for such an unexpected observation, we subsequently refined the Debye-Waller factors separately, while leaving other parameters fixed. We could notice that the atom responsible for this increase is oxygen, and not lithium or the TMs. For example, for pattern #17 (showing the maximum value for B overall = 1.42(9)) the refinement led to B iso (O) = 1.5(1) while B iso (Ni/Mn) = 0.2(2)

MO 6

 6 octahedra with M-O bonds close to 1.90 Å: for that specific composition, the average M-O distance calculated from the Rietveld refinement is fully representative for the homogeneity of the M-O bonds formed at the local scale. We have thus shown that through the inspection of B overall (first) and oxygen's B iso (afterwards) in the spinel structure, operando NPD during electrochemical cycling can be very sensitive to subtle changes in structural parameters and enlighten local structural features.

Figure 3 . 29 :

 329 Figure 3.29: Summary of phase diagrams and neutron powder diffraction patterns obtained for Li1+xMn2-xO4 and LiNi0.4Mn1.6O4.

  Li x VPO 4 O and Li x VPO 4 F (0 ≤ x ≤ 2) 4.

Figure 4 . 1 :

 41 Figure 4.1: Voltage and theoretical capacity of LiVPO4O and LiVPO4F, both exhibiting high gravimetric energy density. The plot only accounts for the extraction of 1 electron/f.u.. The energy density is double considering also the insertion of 1 Li + in their structure, leading to 2 electrons exchanged per f.u..

Figure 4 . 2 :

 42 Figure 4.2: Crystal structure of a generic member of the Tavorite family. Adapted from[START_REF] Marx | The structure of tavorite LiFePO 4 (OH) from diffraction and gga plus u studies and its preliminary electrochemical characterization[END_REF] .

Figure 4 . 3 :

 43 Figure 4.3: Several compounds among Tavorite phosphates in the wide range of available potentials.

. 1 )

 1 V P O 4 + LiF → LiV P O 4 F (4.2) Reaction 4.1 represents the first step where vanadium is introduced in the form of V 5+ 2 O 5 and reduced through CTR to form V 3+ PO 4 . The highly divided carbon is used in slight excess (about 5 wt%) to ensure a complete reduction. The precursors are SPEX ballmilled for 90 minutes (12 hours in case of planetary ball-milling machine), then pressed into a pellet subsequently heated at 350 • C during 8 hours under argon flow (pre-treatment) prior to a grinding and a final treatment at 800 • C during 10 hours, again under argon flow. The intermediate phase VPO 4 is then obtained coated by carbon (estimated around 7-8% by TGA or gas chromatograpy). Reaction 4.2 describes the second step, where VPO 4

4 Figure 4 . 4 :

 444 Figure 4.4: XRPD patterns of phase pure LiVPO4O and LiVPO4F with calculated Bragg positions

Figure 4 . 5 :

 45 Figure 4.5: Representation of the crystal structures of LiVPO4F and LiVPO4O.

  chains running along the [001] P 1 direction (Figure 4.6). The chains are connected to each other via PO 4 tetrahedra through -V-O-P-O-V-sequences. Vanadium lies in two octahedral sites with a very narrow range of V-O distances, 1.96-1.99 Å. The V-F distances along the -F-V-F-V-chain are very homogeneous (constrained by symmetry) with a value of 1.98 Å. LiVPO 4 O

Figure 4 . 6 :

 46 Figure 4.6: Octahedral chains of LiVPO4F (top) and LiVPO4O (bottom), revealing regular bond length distances in the first case (V 3+ ) and long-short alternated bonds in the second one (V 4+ ).

Figure 4 . 5 .

 45 Similar to LiVPO 4 F, it is built on chains of V(1)O 6 and V(2)O 6 octahedra (V(1) and V(2) are two independent vanadium sites) connected alternatively through their corners by oxygen. These chains run along [010] P 1 (Figure 4.5) and are connected to each other by PO 4 tetrahedra characterized by P-O distances between 1.50 and 1.58 Å. The vanadium cations lie within two octahedral

Figure 4 .

 4 7 gathers their behaviour upon galvanostatic cycling in Li-ion batteries (coin cells) made as LiVPO 4 Y // LP30 //

Figure 4 . 7 :

 47 Figure 4.7: Top: Lithium extraction from the structure of LiVPO4F (left) and LiVPO4O (right) upon galvanostatic cycling between 3 V and 4.55 V vs Li + /Li. Bottom: Lithium insertion into the structure of LiVPO4F (left) and LiVPO4O (right) upon cycling (GITT: galvanostatic intermittent titration technique) between 3 V and 1.50 V vs Li + /Li. Adapted from[START_REF] Mba | Synthesis and crystallographic study of homeotypic LiVPO 4 F and LiVPO 4 O[END_REF] .

Figure 4 . 8 :

 48 Figure 4.8: Galvanostatic cycling for three different SPEX ball-milling durations of a mixture of 80 wt% LiVPO4O and 20 wt% Csp. The cycle at the bottom is shown with the respective derivative curve (green). Diffractograms (insets) of the respective crystalline powders obtained after milling are reported.

4 . 1 :

 41 ) Å, b = 5.222(9) Å, c = 7.256(3) Å, α = 109.40(2) • , β = 107.10(1) • and γ = 97.04(6) • . The unit cell volume is V = 171.34(6) Å3 , intermediate between those of LiVPO 4 F and VPO 4 F. The charge is thus divided into two transitions showing volume changes of 2% and 6%, instead of a single transition of ∆V/V = 8% (Figure 4.9). Although this seems to Table Cell parameters of LixVPO4F (x = 0, 0.67, 1, 2). Composition S.G. a ( Å) b

Figure 4 . 9 :

 49 Figure 4.9: Unit-cell volume changes during the global electrochemical reaction LiVPO4F -VPO4F

6 . 5 .

 65 The end members VPO 4 O and Li 2 VPO 4 O were chemically prepared from LiVPO 4 O. In the first case, it was oxidized with a strong oxidizing agent, nitronium tetrafluoroborate (NO 2 BF 4 ) in acetonitrile medium. The resulting yellow powder was then sealed in a 0.2 mm diameter capillary and X-Ray diffraction was performed on a PANalytical diffractometer (Empyrean, Cu Kα 1,2 ) in Debye-Sherrer geometry. In the second case, LiVPO 4 O was reduced with LiAlH 4 in tetrahydrofurane. The resulting dark gray powder was then sealed in a 0.3 mm diameter capillary and X-Ray diffraction was performed on the same diffractometer. Inductively coupled plasma atomic emission spectroscopy (ICP-AES) was used to check the resulting stoichiometry. Neutron diffraction was also carried out on Li 2 VPO 4 O. The powder was put in a 6.5 mm diameter cylindrical vanadium sample holder and measured at λ = 1.594 Å on the high-resolution powder diffractometer D2B

4. 4 . 2

 42 Lithium extraction from LiVPO 4 O -High voltage domain We have previously described the limited electrochemical activity of LiVPO 4 O at high potential (3.95 V vs. Li + /Li). Only half of the theoretical capacity was achieved, the question to be answered being "Li 0.5 VPO 4 O or (1/2 LiVPO 4 O + 1/2 VPO 4 O)?". To address the problem, in situ X-Ray powder diffraction was performed during lithium deintercalation from LiVPO 4 O at a C/50 rate. Diffraction patterns were recorded for 70 minutes each in the angular domain [13 • -44 • ] during galvanostatic cycling. The result of such a measurement is reported in Figure 4.10. The phase diagram clearly shows that when the

Figure 4 . 10 :Figure 4 . 11 .

 410411 Figure 4.10: In situ XRPD patterns (left) of a Li//LP30//LiVPO4O cell upon galvanostatic charge and discharge (middle) at C/50 up to 4.5 V. The evolution of the FWHM of the (200) peak (30 • ) is shown on the top right part of the figure. An enlarged view of the 28.5 • -31 • region is also given at the bottom.

Figure 4 . 12 :

 412 Figure 4.12: XRPD measurement and Rietveld refinement of a -VPO4O powder sealed in a 0.2 mm capillary.

  5), in agreement with the theoretical phase stability. Cell parameters were refined to a = 7.2699(6) Å, b = 6.8773(4) Å, c = 7.2598(5) Å, β = 115.382(2) • (Vol = 327.93(4) Å3 ) and the structure showed the expected alternated long and short V-O distances along the octahedral vanadium chains, with bond lengths of 2.51(2) Å and 1.59(2) Å, respectively. Small distortions are observed both for the in-plane V-O distances (between 1.85(2) Å and 1.93(3) Å) and for the P-O distances (1.55(2) Å, 1.56(4) Å, 1.55(3) Å and a shorter one of 1.48(

Figure 4 .

 4 Figure 4.13: a) Crystal structure before relaxation used for DFT calculations. LiVPO4O from published experimental data (left) and Li0.5VPO4O (right). Li0.5VPO4O is obtained from LiVPO4O with different occupations of the Li1 and Li2 sites. The most stable structure is the one with the site Li1 only occupied. b) Various values of U used for GGA+U calculations applied on the 3d orbitals of V ions and resulting potentials. U = 4 eV represents the best choice. c) Formation energy for Li0.5VPO4O for different U values. The phase would be stable with respect to LiVPO4O and VPO4O only for U = 0.

Figure 4 . 14 :

 414 Figure 4.14: Galvanostatic cycling for a mixture of 80 wt% LiVPO4O and 20 wt% Csp (SPEX ball-milled for 30 minutes). Focus on the low voltage region between compositions Li1.5VPO4O and Li2VPO4O.

Figure 4 . 15 :

 415 Figure 4.15: Operando X-ray diffraction measurement of LiVPO4O cycled at C/48 rate. The first cycle and a second discharge were recorded. (Top) Contour plot and electrochemical curve. (Bottom) An enlarged view of the [26-30 • ] or [27-29 • ] region of the first discharge where important compositions are highlighted (pristine LiVPO4O (pattern #1, blue), Li1.5VPO4O (pattern #14, red), Li1.75VPO4O (pattern #21, green) and Li2VPO4O (pattern #27, brown)).

Figure 4 .Figure 4 . 8 Figure 8 :

 4488 Figure 4.15 the subsequent insertion mechanisms from Li 1.5 VPO 4 O to Li 1.75 VPO 4 O and from Li 1.75 VPO 4 O to Li 2 VPO 4 O do not appear straightforward. As previously mentioned, both a solid solution and a series of two 2-phase reactions had to be considered. At first, a single-phase mechanism (solid solution) seems to be the preferred choice since an evolution of the cell parameters correlated to a shift of the Bragg positions is clear from the contour plot.

Figure 4 . 16 : 123 Figure 9 :

 4161239 Figure 4.16: (Left) Patterns #14 and #21 are considered as extreme members of the biphasic reaction between Li1.5VPO4O and Li1.75VPO4O. A perfect biphasic reaction is simulated as x•pattern #14 + (1-x)•pattern #21 (x = 0.3, 0.4, 0.5, 0.6, and 0.7). The simulations can be compared with the experimental pattern #17 (red), corresponding to a composition close to Li1.6VPO4O. (Right) Patterns #21 and #27 are considered as extreme members of the biphasic reaction between Li1.75VPO4O and Li2VPO4O. A perfect biphasic reaction is simulated as x•pattern #21 + (1-x)•pattern #27 (x = 0.3, 0.4, 0.5, 0.6, and 0.7). The simulations can be compared with the experimental pattern #24 (red), corresponding to a composition close to Li1.87VPO4O.

Figure 4 . 17 :

 417 Figure 4.17: (Top and middle) Refined cell parameters (Le Bail fit) for a single phase solid solution between compositions Li1.5VPO4O and Li2VPO4O. Error bars are within the symbols dimension. (Bottom) χ 2 parameters from the single-phase Le Bail fit of the XRPD scans from #14 to #27, compared to χ 2 for a sequence of two biphasic reactions. End members (in red) are Li1.5VPO4O, Li1.75VPO4O and Li2VPO4O.

  ) gives a useful indication since the "important" single-phase compositions (patterns #14, #21 and #27) show good fits while those intermediate between them correspond to significantly increased χ 2 values.

Figure 4 .

 4 Figure 4.18: Refined cell parameters (Le Bail fit) for a sequence of two biphasic reactions between the compositions Li1.5VPO4O and Li1.75VPO4O (left) and between Li1.75VPO4O and Li2VPO4O (right). Error bars are within the symbols dimension.

prepared Li 2

 2 VPO 4 O through chemical reduction of LiVPO 4 O and measured the resulting powder on a PANalytical Empyrean X-Ray diffractometer and subsequently on the high resolution powder neutron diffractometer D2B at ILL. The patterns were indexed in the triclinic P 1 space group and the cell parameters retrieved are: a = 7.1989(4) Å, b = 7.1012(3) Å, c = 7.7771(3) Å, α = 89.824(3) • , β = 89.812(3) • and γ = 116.319(3) • . The resulting volume of the unit cell is 356.36(3) Å3 . A transformation a' = b, b' = a, c' = -c, α' = 180-β, β' = 180-α and γ' = γ can be used to find a more standard triclinic setting, where the cell parameters are a' = 7.1012(3) Å, b' = 7.1989(4), c' = 7.7771(3) Å, α' = 90.188(3) • , β' = 90.176(3) • and γ' = 116.319(4) • . The first setting will be used in the following to allow a better comparison with the structure of LiVPO 4 O. The obtained parameters are

Figure 4 . 19 :

 419 Figure 4.19: Left: (Top) XRPD measurement and Rietveld refinement of Li2VPO4O powder in a 0.3 mm diameter capillary. (Bottom) NPD measurement and Rietveld refinement of Li2VPO4O placed in a 6.5 mm diameter vanadium container. Right: Crystal structure of Li2VPO4O. Lithium positions are indicated.

between 1 .

 1 98 Å and 2.04 Å and extreme values of 1.88 Å and 2.16 Å. In our structure, the refined values for Li 2 VPO 4 O give an average value of 2.03 Å for V(1)O 6 and of 2.02 Å for V(2)O 6 , with all the V-O bond lengths in good agreement with the expected values. Note how the bonds along the chains are significantly shorter than the in-plane bonds in the octahedra.

Figure 4 . 20 :

 420 Figure 4.20: Octahedral chains of VPO4O (top), LiVPO4O (middle) and Li2VPO4O (bottom), with V-O distances and V-O-V angles along the chains.

Figure 4 . 21 :

 421 Figure 4.21: In situ Synchrotron XRPD measurement and Rietveld refinement of compositions Li1.5VPO4O (top) and Li1.5VPO4O (bottom), isolated during electrochemical discharge of LiVPO4O. Most Bragg reflections originated by the experimental setup are easily excluded from the refinement, except for the binder PTFE that overlaps with important reflections of the phases of interest.

  with the indication obtained by BVS. In Li 1.75 VPO 4 O instead no conclusion can be drawn because both vanadium have long and short bonds and the octahedra are significantly more distorted (possibly because of inhomogeneous distribution of different octahedra). A few interesting remarks can be done on the evolution of the cell parameters during discharge: the biphasic reaction from LiVPO 4 O to Li 1.5 VPO 4 O is quite peculiar because, although the two phases have similar unit cell volume, their cell parameters are significantly different. Contrary to what is expected, the crystallizing phase Li 1.5 VPO 4 O has a shorter b axis length than LiVPO 4 O, hence shorter octahedral chains. c is also slightly shorter, while a is much longer in Li 1.5 VPO 4 O. As for the angles, while α is poorly modified, both β and γ are decreased in Li 1.5 VPO 4 O. The newly forming phase thus privileges increased a and α parameters, indicating bigger distances between neighbouring chains, driven by lithium's insertions into the structure's tunnels (only partially compensated by the shorter

  inter-chains distance along the c axis: ∆a = 0.26 Å, ∆c = -0.13 Å). The strong decrease of b (∆b = -0.23 Å) is instead surprising, as the opposite could be expected from vanadium's reduction. This is probably due to a change in the conformation of the chains, but a detailed analysis would require more precise knowledge of the V-O bond lengths and V-O-V angles along the chains. On the other hand, the reaction from Li 1.5 VPO 4 O to Li 1.75 VPO 4 O to Li 2 VPO 4 O follows a clear trend: b continuously increases and the same is true for a, while c remains almost constant. Regarding the three angles, they show small variations, except for γ which increases from 115.75 • to 116.3 • . Note that Li 1.5 VPO 4 O is the only phase with both α and β slightly bigger than 90 • , while they are slightly smaller in the other two phases. The insertion of 0.5 Li + into Li 1.5 VPO 4 O in this case causes the expectedgradual increase of the chains length, but also further increase of the tunnels size via an augmented a cell parameter; finally, the increase of γ probably relates to the variation of the chains conformation (i.e. the V-O-V angles which can also be modified). From this study we obtained a satisfactory but yet incomplete picture of these intermediate phases Li 1.5 VPO 4 O and Li 1.5 VPO 4 O. They revealed to be quite tricky, because of the difficulty at isolating them ex situ and because of the triclinic nature of their unit cells and the light elements present. In situ NPD would be a desirable choice for a complementary experiment; however we had already attempted this experiment on LiVPO 4 O, but without success mainly because of the difficulty to obtain a proper electrochemical behaviour from 200 mg-electrodes of LiVPO 4 O, but also because of the limited angular resolution of NPD measurements and the limited intensity obtained from operando experiments, both real

4

 4 F and LiVPO 4 O. Both materials show energy densities among the highest achievable in polyanionic compounds, and moreover they have the ability to (de)intercalate two Li + cations per formula unit, which potentially doubles the available capacity. We specifically concentrated on the understanding of the structural modifications occurring upon Li + exchange, since this could be the key to allow the exploitation of the full potential of such materials. Our studies made combined use of in situ & operando XRPD, supported by ex situ neutron powder diffraction measurements for the precise determination of oxygen's and lithium's behaviour inside the triclinic structures of these materials. In the case of LiVPO 4 F, we presented the reactions that bring the material to VPO 4 F, through the extraction of Li + around 4.2 V vs. Li + /Li: these are two biphasic processes, separated by the crystallization of the intermediate phase Li 0.67 VPO 4 F. At lower potential (1.8 V), LiVPO 4 F reacts to form Li 2 VPO 4 F following a single biphasic reaction. Most of the work we carried out concerned LiVPO 4 O, homeotypic to LiVPO 4 F. In its high-voltage domain (Li + extraction at 3.95V vs. Li + /Li) we demonstrated how particles size plays a crucial role during the electrochemical process: in fact, the big µm-size particles we obtain from the ceramic synthesis prevent reaching the theoretical capacity. We proved this by in situ XRPD; the study also indicated a Bragg peaks' broadening, showing how the material undergoes a form of "electrochemical grinding" upon prolonged cycling, which spontaneously improves the obtained capacity. The final member of such a reaction is -VPO 4 O, which we confirmed to belong to the Cc space group. In the lower voltage region, lithiation of LiVPO 4 O can be achieved through a complex series of phase transformations: a first biphasic reaction at 2.5 V leading to Li 1.5 VPO 4 O; a second one at 2.2 V until composition Li 1.75 VPO 4 O, and a final one at 2 V to reach the end member Li 2 VPO 4 O.

Figure 5 . 1 :

 51 Figure 5.1: Voltage profile upon galvanostatic cycling of a typical Li//Na3V2(PO4)2F3 cell between3 -4.6 V vs. Li + /Li. Reprinted from[START_REF] Barker | Hybrid-ion: A lithium-ion cell based on a sodium insertion material[END_REF] .

Figure 5 . 3 :

 53 Figure 5.3: Whole angular range obtained from synchrotron radiation diffraction measurement of Na3V2(PO4)2F3 in situ in our electrochemical cell. Extra Bragg reflections (from sodium and beryllium) are marked with an asterisk.

For reaction 5 Figure 5 . 4 :

 554 Figure 5.4: SQUID measurement of Na3V2(PO4)2F3 between 5 K and 300 K. Inset: SEM image of metalized sample.

5. 2 BianchiniFigure 5 . 5 :

 255 Figure 5.5: Crystal structure of Na3V2(PO4)2F3 in the tetragonal space group P42/mnm (ICSD 88808). Bi-octahedral V2O8F3 (green) and PO4 (yellow) building blocks are showed.

Figure 5 . 6 ,

 56 Figure 5.6, showing a rather good agreement. In the light of this model, we fixed the occupancy factors at values of 1 and 1/2 on the two crystallographic Na(1) and Na(2)

Bianchini et al., Figure 4 XFigure 5 . 6 :

 456 Figure 5.6: Rietveld refinement of Na3V2(PO4)2F3 in the tetragonal space group P42/mnm from XRPD on a laboratory diffractometer (left) and NPD (right) showing a good fit of the data.

5 P4Figure 5 . 7 :

 557 Figure 5.7: Comparison between X-Ray (blue) and synchrotron radiation (red) diffraction data of Na3V2(PO4)2F3. The high resolution of synchrotron data allows to resolve the orthorhombic splitting.

Bianchini et al., Figure 6 TetragonalFigure 5 . 8 :

 658 Figure 5.8: Le Bail fit of synchrotron radiation diffraction data in the P42/mnm space group (top) and in the low-symmetry orthorhombic group Pmmm (bottom).

Figure 5 . 9 :

 59 Figure 5.9: Electron diffraction data recorded with a) a room temperature specimen stage, showing the characteristic extinction corresponding to an A-centered Bravais lattice (weak reflections are indicated by the arrow) and b) with a specimen stage at 353 K. On this latter electron diffraction pattern, the systematic extinctions are consistent with an I-centered Bravais lattice.

Figure 5 . 10 :

 510 Figure 5.10: Combined Rietveld refinement of synchrotron radiation (top) and neutrons (bottom) diffraction data of Na3V2(PO4)2F3 in the Amam space group. Insets zoom on significant peaks in the structure.

Na

Figure 5 . 11 :

 511 Figure 5.11: Distribution of sodium ions in the z = 0 plane in the structure of Na3V2(PO4)2F3. Setting 1 (top) represents the result obtained in the refinement of Figure 5.10, setting 2 (middle) represents the alternative equivalent arrangement observed for sodium in the Amam space group. Bottom: compari-son with the sodium distribution present in literature.

Figure 5 . 12 :

 512 Figure 5.12: Differential scanning calorimetry of Na3V2(PO4)2F3 (two repeated measurements) upon heating from -100 • C to 300 • C at 10 • C/min.

Table 5 . 4 :

 54 Structural parameters obtained from Rietveld refinement of synchrotron radiation diffraction data of Na3V2(PO4)2F3 at T = 400 K. Na 3 V 2 (PO 4 ) 2 F 3 (T = 400 K) S.G. I4/mmm; Z=2 a = b = 6.39271(3) Å; R B = 6.16%; c = 10.75589(6) Å; Rwp = 14.8%; V = 877.544(6) Å3 ; V/Z = 219.386 Å3 . χ 2 = 2.58.

  which are corner-sharing with PO 4 tetrahedra to build the stable open structure. In our work we observe interatomic distances P-O = 1.530(4) Å for the PO 4 tetrahedra and V III -O = 1.985(4) Å, V III -F(1) = 1.981(3) Å and V III -F(2) = 1.97(1) Å for the VO 4 F 2 octahedral

Figure 5 . 14 :

 514 Figure 5.14: Top: Rietveld refinement of synchrotron radiation data for Na3V2(PO4)2F3 at 400 K (high temperature phase, I4/mmm space group). Arrows indicate some of the extinct reflections with respect to the room temperature phase. Bottom: view along the [001] direction of the obtained crystal structure, showing the disordered distribution of sodium ions. The unit cells of the high T and room T phases are highlighted (VroomT = 2 V highT ).

Figure 5 . 15 :

 515 Figure 5.15: Synchrotron radiation XRPD of Na3V2(PO4)2F3 at decreasing temperatures from 300K to 100 K.

235 K

 235 and with a unit cell two times bigger than the room temperature one (a' = b' ≈ a √ 2); however the authors needed a second high-T-like (Na disordered) phase to properly fit their data, leaving some doubts about their structural description. For this reason, and because inconsistent with our observation of b becoming 3 times longer, we did not consider their structural model for Na 3 V 2 (PO 4 ) 2 F 3 . 5.3 Phase diagram of Na 3 V 2 (PO 4 ) 2 F 3 upon Na + extraction: in situ synchrotron radiation XRPD Two outcomes of the previous section -a crystal structure different from the previously accepted one (recalled in Figure 5.16a-b) and fine details in the electrochemical data (Figure 5.2) -contrast quite strongly with the available literature on the extraction of sodium from Na 3 V 2 (PO 4 ) 2 F 3 . In fact the reaction mechanism upon Na + extraction to yield

Figure 2 :Figure 5 .

 25 Figure 2: a) Crystal structure of Na 3 V 2 (PO 4 ) 2 F 3 in the recently proposed Amam space group (ref. 25), showing V 2 O 8 F 3 bi-octahedra, PO 4 tetrahedra and the three different sites for sodium. The c axis is such that c = 2h+d where h is the height of an octahedron and d the height of sodium tunnels. b) top view displaying the a-b plane in the case of room temperature unit cell (solid line indicates the associated space group Amam, dotted line

5 ♦Figure 5 . 17 :

 5517 Figure 5.17: Potential-composition electrochemical curves obtained upon Na + extraction from Na3VPF. The first cell was cycled (GITT) between the compositions Na3VPF and Na2VPF while recording 58 5-minutes diffraction scans; the second one (galvanostatic cycling) between the compositions Na2VPF and NaVPF while recording 95 5-minutes scans. Significant single-phase compositions are highlighted by colored circles. For the 1 st cell they are obtained by the electrochemistry. Cycling of the 2 nd cell resulted in ∆x > 1 because of electrolyte oxidation, hence in this case reported compositions are those obtained from Rietveld refinement. Top line describes the nature of the observed deintercalation mechanism.

Figure 5 .

 5 Figure 5.18 shows the XRPD patterns recorded during GITT relaxation intervals, upon extraction of sodium from Na 3 VPF until the composition Na 2 VPF is reached at the end of the first voltage-composition domain. Note the very high quality of the diffracted data, in terms of both angular and intensity resolution, essential for identifying tricky phenomena occurring in this system. It immediately appears that no continuous shifts in diffracted peak positions occur during this first electrochemical region: those of the pristine phase Na 3 VPF lose intensity right away, while new ones start growing. Specific compositions and their corresponding XRPD patterns are highlighted with colored circles indicating

Figure 4 :Figure 5 .

 45 Figure 4: Different angular domains observed during the extraction of 1 Na + from Na 3 VPF (black curve). Several single-phase compositions are formed through biphasic domains, namely Na 2.4 VPF (blue) , Na 2.2 VPF (orange) and Na 2 VPF (red). a) 17°-17.7° (left) and 24.1°-24.9° (right) angular domains. Peaks are indexed for the Na 3 VPF phase. b) 2.7°-3.3° and 13.5°-14.9° angular domains (weak peaks related to sodium ordering).

Figure 5 :

 5 Figure 5: Detailed view of the initial stages of sodium deintercalation. Selected patterns from #1 (Na 3 VPF) to #38 (Na 2.4 VPF) are presented in the 11.9°-14.55° and 17°-17.7° angular domains. A complex behavior can be noticed in the structured shape of the peaks (200)-(020) and(220). Other peaks as(211) disappear (effect of sodium disordering), while some are almost unaffected(113).

Bianchini et al., fig. 5 Na 3 VPF  Na 2. 4 VPFFigure 5 . 19 :

 534519 Figure 5.19: Detailed view of the initial stages of sodium deintercalation. Selected patterns from #1 (Na3VPF) to #38 (Na2.4VPF) are presented in the 11.9 • -14.55 • and 17 • -17.7 • angular domains.

Figure 5 . 20 :

 520 Figure 5.20: Detailed view of the biphasic reaction between scans #38 (Na2.4VPF) and #47 (Na2.2VPF). At this composition only two peaks at 17.33 • and 17.54 • remain, characteristic of the I4/mmm space group.

Figure 7 :Figure 5 .

 75 Figure 7: a) Rietveld refinement of the intermediate phase Na 2.2 VPF. Missing reflections related to sodium ordering in Na 3 VPF (S.G: Amam) are indicated by arrows. b) Crystal structure of N 2.2 VPF, refined in the I4/mmm space group. Two sites Na1 I and Na2 I are present for sodium. Their occupancy is refined and related sodium amount is reported.

Figure S2 :Figure 5 . 22 :

 S2522 Figure S2: Fourier difference map obtained after Rietveld refinement of diffraction

Figure 8 :Figure 5 . 23 :

 8523 Figure 8: Comparison of composition Na 2 VPF obtained by ex situ chemical oxidation (black), in situ in the first electrochemical cell (blue, after diffraction measurements across the low-voltage-composition plateau) and in situ in the second electrochemical cell (red, before diffraction measurements across the high-voltage-composition plateau). The same Bragg reflections are observed. An * marks peaks not belonging to phase Na 2 VPF (originating from sodium metal in the in situ experiments; from an impurity left as residue of the chemical preparation in the ex situ sample).

Figure S3 :Figure 5 . 24 :

 S3524 Figure S3: Top: Rietveld refinement of the « average» structure of Na 2 VPF in the I4/mmm space group. Bottom: full pattern matching of the superstructure observed, taking into account all Bragg peaks.

ure 5 .

 5 23), by chemical oxidation of Na 3 VPF, yielding a powder with very similar unit-cell parameters and superstructure reflections. At present, and in the following of the paper, we treated Na 2 VPF in the "average" tetragonal unit cell, which gives meaningful results

Figure 5 .

 5 Figure 5.2, the Na + extraction from Na 3 VPF to Na 2 VPF seems to be composed of two

Figure S5 :

 S5 Figure S5: GITT charge of Na 3 V 2 (PO 4 ) 2 F 3.

Figure 5 . 26 :

 526 Figure 5.26: GITT of Na3V2(PO4)2F3. Charge at C/100 for 30 minutes, relaxation until dV/dt < 4mV/h. Electrode mass ≈20 mg.

Figure 9 :

 9 Figure 9: Different angular domains observed during the extraction of 1 Na + from Na 2 VPF (red curve). Na 2 VPF disappears through a biphasic reaction, then a solid solution is present between Na 1.8 VPF and Na 1.3 VPF (both in dark blue); finally Na 1 VPF (green curve) crystallizes through a biphasic reaction. a) 17.25°-17.75° (left) and 24.55°-25.15° (right) angular domains. Peaks are indexed for the Na 1 VPF phase. b) 6.4°-6.8°, 8.6°-9.0° and 12.9°-14.9° angular domains (weak peaks related to sodium ordering).

Figure 5 . 27 :

 527 Figure 5.27: Different angular domains observed during the extraction of 1 Na + from Na2VPF (red curve). Na2VPF disappears through a biphasic reaction, then a solid solution is present between Na1.8VPF and Na1.3VPF (both in dark blue); finally Na1VPF (green curve) crystallizes through a biphasic reaction. a) 17.25 • -17.75 • (left) and 24.55 • -25.15 • (right) angular domains. Peaks are indexed for the NaVPF phase. b) 6.4 • -6.8 • , 8.6 • -9.0 • and 12.9 • -14.9 • angular domains (weak peaks related to sodium ordering).

Figure 11 :Figure 5 .

 115 Figure 11: Parameters obtained from Rietveld refinement (S.G. I4/mmm) during the solid solution reaction occurring in Na x VPF (1.8  x  1.3). Top: vanadium's bond lengths obtained from refinement of fractional atomic coordinates. Middle: Bauer distortion calculated for VO 4 F 2 octahedra. Bottom: amount of sodium/formula unit obtained from the refined site occupancy factor in site Na1 I .

F3Figure 5 . 29 :

 529 Figure 5.29: Structure of NaVPF (full composition NaV2(PO4)2F3) in the Cmc21 space group.

Figure S6 :

 S6 Figure S6: Top: Rietveld refinement of the structure of NaVPF in the Cmc2 1 space group. (110), (112) and (021) peaks are evidenced because they are characteristics of this crystal structure only. Bottom: Fourier difference map obtained after Rietveld refinement of diffraction data, using a structural model not including any sodium.

  3 et +4 on average in plane z=0, but +7 on the Na1 C site Not a filled site (intensity +4) added in the model Intensity between -3 et +3 on average in plane z=0

Figure 5 . 30 :

 530 Figure 5.30: Top: Rietveld refinement of the structure of NaVPF in the Cmc21 space group.(110), (112) and (021) peaks are evidenced because they are characteristics of this crystal structure only. Bottom: Fourier difference map obtained after Rietveld refinement of diffraction data, using a structural model not including any sodium.

Figure 13 :Figure 5 . 31 :

 13531 Figure 13: sodium distribution obtained from Rietveld refinement of the different phases observed upon sodium extraction from Na 3 VPF . Although a superstructure was observed for phase Na 2 VPF, only the average structure was determined, thus the red/black circles indicate that only two positions out of four are expected to be occupied. For Na 1 VPF, an orange dotted circle shows the second sodium site Na1 A which is filled in the structure of Na 3 VPF (dashed cell), while it is now empty.

Na1C

  , partially corresponding to the Na1 A site of the pristine material. Its environment is a capped prism, composed of 4 oxygen and 3 fluorine atoms. Local charge compensation results in longer Na1 C -V1 4.7+ bond-length (3.48(3) Å) than Na1 C -V2 3.3+ (3.35(3) Å). A strong difference is noticed with respect to Na 3 VPF: in both cases the plane z = 0 hosts two Na1 sites, but looking at the two arrangements (Figure 5.31) we notice that for NaVPF one of the two Na1 positions is on the opposite side of the fluorine atom F1, with respect to the Na 3 VPF case. This partially explains the need for a different space group (together with the fact that two V environments are present in NaVPF). To highlight the main crystal structure modifications observed upon sodium extraction from Na 3 VPF, Figure 5.31 gives special emphasis to sodium rearrangement inside the unit cell. In the light of this, the biphasic transition between Na 1.3 VPF and NaVPF discussed above can be understood as follows: during the solid solution Na x VPF (1.8 < x < 1.3) the vanadium polyhedral distortion increases significantly. At composition Na 1.3 VPF, the sodium-and vanadium oxidation-disordered space group I4/mmm is not energetically favorable anymore, and vanadium undergoes disproportionation. The 4 ≈1/4-filled sites stop being equivalent and sodium ions converge on a single site in a bigger unit cell. This ordering happens on several small domains, underestimated by diffraction methods and separated by larger ones which remain disordered. Only when the ordered domains coalesce, diffraction is able to properly quantify them.

Figure 5 . 32 :Figure 5 . 33 :

 532533 Figure 5.32: Evolution of the XRPD diffraction patterns of Na3V2(PO4)2F3 as the Ag + /Na + ion exchange proceeds. The different position of the (111) and (002) peaks are highlighted on the right.

9.0843( 1 )

 1 Å and b = 9.0303(1) Å (b < a now and a/b = 1.006). This implies that while the b unit cell parameter slightly decreases, a strongly increases. The c axis lengthens as well, from c = 10.741(3) Å to c = 10.9942(1) Å. It is interesting to note that this is a direct confirmation of the Amam space group's exactitude for Na 3 VPF. The Ag/Na substitution respects the same symmetry constrains and this space group can be more clearly and undoubtedly confirmed in reason of the presence of Ag, which has two effects: it distorts more the (a,b) plane, making the Bragg peaks' splitting easier to observe; and it

8 <

 8 tially ordered one at ambient temperature. The precise origin of such residual disorder is a challenging problem, currently under investigation. High angular and intensity resolution synchrotron radiation XRPD was then used to study the structural evolution of Na 3 VPF upon Na + extraction in details. The sodium deintercalation reaction, generally reported to be a simple solid solution, reveals instead an extremely complicated phase transformations sequence. The two voltage domains around 3.7 V and 4.2 V vs. Na + /Na have been analyzed separately. The lower voltage region never proceeds through a solid solution. Instead it reveals three biphasic reactions involving two intermediate phases, Na 2.4 VPF and Na 2.2 VPF. The latter displays the same structure as the high-temperature form of Na 3 VPF, crystallizing in the tetragonal space group I4/mmm due to Na + disordering. The former stabilizes instead an ordering on a longer range, up to a ≈18 Å d-spacing, suggesting a superstructural arrangement. At the end of the first voltage-composition plateau, the phase Na 2 VPF is obtained, revealing another possible superstructure due to sodium ordering and/or charge ordering. The higher voltage region shows a biphasic reaction upon which Na 2 VPF disappears and subsequently a wide solid solution of compositions Na x VPF (1.x < 1.3), again sodium-disordered. Thanks to the high quality of these synchrotron data we could follow the reaction in detail and observe the structural modifications (e.g. cell parameters, bond lengths, polyhedral distortion...) and sodium extraction (namely sodium's site occupancy factor) in real time. The end-member NaVPF is finally attained through another biphasic reaction. The structure of this composition is different than those previously encountered and a structural determination was carried out for the first time directly on data collected operando. It revealed a Cmc2 1 space group, leading to a fully occupied sodium site and most importantly and unexpectedly to two different vanadium environments (a V 3+ -V 5+ couple in every bi-octahedron). The extremely small volume change observed from Na 3 VPF to NaVPF, along the overall charge, further qualifies Na 3 VPF as a material of choice for long term cycling stability. These in situ measurements demonstrate how obtaining good angular resolution and high intensity data is crucial because, delivering more detailed information, it can radically change the understanding of a given electrode's

  riety of electrode materials for alkali intercalation-based battery technologies, i.e. Li-ion and Na-ion. Strong motivation for conducting such studies is the belief that the improvement of batteries performances is directly related to a deep understanding of their functioning. In this respect, operando studies are the best choice to observe Li + or Na + (de)intercalation reactions in real time and to obtain detailed information about such processes. Given the crystalline nature of most electrode materials, the characterization technique of choice for determining their structure and structural modifications upon cycling is diffraction. Electrode materials contain heavy transition metals and light cations (Li, Na) and anions (O, F...), thus rarely a single probe is able to observe all of them: combined studies are required. During our diffraction experiments we then tried to exploit several different probes and to take advantage of their combined use to obtain a maximum of details: neutrons, in particular, are sensitive to lithium and oxygen, key elements in battery electrodes, while X-Rays give precise information on transition metals and cell parameters. Synchrotron radiation was also used, as it offers unrivaled angular and time resolution, crucial for operando experiments.

  trolytes. Chapter 2 specifically describes the issues/drawbacks of in situ NPD diffraction and the electrochemical cells developed in the literature and by us to achieve such a goal. All the separate contributions and possible scattering events were considered and discussed and our first successful operando study on LiFePO 4 was described. We demonstrated how we could obtain detailed structural information even during an operando experiment (the charge, or delithiation to composition FePO 4 ) and subsequently use this awareness to carry out new studies on challenging materials belonging to the spinel crystal family. In Chapter 3 we studied in detail the (de)lithiation of materials of strong relevance for applications: three samples in the family Li 1+x Mn 2-x O 4 (x = 0, x = 0.05 and x = 0.10) and a highvoltage spinel LiNi 0.4 Mn 1.6 O 4 . Our experiments and analysis revealed several insights on the phase diagram and (de)lithiation processes of these materials when they are cycled in a battery. Importantly, we confirmed that operando NPD allows us to be sensitive not only to cell parameters, phase fractions and fractional atomic coordinates, but also to more elusive (but carrying much information) parameters as atomic displacement parameters and lithium's site occupancy factors. Therefore we could observe and explain new features of the electrochemical reactions, as for example the voltage-dependent rate of delithiation in Li 1.10 Mn 1.90 O 4 or the distortion occurring on isolated Ni 3+ cations upon charge of LiNi 0.4 Mn 1.6 O 4 . Our results confirmed the feasibility and the richness of information

  ies requiring extremely high angular and intensity resolution. Here, synchrotron XRPD was mainly employed for experiments concerning Na 3 V 2 (PO 4 ) 2 F 3 , a greatly promising material for next-generation Na-ion batteries. The compound was revisited, since it was indexed in a new orthorhombic space group and a new crystal structure was determined, with corrected positions of Na + in the unit cell. Moreover, operando synchrotron XRPD showed an incredibly rich phase diagram upon sodium extraction, resulting from different possible sodium and/or vanadium orderings. Such ordering/disordering phenomena, occurring at different compositions and temperatures in Na x V 2 (PO 4 ) 2 F 3 and detailed in Chapter 5, are the reason for the several phase transitions that the material exhibits, inducing space group modifications and even the creation of superstructures. Synchrotron radiation XRPD also helped complementing other studies spread through this thesis; one in particular deserves to be mentioned, namely the first-time observation of the intermediate phase Li 0.5 Mn 2 O 4

  Résumé développé de la thèse en français Introduction Les batteries Lithium-ion (Li-ion) sont au coeur des dispositifs qui ont permis la "révolution sans fils". Disponibles sur le marché depuis les années '90, elles ont apporté les Smartphones dans nos poches et les ordinateurs portables dans nos sacsà-dos grâce à une importante amélioration des leurs performances. Déjà en 2002 les téléphones portables, et avec eux la technologie Li-ion, étaient partout. Leurs densités d'énergie et de puissance sans précédentes (environ deux fois plus que NiCd et 30% de plus que NiMH) ont permis aux dispositifs électroniques d'être transportés partout sans avoir besoin de piles de rechange. En outre, leurs durées de vie (> 1000 cycles) leur permettent de durer des années et de dominer le marché des batteries avec des millions de cellules vendues chaque année. Cependant beaucoup de travail doit encore être fait pour rendre cette technologie compétitive pour d'autres applications, telles que les véhicules électriques et le stockage d'énergie de masse pour le réseau électrique. Les premiers, considérés depuis une vingtaine d'années, ont connu un lent développement pour des raisons économiques et technologiques, mais aujourd'hui tous les constructeurs automobiles ont rejoint la course pour des voitures électriques meilleures et plus performantes: ils proposent aujourd'hui tous au moins un de ces véhicules (hybrides, plug-in hybrides ou entièrement électriques). Le stockage de l'énergie est un enjeu majeur car il faciliterait significativement l'adoption de sources d'énergie renouvelable (solaire, éolienne...) et donc la diminution des émissions de CO 2 et du réchauffement climatique. En 2012, seulement 5% i de l'énergie produite dans le monde est issue de ces sources, la plus grande limitation étant leur nature instable, ce qui signifie qu'elles sont très dépendantes des conditions atmosphériques et du moment de la journée. Pour cette raison, elles ont besoin de systèmes de stockage fiables et capables d'accumuler de l'énergie pendant les heures de production et de la libérer lorsque nécessaire (la nuit par exemple). Etant le système électrochimique le plus avancé disponible sur le marché, la batterie Li-ion est considérée comme la solution idéale pour fournir ces capacités de stockage. D'autres systèmes de batteries de nouvelle génération sont également développés, comme le Na-ion (sodium-ion), une technologie analogue au Li-ion, mais fondée sur un élément chimique moins cher et plus abondant. Le coeur des batteries Li-ion et Na-ion est constitué par les électrodes, les matériaux aptes à échanger les cations Li + (ou Na + ). En parallèle, ces composés contiennent des métaux de transition qui subissent des réactions d'oxydoréduction afin de fournir les électrons au circuit extérieur. Le développement des batteries passe par la découverte de nouveaux matériaux d'électrodes, ainsi que par une meilleure compréhension des existantes. Ce dernier point en particulier est d'une importance majeure afin de permettre la pleine exploitation de la capacité d'un matériau d'électrode, cet-à-dire l'obtention de la pleine densité d'énergie théorique, à un régime de cyclage suffisamment rapide et avec une durée de vie de milliers des cycles. Une véritable compréhension des matériaux d'électrode nécessite une combinaison de différentes techniques de caractérisations. Afin de comprendre comment ils fonctionnent à l'intérieur d'une batterie, il est important de développer des techniques d'étude in situ, ou, pour aller plus loin, operando, le matériau pouvant être étudié lorsqu'il fonctionne vraiment à l'intérieur de la batterie. Charge et décharge sont en fait des processus qui peuvent induire des transformations profondes dans les électrodes, étant donné que les ions Li + (ou Na + ) sont extraits et insérés (ou, plus correctement, désintercalés et intercalés) et des métaux de transition sont oxydés et réduits. Ces réactions induisent toujours des changements de volume dans le matériau d'électrode, souvent accompagnés d'une ou plusieurs transitions de phase. De telles transformations se produisent souvent hors de l'équilibre, dans des conditions dynamiques, ce qui est la raison de la nécessité d'études menées operando. La diffraction des rayons X, en particulier, a été la technique de choix, à l'aide de diffractomètres de laboratoire et des ii plus puissants rayonnements synchrotrons. De nombreuses études ont été publiées. Objectifs de cette thèse Dans ce travail, nous avons développé plusieurs techniques de diffraction pour comprendre les transformations cristallographiques qui se produisent dans des matériaux d'électrode lorsqu'ils sont lithiés et delithiés à l'intérieur des batteries Li-ion et Na-ion. Pour obtenir un maximum d'informations complémentaires nous avons utilisé plusieurs "sondes", sensibles à différents éléments chimiques dans les matériaux. De manière plus détaillée, nous avons beaucoup utilisé les neutrons qui possèdent des caractéristiques de diffusion particulières; ils interagissent faiblement avec la matière, surtout via les noyaux. Leur diffusion dépend de l'isotope spécifique et ce ne croît pas linéairement avec la masse atomique, à la différence des rayons X. Ceci entraîne plusieurs avantages, les plus importants pour l'application des neutrons aux études des batteries étant que:• ils sont sensibles aux éléments légers comme le lithium et l'oxygène,• ils peuvent générer des contrastes significatifs entre différents métaux de transitions de numéros atomiques voisins,• ils peuvent pénétrer en profondeur dans la matière, ce qui permet d'étudier une électrode entière,• ils conduisent à des intensités diffractées importantes à des valeurs élevées de Q (le vecteur de diffusion), conduisant à des informations importantes au sujet des paramètres de structure atomique comme les occupations des sites cristallographiques et les facteurs de Debye-Waller (agitation thermique). Nous avons aussi beaucoup utilisé les rayons X, plus facilement accessibles tout en donnant beaucoup d'informations précieuses et complémentaires aux neutrons, par exemple sur les métaux de transition et les paramètres de maille. Le rayonnement synchrotron (à SOLEIL-Saclay et ALBA-Barcelone) a été abondamment utilisé dans ce travail, lors d'études nécessitant de hautes résolutions angulaire, temporelle, et en intensité. L'utilisation simultanée de ces différentes sondes s'est avérée être particulièrement adaptée à nos objectifs. Nous avons pu observer de nouvelles fonctionnalités révélées pendant le cyclage électrochimique de plusieurs iii matériaux d'électrodes d'importance pour les batteries Li-ion et Na-ion. Les familles des matériaux analysés dans ce travail sont variées : • les spinelles (Li 1+x Mn 2-x O 4 (x = 0, 0.05, 0.10) et LiNi 0.4 Mn 1.6 O 4 ), • les olivines (LiFePO 4 ), • les tavorites (LiVPO 4 O), • les fluorophosphates pour accumulateur Na-ion (Na 3 V 2 (PO 4 ) 2 F 3 ). Au cours de nos études, pour chacune des "sondes" mentionnées ci-dessus, nous avons réussi à mener des expériences ex situ, in situ et operando. Pour cela, en complément des cellules électrochimiques pour des études in situ en utilisant les rayons X et le rayonnement synchrotron qui étaient disponibles dans nos groupes, une nouvelle cellule pour la diffraction de neutrons a été développée. La diffraction des neutrons sur poudre (NPD) est sûrement la plus compliquée et la moins mature de telles techniques in situ appliquées aux batteries du fait des contributions à la diffraction des différents composants de la batterie. Certains d'entre eux génèrent des pics de diffraction indésirables (collecteurs de courant métalliques, boite de protection ...), certains un bruit de fond élevé (le carbone, les solvants et le sel dans l'électrolyte ...) et certains (le lithium notamment) absorbent les neutrons et réduisent le rapport global signal sur bruit. Développement et validation d'une cellule pour la diffraction de neutrons operando La première étape (et l'objectif principal) de ce travail de thèse était donc de développer un environnement d'échantillon qui puisse convenir à la fois pour l'électrochimie et pour la diffraction des neutrons. La cellule que nous avons développée a dû répondre à des exigences spécifiques:

v

  en utilisant notre cellule, dans laquelle on a préparé une batterie avec LiFePO 4 à l'électrode positive, on a mesuré sur D20 des diagrammes de NPD toute au long de la charge du matériau. Des informations structurales très fiables ont pu être extraites grâce à l'analyse Rietveld des données. On a donc pu observer et quantifier, durant la charge de ce matériau (extraction de Li + ) la formation progressive en FePO 4 selon une réaction bi-phasique; l'évolution structurale des deux phases concernées a pu être étudie en temps réel grâce aux neutrons. La valeur ajoutée réelle de ces expériences est la possibilité de réaliser des affinements structuraux fiables et reproductibles (par la méthode de Rietveld) des paramètres de mailles élémentaires jusqu'aux coordonnées atomiques et même aux facteurs d'occupation de site et aux facteurs d'agitation thermique (facteurs de Debye-Waller). Cette cellule sera désormais disponible à l'ILL pour de futurs utilisateurs potentiels.Mécanismes d'extraction du lithium depuis Li1+x Mn 2-x O 4 Nous avons mené une première étude concernant l'extraction du lithium pendant la charge des matériaux spinelles de composition Li 1+x Mn 2-x O 4 , avec x = 0, 0.05, 0.10. LiMn 2 O 4 est l'un des matériaux les plus étudiés pour les batteries Li-ion, et ce depuis de nombreuses années, pour ses propriétés d'extraction de lithium autour de 4.1 V vs. Li + /Li, montrant une bonne capacité et la possibilité du cyclage à haute régime. Cependant, il a été montré que ces matériaux souffrent de problèmes de rétention de la capacité, causée principalement par la présence d'une quantité importante d'ions Mn 3+ au sein de l'électrode. Une légère augmentation de l'état d'oxydation du manganèse d'origine (+3.5) vers la valeur +4 permet de résoudre en partie ces difficultés, au détriment de la valeur de la capacité théorique. Plusieurs solutions ont été proposées pour résoudre ce problème en réduisant la quantité de Mn 3+ , parmi lesquelles l'utilisation de spinelles stoechiométriques Li 1+x Mn 2-x O 4 (0 < x < 0.33). Nous avons étudié cette famille de compositions en utilisant la diffraction de neutrons operando. L'étude a montré que non seulement le changement de volume induit par la délithiation est réduit en allant de LiMn 2 O 4 à Li1.10 Mn 1.90 O 4 , mais plus important encore que le mécanisme par lequel cela se produit est modifié. En fait, alors que Li 1.10 Mn 1.90 O 4 réagit selon une réaction "simple" monophasique (une solution solide), Li 1.05 Mn 1.95 O 4 montre l'existence d'un processus de solution solide suivi d'une réaction bi-phasique. LiMn 2 O 4 montre même une séquence de deux réactions vi bi-phasiques. Les caractéristiques mentionnées ci-dessus contribuent à faire du composé sur-lithié Li 1.10 Mn 1.90 O 4 un bien meilleur candidat pour une utilisation dans les batteries Li-ion que le LiMn 2 O 4 stoechiométrique standard. Plus précisément, les neutrons nous ont permis d'avoir accès à des paramètres structuraux très pertinents tels que les coordonnées atomiques et même les facteurs d'occupation du site (SOFs) des sites lithium, et donc de les inclure dans notre analyse par la méthode de Rietveld pour augmenter la précision de notre modèle structural, qui se modifie au cours du cyclage. Dans le cas spécifique des spinelles Li 1+x Mn 2-x O 4 , cela signifiait la possibilité de corréler, pour la première fois, l'évolution de l'occupation du site lithium avec les caractéristiques électrochimiques des matériaux, ce qui est d'une importance clé pour la compréhension et donc l'amélioration des matériaux pour batteries Li-ion. Le rayonnement synchrotron a également été utilisé en complément pour répondre à certaines questions laissées sans réponse par la diffraction de neutrons. En particulier, nous avons été en mesure de lever le doute sur la nature de la phase intermédiaire Li 0.5 Mn 2 O 4 , trouvée à mi-chemin lors de la charge et la décharge de LiMn 2 O 4 . Ce matériau a été étudié pendant 30 ans et l'existence de deux régions électrochimiques séparées (en potentiel) durant la charge est bien connue. La cause d'une telle séparation était jusqu'alors attribuée à la possible existence d'une phase intermédiaire ordonnée, sans aucune preuve expérimentale. Nous avons pu montrer que cela est dû à un ordre de charge coopératif sur les sous-réseaux Mn n+et lithium/lacune, au sein de la composition globale Li 0.5 Mn 3+ 0.5 Mn 4+ 1.5 O 4 . La symétrie est réduite par rapport à la symétrie d'origine Fd 3m, la structure devant être décrite:1. tout d'abord à l'aide du groupe d'espace P4 3 32 (résultat de l'ordre de charges à cette composition particulière, avec un rapport 1:3 de différents cations Mn 3+ et Mn 4+ ) 2. enfin à l'aide du groupe d'espace P2 1 3 (résultat de l'ordre lithium/lacune).Nous avons ainsi pu démontrer l'aide précieuse de l'operando XRPD mené avec la haute résolution du rayonnement synchrotron pour l'étude des matériaux de batterie. Nos expériences ont également permis de caractériser finement l'irréversibilité du cyclage électrochimique de LiMn 2 O 4 , dès le premier cycle.Le diagramme de phase est trouvé asymétrique entre la charge et la décharge.De plus, on observe nettement un élargissement significatif des "queues" des pics vii de réflexionsde Bragg, les rendant plus Lorentziennes en raison des diminutions des tailles des domaines cohérents. Mécanismes d'extraction du lithium depuis LiNi 0.4 Mn 1.6 O 4 Un deuxième exemple d'informations pertinentes qui peuvent être récupérées grâce à l'utilisation de la diffraction de neutrons operando au sein d'une batterie en fonctionnement concerne l'étude de l'extraction de lithium depuis le spinelle à haut potentiel LiNi 0.4 Mn 1.6 O 4 . La substitution de Mn par Ni mène à l'extraction de lithium à 4.7 V vs. Li + /Li, un potentiel élevé qui en fait un matériau d'électrode positive prometteur. Notre étude in situ a révélé des phénomènes importants et originaux, tels que les variations non monotones des facteurs d'occupation du site Li et des paramètres de facteurs de Debye-Waller, donnant des informations sur le comportement des atomes dans la matière à différentes échelles de longueur. Plus précisément, pendant la charge, le Manganèse est oxydé de 3+ à 4+ et ensuite le Nickel est oxydé de 2+ à 4+. Lors de ces transformations, les liaisons métal-oxygène se raccourcissent, tandis que le volume de la maille élémentaire diminue. Un comportement intéressant a été constaté lors de l'apparition du cation Ni 3+ , qui est Jahn-Teller déformé et dont la présence a pu être observée indirectement via une augmentation du facteur de Debye-Waller des atomes d'oxygène l'entourant. Insertion ou extraction de lithium dans/depuis les Tavorites LiVPO 4 X (X = O, F) Les composés à charpente polyanionique (phosphates, silicates, sulphates, ...) constituent des électrodes positives de grand intérêt, grâce en particulier à leur versatilité pour l'utilisation de plusieurs couples redox de métaux de transition et plusieurs groupes polyanioniques. Les matériaux de structure Tavorite (dont la formule chimique générale est AMXO 4 Y avec A comme ion alcalin, M un métal de transition ou métal alcalino-terreux, X comme le phosphore ou le soufre et Y comme un halogénure, un hydroxyde, un oxygène, ou un halogénure/hydroxyde mixte) sont largement étudiées dans la littérature. Ils peuvent conduire à une grande variété de potentiels redox vs Li + /Li lorsqu'ils sont utilisés comme électrodes. Le vanadium, en particulier, est le seul métal de transition capable d'exploiter 3 couples redox, de V 2+ à V 5+ , ce qui le rend extrêmement polyvalent. Il est alors facile de comprendre la raiviii son de la grande attention accordée aux matériaux Tavorite dans la communauté des batteries, et aux phosphates de vanadium en particulier dans notre groupe. En fait, les compositions LiVPO 4 O et LiVPO 4 F y sont étudiées depuis 2011: elles possèdent parmi les plus hautes densités d'énergie gravimétrique. Dans ce travail, nous avons concentré notre intérêt sur la composition LiVPO 4 O, de structure connue, construite par des chaines d'octaèdres de vanadium VO 6 , lies entre elles par de tétraèdres PO 4 . Cet arrangement génère des canaux dans lesquels les cations Li + peuvent se déplacer. Cet oxyphosphate montre la capacité d'exploiter deux couples redox, V 5+ / V 4+ à 3.95 V vs. Li + /Li et V 4+ / V 3+ à un potentiel moyen de 2.3 V vs. Li + /Li lors de l'extraction et de l'insertion des ions Li + , respectivement. Les deux domaines présentent des différences marquées à la fois dans la signature électrochimique et dans le diagramme de phase. Dans le domaine des hauts potentiels, LiVPO 4 O exploite le couple redox V 5+ / V 4+ et se transforme par l'extraction du lithium en -VPO 4 O. Cette réaction n'est pas complète après le 1er cycle, car seule la composition "Li 0.5 VPO 4 O" peut être atteinte, mais la capacité s'améliore de manière significative durant le cyclage et elle peut atteindre sa valeur théorique après 30 cycles (un effet de broyage électrochimique est observé par l'élargissement des pics de diffraction). Les rayons X in situ confirment que "Li 0.5 VPO 4 O" n'est pas une phase stable et que la désintercalation du lithium est limitée par les faibles propriétés de transport au sein de grosses particules de LiVPO 4 O. La structure cristalline de la forme délithiée -VPO 4 O a été déterminée à l'aide de calculs DFT et affinements Rietveld, confirmant qu'elle appartient au groupe d'espace Cc. Dans le domaine des bas potentiels, le lithium est inséré dans LiVPO 4 O par réduction du vanadium en V 3+ . Ici aussi, la pleine capacité n'est atteinte que lorsque le matériau est broyé (ball-milling) de manière significative afin de réduire la taille des particules. La série complexe de transformations de phases présentes dans le diagramme de phase de LiVPO 4 O a été étudiée grâce à la technique in situ XRPD. Deux phases intermédiaires, Li 1.5 VPO 4 O et Li 1.75 VPO 4 O, ont été clairement identifiées. La première étape de réaction entre LiVPO 4 O à Li 1.5 VPO 4 O est une réaction bi-phasique parfaite, avec un petit changement de volume. La formation de Li 1.75 VPO 4 O et Li 2 VPO 4 O, au contraire, se passe par une séquence de réactions à deux phases qui sont particulières car la variation de volume entre les éléments extrêmes est importante et ca ix entraine que du stress est induit pendant la réaction d'intercalation / désintercalation. Cela signifie qu'il est nécessaire de permettre un léger changement de la valeur des paramètres de maille pendant les réactions bi-phasiques pour compenser de telles contraintes. Enfin, la composition "extrême" Li 2 VPO 4 O a été isolée et sa structure déterminée pour la première fois grâce à XRPD et NPD ex situ . L'étude par rayonnement synchrotron in situ a aussi partiellement révélé les structures des compositions Li 1.5 VPO 4 O et Li 1.75 VPO 4 O (sauf pour les positions de lithium). Grâce à ces déterminations structurales, les changements précis dans l'environnement de vanadium et des liaisons chimiques peuvent être suivis lorsque le vanadium est réduit de -V V PO 4 O -LiV IV PO 4 O -Li 2 V III PO 4 O: les liaisons V-O changent de liaisons du type vanadyle alternées longues-courtes pour devenir enfin régulières, tandis que la conformation des chaînes octaédriques est également modifiée fortement. Cela prouve que l'état d'oxydation du vanadium est vraiment le moteur qui dirige la modification structurale des chaines des octaèdres. Un matériau prometteur pour les batteries au sodium: Na 3 V 2 (PO 4 ) 2 F 3 La structure cristalline de ce composé a été re-déterminée avec précision ainsi que le diagramme de phases obtenues lors de l'extraction réversible de sodium. En fait, bien que la technologie Li-ion est désormais la technologie de choix pour les applications électroniques portables et même vers le monde de l'automobile, des préoccupations ont été soulevées récemment à propos de la future disponibilité et du prix des ressources de lithium. De nombreuses alternatives sont explorées et une grande quantité de recherches sont actuellement consacrées à la technologie Na-ion, du fait que le sodium n'est pas cher, est abondant et que la connaissance acquise sur la chimie des matériaux pour l'intercalation du lithium peut rendre le développement de matériaux pour batteries Na-ion plus rapide. Nous avons choisi de concentrer nos efforts sur le composé polyanionique à base de vanadium Na 3 V 2 (PO 4 ) 2 F 3 . Un tel matériau présente une capacité théorique très intéressante de 192.4 mAh/g pour l'extraction de 3 Na + , bien que l'extraction de seulement deux d'entre eux ait pu être démontrée jusqu'à présent expérimentalement, lorsque le matériau est cyclé vs. Na. Le matériau est également intéressant du point de vue de la structure cristalline, puisque toute la famille de compositions Na 3 V 2 O 2x (PO 4 ) 2F 3-2x (0 ≤ x ≤ 1, avec l'état d'oxydation du vanadium allant de 3+ à 4+), montre un très riche ensemble x de transformations de phases en fonction de la température et de la composition, cet-à-dire un diagramme de phase très riche. Dans le cas de Na 3 V 2 (PO 4 ) 2 F 3 (x = 0), la structure cristalline a été étudié en 1999 par Le Meins et al., qui lui ont attribué le groupe d'espace quadratique P4 2 /mnm, utilisé jusqu'à présent, bien que des divergences importantes dans les paramètres de maille rapportés soient trouvés dans la littérature. Nous avons constaté une petite distorsion orthorhombique dans Na 3 V 2 (PO 4 ) 2 F 3 (a = 9.028 Å, b = 9.044 Å) qui ne pouvait être observée que grâce à la très haute résolution angulaire disponible dans une expérience de diffraction avec le rayonnement synchrotron. Cela a abouti à une nouvelle détermination structurale complète dans le groupe spatial Amam, conduisant à une distribution différente des ions sodium, ce qui constitue la propriété la plus importante pour un matériau d'électrode. Nous avons également démontré l'existence de transitions de phase à différentes températures: une transition orthorhombique -quadratique lors d'un chauffage à 400 K, causée par le désordre des ions sodium à cette température, ce qui augmente la symétrie du matériau. Au-dessous de 200 K, par contre, le matériau présente des réflexions supplémentaires typiques d'une maille 3 fois plus grande dans la direction de l'axe b, qui est un exemple de formation d'une surstructure due à une mise en ordre ordre des ions sodium, bien que l'origine exacte de cette ordre n'ait pas encore été trouvée. En ce qui concerne le mécanisme d'extraction de sodium depuis Na 3 V 2 (PO 4 ) 2 F 3 , il a toujours été rapporté comme opérant via une simple solution solide de symétrie quadratique P4 2 /mnm, avec contraction de la maille élémentaire. Cependant, différents faits suggèrent le contraire: d'une part, la constatation d'un groupe d'espace différent pour Na 3 V 2 (PO 4 ) 2 F 3 mentionné ci-dessus; d'autre part, un travail récent où le diagramme de phase calculé/prédit être plus compliqué que celui d'une simple solution solide: enfin, des expériences in situ ont été réalisées par d'autres groupes sur les matériaux de la famille Na 3 V 2 O 2x (PO 4 ) 2 F 3-2x (x = 0.8, 1), montrant un comportement complexe. Ceci n'est d'ailleurs pas trop surprenant pour ce composé d'intercalation du sodium, où on observe généralement une forte tendance à la stabilisation de phases intermédiaires. Nous avons décidé de ré-étudier le diagramme de phase de Na 3 V 2 (PO 4 ) 2 F 3 , en utilisant la technique XRPD avec le rayonnement synchrotron in situ (operando) lors de l'extraction Na + . Nous avons observé pour la première fois une séquence extrêmement compliquée de réactions bixi phasiques et monophasiques entre Na 3 V 2 (PO 4 ) 2 F 3 et NaV 2 (PO 4 ) 2 F 3 , avec plusieurs phases intermédiaires formées lors de la charge. Le sodium s'ordonne à travers de sites cristallographiques différents, ce qui induit des changements de symétrie du groupe d'espace et de la structure cristalline.

  Ce travail de thèse a tenté d'adopter une approche globale à l'utilisation de techniques de diffraction, ex situ, in situ et operando, pour dévoiler les modifications de xii structures cristallines qui se produisent dans les matériaux d'électrodes pour les batteries Li-ion et Na-ion pendant leur fonctionnement en cyclage électrochimique. Les connaissances obtenues révèlent les interconnexions entre les structures cristallines et les performances électrochimiques dans les matériaux d'électrodes, ceci ayant une importance clé pour mieux les comprendre et envisager des améliorations notables des prochaines générations de batteries. xiii Résumé de la Thèse en Français Ce travail vise à étudier les matériaux d'électrodes pour batteries Li-ion et Na-ion lors qu'ils fonctionnent à l'intérieur des batteries. Afin de comprendre l'évolution structurelle des matériaux alors que les ions Li + ou Na + sont insérés/extraits de leur cadre, on utilise principalement la diffraction, exploitant neutrons, rayons X et le rayonnement synchrotron (SR). Nous avons adopté une approche combinée des mesures ex situ, in situ et operando. Au début, nous avons conçu une cellule électrochimique pour mesures de diffraction de neutrons sur poudre (NPD) in situ, avec un alliage en (Ti,Zr) "transparent aux neutrons"; cette cellule s'est ajoutée à l'ensemble de nos outils pour effectuer des études de type operando. Nous avons démontré leur faisabilité en utilisant LiFePO 4 , montrant des bonnes performances électrochimiques et des données NPD de haute qualité pour affinements structurales Rietveld. Ensuite, nous avons réalisé des études des spinelles Li 1+x Mn 2-x O 4 (x = 0, 0.05, 0.10) et LiNi 0.4 Mn 1.6 O 4 : pendant le cyclage, nous avons rapporté des évolutions structurelles, des diagrammes de phases et des paramètres subtils tels que le comportement du Li, ou les facteurs de température. L'utilisation complémentaire du SR a clarifié la nature de la phase ordonnée Li 0.5 Mn 2 O 4 . Nos études combinées ont concernées d'autres matériaux d'électrodes prometteurs: LiVPO 4 O et Na 3 V 2 (PO 4 ) 2 F 3 . Les deux révèlent des comportements complexes pendant la (de)intercalation du Li + /Na + . Les données de haute qualité ont permis des analyses quantitatives, dévoilant la structure d'un grand nombre des phases ordonnées et menant à la compréhension du comportement des cations dans ces matériaux.

NPD using LiFePO 4 ,

 4 showing good electrochemical performances and high-quality NPD patterns for Rietveld structural refinements. Then we carried out detailed studies of spinels Li 1+x Mn 2-x O 4 (x = 0, 0.05, 0.10) and LiNi 0.4 Mn 1.6 O 4 : we reported phase diagrams, structural evolutions and subtle parameters as lithium's behavior inside the spinel framework, or thermal displacement parameters, directly upon cycling. Complementary use of SR shed light on other features, as the nature of the ordered phase Li 0.5 Mn 2 O 4 . Our combined studies concerned other promising electrode materials: LiVPO 4 O and Na 3 V 2 (PO 4 ) 2 F 3 . Both revealed complex behaviors upon Li + /Na + (de)intercalation. High quality data allowed quantitative analyses, unveiling the nature and detailed structure of many ordered phases encountered upon cycling and leading to deeper understanding of Li + /Na + behavior in these material.

Table 1 . 1 :

 11 Comparison of lithium and sodium properties relevant to the battery technology.

		Cation	Atomic Weight V vs. Cost ($/ton)	Capacity
		Radius ( Å)	(g/mol)	SHE (carbonates) (mAh/g) (metal)	Preferred coordination
	Lithium	0.70	6.9	-3.04	5000	3829	Octahedral & Tetrahedral
	Sodium	1.20	23.7	-2.71	150	1165	Octahedral & Prismatic

  Table2.1 summarizes the scattering properties of lithium. In all the experiments of this work, natural lithium was used, i.e. 6.[START_REF] Morcrette | In situ x-ray diffraction techniques as a powerful tool to study battery electrode materials[END_REF] Li composed of 92.5% 7 Li and only 7.5%6 Li.7 Li being the most abundant isotope is certainly an advantage because it is the one having negative scattering length and a relatively small absorption cross section. Isotopic enrichment (the use of a specific isotope instead of the naturally-occurring composition) is sometimes performed in neutron scattering facilities because it can lead to additional experimental information by controlling the element's absorption. In our case this possibility was ruled out because of the different lithium

contributions present in a battery (in the positive electrode, in lithium metal and in the lithium salt in the electrolyte) that would have made a proper enrichment very complicated and expensive.

Table 2 .

 2

1: Neutron scattering properties of

1 :

 1 Neutron scattering lengths for most elements (natural abundance) in the periodic table. Those in red are strong neutron absorbers.

Li 1.1 Mn 1.9 O 4

	The chosen active material 213 mg C/16 (LP30) 19 mg C/4 (LP30) was mixed with an appropriate amount of Carbon Super P (12 wt% for LiFePO 4 ) and the a) 4.4 + /Li) electrode mixture was ground in a mortar. No binder was used in these first tests. Batteries were assembled with glass fiber separators and either the commercial LP30 electrolyte (SelectiLyte TM , Merck company, 1M LiPF 6 in EC:DMC (1:1) (wt%)) or a home-made deuterated electrolyte (1M LiPF 6 (Sigma Aldrich) in d-Ethylene Carbonate : d-Dimethyl Voltage Li 4.0 (Volts vs. Volts vs Li + /Li 3.0 3.5 4.0 4.5 (dV/dx) -1 -0.2 0.0 0.4 3.6 4.2 + /Li 0.2 vs. Li 3.8 3.2 3.4 Volts 3.0 2.8 Capacity (mAh/g) 0 20 40 60 80
	Carbonate 1:4 wt% (Armar Chemicals)). Lithium metal was used as anode. Composition (x in Li x Mn 1.9 O 4 ) 1.1 0.5 0.6 0.7 0.8 0.9 1.0
	4.0 + /Li) Li 3.6 (Volts vs. 3.2 2.8 Voltage 2.4	b)	LiFePO 4	Li 4.0 + /Li 3.6 Volts vs. 2.8 3.2	0	31 mg C/10 (LP30) 33 mg C/10 (deut.electrolyte) 105 mg C/24 (deut.electrolyte) Capacity (mAh/g) 60 120 180
		0.0	0.1 0.2 0.3		0.4 0.5	0.6 0.7	0.8 0.9	1.0
					Composition (x in Li x FePO 4 )
							3

Table 2

 2

	.3). However, a 3 by

Bianchini et al., figure 3

Table 2 .

 2 3: Structural parameters obtained after Rietveld refinement of Neutron diffraction data from phase pure LiFePO4 recorded in the in situ lithium cell on the diffractometer D20. For comparison purposes, those obtained for the same powder recorded as pure on the diffractometer D2B are reported in bold. The same parameters were refined in the two cases, except for Biso that was not refined at the same time of Li SOF for the in situ cell because of the small angular domain (less than 120 • ).

				LiFePO 4
	S.G. Pnma; Z=4
	a = 10.320(1) Å; b = 6.004(1) Å; c = 4.6907(7) Å;		D20: Rwp = 16.7%;
	V = 290.68(7) Å3 ; V/Z = 72.67 Å3 .		R B = 6.51%; χ 2 = 1.60
	a = 10.3233(2) Å; b = 6.0044(1) Å; c = 4.6918(1) Å;	D2B: Rwp = 11.0%;
	V = 290.83(1) Å3 ; V/Z = 72.71 Å3 .		R B = 3.98%; χ 2 = 2.54
				Atomic Parameters
				Atomic Positions
	Atoms Wyckoff	x/a	y/b	z/c	SOF	B iso
	Li	4a	0	0	0	1	1.6(4)
			0.282(1)		0.974(4)		0.63
	Fe	4c		0.25		1
			0.2816(4)		0.9749(8)		0.63(5)
			0.094(2)		0.414(4)		0.43
	P	4c		0.25		1
			0.0952(6)		0.418(1)		0.43(9)
			0.097(2)		0.748(5)		0.8
	O(1)	4c		0.25		1
			0.0966(7)		0.743(1)		0.8(1)
			0.457(2)		0.204(5)		0.7
	O(2)	4c		0.25		1
			0.4566(6)		0.206(1)		0.7(1)
			0.167(2)	0.045(2)	0.285(3)		0.66
	O(3)	8d				1
			0.1655(4) 0.0469(6)	0.2836(8)		0.66(6)
	viously discussed, we note that neutrons allow obtaining high-intensity diffraction peaks
	at high angles (≥ 100 • in 2θ at λ ≈1.5 Å). As shown by the results given in Figure 2.10
	(good minimization of the difference between the observed and calculated data) and by the
	good reliability factors given in Table 2.3 and Table 2.4, single phase data refinements of
	positive electrode materials can be achieved within a lithium based electrochemical cell.
	The obtained structural parameters are listed in these tables and match very well with
	those obtained from high-resolution data.
	As already mentioned in the introductory chapter, LiFePO 4 belongs to the olivine-type
	structural family, described in an orthorhombic unit cell (space group Pnma, Figure 2.11)
	with a = 10.3233(2) Å, b = 6.0044(1) Å and c = 4.6918(1) Å. The structure is built on
	layers of corner-sharing distorted FeO 6 octahedra linked through PO 4 tetrahedra and with

Table 2 . 5 :

 25 Selected bond lengths ( Å) in the structures of LiFePO4 and FePO4 at different key compositions of the phase diagram xLiFePO4 • (1-x)FePO4 obtained from NPD data recorded operando in the in situ electrochemical cell on the diffractometer D20. Expected and refined fractions of each phase are reported in red. Polyhedral distortion is calculated as

Table 2

 2

.2, Figure 2.3 and Figure

Table 3 . 1 :

 31 Electrochemical and crystallographic characterization of pristine materialsLi1+xMn2-xO4 (x = 0, 0.05, 0.10) from XRPD, NPD and galvanostatic cycling. Statistical errors are reported (3σ). For sample S1 the refined value of x is different than in Figure3.5, because in that case oxygen's SOF is also refined.

	Pristine	a = b = c ( Å)	Refined Mn oxid.	Measured/Expected fully
	Material		x (ND) state (calc)	oxid. compos.
		XRD: 8.2484(2)
	S1: LiMn2O4		0.00(7)	+3.5	Li0.04Mn2O4 / Li0.0Mn2O4
		ND: 8.2487(1)
		XRD: 8.2307(4)
	S2: Li1.05Mn1.95O4		0.05(8)	+3.56	Li0.19Mn1.95O4 / Li0.20Mn1.95O4
		ND: 8.2355(1)
		XRD: 8.2188(3)
	S3: Li1.10Mn1.90O4		0.10(8)	+3.63	Li0.40Mn1.90O4 / Li0.40Mn1.90O4
		ND: 8.2218(1)

  1.05 Mn 1.95 O 4

  1.10 Mn 1.90 O 4 as[Li] 8a [Li 0.10 Mn 1.90 ] 16d O 4 . It is generally admitted that only Li 8a is electrochemically active, i.e. Li 16d cannot be extracted from the structure[START_REF] Kim | Significance of the Tetrahedral A Site on the Electrochemical Performance of Substituted Li 1[END_REF] . The oxidized composition is thus [Li 0.30 ] 8a [Li 0.10 Mn 1.90 ] 16d O 4 . Note that, to the best of our knowledge and due to the lack of sufficiently sensitive experimental techniques, this has never been proved experimentally. We verified this important point by choosing selected compositions (the one in Figure3.11b, for example) and by refining the lithium content in each site (Li 8a , Li 16d

  + extraction from Li 1.05 Mn 1.95 O 4 (sample S2) In Li 1.05 Mn 1.95 O 4 , Mn is in the average oxidation state +3.56 and therefore only 0.85 Li + can be theoretically extracted, leading to the final composition Li 0.20 Mn 1.95 O 4 (namely [Li 0.15 ] 8a [Li 0.05 Mn 1.95 ] 16d O 4 ). The same rate of C/20 was used while charging the battery and the high electrode loading resulted again in the presence of an unreacted phase, estimated at 10-15% from refinements. Figure 3.12a shows all the significant refined parameters extracted from operando NPD as a function of the global Li content, y, in Li y Mn 1.95 O 4 .

Li + extraction first proceeds through a solid solution (single phase) mechanism across the first electrochemical feature at 4.05 V vs. Li + /Li. Concurrently, the unit cell parameter

  1. This intermediate phase (2) subsequently evolves to final values of a 2 = 8.156(5) Å and Li 8a SOF = 0.63(21). As observed for sample S2 at composition Li ≈0.6 Mn 1.95 O 4 , we notice that the final composition reached at this stage is not Li 0.5 Mn 2 O 4 . Figure 3.12b shows the Rietveld refinement of the observed intermediate phase of composition Li 0.67 Mn 2 O 4 . As previously mentioned, several authors proposed an ordered intermediate phase Li 0.5 Mn 2 O 4 to be responsible for the separation of the two electrochemical features at 4.05 V and 4.15 V vs. Li + /Li

Table 3 . 2 :

 32 Structural parameters obtained from Rietveld refinement of Li0.5Mn2O4. (-) indicates that a value has not been refined in P213, but it was kept as refined in the P4332 space group.

				Li 0.5 Mn 2 O 4
	S.G. P2 1 3; Z=8
	a = b = c = 8.1529(1) Å;			Rwp = 18.9%;
	V = 541.92(1) Å3 ; V/Z = 67.74(1) Å3 .		R B = 8.06%; χ 2 = 60.2
	Main Li 0.5 Mn 2 O 4 phase = 96(1) wt%;
	Secondary LiMn 2 O 4 -like phase = 3.3(2) wt% (Fd 3m, a = 8.2390(4) Å)
			Atomic Parameters
			Atomic Positions
	Atoms Wyckoff	x/a	y/b	z/c	SOF	B iso
	Mn1	4a	0.625(7)	0.625(7)	0.625(7)	1	2.6(-)
	Mn2	12b	0.128(6)	0.380(4)	-0.127(4)	1	2.6(-)
	O(1)	4a	0.387(21)	0.387(21)	0.387(21)	1	2.3(-)
	O(2)	12b	0.142(25) -0.135(16) 0.136(19)	1	2.3(-)
	O(3)	4a	0.869(18)	0.869(18)	0.869(18)	1	2.3(-)
	O(4)	12b	0.104(19)	0.119(16)	0.396(17)	1	2.3(-)
	Li(1)	4a	0.011(-)	0.011(-)	0.011(-)	1	1.0(-)

Table 3 .

 3 3: Significant bond length distances ( Å) obtained from Rietveld refinement of Li0.5Mn2O4 in the P213 space group, compared to those obtained for the P4332 one. Error bars are reported as 3σ. Polyhedral distortion is calculated as ∆ = 1/N i (di -d / d ) 2 , bond valences as reported in[255] .Li 0.5 Mn 2 O 4 (P2 1 3 vs. P4 3 32)

			O1	O2	O3	O4	BVS	Distort.
	Mn(1)	P2 1 3	-	1.94(15) x3		2.01(15) x3	3.3(6)	2.9E-4
		P4 3 32	-	1.99(4) x6		-	3.2(2)	0.001E-4
		P2 1 3	1.91(18)	1.94(18) x2 1.97(15) 1.90(15) x2	3.8(6)	2E-4
	Mn(2)			1.94(5) x2
		P4 3 32 1.92(7) x2	1.90(4) x2	-	-	3.8(2)	0.839E-4
	Li(1)	P2 1 3	-	1.90(18) x3 2.00(18)	-	1.2(3)	6E-4
		P4 3 32	2.08(7)	1.92(4) x3	-	-	1.07(7)	11E-4

Table 3 .

 3 2 and Table3.3 gather and compare the structural informations obtained for Li 0.5 Mn 2 O 4 in both the P4 3 32 and P2 1 3 space groups while the arrangements of cations and lithium/vacancy ordered distributions in Li 0.5 Mn 2 O 4 are displayed in Figure3.21.

Table 3 . 4 :

 34 Structural parameters obtained from Rietveld refinement of Li0.68Ni0.4Mn1.6O4 (scan #17).

				Li 0.68 Ni 0.4 Mn 1.6 O 4
	S.G. Fd 3m; Z=8
	a = b = c = 8.11124(4) Å;				Rwp = 23.7%;
	V = 533.88(4) Å3 ; V/Z = 66.74(4) Å3 .		R B = 7.63%; χ 2 = 2.02
				Atomic Parameters
				Atomic Positions
	Atoms Wyckoff	x/a	y/b	z/c	SOF*	B iso
	Ni	16d	0	0	0	1	0.2(2)
	Mn	16d	0	0	0	1	0.2(2)
	O	32e	0.2373(5) 0.2373(5) 0.2373(5)	1	1.5(1)
	Li	8a	3/8	3/8	3/8	0.68(15)	0.9(5)

*Occupancy and B iso refined separately

LiTi IV PO 4 O Li 2 Ti III PO 4 O 1.5 V LiTi III PO 4 F Li 2 Ti II PO 4 F Ti IV PO 4 F 2.9 V LiFe III PO 4 OH Li 2 Fe II PO 4 OH HFe III PO 4 OH LiHFe II PO 4 OH LiFe III PO 4 F Li 2 Fe II PO 4 F LiV IV PO 4 O Li 2 V III PO 4 O ~2.3V

Ti III /Ti IV and Ti II /Ti III /Ti IV redox couples Fe II /Fe III redox couple V III /V IV /V V and V II /V III /V IV redox couples

				1								2		3	4	5
														Potential
														vs. Li +	/Li
	Li	1 PO 2 Ti III	4 O		1.5 V	2 LiTi IV	PO	4 O	3	4 Ti III /Ti IV	and	5 Potential
														Ti II	/Ti III	/Ti IV	vs. Li + /Li
								1.5 V					2.9 V
	Li	2 Ti II PO	4 F				LiTi III PO	4 F	Ti IV	PO	4 F	redox couples
														2.6 V
								Li	2 Fe II PO	4 OH	LiFe III PO	4 OH
									LiHFe II PO	4 OH 2.6 V	2.8 V	HFe III PO	4 OH	Fe II	/Fe III
														redox couple
										Li	2 Fe II PO	4 F	2.8 V 2.9 V	LiFe III PO	4 F
														2.9 V
													~2.3V	3.95 V
						Li	2 V III PO	4 O				LiV IV	PO	4 O	V V	PO	4 O	V III	/V IV	/V V	and
														V II	/V III	/V
										1.80 V	4.26 V
			Li	2 V II PO	4 F						LiV III PO	4 F	V IV	PO	4 F

IV redox couples LiMn III PO 4 OH Mn IV PO 4 OH 3.25 V Mn III /Mn IV redox couple

  3+ to V 2+ . The absolutely flat shape of the profile is indicative of a biphasic reaction between the end members LiVPO 4 F and Li 2 VPO 4 F. In the high-voltage region, where lithium is extracted from LiVPO 4 F, we notice instead a different behaviour. Although at a first glance it seems It can be clearly observed in the right part of Figure 4.7. The extraction of Li + occurs at an average potential of 3.95 V versus Li + /Li at C/50 regime: this leads upon 1 st charge to a global composition of "Li 0.5 VPO 4 O", raising the question whether (i) such a composition is actually the stable one obtained upon oxidation or (ii) the reaction could not be completed because of the poor electrochemical reactivity of LiVPO 4 O. Given the strict relation with its phase diagram, this matter will be addressed in the next section. Note that LiVPO 4 O's ability to deintercalate lithium ions by exploiting the vanadium V 4+ /V 5+ redox couple has been addressed in the past by Azmi et al. focusing mainly on the orthorhombic β-LiVPO 4 O phase

	that the reaction proceeds as a plateau around 4.2 V, a closer inspection reveals a sequence
	of two flat regions, at 4.24 V and 4.28 V vs. Li + /Li. These two electrochemical features
	are well-separated and they suggest the presence of an intermediate phase of composition
	Li 0.67 VPO

4

F we notice immediately a very flat voltage-composition plateau at 1.80 V vs. Li + /Li that occurs upon insertion of lithium into the structure, with concurrent reduction of V 4 F, before reaching the fully delithiated V 4+ PO 4 F. In both domains, LiVPO 4 F electrodes reach a capacity very close to the theoretical one.

Despite the structural similarity between LiVPO 4 F and LiVPO 4 O, the latter shows a significantly different electrochemical behavior.

  VPO 4 O to Li 1.75 VPO 4 O and the final short plateau at 2.04 V vs. Li + /Li to reach the end member Li 2 VPO 4 O. The detailed mechanisms associated with these reactions as well as the description of the crystal structures involved is made in paragraph 3.4.4. Note the drastic voltage difference experienced by Li x VPO 4 Y, for the "same" V 3+ /V 4+ redox couple, when Y is changed from O to the more electronegative F: this is partly due to the inductive effect of the Y cation, but also to the fact that in Li x VPO 4 O the electrochemically active reaction is done on the vanadyl bond VO 2+ , absent in Li x VPO 4 F, and finally to the

1.76 VPO 4 O (and β-Li 1.47 VPO 4 O). This suggested that the Tavorite polymorph of LiVPO 4 O can accommodate more lithium than the orthorhombic one. In their study, Allen et al. also showed a significantly modified XANES signal between the pristine LiVPO 4 O and the lithiated Li 1.76 VPO 4 O, both in the pre-edge and edge features. They notice how the vanadium's environment is modified, namely losing the shortest V-O bond present in LiVPO 4 O as a result of vanadium's reduction. In our GITT measurement (Figure 4.7), we observe 3 peculiar features similar to those reported by Allen et al.: the 1 st long voltage-composition plateau at 2.45 V vs. Li + /Li between LiVPO 4 O and Li 1.5 VPO 4 O, the second "pseudo-plateau" at 2.21 V vs. Li + /Li, from Li 1.5 fact that 0 ≤ x ≤ 1 for Li x VPO 4 F while 1 ≤ x ≤ 2 for Li x VPO 4 O.

  The cell parameters retrieved from Le Bail fitting by Ateba Mba are a =

	7.227(4) Å, b = 7.949(4) Å, c = 7.316(5) Å and β = 116.81(6) • (Table 4.1), in excellent
	agreement with those reported by Ellis et al. The volume is V = 375.16(1) Å3 (V/Z =
	93.79 Å3 ), bigger (as expected) than that of LiVPO 4 F as a result of the V 2+ ionic radius
	(0.088 nm) bigger than that of V 3+ (0.074 nm).

Table 4 .

 4 2: Structural data for different polymorphs of VPO4O. Space groups and Vanadium-Oxygen bond lengths are reported.

	Polymorph	Symmetry	Space group V=O ( Å) V-O ( Å)
	-VPO 4 O (this work)	Monoclinic	Cc	1.59	2.51
	-VPO 4 O (this work)	Monoclinic	P2 1 /n	1.59	2.51
	-VPO 4 O (ICSD 415924 [293] )	Monoclinic	Cc	1.57	2.56
	δ-VPO 4 O (ICSD 420073 [294] )	Tetragonal	P4 2 /mbc	1.62	1.81
	γ-VPO 4 O (ICSD 415213 [295] )	Orthorhombic	Pbam	1.50 1.62	2.70 1.81
	β-VPO 4 O (ICSD 9413

Table 4 .

 4 3: Formation energies calculated in meV/f.u. for the different structural hypothesis for VPO4O with GGA and GGA + U vs. the most stable phase (the one described in Cc).

	V P O 4 O	GGA		GGA+U
			U = 3 eV U = 4 eV U = 4.5 eV
	Cc	0	0	0	0	most stable
	P2 1 /n	7	7	7	8
	P 1	33	28	27	27
	P2/c	420	361	343	334

4

O and removing all Li + ions. All structures were fully relaxed and the corresponding structural parameters are given in Table

4

.4. The lower energy was obtained for VPO 4 O in Cc in both GGA and GGA+U calculations. In Table

4

.3 we give the formation energy per formula unit for each case versus this most stable phase. It appears that VPO 4 O described in P2 1 /n is only slightly less stable than the one described in Cc by only about 7 meV/Formula unit (which is lower than kT at ambient temperature (25 meV)). VPO 4 O described in P 1 is less stable by about 27 meV/Formula unit. The largest energy difference is obtained for VPO 4 O described in C2/c where all

Table 4 . 4 :

 44 Cell parameters and V-O bonds distances resulting from the structural optimization using GGA + U (U = 4eV) with the VASP code.

		GGA+U (U = 4 eV)
	V P O 4 O	Cc	P2 1 /n	P 1	C2/c
	a ( Å)	7.326	7.311	6.962	7.221
	b ( Å)	7.07	7.135	7.705	7.304
	c ( Å)	7.371	7.408	7.598	7.24
	α ( • )	90	90	90.78	90
	β ( • )	115.19 115.02	90.23	121.54
	γ ( • )	90	90	119.61	90
		distance V-O ( Å)
	V(1)-O	1.609	1.609	1.612	1.819 x2
		1.884	1.887	1.892	1.903 x2
		1.917	1.905	1.895	1.929 x2
		1.919	1.909	1.912
		1.919	1.917	1.922
		2.574	2.585	2.524
	V(2)-O	-	-	1.611	-
				1.891
				1.909
				1.914
				1.925
				2.497

Table 4 . 5 :

 45 Refined parameters for VPO4O. Comparison between Cc and P21/n space groups.

	-V P O 4 O	Cc	P2 1 /n
	χ 2 , R B , Rwp	2.83, 3.9%, 12.3%	3.57, 6.77%, 14.8%
	a, b, c, ( Å)	7.2699(6), 6.8773(4), 7.2598(5),	7.2684(6), 6.8772(4), 7.2605(6),
	γ ( • ), Vol ( Å3 )	115.382(2), 327.93(4).	115.384(3), 327.89(4).
	V-O distances ( Å)	1.85(2), 1.86(3), 1.86(2),	1.83(3), 1.82(2), 1.88(1),
		1.93(2), 1.59(2), 2.51(2).	1.95(3), 1.58(2), 2.52(2).
	Distortion	41.95 • 10 -4	48.07 • 10 -4
	P-O distances ( Å)	1.55(2), 1.56(3), 1.55(3), 1.48(2) 1.52(2), 1.63(3), 1.50(3), 1.60(2)
	Distortion	4.98 • 10 -4	12.36 • 10 -4

Table 4 . 6 :

 46 Cell parameters of selected LixVPO4O compositions, refined in the space group P 1. Vanadium chains run along b.

Table 4 .

 4

6 reveals another interesting fact. The unit cell volume changes only slightly between LiVPO 4 O and Li 1.5 VPO 4 O (∆V/V = 0.14%), while it changes significantly from Li 1.5 VPO 4 O to Li 2 VPO 4 O (3.92%). This strong difference may be the explanation for such a dissimilar phase behavior between these composition ranges. The transition from LiVPO 4 O to Li 1.5 VPO 4 O involves a very small volume change and it can therefore happen via a perfect first order reaction. On the contrary, the transitions from Li 1.5 VPO 4 O to Li 1.75 VPO 4 O and from Li 1.75 VPO 4 O to Li 2 VPO 4 O involve a significant volume change

Table 4 .

 4 7: Structural parameters obtained from Rietveld refinement of XRPD and Neutron diffraction data of Li2VPO4O. Parameters refined using XRPD data are in bold. Isotropic thermal displacement parameters were constrained to be equal for the same type of atom.

				Li 2 VPO 4 O
	S.G. P 1; Z=4
						XRPD: Rwp = 14.8%;
	a = 7.1989(4) Å; b = 7.1012(3) Å; c = 7.7771(3) Å; R B = 10.5%; χ 2 = 2.82
	α = 89.824(3) • ; β = 89.812(3) • ; γ = 116.319(3) • .		NPD: Rwp = 12.6%;
	V = 356.36 (3) Å3 ; V/Z = 89.09 Å3		R B = 6.55%; χ 2 = 2.36
				Atomic Parameters
				Atomic Positions
	Atoms Wyckoff	x/a	y/b	z/c	SOF	B iso
	V(1)	2i	0.748(3) -0.004(3)	-0.752(3)	1	1.5(2)
	V(2)	2i	0.734(3) -0.505(3)	-0.755(3)	1	2.5(2)
	P(1)	2i	0.24(1)	-0.248(9)	-0.612(8)	1	0.8(2)
	P(2)	2i	0.27(1)	-0.743(9)	-0.885(8)	1	0.8(2)
	O(1)	2i	0.563(5)	-0.910(5)	-0.310(4)	1	0.98(5)
	O(2)	2i	0.07(1)	-0.359(9)	-0.755(6)	1	0.98(5)
	O(3)	2i	0.721(7)	-0.591(8)	-0.499(6)	1	0.98(5)
	O(4)	2i	0.161(8)	-0.117(7)	-0.496(7)	1	0.98(5)
	O(5)	2i	0.232(9)	-0.259(8)	-0.152(7)	1	0.98(5)
	O(6)	2i	0.064(5)	-0.883(5)	-0.784(4)	1	0.98(5)
	O(7)	2i	0.230(7)	-0.588(8)	-0.993(6)	1	0.98(5)
	O(8)	2i	0.728(8)	-0.260(8)	-0.652(7)	1	0.98(5)
	O(9)	2i	0.57(1)	-0.354(9)	-0.259(6)	1	0.98(5)
	O(10)	2i	0.337(8)	-0.877(7)	-0.008(7)	1	0.98(5)
	Li(1)	1d	1/2	1/2	1/2	1	2.2(7)
	Li(2)	1h	0	1/2	0	1	2.2(7)
	Li(3)	2i	0.10(1)	0.27(1)	0.46(1)	1	2.2(7)
	Li(4)	2i	0.36(1)	0.82(1)	0.04(1)	1	2.2(7)
	Li(5)	2i	0.42(1)	0.15(1)	0.45(1)	1	2.2(7)
	both patterns were exploited to obtain the final crystal structure, via successive refine-
	ment iterations between the X-Ray and neutron diffraction patterns. For instance, oxygen
	positions obtained from the X-Ray pattern are not accurate because of the high number
	of oxygen coordinates (30 independent parameters) and the limited sensitivity of X-Rays
	to light elements. The obtained results are shown in Figure 4.19, with the resulting rep-
	resentation of the crystal structure. The refined parameters are reported in Table 4.7 as

Li 2 VPO 4 O shows a double cell analogous to that of LiVPO 4 O. Since the two different probes are sensitive to different structural parameters, obtained from the neutron diffraction data, with the exception of cell parameters, vanadium's fractional atomic coordinates and isotropic atomic displacement parameters. Bond

Table 4 . 8 :

 48 Significant bond length distances of Li2VPO4O obtained from Rietveld refinement of XRPD and Neutron diffraction data. Only distances shorter than 2.5 Å are considered. V-O distances along the chains are highlighted in bold. Polyhedral distortion is calculated as ∆ = 1/N i (di -d / d ) 2 , bond valences as reported in[255] .

					Li 2 VPO 4 O
		V(1)	V(2)	P(1)	P(2)	Li(1)	Li(2)	Li(3)	Li(4)	Li(5)
	Coord.	6	6	4	4	6	6	4	5	6
										2.23(9)
	O(1)	2.09(4)	-	1.51(7)	-	-	-	-	2.17(7)
										2.09(9)
	O(2)	-	2.17(6) 1.57(8)	-	-	2.11(5) x2	-	2.48(8)	-
	O(3)	-	2.07(5) 1.57(9)	-	1.96(6) x2	-	2.10(9)	-	2.15(9)
	O(4)	2.10(5)	-	1.55(9)	-	-	-	1.75(9)	-	2.03(9)
	O(5)	1.96(7) 1.94(7)	-	-	-	2.13(5) x2	-	1.75(8)	-
	O(6)	2.06(4)	-	-	1.56(6)	-	-	2.15(8)	-	-
	O(7)	-	2.04(5)	-	1.50(9)	-	2.01(6) x2	-	-	-
	O(8)	1.92(7) 1.93(7)	-	-	2.12(5) x2	-	1.93(9)	-	2.21(13)
	O(9)	-	1.95(6)	-	1.56(8) 2.10(5) x2	-	-	-	2.07(10)
									2.29(9)
	O(10)	2.03(5)	-	-	1.58(9)	-	-	-		-
									2.01(9)
	Distor.(•10 -4 )	11.1	18.4	2.6	4.1	10.9	2.6	62.0	135	11.9
	BVS	2.8(2)	2.9(2)	4.8(6)	4.8(5)	1.22(8)	1.13(7)	1.1(2)	1.0(1)	1.0(1)

length distances and polyhedral coordinations are reported in Table

4

.8. Lithium's fractional atomic coordinates were determined thanks to Fourier difference maps, their location being not straightforward. Indeed, the first 4 lithium positions (Li1 and Li2, Wyckoff positions 1c and 1h, and Li3 and Li4, positions 2i) emerged quite clearly from the maps. The last site(s), required to respect the stoichiometry, was less easily detectable. Finally, the best solution was found from the map with the Li5 atom placed in a 2i site. As can be observed in

Table 4 .

 4 8, V and P environments are in line with those expected, although with significant error bars due to the large number of refined parameters; lithium local environments are also equally plausible, despite two short Li-O distances. No Li-Li distance shorter than 2.3 Å is observed. For all the cations (P 5+ , V 3+ and Li + ) the bond valences calculated are in very good agreement with those expected from the chemical formula Li 2 VPO 4 O. Regarding the vanadium environment, the V(1)O 6 and V(2)O 6 octahedra in Li 2 VPO 4 O can be compared to what is expected for V 3+ O 6 polyhedra from the survey of Schindler et al.

Table 4 . 9 :

 49 Structural parameters obtained from Rietveld refinement of in situ synchrotron XRPD data of Li1.5VPO4O. Isotropic thermal displacement parameters were constrained to be equal for the same type of atom. Soft constrains are used on P-O bonds (= 1.530 +/-0.005). Their structural parameters are reported in Table4.9 and Table4.10, while bondlength distances are in Table4.11. The 3D framework of Li 1.5 VPO 4 O and Li 1.75 VPO 4 O clearly resembles very much LiVPO 4 O's one. The observed decrease of the unit cell volume is in good agreement with vanadium's gradual reduction, as are the calculated vanadium bond-valence sum (BVS) values. In Li 1.5 VPO 4 O, the presence of two sites V(1) 3.8(5)+

				Li 1.5 VPO 4 O
	S.G. P 1; Z=4
	a = 6.9930(2) Å; b = 6.9778(2) Å; c = 7.7921(2) Å;		Rwp = 15.3%;
	α = 90.133(2) • ; β = 90.409(2) • ; γ =115.727(2) •	R B = 11.3%; χ 2 = 21.6
	V = 342.52(3) Å3 ; V/Z = 85.63 Å3
			Atomic Parameters
			Atomic Positions
	Atoms Wyckoff	x/a	y/b	z/c	SOF	B iso
	V(1)	2i	0.750(5) 0.992(5) -0.236(3)	1	1.6(2)
	V(2)	2i	0.753(5) 0.507(5) -0.259(4)	1	1.6(2)
	P(1)	2i	0.267(2) 0.766(2) -0.102(2)	1	2.2(3)
	P(2)	2i	0.221(2) 0.268(2) -0.409(2)	1	2.2(3)
	O(1)	2i	0.73(1)	0.24(2)	-0.34(1)	1	2.6(3)
	O(2)	2i	0.22(1)	0.23(1)	-0.826(9)	1	2.6(3)
	O(3)	2i	0.352(9) 0.632(9)	0.010(6)	1	2.6(3)
	O(4)	2i	0.22(1)	0.939(9) -0.006(6)	1	2.6(3)
	O(5)	2i	0.068(6) 0.631(9) -0.219(5)	1	2.6(3)
	O(6)	2i	0.42(1)	0.83(1)	-0.260(6)	1	2.6(3)
	O(7)	2i	0.145(9) 0.414(9) -0.515(6)	1	2.6(3)
	O(8)	2i	0.27(1)	0.103(9) -0.515(6)	1	2.6(3)
	O(9)	2i	0.09(1)	0.15(1)	-0.243(6)	1	2.6(3)
	O(10)	2i	0.442(5) 0.410(9) -0.322(6)	1	2.6(3)

refinement (Figure

4

.21) we obtained the two structures nonetheless (except for the lithium sites).

Table 4 .

 4 10: Structural parameters obtained from Rietveld refinement of in situ synchrotron XRPD data of Li1.75VPO4O. Isotropic thermal displacement parameters were constrained to be equal for the same type of atom. Soft constrains are used on P-O bonds (=1.530 +/-0.005).

				Li 1.75 VPO 4 O
	S.G. P 1; Z=4
	a = 7.1019(3) Å; b = 7.0414(3) Å; c = 7.7926(3) Å;		Rwp = 18.0%;
	α = 89.815(3) • ; β = 89.742(2) • ; γ =116.015(3) •	R B = 13.1%; χ 2 = 28.2
	V = 350.19(3) Å3 ; V/Z = 87.55 Å3
			Atomic Parameters
			Atomic Positions
	Atoms Wyckoff	x/a	y/b	z/c	SOF	B iso
	V(1)	2i	0.750(5) 0.992(5) -0.236(3)	1	1.6(2)
	V(2)	2i	0.753(5) 0.507(5) -0.259(4)	1	1.6(2)
	P(1)	2i	0.267(2) 0.766(2) -0.102(2)	1	2.2(3)
	P(2)	2i	0.221(2) 0.268(2) -0.409(2)	1	2.2(3)
	O(1)	2i	0.73(1)	0.24(2)	-0.34(1)	1	2.6(3)
	O(2)	2i	0.22(1)	0.23(1)	-0.826(9)	1	2.6(3)
	O(3)	2i	0.352(9) 0.632(9)	0.010(6)	1	2.6(3)
	O(4)	2i	0.22(1)	0.939(9) -0.006(6)	1	2.6(3)
	O(5)	2i	0.068(6) 0.631(9) -0.219(5)	1	2.6(3)
	O(6)	2i	0.42(1)	0.83(1)	-0.260(6)	1	2.6(3)
	O(7)	2i	0.145(9) 0.414(9) -0.515(6)	1	2.6(3)
	O(8)	2i	0.27(1)	0.103(9) -0.515(6)	1	2.6(3)
	O(9)	2i	0.09(1)	0.15(1)	-0.243(6)	1	2.6(3)
	O(10)	2i	0.442(5) 0.410(9) -0.322(6)	1	2.6(3)

Table 4 .

 4 11: Significant bond length distances of Li1.5VPO4O and Li1.75VPO4O obtained from Rietveld refinement of XRPD and Neutron diffraction data. V-O distances along the chains are highlighted in bold. Polyhedral distortion is calculated as ∆ = 1/N i (di -d / d ) 2 , bond valences as reported in[255] .

	Li 1.5 V P O 4 O	V(1)	V(2)	P(1)	P(2)	Li 1.75 V P O 4 O	V(1)	V(2)	P(1)	P(2)
	O(1)	1.98(12) 1.91(11)	-	-		1.67(9) 2.21(9)	-	-
	O(2)	1.70(12) 1.89(11)	-	-		2.01(9) 1.73(9)	-	-
	O(3)	-	2.16(6) 1.57(7)	-		2.22(6)	-	1.57(6)	-
	O(4)	1.93(5)	-	1.58(7)	-		2.24(5)	-	1.57(3)	-
	O(5)	-	2.00(5) 1.58(4)	-		-	1.95(5) 1.56(3)	-
	O(6)	2.09(8)	-	1.57(4)	-		-	2.00(6) 1.56(6)	-
	O(7)	-	1.90(5)	-	1.57(7)		-	2.13(5)	-	1.56(6)
	O(8)	2.03(5)	-	-	1.57(7)		-	2.11(5)	-	1.57(5)
	O(9)	2.15(8)	-	-	1.59(5)		1.91(5)	-	-	1.57(6)
	O(10)	-	2.03(5)	-	1.58(3)		1.99(5)	-	-	1.57(4)
	BVS	3.8(5)	3.2(3)	4.5(4) 4.4(4)		3.4(3)	3.1(3)	4.6(3) 4.6(3)
	Dist.(•10 -4 )	53.1	22.5	0.09	0.2		91.3	58.8	0.2	0.2

  1.5 VPO 4 O and Li 1.75 VPO 4 O, which

Table 5 . 1 :

 51 Space group and cell parameters of Na3V2(PO4)2F3 (and otherNa3V2O 2δ (PO4)2F 3-2δ compositions) as gathered from the literature. # combined refinement.

	Reference	Space	a ( Å)	b ( Å)	c ( Å)	Vol. ( Å3 )	Announced
		group					composition
	Hao [313]	P42/mnm	9.15	9.15	10.86	909.22	Na3V2(PO4)2F3

Table 5 .

 5 2: Structural parameters obtained from combined Rietveld refinement of synchrotron radiation and neutron diffraction data of Na3V2(PO4)2F3.

			Na 3 V 2 (PO 4 ) 2 F 3
	S.G. Amam; Z=4
	a = 9.02847(3) Å;			Synchrotron:
	b = 9.04444(3) Å;		Rwp = 14.8%; R B = 4.45%; χ 2 = 2.58.
	c = 10.74666(6) Å;
	V = 877.544(6) Å3 ;			Neutrons:
	V/Z = 219.386 Å3 .		Rwp = 17.4%; R B = 9.89%; χ 2 = 2.58.
			Atomic Parameters
				Atomic Positions
	Atoms Wyckoff	x/a	y/b	z/c	SOF	B iso
	V	8g	1/4	0.2536(5) 0.1844(2)	1	0.40(3)
	P	8e	0	0	0.2472(6)	1	0.46(5)
	O(1)	16h	0.0960(8) 0.0960(8) 0.1618(8)	1	0.9(2)
	O(2)	16h	0.0943(8) 0.4038(8) 0.1659(8)	1	0.7(2)
	F

Table 5 .

 5

3: Significant bond length distances ( Å) of Na3V2(PO4)2F3 obtained from Rietveld refinement of combined synchrotron radiation and neutron diffraction data. Distances shorter than 2.8 Å were considered. Polyhedral distortion is calculated as ∆

Table 5 . 5 :

 55 Comparison between Rietveld refinement obtained for Na3V2(PO4)2F3 in a capillary in Debye-Scherrer geometry (black, top lines) and for the same material measured in situ in transmission in our electrochemical cell (blue, bottom lines).

			Na 3 V 2 (PO 4 ) 2 F 3
			Our work ( [312] ) vs. refined in situ
	S.G. Amam; Z=4
					Synchrotron: Rwp = 14.8%;
	a = 9.02847(3) Å; a = 9.0262(2) Å;	R B = 4.45%; χ 2 = 2.58.
	b = 9.04444(3) Å; b = 9.0418(2) Å;	Neutrons: Rwp = 17.4%;
	c = 10.74666(6) Å; c = 10.7434(3) Å;	R B = 9.89%; χ 2 = 2.58.
	V = 877.544(6) Å3 ; V = 876.80(1) Å3	Synchro. in situ: Rwp = 11.4%;
	V/Z = 219.20(1) Å3 ; V/Z = 219.386 Å3 .	R B = 6.36%; χ 2 = 18.1.
				Atomic Positions
	Atoms	Wyckoff	x/a	y/b	z/c	SOF	B iso
				0.2536(5)	0.1844(2)		0.40(3)
	V	8g	1/4			1
				0.2529(9) 0.1848(3)		1.36(8)
					0.2472(6)		0.46(5)
	P	8e	0	0		1
					0.244(1)		1.6(1)
			0.0960(8)	0.0960(8)	0.1618(8)		0.9(2)
	O(1)	16h				1
			0.096(1)	0.097(1)	0.159(1)		1.2(1)
			0.0943(8)	0.4038(8)	0.1659(8)		0.7(2)
	O(2)	16h				1
			0.091(1)	0.404(1)	0.164(1)		1.2(1)
				0.253(2)			0.6(1)
	F(1)	4c	1/4		0	1
				0.253(2)			1.4(1)
				0.756(1)	0.1325(5)		1.2(1)
	F(2)	8g	1/4			1
				0.756(2)	0.1349(6)		1.4(1)
				0.023(1)			2.3(3)
	Na(1)	4c	3/4		0	1
				0.024(2)			3.8
			0.536(1)	0.283(1)		0.65(3)	1.4(3)
	Na(2)	8f			0
			0.538(2)	0.289(2)		0.8(1)	3.8
			0.593(3)	0.364(4)		0.30(3)	3.1(9)
	Na(3)	8f			0
			0.623(5)	0.393(6)		0.2(1)	3.8

Table 5 . 6 :

 56 Compositions obtained upon Na + extraction from Na3VPF. Space groups, cell parameters and volumes are reported. # The actual space group of composition Na2VPF in its superstructural arrangement is not known, so the low-symmetry space group Pmmm is used to

		index all observed reflections.
	Composition	S.G.	a ( Å)	b ( Å)	c ( Å)

Na 2.4 VPF  Na 2.2 VPF Figure 6:

  Detailed view of the biphasic reaction between scans #38 (Na 2.4 VPF) and #47 (Na 2.2 VPF). At this composition only two peaks at 17.33° and 17.54 ° remain, characteristic of the I4/mmm space group.

Bianchini et al., fig. 6

Table 5 .

 5 6). The crystal structure of Na 2.2 VPF was refined by the Rietveld method (Figure 5.21). Sodium ions adopt a disordered arrangement, and Fourier difference maps (re-

	Bianchini et al., fig. S2

  • -25 • 2θ region shows that the splitted (400) and (040) peaks of Na 3 VPF are again merged into one single peak in Na 2 VPF, suggesting a tetragonal space group. A more detailed look reveals however that this phase Table5.7: Bond-lengths and sodium content per formula unit obtained from Rietveld refinement of selected deintercalated phases observed in situ during Na + extraction from Na3VPF.

Bianchini et al., fig. S4 Figure S4:

  Fourier difference map obtained after Rietveld refinement of diffraction data at composition Na 2 VPF. Top: structural model for refinement not including any sodium. Bottom: structural model with Na1 I site only included. Fourier difference maps obtained after Rietveld refinement of diffraction data at composition Na2VPF. Top: structural model for refinement not including any sodium. Bottom: structural model with Na1I site only included.features at 3.68 V and 3.70 V vs. Na + /Na (i.e. separated by only 20 mV), suggesting a sequence of two biphasic reactions with an intermediate phase around the composition Na ≈2.4 V 2 (PO 4 ) 2 F 3 . At the end of section 5.2.1 we made the hypothesis that this intermediate phase could actually be Na 7/3 V 2 (PO 4 ) 2 F 3 , crystallized following the extraction of the first 2/3 Na/f.u., namely that the Na3 A site was emptied first. However our structural data recorded in situ point towards three biphasic reactions Na 3 VPF -Na 2.4 VPF, Na 2.4 VPF -Na 2.2 VPF and Na 2.2 VPF -Na 2 VPF. Hence our hypothesis must be rejected, in favor of multiple biphasic reactions caused by the several stable configurations for sodium ions in the structure. A similar case of electrochemistry / diffraction "disagreement" (or "difference in sensitivity") was recently reported for the Na + extraction from NaFePO 4 , towards an intermediate phase Na 2/3 FePO 4 . This intermediate phase is observed by diffraction

		No sodium in the structure 1	Na 2 VPF
			1
			.9	.9	Four main intensities,
			.8	.8	corresponding to site
	y/b	y/b	.4 .5 .6 .7	.5 .6 .7	Na1 I Na/site	Density	10 20 30 40 50 60
			0 .1 .2 .3	.2 .3 .4	Na1 I = 2.05(6) Total: 2.05(6) Na/f.u.	.9 1 -10 0	.8	.5 .6 D .7 e n s i t y y /b	.4	.3	.2	.1	0	0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 x /a
				.1
				0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
				x/a
				0
		1 Site Na1 I added in the model 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 x/a
			1
			.9	.9	Same residual
	y/b	y/b	.8 0 .1 .2 .3 .4 .5 .6 .7	.8 .2 .3 .4 .5 .6 .7	intensity on both Na1 I and Na2 I with 0 average value Na2 I Na1 I	12 14 .9 1 -10 -8 -6 -4 -2 0 2 4 6 8 10 Density	.8	.5 .6 y /b .7 D y t i s n e	.4	.3	.2	.1	0	0 .1 .2 .3 .4 .5 .6 x /a .7 .8 .9 1
			0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 .1
				x/a
				0
				0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
	Figure 5.25:			x/a

Table 5 . 8 :

 58 Structural parameters obtained from Rietveld refinement of in situ synchrotron radiation data for fully charged NaVPF, in the space group Cmc21. Because of the floating origin of this space group, z/c of V1 is not refined.

			NaV 2 (PO 4 ) 2 F 3
						S.G. Cmc2 1 ; Z=4
	a = 8.7822(3) Å;
	b = 8.7961(3) Å;				Rwp = 14.8%;
	c = 11.0015(2) Å;				R B = 4.45%;
	V = 849.86(1) Å3 ;				χ 2 = 2.58.
	V/Z = 212.47(1) Å3 .
			Atomic Parameters
				Atomic Positions
	Atoms Wyckoff	x/a	y/b	z/c	SOF	B iso #
	V1	4a	1/2	0.248(4)	0.338(-)	1	0.63
	V2	4a	0	0.251(3) 0.1908(7)	1	0.63
	P##	8	0.244(2) 0.501(3)	0.276(1)	1	0.96
	O1	8	0.357(5) 0.098(6)	0.368(3)	1	1.07
	O2	8	0.347(7) 0.397(7)	0.361(3)	1	1.07
	O3	8	0.157(7) 0.100(7)	0.193(3)	1	1.07
	O4	8	0.163(5) 0.423(5)	0.170(2)	1	1.07
	F(1)	4a	1/2	0.247(6)	0.520(6)	1	0.59
	F(2)	4a	1/2	0.24(1)	0.875(2)	1	0.59
	F(3)	4a	1/2	0.232(8)	0.187(3)	1	0.59
	Na(2)	4a	1/2	0.071(2)	0.025(8)	0.88(9)	3.0
	# refined in the final stages of refinement and then fixed
	## soft constraints used on P-O distances (P-O = 1.54 Å+/-0.02 Å)

  (PO 4 ) 2 F 1.4 , obtained by sodium deintercalation from the pristine compound Na

	4.8+ 2	O 1.6

Table 5 . 9 :

 59 Ion exchange as a function of elapsed time. Cell parameters obtained from LeBail fit of XRPD data are reported. The last column shows the silver amount measured via MEB-EDX (except for t=15min because of the insufficient amount of material recovered).Figure 5.32 and Table5.9 show the ion exchange evolution over time. Note that after 15 min Bragg peaks are in similar positions but with modified intensity, indicative of the initial substitution of Ag for Na. After 20 hours the diffraction pattern is clearly modified from the pristine one, as the reflections significantly change position and intensity, while after 60 hours they show only slight changes. These first observations suggest a solid solution domain present close to the extremes of Na 3-x Ag x V 2 (PO 4 ) 2 F 3 , but they are not sufficient to support the total absence of a miscibility gap.As measured from MEB-EDX after 60 hours we obtained Ag 2.70 Na 0.38 V 2 (PO 4 ) 2 F 3 , still containing sodium but significantly Ag-rich, and the compound will be referred to as Evolution of the XRD diffraction patterns of Na 3 V 2 (PO 4 ) 2 F 3 as the Ag + /Na + ion exchange proceeds.

	Time	a ( Å)	b ( Å)	c ( Å)	V/Z ( Å3 )	a/b	x in Na3-xAgxV2(PO4)2F3
	0	9.028(3)	9.042(3)	10.741(3)	219.2	0.998	0
	15 min	9.043(3)	9.037(3)	10.767(3)	220.0	1.000	unknown
	20 hrs	9.075(3)	9.035(3)	10.916(3)	223.8	1.004	2.4
	60 hrs	9.082(2)	9.028(2)	10.945(2)	224.3	1.006	2.8

Table 5 .

 5 10: Structural parameters obtained from combined Rietveld refinement of synchrotron XRPD and neutrons diffraction data of Ag3VPF. Ag 2.70 Na 0.38 V 2 (PO 4 ) 2 F 3 (Ag 3 VPF)

	S.G. Amam; Z=4
					Combined: χ 2 = 6.56.
	a = 9.0843(1) Å;
	b = 9.0303(1) Å;			Synchrotron:
	c = 10.9442(1) Å;			Rwp = 16.7%; R B = 7.88%.
	V = 897.796(1) Å3 ;				Neutrons:
	V/Z = 224.449(1) Å3 .		Rwp = 18.9%; R B = 12.6%.
			Atomic Parameters
			Atomic Positions
	Atoms Wyckoff	x/a	y/b	z/c	SOF	B iso #
	V1	8g	1/4	0.2525(6) 0.1820(4)	1	0.5(1)
	P1	8e	0	0	0.2396(9)	1	0.7(1)
	O1	16h	0.099(1)	0.094(1)	0.156(1)	1	0.7(2)
	O2	16h	0.093(1)	0.402(1)	0.175(1)	1	0.7(2)
	F1	4c	1/4	0.265(2)	0	1	0.8(3)
	F2	8g	1/4	0.742(2)	0.140(1)	1	1.0(3)
	Ag1	4c	1/4	0.9610(5)	0	0.92(1)	2.1(1)
	Ag2	8f	0.9598(7)	0.792(1)	1/2	0.51(6)	1.2(2)
	Ag3	8f	0.942(1)	0.856(2)	1/2	0.38(6)	1.6(3)
	Na1	4c	1/4	0.9610(5)	0	0.08(1)	2.1(1)
	Na2	8f	0.9598(7)	0.792(1)	1/2	0.15(3)	1.2(2)

Total amount of Na (0.38) is set to the value found by MEB-EDX.

Table 5 .

 5 11: Significant bond-length distances ( Å) (upper right part), angles ( • ) (down left part), polyhedral distortion and Bond-Valence Sum calculations for PO4 tetrahedra in Ag3VPF.

	P O4	O(1)	O(1)	O(2)	O(2)
	O(1) 1.54(1)	2.47(2)	2.55(2)	2.54(2)
	O(1) 106.8(3) 1.54(1)	2.54(2)	2.55(2)
	O(2) 111.7(3) 110.8(2) 1.54(1)	2.45(2)
	O(2) 110.8(2) 111.7(3) 105.2(3) 1.54(1)
	Distortion ∆ = 0.11•10 -5 , BVS = +4.94(9)

Table 5 .

 5

	V O4F2	O(1)	O(1)	O(2)	O(2)	F(1)	F(2)
	O(1)	2.01(1)	2.74(1)	2.80(2)	3.95(2)	2.68(1)	2.94(2)
	O(1)	86.2(2)	2.01(1)	3.95(2)	2.80(2)	2.68(1)	2.94(2)
	O(2)	89.5(1)	169.1(2) 1.96(1)	2.85(2)	2.69(2)	2.87(2)
	O(2)	169.1(2)	89.5(1)	92.9(2)	1.96(1)	2.69(2)	2.87(2)
	F(1)	84.1(1)	84.1(1)	85.5(1)	85.5(1)	1.995(5)	3.95(2)
	F(2)	96.1(2)	96.1(2)	94.3(2)	94.3(2)	179.7(2)	1.95(1)
		Distortion ∆ = 1.174•10 -a , BVS = +3.04(4)

12: Significant bond-length distances ( Å) (upper right part), angles ( • ) (down left part), polyhedral distortion and Bond-Valence Sum calculations for VO4F2 octahedra in Ag3VPF.

See for example the 2006 documentary Who killed the electric car?, Sony Pictures Classic.

1.3. Li-ion batteries

see for example X-Ray Diffraction by B.E. Warren

Acknowledgements

Bibliography

Résumé de la thèse en français i

Acknowledgements

These three amazing years of PhD have been an extremely formative experience from the scientific and personal point of view and there are many people I need to thank for it.

Firstly, my supervisors Laurence, Emmanuelle and Christian.

They have been great teachers, those I needed to tackle a subject new to me and to

Experimental

Characterization of Na 3 V 2 (PO 4 ) 2 F 3

The static molar magnetic susceptibility of Na 3 V 2 (PO 4 ) 2 F 3 , (χ(T) = M(T)/H with H = 1 T as the magnetic field and M as the magnetization) was measured between 5 and 300 K using a SQUID magnetometer (Quantum Design). The zero-field cooled χ values were obtained by cooling the sample in zero field down to 5 K and then heating it under the measuring field. The diamagnetic contributions were corrected using the atomic values from Bain and Berry [START_REF] Gordon | Diamagnetic corrections and pascal's constants[END_REF] , yielding the final paramagnetic susceptibility χ M .

High resolution scanning electron microscopy (SEM) analysis of metalized samples (Pd deposited) was performed using a Hitachi S-4500 microscope. Prior to the observation by electron microscopy, a suspension was obtained by grinding the material in hexane, a droplet of this suspension being deposited on a formvar carbon film supported on a copper grid.

Electron diffraction experiments were carried out on many crystallites and very reproducible results were observed. The particles studied were chosen as isolated as possible. Electron diffraction patterns were obtained using a JEOL 2100. The electrochemical signature of the Na 3 V 2 (PO 4 ) 2 F 3 active material was measured in Swagelok cells. The composite electrodes were prepared using 75 wt.% of active material, 12.5 wt.% of Carbon Super P and 12.5 wt.% of PVDF binder. Then the slurry of this mixture was cast on an Al foil with a 25 µm casting thickness and dried at 85 • C for 24 hours. A 1 M solution of NaPF 6 in PC (Aldrich) was used as electrolyte. Glass microfiber filters (Whatman) were used as separators and metallic sodium was used as negative electrode. During galvanostatic cycling the electrochemical is a stronger scatterer of X-Rays (Z = 47 vs. Z=11 for Na), thus dominating the intensity of reflections and leaving no doubt about its position in the structure.

Based on the combined Rietveld refinement of diffraction patterns (Figure 5.33 and Table 5.10), the crystal structure of Ag 3 VPF was obtained and it is shown in Figure 5.34. The basic structural framework of Na 3 VPF, consisting of V 2 O 8 F 3 bi-octahedra, is preserved.

Such bioctahedral environments are bridged by corner-sharing PO 4 tetrahedra, building a stable structure where large tunnels are present along the [110] and [1-10] directions.

These are responsible for the facile sodium extraction from Na 3 VPF and for its promising electrochemical activity as a positive electrode for Na-ion batteries, but also for the relative ease of ion exchange with silver without consequent disruption of the 3D framework of the material. Table 5.11 and Table 5.12 report all significant structural information on PO 4 tetrahedra and VO 4 F 2 octahedra, respectively. The most important differences between the parent structural framework and the one obtained after Ag/Na ion exchange can be summarized as follows:

• more pronounced orthorhombic distortion and longer c axis, as discussed above. like it, a lot. Not only that, they have also been models and friends. We made a very efficient team and working together was always a pleasure. I will never forget our fruitful beamtimes, when we multi-tasked among experiments, data analysis and, while waiting the measurements, we planned and even wrote papers. I also want to thank François Fauth, Three years of PhD do not pass without making many friends, especially while often traveling among different labs. These are the people who shared most every-day moments, extra coffees to keep working long enough, tough moments while facing scientific issues...and finally beers to forget them. So although they won't probably read this, it's a pleasure to mention all of them: Francesco, Federica, Yuri, Giacomo, Alessio, Ernesto, Pippo, Daria, Annalisa, Valentino, Elodie, Cedric, Stephane, Vincent, Manu, Laurent, Florian, Laura, Thibault, Sylvain, Fabien, Yue, Lionel, Amina, Hania, Robin, Wan-Si, Huikyong, Liang, Michal...and if I forgot someone, I hope they will forgive me.

Finally I want to thank my family, for being the constant presence that, regardless the