Danielle Laurencin

Nicolas Dupre

Axelle Rmn

Estelle Grelard

Morvan

Eric Lebraud

Stanislav Pechev

Francois Fauth

Mortemard Benoit

Stéphane De Boisse

Didier Toulin

Abder Campagne

Salhi

Je

Marie Guignard

Liliane Guerlou-Demourgues

Jacob Olchowka

Emmanuel Petit

Jérôme Kalisky

Frédéric Brigitte Pecquenard

L E Cras

François Weill

Damien Cindy

Maël, Kenneth Camille Fiona

Adrien Julien

Manon Clémence

Léopold Pauline Patrick

Clément, Maxence, Grégoire Alex Thibault

Nikko Jacques Pascal

Seb, Fab', César, Yann Greg Ainsi

Danielle Dave

Chelsey

Blosom

Kris

Annie-Kim « Canadab

Adrien « La Bière C'est De L'eau »

Fatima « Ronando

Wallah

Gwen

Valentin « Vola

Vadim, Léah, Edgar, Sunkyu, Damieng, Elodie, Cedric Très Tchatcheur »

Thibault, Céline Vincent Paula

Ségolène, Louisiane, Tahya Alberto Laura

Max Florian

Charlotte « Va

Dans un premier temps, je voudrais remercier tout particulièrement mon encadrante de thèse, Dany CARLIER pour sa bienveillance et la confiance qu'elle m'a accordé pour mener ce projet. Je tiens également à remercier mes co-encadrants, Claude DELMAS pour son et Gillian GOWARD pour son accueil au sein de son équipe pendant deux mois.

Je tiens également à remercier Mario MAGLIONE en sa qualité de directeur du laboratoire mais aussi en sa

General Introduction

The lamellar oxides, AxMO2 (A = alkali ions, M = transition metal ions) are phases largely studied in solid-state chemistry. They can be described as an alternation of MO2 slabs formed by CoO6 octahedra and interslab spaces in which x A + ions are intercalated. Depending of the slabs packing, the alkali ions can intercalate in sites with different possible geometries. For instance, on Figure GI-1, the A + ions are represented in octahedral sites. In order to describe easily the lamellar oxides, Delmas et al. [START_REF] Delmas | Structural classification and properties of the layered oxides[END_REF] proposed a specific nomenclature in 1980. This nomenclature is composed of letter(s) which correspond to the intercalation site geometry for the alkali ions and one number corresponding to the number of Ax interslab spaces necessary to describe the hexagonal unit cell.

If the cell undergoes a distortion (monoclinic or orthorhombic), then a ' symbol is used in the structure name. Generally, for the LiMO2 phases, the Li + ions are intercalated in octahedral sites and it is necessary to include three interslab spaces in the structure to describe the unit cell of the materials leading to an O3 structure. For instance, the O3-LiCoO2 phase is well-known because of its high electrochemical performances as positive electrode material for Li-ion batteries. It was commercialized by SONY in 1991 for mobile applications. On this system, Li deficient phases can be only prepared by chemical or electrochemical deintercalation. Several other stacking sequences can be thus observed as O1 2 .

If Li + ions are replaced by Na + ions, the variety of layered NaxMO2 phases that can be synthetized is much larger. The larger Na + ions size (0.99 Å) compared to Li + (0.59 Å) 3 can be localized either in octahedral or in prismatic sites with two or three interslab spaces in their unit cell (usually O2, P2 and P3 structures) depending on the synthesis conditions like the nature of the transition metal ions, the synthesis temperature or the initial Na + /M ratio used for the synthesis [4][5][START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] . Figure GI-2 proposes an overview of the different polytypes that can be synthetized for NaxCoO2 depending of the temperature and initial Na + /Co ratio and highlights the rich phases diagram of the NaxCoO2 systems.

Figure GI-2:

Phases diagram of NaxCoO2. The grey zones represent the single phase synthesis zones while the white zones are the multiple phases synthesis zones. Extracted from [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Many NaxMO2 systems are (re)investigated as positive electrode material for Na-ion batteries because of a drastic decrease of the Li resources amount involving a large increase of the Li materials precursors price compared to the Na precursors like Na2CO3 [START_REF] Eshetu | Comprehensive Insights into the Reactivity of Electrolytes Based on Sodium Ions[END_REF][START_REF] Yabuuchi | Research Development on Sodium-Ion Batteries[END_REF] . The interest for P2-NaxMO2 and especially, the P2-NaxCoO2 system was reactivated with reports concerning the Na0.5CoO2 phase in 1997 [START_REF] Terasaki | Large thermoelectric power in NaCo2O4 single crystals[END_REF][START_REF] Takada | Superconductivity in two-diemnsional CoO2 layers[END_REF] and later the hydrated NaxCoO2 phases, showing interesting thermoelectric power and superconductivity performances [START_REF] Chou | Thermodynamic and transport measurements of superconducting Na0.3CoO2• 1.3 H2O single crystals prepared by electrochemical deintercalation[END_REF][START_REF] Landron | Ab initio evaluation of the local effective interactions in the superconducting compound Na0.35CoO2•1.3 H2O[END_REF] . Lee et al. [START_REF] Lee | Large enhancement of the thermopower in NaxCoO2 at high Na doping[END_REF][START_REF] Lee | Enhancement of the thermopower in NaxCoO2 in the large-x regime (x>0.75)[END_REF] also showed an enhancement of the thermopower for x > 0.75 in P2-NaxCoO2. In 2004, Huang et al. [START_REF] Huang | Low temperature phase transitions and crystal structure of Na0. 5CoO2[END_REF] showed that the ordered phase Na1/2CoO2 exhibits a metal-insulator transition at 53 K, increasing the interest about this system and its peculiar phases. KxCoO2 proposed, also interesting physical properties and especially magnetic and electronic properties for different x values (x = 0.67, x = 0.5 [START_REF] Delmas | Les bronzes de cobalt KxCoO2 (x< 1). L'oxyde KCoO2[END_REF] and x = 0.36 [START_REF] Fu | Structural, Transport and Magnetic Properties of KxCoO2 (x = 0.36)[END_REF] ). K0.36CoO2 has a semi-conductor behavior while K0.5CoO2 and K0.67CoO2 have a metallic behavior. KxMO2 systems were investigated as positive electrode material for K-ion batteries as an alternative to the Na and Li-ion batteries. Komaba and coworkers [START_REF] Hironaka | P2-and P3-KxCoO2 as an electrochemical potassium intercalation host[END_REF] proposed the first investigation of KxCoO2 as positive electrode material with two different polytypes, P2 and P3 after the first report of the phases synthesis in 1975 [START_REF] Delmas | Les bronzes de cobalt KxCoO2 (x< 1). L'oxyde KCoO2[END_REF] . Note that other lamellar oxides were tested for K-ion batteries as KxFe0.5Mn0.5O2 20 , KxMnO2 [START_REF] Vaalma | Non-aqueous K-ion battery based on layered K0. 3MnO2 and hard carbon/carbon black[END_REF][START_REF] Liu | Layered potassium-deficient P2-and P3-type cathode materials KxMnO2 for K-ion batteries[END_REF] , KxMn0.9Mg0.1O2 23 or KxCrO2 [START_REF] Hwang | Development of P3-K0. 69CrO2 as an ultra-high-performance cathode material for K-ion batteries[END_REF] . Moreover, many studies focused on other phases as polyanionic or Prussian blue compounds which present, also, interesting electrochemical performances [START_REF] Hosaka | Polyanionic Compounds for Potassium-Ion Batteries[END_REF] .

In this manuscript, we propose to study the average structure of different layered systems used as battery positive electrode materials by ex-situ and in-situ X-Ray Diffraction (XRD) but also the local structure and electronic structure by solid state Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR). MAS NMR was already performed successfully in the solid state chemistry field for the investigation of many local and electronic structures and especially in the group, for NVPF [START_REF] Nguyen | Stability in water and electrochemical properties of the Na3V2(PO4)2F3-Na3(VO)2(PO4)2F solid solution[END_REF] , phosphate [START_REF] Castets | Analysis of the 7 Li NMR signals in the Monoclinic Li3Fe2(PO4)3 and Li3V2(PO4)3 Phases[END_REF] or tavorite [START_REF] Boivin | LiVPO4F1-yOy Tavorite-Type Compositions: Influence of the Concentration of Vanadyl-Type Defects on the Structure and Electrochemical Performance[END_REF] structures for example. MAS NMR is a powerful technique which can be used in the battery domain [START_REF] Grey | NMR Studies of Cathode Materials for Lithium-Ion Rechargeable Batteries[END_REF][START_REF] Pecher | Materials' methods: NMR in battery research[END_REF] . In fact, NMR allows the investigation of different parts of a battery as the electrodes, the electrolyte, the interfaces or the SEI [START_REF] Dupré | Positive electrode materials for lithium batteries based on VOPO4[END_REF][START_REF] Trease | In situ NMR of lithium ion batteries: Bulk susceptibility effects and practical considerations[END_REF][START_REF] Kitada | Unraveling the Reaction Mechanisms of SiO Anodes for Li-Ion Batteries by Combining in Situ 7 Li and ex Situ 7 Li/ 29 Si Solid-State NMR Spectroscopy[END_REF][START_REF] Key | Real-time NMR investigations of structural changes in silicon electrodes for lithium-ion batteries[END_REF][START_REF] Dupré | Electrode/electrolyte interface studies in lithium batteries using NMR[END_REF][START_REF] Dupré | Relationship between surface chemistry and electrochemical behavior of LiNi1/2Mn1/2O2 positive electrode in a lithium-ion battery[END_REF][START_REF] Marino | Study of the Electrode/Electrolyte Interface on Cycling of a Conversion Type Electrode Material in Li Batteries[END_REF][START_REF] Bouayad | Improvement of electrode/electrolyte interfaces in highvoltage spinel lithium-ion batteries by using glutaric anhydride as electrolyte additive[END_REF] . Moreover, NMR is an interesting technique to get information about the mechanisms occurring during an electrochemical cycling [START_REF] Clément | Direct evidence for high Na mobility and high voltage structural processes in P2-Nax[LiyNizMn1-y-z]O2 (0< x, y, z< 1) cathodes from solid-state NMR and DFT calculations[END_REF][START_REF] Clément | Short-range order and unusual modes of nickel redox in a fluorine-substituted disordered rocksalt oxide lithium-ion cathode[END_REF] .

In this work, two original layered oxides are, firstly, reported in the chapters II and III, respectively, OP4-(Li, Na)CoO2 and O4-LiCoO2. The OP4 phase was reported for the first time by Balsys and Davis in 1994 [START_REF] Balsys | The structure of Li0. 43Na0. 36CoO1. 96 using neutron powder diffraction[END_REF] and can be described as an 1:1 alternation of Na and Li interslab spaces intercalated between the CoO2 slabs along the c axis while the O4-LiCoO2 phase proposed an 1:1 alternation of O3 and O2-type Li interslab spaces. Both phases were already investigated in the group during Romain Berthelot PhD [START_REF] Berthelot | Synthesis and Investigations on an O4-LiCoO2 Polytype[END_REF][START_REF] Berthelot | Contribution à l'étude électrochimique du système P2-NaxCoO2. Synthèse et caractérisation de nouveaux oxydes lamellaires ordonnés (A/A')CoO2 (A[END_REF][START_REF] Berthelot | Reinvestigation of the OP4-(Li/Na)CoO2 -Layered System and First Evidence of the (Li/Na/Na)CoO2 Phase with OPP9 Oxygen Stacking[END_REF] . He mainly studied their average structures by XRD, the influence of the temperature on their structures and their electrochemical properties. In this work, we correlated together, thanks to NMR acquisitions, the average, the local and the electronic structures of both phases. A specific attention was also given to the understanding of the chemical formula of both materials and to the ionic mobility of the Li + ions in both structures with 2D MAS NMR acquisitions. I investigated the dynamics of the Li + ions in both phases in McMaster University (Hamilton, Canada) under the supervision of Gillian Goward during two one-month visits in 2017 and 2018.

Then, we focused our study on layered oxides for Na-ion batteries, P2-NaxCoyMn1-yO2 (y = 2/3, 1/2, 1/3 and 1) and O3-NaxRuO3 which propose interesting electrochemical properties [START_REF] Carlier | The P2-Na2/3Co2/3Mn1/3O2 phase: structure, physical properties and electrochemical behavior as positive electrode in sodium battery[END_REF][START_REF] Mortemard De Boisse | Intermediate honeycomb ordering to trigger oxygen redox chemistry in layered battery electrode[END_REF] . A new formulation of electrolytes allows to reach, reversibly, higher voltages than previously. Therefore, a new part of the P2-NaxCoO2 phases diagram can be reached for low Na + contents, in fact, Berthelot et al. [START_REF] Berthelot | Electrochemical investigation of the P2-NaxCoO2 phase diagram[END_REF] studied this system by in-situ XRD but limited his investigations to x > 1/2. In the chapter IV, we report the electrochemical properties of the P2-NaxCoyMn1-yO2 (y = 2/3, 1/2, 1/3 and 1) systems in two voltage ranges. Moreover, we propose the investigation of the structural evolution of these systems during the Na + deintercalation by in-situ XRD.

The chapter V focuses on the P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 systems. Different phases were synthetized at specific voltages by an electrochemical technique and analyzed by ex-situ XRD and 23 Na MAS NMR in order to understand the mechanisms involved by the Na + deintercalation.

Finally, the chapter VI proposes the investigation of the local structure evolution of the O3-NaxRuO3 system by ex-situ 23 Na MAS NMR in collaboration with Benoît Mortemard de Boisse (from Pr. Yamada group in Tokyo). Previous studies [START_REF] Mortemard De Boisse | Intermediate honeycomb ordering to trigger oxygen redox chemistry in layered battery electrode[END_REF][START_REF] Mortemard De Boisse | Coulombic self-ordering upon charging a large capacity layered cathode material for rechargeable batteries[END_REF] reported an extra capacity due to the participation of the oxygen ions in the redox process. The different phases were synthetized in Japan with the same technique than in the chapter V and only the 23 Na MAS NMR results are proposed in this chapter.

The lamellar oxides

O3-NaFeO2 structure

In 1933, Goldzstaub [START_REF] Goldsztaub | Structure cristalline du ferrite de sodium[END_REF] The hexagonal description allows to represent the cell as a stacking of FeO2 and NaO2 slabs with a 1:1 alternation in the case of O3-NaFeO2 (Figure GI-1). The atomic positions are reported by Takeda et al. [START_REF] Takeda | Sodium deintercalation from sodium iron oxide[END_REF] as Na (3a, 0, 0, 0), Fe (3b, 0, 0, 1/2) and O (6c, 0, 0, ZO).

The different polytypes and their intercalation sites

The other lamellar oxide polytypes can be obtained by considering elemental symmetry operations on the O3 structure as translations or rotations. By considering these operations, changes in the intercalation sites and in the oxygen ions positions lead to the P2, P3 or O2 structures (Figure I-3). P sites correspond to prismatic interstitial sites for the alkali ions intercalation. In this report, materials with prismatic and octahedral sites are reported that's why a short overlook of every stacking is necessary. Note that other intercalation sites are reported in the literature like tetrahedral (T) [START_REF] Tournadre | The T # 2-Li2/3Co2/3Mn1/3O2 System[END_REF] or linear (D for Dumbbell) [START_REF] Shin | Preparation and magnetic properties of some new layer rocksalt-and mixed delafossite-type oxides[END_REF] . The O3 structures are obtained for A + /M ratio close to one. Note that lamellar oxides O3-LiMO2 can be synthetized only for M = Cr, Co, Ni or V while the panel of 3d transition metals is larger concerning the synthesis of O3-NaMO2 (for instance O3-NaCoO2 [START_REF] Siegel | 59 Co, 23 Na NMR and electric field gradient calculations in the layered cobalt oxides NaCoO2 and HCoO2[END_REF] ).

 In the P3 structure, the A + ions share simultaneously edges and faces with the surrounding MO6. They are usually synthetized at moderate temperature (≈500°C) and for low A + /M ratio (≈0.6) [START_REF] Delmas | Structural classification and properties of the layered oxides[END_REF] .

Chapter I

 In the P2 structure, the prismatic sites can either share edges (site labelled Ae) or faces (site labelled Af) with the surrounding MO6. As the electrostatic repulsions are more intense between the A + in Af sites and the M ions, the Ae sites are favored for the A + intercalation involving amount of A + ions in Ae twice bigger than in Af.

Finally, for the structures with prismatic sites, filling the whole interslab spaces with Na + ions is impossible due to the too large Na + ions size compared to the distance between the neighbor sites.

This point isn't true for lithium in octahedral sites and explained why the Li interslab spaces are totally full after thermal treatment. Moreover, each structure can be described by a specific space group and specific atomic positions. These data are summarized in Table I.1.

Structure Space Group

Atomic positions A M O A e

A f O3 R𝟑 ̅ m (#166) 3b (0, 0, 1/2) 3a (0, 0, 0) 6c (0 0 z) z ≈ 0.27

P3

R𝟑 ̅ m (#166) 6c (0, 0, z) z ≈ 0.84 3a (0, 0, 0) 6c (0 0 z) z ≈ 0.4

P2

P6 3 /mmc (#194) 2b (2/3, 1/3, 1/4) 2d (0, 0, 1/4) 2a (0, 0, 0) 4f (1/3, 2/3, z) z ≈ 0.09 However, there is a large debate concerning the stabilized orbital(s) between a1g and eg'. In fact, the band structures [START_REF] Singh | Electronic structure of NaCo2O4[END_REF][START_REF] Baskaran | Electronic Model for CoO2 Layer Based Systems: Chiral Resonating Valence Bond Metal and Superconductivity[END_REF] , ab-initio calculations [START_REF] Landron | Ab initio evaluation of the local effective interactions in the superconducting compound Na0.35CoO2•1.3 H2O[END_REF] or angle-resolved photoemission spectroscopy (ARPES) experimental measurements [START_REF] Yang | Fermi surface evolution and Luttinger theorem in NaxCoO2: a systematic photoemission study[END_REF] suggest that the orbitals eg' are stabilized at a lower energy than a1g while LDA calculations [START_REF] Johannes | Nesting, Spin Fluctuations, and Odd-Gap Superconductivity in NaxCoO2• y H2O[END_REF] found the opposite result. Landron and Lepetit [START_REF] Landron | An ab initio evaluation of the local effective interactions in the NaxCoO2 family[END_REF] showed that the controversy was due to an incorrect treatment of the correlation integrals within the 3d shell. They proposed as model to consider the two cobalt sites Co (1) and Co(2) in Na0.5CoO2. For both cobalt sites, the a1g orbitals are much energetically higher than the eg' orbitals. The model proposes also at the Fermi level, providing "heavy" and "light" charge carriers. This point suggests that delocalized and localized electrons contribute to the electronic structure for NaxCoO2. Chapter I 20

Na-ion and Na batteries 2.1 Principles

The Na and Na-ion batteries are technologies composed of a positive electrode, a negative electrode and an electrolyte (Figure I-9a). During this report, the terms negative and positive electrode are favored instead of cathode and anode in order to avoid any misunderstanding as the cathode and anode side changes depending if the battery is charging or discharging. The electrolyte separates both electrodes and is usually a sodium salt dissolved in an organic or aqueous solvent. The electrolyte ensures the ionic conductivity from one electrode to the other. It is important to distinguish the difference between a Na battery and a Na-ion battery, in fact, both terms differ by the nature of the material used as negative electrode. For the Na batteries, the negative electrode is sodium metal (Na(s)). The Na-ion batteries term is used for the batteries with an Na + intercalation material as negative electrode. These materials involve no reduction or oxidation of the Na + ions but only, as their name indicates, an intercalation. In this work, we only made Na-batteries.

During the charge of a Na battery, a current is applied imposing the electrons flux from the positive to the negative electrode through the external circuit. In order to balance the charge neutrality of the positive electrode material, Na + ions are removed from the interslab spaces into the electrolyte and reach the negative electrode where they are reduced. Moreover, the extraction of the electrons from the positive electrode involved an oxidation of the metal transition ions. The following equations summarize the phenomena happening during the charge.

𝑁𝑎 𝑥 𝑀𝑂 2 → 𝑁𝑎 𝑥-𝑥 ′ 𝑀𝑂 2 + 𝑥 ′ 𝑁𝑎 + + 𝑥 ′ 𝑒 -(𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒) 𝑥 ′ 𝑁𝑎 + + 𝑥 ′ 𝑒 -→ 𝑥 ′ 𝑁𝑎(𝑠) (𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒)

During the discharge (no applied current), the phenomena are reversed involving a reduction of the transition metal ions in the positive electrode material and an intercalation of the Na + ions inside Peculiar phase. This behavior is characterized by an abrupt voltage jump (in charge) or drop (in discharge) on the galvanostatic curve. It highlights the presence of a single phase obtained for a specific Na + content with a Na + /vacancy ordering in the interslab spaces. Usually, the Na + /vacancy

Chapter I

ordering involves the appearance of a supercell and therefore superstructures peaks on the XRD patterns.

Biphasic domain. Two phases are in equilibrium involving a voltage plateau. Along the plateau, only the proportion of both phases in equilibrium is changing.

Solid Solution. The E = f(x or t) curves evolve smoothly and it means that the structure remains the same while only the Na + content is modified during the cycling.

The other technique reported in this work is the potentiostatic experiment which consists of applying a constant voltage and to monitor the current evolution as a function of time or x. The combination of both techniques was useful in order to synthetize phases at selected voltage on the different studied systems and will be discuss later in this chapter.

Electrochemical properties

In order to characterize the electrochemical performances of the different materials, it is necessary to introduce different variables.

Sodium content (x) and capacity (Q)

These variables are the most used in this report and are directly correlated one to each other. x corresponds to the concentration of Na + ions in the NaxMO2 materials at a specific moment. x is dimensionless. Q represents the electrical charge that the battery can store or deliver. Q is expressed in A.h and can be expressed as follows: ∆𝑥: number of (de)intercalated sodium at a specific time m: weight of active material (g) M: molecular weight of active material at t = 0 (g.mol -1 )

For NaxMO2 materials, ∆𝑥 is included between 0 and 1.

Specific capacity (𝑄 𝑚 )

Usually the capacities values correspond to the discharge one and are expressed per weight of active material in order to be comparable to other systems. This value is labelled 𝑄 𝑚 and called specific capacity. It is expressed in A.h.g -1 .

Charge and discharge voltages

In order to realize electrochemical cycling and especially for the galvanostatic measurements, two voltages have to be introduced. The cutoff voltage represents the maximal voltage value imposed during a charge while the discharge voltage is the minimal voltage value imposed during a discharge. In this report, the voltage values are reported against the Na + /Na redox couple because our reference electrode was the negative electrode, Na(s).

Cycling rate

The rate is directly correlated to the applied current for a galvanostatic measurement. It corresponds to the time (t) that needs the system to reach the maximal charge/discharge capacity for ∆𝑥 = 1.

Chapter I

25

𝐼 = 𝑄 𝑚 𝑡 ⁄

This rate is labeled C/t. For example, C/20 means that 20 h are necessary to (de)intercalate 1 mol of Na + ions.

2.4 Preparation for the galvanostatic measurements

Positive electrode preparation for galvanostatic cycling

In this report, the positive electrodes were a mixture of the studied material, black carbon (a mixture of graphite and soot) and polytetrafluoroethylene (PTFE) for the galvanostatic cycling in an 88:10:2 wt ratio. All the powders were ground together in an Ar-filled glovebox. The black carbon is used in order to improve the electric conductivity of the electrode while PTFE allows to maintain all the compounds together and therefore, to obtain electrodes easier to handle. After the mixing, a paste is obtained and a circular electrode with 10 mm diameters was cut with a mass included between 20 and 50 mg.

Coin Cell assembly

In this work, the galvanostatic measurements were performed in sealed coin cells assembled in a Ar-filled glovebox in order to avoid either the reaction of the metal sodium with water or the oxidation of the solid sodium with the air. After sealing, the coin cell can be removed from the glovebox and be connected to a galvanostat.

The ECLAB software was used to set up all the electrochemical measurements and to monitor the evolution of the current as a function of time or x.

Synthesis by electrochemical (de)intercalation

In this report, some phases were synthetized by electrochemical (de)intercalation. This technique needs two steps: (1) a galvanostatic (dis)charge to the targeted voltage at a selected C/t rate. ( 2

Characterization techniques

X-Ray Diffraction (XRD)

XRD was used as a structural characterization technique to determine for example, the lattice parameters of the synthetized powders, the space group or the atomic positions, in fact, XRD gives information about the average structure of an analyzed sample. In this work, as the studied materials were air-sensitive, the samples were packed in airtight systems for the XRD characterization.

Ex-situ XRD

Many diffractometers are available at ICMCB and have their own advantages and drawbacks. In this manuscript, the XRD patterns were mainly collected on two of them using two different techniques of samples packing.

 PANalytical X'Pert Pro uses Co K𝛼 1,2 radiations. The air-sensitive samples have to be placed in an airtight sample holder for the analyses on this diffractometer. The none airsensitive samples can also be analyzed easily with this diffractometer.

 PANalytical X'Pert 3 Powder uses Cu K𝛼 1,2 radiations. The air-sensitive samples have to sealed in an airtight capillary for the analyses on this diffractometer. The samples were ground for a long time before the packing because the capillaries have a small diameter of 0.3 mm for the acquisitions at ICMCB. The powder was, then, loaded in the capillary inside the glovebox and sealed with a flame to ensure the airtightness outside the glovebox. In this report, only glass capillaries were used. The advantage of this technique is the use of a low amount of powder but only Cu K𝛼 1,2 radiations were available on the corresponding diffractometer.

In-situ XRD (Synchrotron radiations)

Some samples were analyzed using Synchrotron radiations. For the Synchrotron XRD characterization, the filling and sealing techniques of the capillaries were the same than for the laboratory acquisitions but with 0.5 mm diameter capillaries. The acquisitions were performed on the BL04-MSPD beamline of the ALBA synchrotron facilities (Cerdanyola del Vallès, Spain) in collaboration with Francois Fauth. The data were collected for 2θ from 2° to 73° with a wavelength of λ = 0.8261 Å.

Moreover, XRD acquisitions in-situ i.e. during the charge and the discharge of the battery were also performed. We used a specific home-made coin cell in order to let the beam pass through the electrochemical cell without any air contamination.

In-situ XRD allows to monitor the materials structural evolution during the Na + (de)intercalation in order to have an insight of the structural changes occurring during the charge and the discharge.

In order to let the beam pass through the coin cells, 3 mm diameters holes had been drilled at ICMCB in both current collectors and in the support where the metal sodium negative electrode was deposed. Moreover, to ensure the airtightness of the cell, a 7 mm diameter polyimide had been stuck on both current collector holes (Figure I-14b). Moreover, to improve the sticking, the Kapton film and the current collectors faces had been abraded. Finally, a 10 mm diameter thin aluminum foil had been inserted between the positive electrode and the positive current collector to improve the conductivity between both. The next steps of the assembly were the same than for the usual coin cell. Some tests had been realized before assembling on the drilled coin cells in order to see if the electrolyte reacts or not with the glue. The electrolyte had been poured in the current collectors and after one day, no leakage had been observed between the polyimide film and the current collectors.

In ALBA, four coin cells were plugged to a galvanostat/potentiostat at the same time. The data were collected from 2° to 45° while the batteries were cycled. Some additional peaks on the patterns are due to the different elements like the graphite in the black carbon, the PTFE, the aluminum or the sodium foil.

Nuclear Magnetic Resonance (NMR)

Generalities

Zeeman effect

Each atom is characterized by a specific quantum number, I (also called nuclear spin quantum number). I value depends of the nucleons number A and the Z number parity. If A and Z are both even, I is null. If A is odd, I is half integer and if A is even and Z odd, I is a whole number. The NMR measurements are only possible on non-null I value atoms.

If I is different from zero, I is associated to a spin magnetic moment without any preferential orientation without a magnetic field. But by applying a magnetic field 𝐵 0 ⃗⃗⃗⃗ , the spin magnetic moment can be aligned either in the parallel or in the anti-parallel direction to 𝐵 0 ⃗⃗⃗⃗ . Two energy levels are, then, created by the magnetic field ( The samples are placed under a 𝐵 0 ⃗⃗⃗⃗ magnetic field which induces the Zeeman effect described previously. The spin excess in the 𝐵 0 ⃗⃗⃗⃗ direction involves the appearance of a macroscopic nuclear magnetization 𝑀 ⃗⃗ also aligned with the magnetic field. In order to provide the adequate energy quantum 𝜔 0 = 𝛾𝐵 0 necessary to the transition between the Zeeman levels, an additional 𝐵 1 ⃗⃗⃗⃗ magnetic field is used. This additional magnetic field oscillates in a plane perpendicular to 𝐵 0 ⃗⃗⃗⃗ and at the 𝜔 0 frequency. Consequently, the population of both spins (up and down) tends thus to become similar. When the magnetic field 𝐵 1 ⃗⃗⃗⃗ is cut off, the system recovers its equilibrium state.

By applying 𝐵 1 ⃗⃗⃗⃗ , the magnetization is removed from its equilibrium position (along 𝐵 0 ⃗⃗⃗⃗ ) with an angle 𝛼 = 𝛾𝐵 1 𝜏 where 𝜏 is the time during which 𝐵 1 ⃗⃗⃗⃗ is applied. Due to the angular momentum theorem, the magnetization have a precession movement around the 𝐵 0 ⃗⃗⃗⃗ axis. This precession frequency is called Larmor frequency and is equal to 𝜔 0 . For a magnetization brought in the plane After the perturbation, the measured signal decreases due to two relaxation mechanisms:

-The T2-type relaxation which expresses the defocusing of the magnetizations induced by the different interactions on the individual spins in the (x',y') plane.

-The T1-type relaxation which expresses the recovery of M ⃗⃗⃗ along 𝐵 0 ⃗⃗⃗⃗ .

In solid state NMR, T1 >> T2 and the temporal evolution of magnetization measured in the (x',y') plane is called Free Induction Delay (FID). A Fourier transformation of the FID monitored in the (x',y',z') plane gives the NMR spectrum in Hz or ppm. An NMR acquisition corresponds at the repetition of this experiment in order to increase the quality (signal/noise ratio) of the NMR spectrum. A 𝐷 0 time is added between each experiment in order to allow the system to come back to equilibrium (𝐷 0 ≈ 5 * 𝑇1). Experimentally, the samples are packed in a rotor and are placed at the 𝜃 𝑅 magic angle formed with 𝐵 0 ⃗⃗⃗⃗ at fast spinning. Different NMR spectrometers with different magnets are commercialized and, therefore, different magnetic fields can be used for the acquisitions. By using the MAS, the spinning side bands become closer when the magnetic field increases. Chapter I 35

Hyperfine interaction

NMR is sensitive to the presence of single electrons in the probed nucleus environment. The hyperfine coupling between a single electron and the probed nucleus involves a NMR shift and a signal broadening. The Hamiltonian of the hyperfine interaction 𝐻 𝑆𝐼 between single electrons can be written as follows: Regarding, the Hamiltonian formula, the hyperfine interactions have two contributions: The Fermi contact interaction and the dipolar interaction.

𝐻 𝑆𝐼 = 𝐴

Fermi contact interaction

This interaction is due to the presence of single electrons spin density transferred from the transition metal ion (M) orbital to the s orbital of the alkali ion via the 2p orbital of the oxygen ion leading to M-O-A bond pathway .The Fermi contact involves, generally, important NMR shifts called Fermi contact shifts and is observed for paramagnetic compounds. The NMR shift signal due to Fermi contact can be expressed as follows [START_REF] Bertini | Magnetic susceptibility in paramagnetic NMR[END_REF] : By combining both expressions, one obtained an easier expression considering only magnetic susceptibility and the spin density at the probed nucleus:

𝛿 𝑖𝑠𝑜 𝑖 = 𝐴 𝑖 ħ 𝜒 𝑀 (𝑇) 𝜇 0 𝛾 𝑖 𝑔 𝑒 𝜇 𝐵
𝛿 𝐹𝑒𝑟𝑚𝑖 𝑖 = 1 3𝑆𝑁 𝐴 𝜌 𝑖 (0)𝜒 𝑀 (𝑇)
If the nucleus environment is composed of many paramagnetic transition metal ions, the Fermi contact shifts are cumulative, each contribution is added in order to get the total shift. Moreover, the Fermi contact is also temperature dependent as shown by 𝜒 𝑀 (𝑇) in the previous equations.

Schematically, the Fermi contact represents the amount of electronic spin transferred from a metal transition ion to the probed nucleus through bonds (Figure I-18 in the case of 23 Na MAS NMR and a 90° interaction). Note also that the sign and magnitude of the individual shift strongly depend of the geometry of the material, the covalency of the bond pathway, the occupation of the t2g and eg orbitals occupation and the magnetic state of the material.

Figure I-18:

Representation of the Fermi contact shift for a 90° interaction between a half-filled t2g orbital of a M ion and a Na nucleus via an 2p orbital of the oxygen ion.

Dipolar interaction

Dipolar interaction is an interaction between the electronic spin and the probed nuclear spin trough the space and have a 1/r 3 dependence. Thus, the dipolar interaction strongly depends of the distance between the single electrons and the probed nucleus. As explained previously, this interaction (as every dipolar interaction) is partially removed by the MAS due to an anisotropic nature contribution. However, the isotropic contribution is called dipolar shift or "pseudocontact".

Usually, the Fermi contact shift contribution is stronger than the pseudo-contact. For instance, in the oxides NMR [START_REF] Mustarelli | Transferred hyperfine interaction and structure in LiMn2O4 and Li2MnO3 coexisting phases: A XRD and 7 Li NMR-MAS study[END_REF][START_REF] Lee | 6 Li and 7 Li MAS NMR Studies of Lithium Manganate Cathode Materials[END_REF] , the pseudo-contact shift can be neglected compared to the Fermi contact. It is also the case for the lamellar oxides with transition metal ions in their structure. If the spinning (at Magic Angle) is not fast enough, an anisotropic contribution of the hyperfine interaction is in charge of the signal broadening and have consequences on the isotropic signal position. Thus, it is necessary to spin the rotors at the maximum rate that the rotor size allows.

Chapter I 38

Knight shift

The Knight shift is observed for metallic phases and is due to the electronic spin density on the probed nucleus. However, contrary to the Fermi contact, the electronic density depends of the participation of the electrons in the "s" orbitals contribution at the Fermi level of the probed nucleus

Quadrupole Coupling

The quadrupolar coupling magnitude depends on the interaction between an electric field gradient (EFG) and on the nuclear electric quadrupole moment at the probed nucleus (Q). The Hamiltonian for the first order can be written as follows: . MAS allows to remove completely or partially, the first and second order isotropic signal broadening effects. However, a part of the second order term of HQ can't be removed by MAS and broadens the central transition signal. This second-order term involves a small additional contribution to the total shift which varies inversely to B0 2 , with B0 the strength of the magnetic field. Consequently, high magnetic fields reduce the magnitude of this contribution and therefore, the broadening of the spectral line due to the quadrupolar interaction. The signals can be fitted using the DMFit software [START_REF] Massiot | Modelling one-and two-dimensional solid-state NMR spectra[END_REF] in order to determine the different quadrupolar parameters. [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li, [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li and 23 Na nuclei. Table I-2 shows the that 6 Li, [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li and 23 Na are quadrupolar nuclei because I > 1/2. The large quadrupole moment Q of the 23 Na nucleus compared to the two Li isotopes suggests that the quadrupolar interactions can't be neglected for 23 Na MAS NMR and that the first and second order quadrupolar terms have to be taken into account to interpret the 23 Na MAS NMR spectra. As the [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li and [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li quadrupolar moments are low compared to the hyperfine interactions, the quadrupolar contribution can be neglected for these nuclei. Figure I-20 represents the influence of the first and second orders quadrupolar terms on the 23 Na energy level. The first order term doesn't affect the central transition for 23 Na. However, the second order quadrupolar interaction affects all the energetic transitions. Note that in many cases, the broadening of the satellite transitions (ST) is so important that only the central transition can be observed on the different spectra.

𝐻 𝑄 = 𝑒𝑄 2𝐼(𝐼 -
Chapter I 41

1D NMR pulse sequences

Many parameters can be modified in an NMR pulse sequence. For 1D NMR, two pulse sequences had been mainly used during this work, simple pulse and Hahn Echo.

Simple pulse sequence

This experiment is the most basic one in NMR and is similar to the description made previously

(

NMR for dynamics

The 2D NMR experiments have been developed in order to have information about the ionic dynamics in different phases. By performing dynamics NMR experiments in temperature, it is possible to experimentally probe the intermolecular potential in order to determine the dynamics rates [START_REF] Smiley | An Improved Understanding of Li + Hopping Pathways and Rates in Li3Fe2(PO4)3 Using Selective Inversion 6 Li NMR Spectroscopy[END_REF] . The dynamics NMR is based on the fact that the nuclear spin interactions depend of the molecular orientation within the applied magnetic field. In fact, the change of orientation is correlated with a change in some interaction strengths. 2D methods allow to study very slow dynamics by introducing a mixing time, 𝜏 𝑚 during which the molecular reorientation can occur.

Two periods in two different dimensions should also be considered: t1 and t2. During the t1 period, the strength of a particular nuclear spin interaction is monitored while during the t2, the new strength after the reorientation of the interaction is monitored. In order to obtain the 2D NMR spectrum, the interaction strengths during t1 and t2 are correlated. Finally, this experiment is repeated with different mixing times. In the 2D NMR experiments through this report, mixing times allow a chemical exchange between the different sites observed with 1D MAS NMR. Extracted from [START_REF] Duer | Solid-state NMR spectroscopy: principles and applications[END_REF] .

The limitation of this technique concerns the time scales because one supposes that there are no molecular dynamics or chemical exchange during t1 and t2 and that all the dynamics/exchanges occur during the mixing times. That's why it is necessary that 𝜏 𝑚 >> t1, t2. For the solid state NMR, these experiments have to be performed with the MAS which allows to monitor only the chemical exchanges. In our case, MAS NMR suggested the presence of several sites in 1D NMR and allowed us to study potential correlations between the different sites.

Chapter I 46

DFT calculations

Principle

Hohenberg and Kohn are at the origin of DFT calculations by proving that the total energy of a gas of electrons in attendance of a extern potential Vext(𝑟 ) can be expressed as :

𝐸(𝜌) = ∫

In the case of colbatates

The first principles calculations were performed within the Density Functional Theory (DFT)

framework. In a previous study of the group, they showed that PAW-PBE potentials as implemented in the Vienna ab initio Simulation Package (VASP) code [START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF] can be used to compute theoretically the Fermi contact shifts in paramagnetic materials [START_REF] Bamine | Understanding Local Defects in Li-Ion Battery Electrodes through Combined DFT/NMR Studies: Application to LiVPO4F[END_REF] . A plane wave energy cut-off of 600 eV and a k-mesh dense enough to reach a convergence were used. All the calculations were done with a ferromagnetic ordering which is considered appropriate for the Fermi contact shift, as described in reference [START_REF] Carlier | Understanding the NMR shifts in paramagnetic transition metal oxides using density functional theory calculations[END_REF] . In the Generalized Gradient Approximation (GGA), the inherent self-

Chapter I

47 interaction error has detrimental effect on localized transition-metal d (or rare earth f) orbitals.

Although, the addition of a Hubbard U correction can produce theoretical average potentials or Fermi contact shifts in better agreement with experiments [START_REF] Aykol | van der Waals Interactions in Layered Lithium Cobalt Oxides[END_REF] , this method is not used in this study it has been shown to yield some unphysical results for layered cobalt oxide systems: phase stability inversion between O1 and O3 in CoO2 and incorrect phase diagram for the P2-NaxCoO2 system [START_REF] Hinuma | Temperature-concentration phase diagram of P2 NaxCoO2 from first-principles calculations[END_REF] .

On the contrary, GGA has been successfully used to describe the phase diagram of the LixCoO2 system [START_REF] Van Der Ven | First-principles investigation of phase stability in LixCoO2[END_REF] . The difficulty to properly model layered cobalt oxides probably comes from the dual character of the electronic properties: some electrons are fully delocalized leading to metallic conduction in plane [START_REF] Levasseur | Evidence for structural defects in non-stoichiometric HT-LiCoO2: electrochemical, electronic properties and 7 Li NMR studies[END_REF] and some are localized leading to a Curie-Weiss type paramagnetism [START_REF] Igarashi | Precise Control of Na Content in the Layered Cobaltate γ-NaxCoO2[END_REF] .

NMR shift calculation

The following equation is used to calculate the spin density, and uses the hyperfine coupling constant (𝐴 𝐹𝐶 ) determined by VASP in addition to the total number of unpaired electrons in the unit cell and gyromagnetic ratio of the nucleus to which spin density is being transferred to determine the total amount of spin density at each Na nucleus.

𝜌(0) = 𝐴 𝐹𝐶 3𝑆 𝜇 0 ℏ𝛾 𝐼 𝑔 𝑒 𝜇 𝐵
where 𝜇 0 is the permeability of free space, ℏ is the reduced Planck constant, 𝛾 𝐼 is the gyromagnetic ratio of the NMR observed nucleus, 𝑔 𝑒 is the electron g-factor, and 𝜇 𝐵 is the Bohr magneton. The expected paramagnetic contribution to the NMR shift can then be determined by taking into account the spin density at the nucleus (ρ(0)) and the magnetic susceptibility of the material (χ 𝑀 ) according to:

δ 𝑖𝑠𝑜,𝐹𝐶 = 1 3S ρ(0)χ 𝑀 Part A:
Study of the average structure, electronic structure and dynamics of the Li + ions in OP4-(Li,Na)CoO 2 and O4-LiCoO 2

Introduction

In this chapter, we were interested in a unique (Li/Na) mixed lamellar oxide with stacking of edge-shared CoO6 octahedra layers forming CoO2 slabs with an alternative occupation of the interslab spaces by Na + and Li + (Figure II-1) and first reported in 1994 by Balsys and Davis [START_REF] Balsys | The structure of Li0. 43Na0. 36CoO1. 96 using neutron powder diffraction[END_REF] .

This material was synthetized from the O3-LiCoO2 and P2-Na0.7CoO2 precursors in a 1:1 molar ratio, therefore the Li0.5Na0.35CoO2 ideal formula was, firstly, expected. However, the presence of LiCoO2 as impurity called the theoretical formula into question and a Li0.43Na0.36CoO1.96 phase composition was deduced from a Rietveld refinement on neutron diffraction data. The alkali ions keep the intercalation site symmetry of the used precursors: O3-LiCoO2 and P2-Na0.7CoO2, i.e.

octahedral and trigonal prismatic for the lithium and sodium ions respectively thus forming an OP4 stacking [START_REF] Delmas | Electrochemical intercalation of sodium in NaxCoO2 bronzes[END_REF] . Na + ions can, therefore, occupy either the Nae or the Naf sites [START_REF] Huang | Coupling between electronic and structural degrees of freedom in the triangular lattice conductor NaxCoO2[END_REF] By using O3-LiCoO2 and P2-Na0.7CoO2 as precursors for their synthesis, Balsys and Davis indicated the difficulty to obtain a pure phase. Additional publications proposed the synthesis of this phase without any consensus concerning the best precursors or thermal treatment to obtain the purest phase [START_REF] Berthelot | Reinvestigation of the OP4-(Li/Na)CoO2 -Layered System and First Evidence of the (Li/Na/Na)CoO2 Phase with OPP9 Oxygen Stacking[END_REF][START_REF] Ren | Enhanced thermopower in an intergrowth cobalt oxide Li 0.48Na0.35CoO2[END_REF][START_REF] Bos | Magnetic and thermoelectric properties of layered LixNayCoO2[END_REF][START_REF] Semenova | Raman spectroscopy study of sodium-lithium cobaltite[END_REF][START_REF] Kellerman | 23 Na NMR in binary lithium-sodium cobaltite[END_REF][START_REF] Mesilov | X-ray spectra and specific features of the structure of lithium-sodium cobaltite LixNayCoO2[END_REF][START_REF] Yabuuchi | A comparative study of LiCoO2 polymorphs: structural and electrochemical characterization of O2-, O3-, and O4-type phases[END_REF] . Table II-1 summarizes the chemical compositions and cell parameters reported in the literature for the OP4 phases. [START_REF] Berthelot | Reinvestigation of the OP4-(Li/Na)CoO2 -Layered System and First Evidence of the (Li/Na/Na)CoO2 Phase with OPP9 Oxygen Stacking[END_REF] .

In this chapter, since the layered OP4 phase is really original in solid state chemistry and might exhibit peculiar properties, especially because of a different occupation ratio of the alkaline layers, we decided to reinvestigate further its structure in order to have a better insight of the correlation between its chemical formula and its structure. We will investigate the local structure, the electronic structure and the dynamics of the Li + ions by NMR as a local probe. Note that the ionic mobility in the positive electrode materials was already probed in the literature by different technique as exchange spectroscopy [START_REF] Cahill | The challenge of paramagnetism in twodimensional 6, 7 Li exchange NMR[END_REF][START_REF] Davis | Study of lithium dynamics in monoclinic Li3Fe2(PO4)3 using 6 Li VT and 2D exchange MAS NMR spectroscopy[END_REF][START_REF] Cahill | 7 Li NMR and two-dimensional exchange study of lithium dynamics in monoclinic Li3V2(PO4)3[END_REF] , Variable Temperature 85 or rotational-echo double resonance [START_REF] Cahill | 6 Li{ 31 P} Rotational-Echo, Double-Resonance Studies of Lithium Ion Site Dynamics in Li3V2(PO4)3[END_REF] .

Selective inversion is also a technique, detailed in this chapter, to study the ionic mobility 67 .

Synthesis, average structure characterization and physical properties

While by reproducing the synthesis many times with slightly different alkaline initial compositions, a real pure OP4 phase could not be, easily, synthetized. Among all the prepared samples, we selected for the discussion in this chapter, three of them, representative of all the resulting powders.

The samples are labelled A, B, and C in this chapter.

Synthesis route

In the literature, the syntheses were performed using either alkaline carbonates and cobalt oxide All the OP4 phases were then stored and prepared for characterization in a glovebox in order to avoid any air contamination.

Typical SEM images of the sample A can be found in Å. The sample C exhibits only traces of the OPP9 phase as an impurity on its pattern.

Thus, our quenching procedure was fast enough to avoid the OP4 phase decomposition in O3-LiCoO2 and P2-𝑁𝑎 ~0.7 CoO2 as observed previously [START_REF] Berthelot | Reinvestigation of the OP4-(Li/Na)CoO2 -Layered System and First Evidence of the (Li/Na/Na)CoO2 Phase with OPP9 Oxygen Stacking[END_REF] . The XRD patterns of all the phases were first refined using the Le Bail method to extract the cell parameters which are summarized in Table II

Physical properties 3.1 Electronic conductivity

In Figure II-5, the electrical conductivity of a sample synthetized during R. Berthelot PhD is plotted as a function of temperature in the 6 K -300 K range. The electronic conductivity was measured using a standard four probe technique. Note that no sintering of the pellet could be done due to the fast quench required to avoid the decomposition of the OP4 phase. The evolution of the conductivity denotes a semi-conductive behavior probably due to inter particles boundaries resistivity. Ren et al. [START_REF] Ren | Enhanced thermopower in an intergrowth cobalt oxide Li 0.48Na0.35CoO2[END_REF] reported similar data as well as Seebeck coefficient measurements that showed that the OP4 phase should exhibit a metallic conductivity in the (a, b) plane relatively similar to the P2-NaxCoO2 [START_REF] Takahata | Low thermal conductivity of the layered oxide (Na,Ca)Co2O4: Another example of a phonon glass and an electron crystal[END_REF][START_REF] Motohashi | Simultaneously enhanced thermoelectric power and reduced resistivity of NaxCo2O4 by controlling Na nonstoichiometry[END_REF] and O3-LixCoO2 74 phases. emu.mol -1 . The C value is relatively high compared to the theoretical one (Cth = 0.05 emu.K.mol -1 ) by considering the Li0.42Na0.38CoO2 formula with 0.2 LS-Co IV and 0.8 LS-Co III . This difference indicates that the material doesn't completely follow a Curie-Weiss law and a part of the susceptibility can be due to delocalized electrons. This point will be discussed again regarding the variable temperature [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR spectra.

Magnetic measurements

DFT calculations

Description of the considered cell

A model compound was considered with the Li1/2Na1/3CoO2 stoichiometry, considering full Li interslab spaces as in O3-LiCoO2 and the a Na + /vacancy ordering as reported by Platova et al. [START_REF] Platova | Nuclear quadrupole resonance and X-ray investigation of the structure of Na2/3CoO2[END_REF] for P2-Na2/3CoO2 (Figure II-10). The used supercell formula is Li24Na16Co48O96. A quasi-Newton algorithm was used for the ionic relaxations. To obtain accurate final energies, all the relaxations were followed by a final static calculation with the linear tetrahedron method. For the magnetic susceptibility we used 𝜒 = 𝐶/(𝑇 -𝜃 𝑝 ), with C and 𝜃 𝑝 determined from the linear fit of the inverse of the magnetic susceptibility (1/ χ) versus temperature using the modified Curie-Weiss law Chapter II 66

(

Results

Even if the stoichiometry is slightly different from the real one and eventhough in our Generalized Gradient Approximation (GGA) approach, all the cobalt ions are partially oxidized, the calculations showed that considering a specific Na ordering tends to partially localize the charges. The global spin calculated in the cell is in agreement with the expected value for 1/6 LS-Co 4+ (t2g As expected from the larger C value experimentally calculated, the resulting shifts magnitude is larger than by using the theoretical Cth. Whatever the method used, the experimental data cannot be properly simulated

(Figure II-12).
This emphasizes the difficulty to model the electronic structure for layer cobalt oxides as discuss in chapter I. In our modelling, the t2g orbitals degeneracy is lifted because of the CoO6 distortion along the c axis leading to the a1g and eg' orbitals [START_REF] Landron | An ab initio evaluation of the local effective interactions in the NaxCoO2 family[END_REF] . Note that the 3D spin density map clearly shows that the a1g orbital resulting from a recombination of the t2g orbitals as discussed in chapter I (section 1.

Dynamics of the Li + ions in the interslab spaces

Selective inversion is a technique used to investigate the dynamics of Li + ions in the OP4 material in order to investigate a possible deficit of Li + inside the Li layers. This technique introduces a mixing time which allows a chemical exchange between the different Li sites by hopping. In order to apply a coherent mixing times range, the longitudinal relaxation time T1 of each Li signal have to be determined. For that, the inversion recovery technique was processed at different temperatures.

T1 measurements

Figure II-18 : Pulse sequence of the inversion recovery. Extracted from reference 61

This technique consists of applying two pulses separated by a 𝜏 𝑚 delays. The pulse sequence is repeated many times with different 𝜏 𝑚 delays. The first pulse allows to invert the population distribution while the 𝜏 𝑚 delays allows the relaxation of the populations. Finally, the second pulse allows to convert the population difference into coherences.

In order to determine the T1 value, the evolution of the signals intensity as a function of 𝜏 𝑚 delays is plotted using the formula as follows:

𝐼(𝑡) = 𝐼 0 + 𝐴 * exp (-𝑡 𝑇1 ⁄ ) eq(II-5)
Where 𝐼 0 and A are constant values.

The TopSpin software allows measuring the intensity of each signal and calculating for each T1 value. The full recovery of the magnetization has to be reached for the longest mixing times that's why a criterion for a good inversion recovery acquisition is to have 𝜏 𝑚 ~ 5*T1. The Similar plots were obtained at 310 K, 320 K and 340 K. The fitted T1 values are reported in Table II-7 for each temperature and signal. The signal 4 shows a low modification of its intensity with the increasing 𝜏 𝑚 delays that's why it is not plotted in this manuscript. Moreover, the signal 5 is located under a spinning side band at this magnetic field. The T1 values are almost constant whatever the considering temperature for each site. Moreover, the small differences between some values are probably due to the low resolution between the different signals on the NMR spectra. Therefore, it is difficult to the define the range of each signal and to process a proper integration.

Chapter II 76

Selective Inversion

Selective inversion consists of a succession of two pulses separated by the mixing time, 180°-𝜏mix-90°. The 180° pulse is a soft power Gaussian shaped pulse with a longer length than the usual pulses [START_REF] Smiley | An Improved Understanding of Li + Hopping Pathways and Rates in Li3Fe2(PO4)3 Using Selective Inversion 6 Li NMR Spectroscopy[END_REF]

Na + ions in Li interslab spaces

As NMR shows full Li interslab spaces and stacking fault simulations discredit the hypothesis of plenty of successive Na layers in the material [START_REF] Berthelot | Contribution à l'étude électrochimique du système P2-NaxCoO2. Synthèse et caractérisation de nouveaux oxydes lamellaires ordonnés (A/A')CoO2 (A[END_REF] in order to explain the chemical formula of the OP4 phase, it becomes difficult to explain the difference between the expected (Li0.5Na0.35CoO2) and the experimental (Li0.42Na0.38CoO2) chemical formula for the OP4 pure phase. Another idea to explain the gap between the formulas is to consider Na + ions intercalated in the Li layers after the thermal treatment. 23 Na MAS NMR was performed in order to confirm this hypothesis. and can be assigned to Na + in environments similar to the P2 phase (P2 and OPP9 impurities).

1D NMR

Magnetic field comparison

Comparison of the samples

Table II-8 shows that the major signal is the one labelled 2 on Figure II-23b. This signal corresponds to the average signal for the Na + ions in the Nae and Naf sites in the Na interslab spaces.

Therefore, we can confirm that the presence of Na + ions in the Li layers are at the origin of this signal 1. The Co-O-Na distance in that case should be shorter, making the hyperfine interaction larger [START_REF] Berthelot | Reinvestigation of the OP4-(Li/Na)CoO2 -Layered System and First Evidence of the (Li/Na/Na)CoO2 Phase with OPP9 Oxygen Stacking[END_REF] . The presence of Na + ions in Li layers will be discussed again with the Rietveld refinement performed on SXRD data.

Sample B 7 93

Sample A 2 98

Table II-8:

Repartition of the areas of the two signals highlighted on the 23 Na MAS NMR spectra for Na + ions for the three studied samples. The signals around 370 ppm on the samples B and C spectra are not considered because they are due to Na impurities.

23 Na Mas NMR Variable Temperature measurements (VT)

23 Na MAS NMR VT was also performed with a spinning frequency of 13 kHz for temperatures between 265 and 450 K (Figure II-24). Note that using a 13 kHz spinning frequency and a 7.05 T magnetic field, the resolution was not sufficient to follow the change for the signal 1. The temperature increase results in a sharpening of the signal 2 that exhibits at 450 K a well-defined 2 nd order line shape as would exhibit a 23 Na nucleus in a unique site with an axial symmetry of the electric field gradient (EFG). This signal modification can be interpreted by i) an increase of the Na + ions dynamics in the interslab spaces that is not fully achieved at room temperature compared to the NMR timescale and ii) a decrease of the dipolar part of the nuclear -electron spin coupling as also observed for the P2-NaxCoO2 [START_REF] Carlier | Sodium Ion Mobility in NaxCoO2 (0.6 < x < 0.75) Cobaltites Studied by 23 Na MAS NMR[END_REF] . A decrease of the shift values is also observed for the increasing temperature as expected for paramagnetic shifts. However, in the case of 23 Na MAS NMR, contrary to [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li, one cannot neglect the quadrupolar shift contribution to the total shift in addition to the Fermi contact and the Knight shifts. The analysis of the isotropic shift position versus the temperature is therefore more complex than for [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li.

Determination of the composition by Rietveld refinement

High angular resolution synchrotron powder X-ray diffraction (SXRD) experiments were performed on the BL04-MSPD beamline of the ALBA Synchrotron (Cerdanyola del Vallès, Spain)

for only the sample A where the targeted composition was Li0.44Na0.38CoO2 (Table II-2 Chapter II 87

O Na 4e 0 0 0.3363(7) 0.79(1) 1
O Li 4f 1/3 2/3 0.4248(7) 0.42 (1) 1 Rp

Table II-9: Calculated parameters, atomic positions and atomic occupancies obtained for the refined SXRD data performed on the sample A (SXRD pattern on Figure II-25) with the P63/mmc space group. ONa represent the O ions between a Na layers and Co layers while OLi are the O ions between a Li layers and a Co layers.

Conclusion

The objective of this chapter was to reinvestigate the complex structure of the OP4-(Li,Na)CoO2 phase in order to understand some unclear points and especially the gap between the theoretical, Li0.5Na0.35CoO2 chemical formula and the experimental one, Li~0.4Na~0.4CoO2 obtained in many papers. The presence of a low amount of stacking faults can't explain the important gap between both chemical formulas and suggests that its origin concerns more a deficit of Li + ions than an excess of Na + ions in the structure. In this aim, three samples with controlled amount of impurities were synthetized in order to investigate their average structure by XRD and their local and electronic structure by [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li and 23 Na MAS NMR. The three samples showed five different environments for the Li + ions but DFT calculations were not able to assign properly each signal because of the dual behavior of the OP4 phase with the presence of localized and delocalized electrons. Selective inversion technique was performed and highlighted the absence of Li + ions mobility allowing to confirm that the Li interslab spaces are almost full.

Finally, 23 Na MAS NMR highlighted the presence of two environments for the Na + ions in the OP4 structure: (1) a major signal for Na + in prismatic sites in the Na interslab spaces (2) a minor signal for Na + in octahedral sites in the Li interslab spaces. The presence of Na + ions allows to fill almost the whole Li interslab spaces explaining why there is no mobility of the Li + ions in the structure.

A Rietveld refinement on SXRD data allowed, finally, to determine the OP4-[Li0.42Na0.05]Na0.32CoO2 chemical formula for the pure OP4 phase.

III.

Chapter III 90

The different LiCoO 2 polytypes

Among the different polytypes of LiCoO2, O3-LiCoO2 is the most famous one because it can be easily synthetized by a solid-sate route and exhibits good electrochemical performances firstly investigated by Goodenough and coworkers [START_REF] Mizushima | LixCoO2 (0< x<1): A new cathode material for batteries of high energy density[END_REF] .

The O2 polymorph was reported for the first time by Delmas et al. in 1981 [START_REF] Delmas | A new variety of LiCoO2 with an unsual oxygen packing obtained by exchange reaction[END_REF] . They synthetized the phase by a Na + /Li + ion-exchange from the P2-Na0.7CoO2 phase. During the exchange, one CoO2 over two slides to generate octahedral sites in the interslab spaces [START_REF] Tournadre | On the mechanism of the P2-Na0. 70CoO2→ O2-LiCoO2 exchange reaction-Part I: proposition of a model to describe the P2-O2 transition[END_REF][START_REF] Tournadre | On the mechanism of the P2-Na0. 70CoO2→ O2-LiCoO2 exchange reactionPart II: an in situ X-ray diffraction study[END_REF] repulsions are stronger in the O2 stacking due to the sharing of one face (in O3 structure, LiO6 octahedra only share edges with the surrounding CoO6). Delmas et al. [START_REF] Delmas | A new variety of LiCoO2 with an unsual oxygen packing obtained by exchange reaction[END_REF] showed that the O2 stacking is metastable, in fact, the structure reorganizes itself irreversibly into the O3 structure when heated. The O2 structure was also studied by [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR where only a diamagnetic signal is observed [START_REF] Carlier | A New Polymorph of Layered LiCoO2[END_REF] . This point confirms that the interslab spaces are fully occupied by Li + ions after the exchange and only surrounded by diamagnetic Co 3+ in a similar case than O3-LiCoO2 [START_REF] Menetrier | Cobalt segregation in the LiNi1-yCoyO2 solid solution: a preliminary 7 Li NMR study[END_REF][START_REF] Ménétrier | The insulator-metal transition upon lithium deintercalation from LiCoO2: electronic properties and 7 Li NMR study[END_REF] .

Figure III-1 : Representation of the CoO2 gliding to generate octahedra sites and form the O2 polytype. From 43

Concerning the O4 polytype, few publications report the synthesis of the O4-LiCoO2 material [START_REF] Berthelot | Synthesis and Investigations on an O4-LiCoO2 Polytype[END_REF][START_REF] Yabuuchi | A comparative study of LiCoO2 polymorphs: structural and electrochemical characterization of O2-, O3-, and O4-type phases[END_REF]100 . As the OP4-(Li/Na)CoO2 phase proposes a good alternation of P2-type and O3type layers, we expected, therefore, that a Na + /Li + ion-exchange leads to an O4-LiCoO2 with an perfect alternation of O3-type and O2-type layers by considering only glidings of the P2 layers to (2) Berthelot et al. [START_REF] Berthelot | Synthesis and Investigations on an O4-LiCoO2 Polytype[END_REF] proposed an ion-exchange with melted salts LiNO3 in excess and KNO3.

The mixture is heated at 150 °C and washed many times to remove potential traces of Chapter III 92 nitrate. This way of synthesis was similar to this used previously by Delmas et al. [START_REF] Delmas | A new variety of LiCoO2 with an unsual oxygen packing obtained by exchange reaction[END_REF] to stabilize the O2-LiCoO2 structure from P2-Na0.7CoO2.

The ideal O4 stacking is composed of a 1:1 alternation of O2-type and O3-type slabs ( [START_REF] Berthelot | Contribution à l'étude électrochimique du système P2-NaxCoO2. Synthèse et caractérisation de nouveaux oxydes lamellaires ordonnés (A/A')CoO2 (A[END_REF] .

By using the ICP-AES technique to determine the chemical compositions of the synthetized phase, Berthelot et al. [START_REF] Berthelot | Synthesis and Investigations on an O4-LiCoO2 Polytype[END_REF] suggested the presence of 0.8 Li + ions, Komaba et al. 100 showed the presence of 0.85 Li + ions in O4 structure and Yabuuchi et al. [START_REF] Yabuuchi | A comparative study of LiCoO2 polymorphs: structural and electrochemical characterization of O2-, O3-, and O4-type phases[END_REF] determined 0.9 Li + ions with a negligible amount of remaining Na + ions from the OP4 phase in the O4-LiCoO2 phase. Therefore, the Li interslab spaces are not completely filled and it is important to keep in mind that the alkali ions amount in the structure strongly depends of the exchange conditions.

Note that On-LixCoO2 (x < 1) phases with different stacking were also reported. The O1 stacking is obtained for structures largely deintercalated labelled 𝐿𝑖 𝜀 𝐶𝑜𝑂 2 from O3-LiCoO2 [START_REF] Tournadre | The T # 2-Li2/3Co2/3Mn1/3O2 System[END_REF]105 and its structure is derived from the O2 stacking which undergoes layers glidings along a (1/3, 1/6, 0) vector. This stacking is obtained for x values between 0.52 and 0.72 during Li + deintercalation from O2-LixCoO2. The aim of this chapter is to obtain new information concerning the average structure and the local structure of the O4-LiCoO2 phase. For this study, solid state NMR was used on two different samples prepared in two different ion-exchange conditions in order to isotopically mark the Li + ions in the different layers using [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li and [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li ions (Figure III-4). Again, the Li + ions mobility was tested on both samples after observing many signals by 1D NMR. 23 Na MAS NMR and ICP-OES were performed in order to confirm or not the presence of remaining Na + ions in the structure.

Figure III-4:

Representation of the expected O4 structure after ion-exchange from the OP4 phase enriched with [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li ions

Chapter III 94

Synthesis conditions

Before realizing the ion-exchange, an OP4-(Li, Na)CoO2 phase was synthetized enriched with [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li.

The synthesis conditions were the same than those described in the chapter II except the use of Li2CO3 enriched in [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li instead of traditional Li2CO3.

We choose to synthetize two different O4 phases by ion-exchange with the "in solution" technique.

Both syntheses were realized in a 1M LiCl solution and the synthesis conditions are summarized in Table III

Figure III-6: Experimental XRD patterns of both samples compared to the theoretical one using Berthelot et al. data 43

Chapter III 98

Chemical compositions

In order to determine the chemical compositions of both EIE and SIE samples, ICP-OES was performed. The samples were previously solubilized in a HCl/HNO3 mixture before the measurement. The samples were tested in order to determine the Co and Li + ions amount but also the amount of eventual remaining Na + ions.

ICP-OES shows different Li/Co ratio for both samples in good agreement with the ion-exchange conditions used to synthetize the two samples. The Li + ions compositions are 0.79(4) and 0.68 (7) for, respectively, EIE and SIE-O4-LiCoO2 in good agreement with the synthesis conditions of the two samples. However, it is important to note that a small part of the Li + ions in the EIE sample can be due to O3-LiCoO2 present as an impurity. Additionally, ICP-OES shows the presence of ~ 0.1(1) Na + ions in both samples but it is also to qualify because of the important uncertainty. The presence of Na + ions could be explained by the presence of local Na + ions which are still intercalated in the structure either in remaining P-type layers or in O-type layers. This point will be discussed later in this manuscript regarding the 23 Na MAS NMR spectra. A partial filling of the O4 structure is proposed regarding the ICP results with vacancies in the layers whatever the synthesis conditions in opposition with the synthesis by ion-exchange of the O2 polytype which proposes full Li interslab spaces. Regarding these results, the samples will be relabeled 'O4-LixCoO2' until the end of this chapter.

4. 6/7 Li and 23 Na MAS NMR

Standard sample

Before showing the NMR spectra of the EIE and SIE samples, we studied a sample without any enrichment in [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li. The presence of potential [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li ions in this sample is only due to the natural abundance of this isotope (natural abundance 6 Li: 7.6 % vs 7 Li : 92.4 %). It had been synthetized

before the beginning of my PhD using an "usual" OP4 phase as precursor and in the same synthesis condition than the EIE sample. This sample is labeled "standard" sample in this work. Chapter III 100 4.2 A selective exchange?

7 Li and [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li MAS NMR were performed with the Hahn Echo sequence on the EIE-and SIE-O4-LixCoO2 samples in order to check which Li sites are occupied by [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li and [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li ions. The spectral width was set to 1 MHz, and the recycle time D0 = 10 s, is long enough to avoid T1 saturation effects. The acquisitions were performed on a 7.05 T magnet using a spinning frequency of 30 kHz and with a Hahn echo sequence. Chapter III 102

Evidence of Na + ions in the structure

ICP-OES introduced a potential presence of remaining Na + ions after the ion-exchange. However, due to the important uncertainty concerning the amount of Na + ions, it is important to confirm by another technique if some Na + ions remains or not in the O4 phases. 23 Na MAS NMR was also performed on both samples on a 7.05 T magnet using a simple pulse sequence and with a baseline removal on the software DMFit [START_REF] Massiot | Modelling one-and two-dimensional solid-state NMR spectra[END_REF] . The spectral width was set to 1 MHz, and the recycle time D0 = 0.5 s, is long enough to avoid T1 saturation effects. 23 Na MAS NMR spectra (Figure III-9)

highlight that a certain amount of Na + ions remains in the structure after the ion-exchange. Note that more Na + ions remain in the phase obtained in the stoichiometric exchange condition than with the Li + excess exchange condition as expected. Moreover, two environments can be evidenced by 23 Na MAS NMR as two signals at 176 ppm and around 400 ppm are observed. The 176 ppm signal is located at a similar position than the major signal recorded on the OP4 phase before the ionexchange and could be due to a slight amount of remaining OP4 phase as impurity. The large shift value of the major signal around 400 ppm is not in agreement with Na + ions in prismatic sites. The value is more in agreement with local remaining Na + ions in octahedral sites and therefore in the O3-type Li interslab spaces. Three times more Na + ions remain in SIE sample than in EIE sample but it is still difficult to determine the chemical formulas including the Na + ions because of the high uncertainty of the ICP results. It is however complicated to conclude something about the third signal because of its low intensity.

We can't conclude clearly about the Li + ions mobility regarding the EXSY experimental results, indeed, it is not obvious if cross-peaks appear really or if it is just background noise. 23 Na MAS NMR spectrum were only performed on sample SIE using an EXSY measurements of EIE at room temperature with a mixing time of 0.3 s (4.7 T magnet, spinning frequency of 60 kHz)

Figure III-10:

Selective inversion was introduced in the previous chapter and is a complementary technique to EXSY in order to confirm or deny that the cross-peaks are due to a Li + mobility in the layers.

Moreover, the selective inversion measurements were easier to set up for this material as for the OP4 phase because of the higher separation between the signals.

Conclusion

The O4 phase was successfully synthesized from OP4 phase with a solution route and proposed different amounts of Li + ions following the exchange conditions. It is, however, difficult to synthetize a phase with no stacking faults. During the ion-exchange, all the Li + ions are mobile and participate to the exchange as suggested by [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li and [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR spectra. ICP-OES, 1D NMR and 2D NMR suggest that Li layers are not completely filled and that a Li + ions amount limit is reached for longer exchanges. Moreover, Li + ions are present in three different sites: a diamagnetic environment, probably surrounded only by Co 3+ and two paramagnetic environments due to a repartition of Co 4+ in the CoO2 layers. Selective inversion shows that two Li sites are in the same layer due to the possibility of Li + ions to hop from one site to the other. The origin of the signals is still complex to assign and needs more investigations for example by variable temperature NMR to observe or not delocalized electrons like on the OP4 phase. This point needs to be investigated more largely. Finally, 23 Na MAS NMR suggests that Na + ions occupy octahedral sites in Li interslab spaces as already observed in the OP4 phase. O4-phase structure and electronic structure are also difficult to understand and peak assignment needs to be investigate more carefully to explain their origin.

Introduction

NaxCoO2 was introduced in 1973 and investigated as positive electrode material, for the first time in 1981 [START_REF] Delmas | Structural classification and properties of the layered oxides[END_REF][START_REF] Delmas | Electrochemical intercalation of sodium in NaxCoO2 bronzes[END_REF]106 . As shown in the general introduction, different polytypes of NaxCoO2 pristine phases can be synthetized depending on the Na + content and synthesis conditions [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] That also allowed to describe more precisely the different domains depending on the Na + content.

The chex parameter decreases as the Na + intercalated amount increases due to the screening effect of the Na + ions which limits the O-O repulsions between the successive layers. Note that the ahex lattice parameter slightly increases during the discharge because the Co 3+ ion radius (0.545 Å) is larger than the Co 4+ radius (0.53 Å) 3 .

Concerning the peculiar phases, Cava and coworkers 107,108 were the first to highlight the superstructure peaks by electronic microscopy for the x = 1/2 composition. These particular structures can be, usually, described in a hexagonal or orthorhombic cell but sometimes modulation vectors are necessary to describe incommensurable superstructures. Table IV-1 summarizes the peculiar phases observed for x ≥ 0.5, their voltage vs Na + /Na of formation and their superstructure expressed from the original hexagonal cell (in the P63/mmc space group). The Na1/2CoO2 and Na2/3CoO2 (described by Platova et al. [START_REF] Platova | Nuclear quadrupole resonance and X-ray investigation of the structure of Na2/3CoO2[END_REF] ) phases and were also stabilized by electrochemical deintercalation by Berthelot et al. [START_REF] Berthelot | Electrochemical investigation of the P2-NaxCoO2 phase diagram[END_REF] Extracted from reference [START_REF] Berthelot | Contribution à l'étude électrochimique du système P2-NaxCoO2. Synthèse et caractérisation de nouveaux oxydes lamellaires ordonnés (A/A')CoO2 (A[END_REF] .

Na 2/3 CoO 2 2.8 V R3 ̅ c : 2√3a x 2√3a x 3c

Table IV-1:

The peculiar phases already reported on the NaxCoO2 system for x ≥ 0.5 with the associated voltages of formation, space groups and superlattices

The Mn-substituted P2-NaxCoO2 phases are also interesting positive electrode materials for Naions batteries. The influence of the Co/Mn ratio had been largely studied by Paulsen and Dahn 117 .

P2-NaxCo2/3Mn1/3O2 exhibits interesting electrochemical performances [START_REF] Carlier | The P2-Na2/3Co2/3Mn1/3O2 phase: structure, physical properties and electrochemical behavior as positive electrode in sodium battery[END_REF]

Table IV-2: Electrochemical performances of some NaxCoyMn1-yO2 systems reported in the literature

The previous studies in our group and in most of the studies in the literature at the beginning of this PhD were realized using NaClO4 in an organic solvent as electrolyte. Unfortunately, this electrolyte is not stable enough to investigate cycling above 3.8 V vs Na + /Na. Preliminary studies realized by Cedric Constantin in collaboration with Anthony Baux, in 2015, in our group showed that rather good cycling properties in the 1.5 -4.3V vs Na + /Na voltage range could be achieved using NaPF6 in 1M in PC + 2% wt FEC as electrolyte in a Na(s) // P2-NaxCoO2 cell (Figure IV-3). We, thus, decided to further investigate this system using this electrolyte, with a particular interest for the mechanisms occurring at high voltage. In Table IV- The hexagonal shape can be observed on many P2 phases in literature 125,126 .

Morphology of NaxCoO2

Figure IV-6b
highlights the presence of an alternation of layers which characterizes the layered oxides structure.

Small imperfections represented by white particles on the surface are due to an air exposure during the very short transit at air before the gold sputtering. These white particles can also correspond to remaining Na2CO3 precursor grown in air.

Structural characterization

The laboratory XRD study of the pristine materials (not shown here) indicated that all the phases were pure and crystallized in the P63/mmc space group. All the phases were also analyzed at ALBA Synchrotron facilities on the MSD04 beamline in a 2° to 73° 2θ range at a wavelength of λ = 0.8261 Å. The samples were packed in 0.5 mm diameter sealed capillaries as explained in chapter I. The XRD patterns were refined with the Le Bail method using the hexagonal cell described in P63/mmc without considering any Na + /vacancy ordering (Figure IV-7). The match is not perfect since some additional superstructure peaks can also be observed in the 15° -23° range. Therefore, a correct indexation of the complete patterns could not be found in those cases. Note that the XRD pattern of the P2-𝑁𝑎 ~2/3 𝐶𝑜 2/3 𝑀𝑛 1/3 𝑂 2 exhibits a shoulder on the right side of the (002) peak indicating either an heterogeneity of the material or that the composition of the material falls in a biphasic domain.

The refined cell parameters (Table IV- ). Note that the NaxCoO2 pristine phase was not the same than the refined one and it seems that its composition was close to 0.76 which is possible due the large P2 existence domain [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] .

For NaxCo1/2Mn1/2O2 and NaxCo1/3Mn2/3O2, the polarization is higher and the capacity retention is Another interesting point is the shape of the electrochemical curve of the different systems.

Whereas, the NaxCoO2 galvanostatic curve shows many accidents, the Co-Mn systems exhibit much less slope breaks. Only one is clearly observed on the NaxCo2/3Mn1/3O2 system for x = 1/2 that might correspond to a phase with a specific Na + /vacancy ordering [START_REF] Carlier | The P2-Na2/3Co2/3Mn1/3O2 phase: structure, physical properties and electrochemical behavior as positive electrode in sodium battery[END_REF] . The voltage evolution of the NaxCo2/3Mn1/3O2, NaxCo1/2Mn1/2O2 and NaxCo1/3Mn2/3O2 systems suggests solid solution behaviors in their low voltage range.

Galvanostatic cycling in high voltage range

In order to investigate the performances under "extreme" conditions of the systems, the batteries were cycled at C/20 up to 4.6 V vs Na + /Na for NaxCoO2 and 4.5 V for NaxCo2/3Mn1/3O2 (Figure At high voltage, it is possible that, a proportion of the P2-NaxMO2 phase is, irreversibly, disordered due to some sheets glidings. By charging the battery and therefore by removing Na + ions, O-O repulsions increase and sheets glidings occur to stabilize the structure 128 . This point will be investigated in the following using operando XRD measurements and in the next chapter using

IV

Structural evolution by in-situ Synchrotron XRD

The structural evolution of the different P2 phases were investigated by operando XRD on the BL-04-MSPD beamline of the ALBA synchrotron (Barcelona, Spain) with the collaboration of François Fauth. Each system was cycled at a C/10 rate using drilled coin cells as described in the first chapter and operando measurements were realized up to 4.6 V or 4.5 V using the fast MYTHEN detector 129 . Moreover, a PITT (Potentiostatic Intermittent Titration Technique) was realized on the P2-NaxCoO2 system for different high voltages from 4.1 V to 4.8 V vs Na + /Na.

NaxCoO2 system

Operando measurements

Starting from a Na(s)//P2-𝑁𝑎 ~0.7 𝐶𝑜𝑂 2 cell, the first charge and second discharge were investigated in the 1.5 V -4.6 V range at C/10. Chapter IV 139

PITT

The cell for this study was first charged using a C/10 regime until 4.1 V and then, different voltages

NaxCo2/3Mn1/3O2 system

The first charge following the first discharge from a P2-𝑁𝑎 ~2/3 𝐶𝑜 2/3 𝑀𝑛 1/3 𝑂 2 // Na cell has also been studied by operando synchrotron XRD from 1.25 V to 4.5 V at a rate of C/10. As for the NaxCoO2 system, the 2𝜃 positions of the (002) and (004) peaks decrease during the Na + ions deintercalation indicating a global increase of the chex lattice parameter during the charge (Figure

IV-19).

The system also reaches a limit chex value for x = 0.4 (11.30(1) Å). This system is less complex than NaxCoO2, in fact, only few superstructure peaks appear during the charge to 4.5 V.

For 0.67 < x < 0.8 many contributions are observed as seen in the red frame zooms. The ionic and electronic conductivities in this composition are probably worth than for x < 0.67 leading to composition heterogeneities in the electrodes. Indeed, for x > 2/3, no Co 4+ is present that usually leads to conductivity improvement and the system exhibits less Na vacancies. Globally, NaxCo2/3Mn1/3O2 has a solid solution behavior with only one clear ordered phase at x = 1/2.

Na1/2Co2/3Mn1/3O2 (red XRD pattern), in first approximation, was Le Bail refined in the same space group than Na1/2CoO2 (Pnmm) and with same relation between the hexagonal lattice parameters and the orthorhombic one (√3 𝑎 ℎ𝑒𝑥 x 2 𝑎 ℎ𝑒𝑥 x 𝑐 ℎ𝑒𝑥 ).

NaxCo1/2Mn1/2O2 system

The first charge following the first discharge from a P2-𝑁𝑎 ~0.6 𝐶𝑜 1/2 𝑀𝑛 1/2 𝑂 2 // Na cell has also been studied by operando synchrotron XRD from 1.25 V to 4.5 V at a rate of C/10. The first charge is reported in this manuscript (Figure IV-21). Again, the P2-structure is maintained in the 0.18 <

x < 0.7 range. As previously showed, the galvanostatic curve only exhibits one voltage jump for x = 1/3 and a slope change around x = 1/2. Globally, the (002) and (004) peaks evolution denotes an increase of the chex lattice parameter during the charge. For 0.45 < x < 0.7, an important heterogeneity in the electrodes is also at the origin of the presence of many contributions as seen in the red framed zoom. As for the NaxCo2/3Mn1/3O2 system, no Co 4+ should be present in this particular range involving bad ionic and electronic conductivities. For x < 0.45, the expected presence of Co 4+ ions improves the conductivity in the electrode and leads to the observation of one well-defined (004) peak (blue framed zoom). Moreover, a solid solution behavior can be observed. The system reaches a chex lattice parameter maximal value at x ≈ 0.4 (11.33(1) Å). The zoom in the 13.5 -14° range highlights the presence of a superstructure peak appearance for x around 1/3 on the red XRD pattern which corresponds to the formation of the Na1/3Co1/2Mn1/2O2 peculiar phase. A Le Bail refinement was realized on the XRD data of this phase using the same space group than for Na1/3CoO2. However, we are not able to refine correctly the XRD pattern of this phase with the P63/mmc space group due to a possible distortion of the corresponding cell.

Discussion

To summarize the results extracted from this study for the four P2-NaxMO2 (M = Co,Mn) systems: the P2-structures remain during the Na + deintercalation with our acquisition conditions at C/10.

For each system, a maximal chex value is reached for x around 0.4. The lattice parameters in Table IV-6 correspond to the calculated values from Le Bail refinements realized on the XRD patterns on which the (004) peaks is at its minimal 2θ position. As expected, the chex lattice parameters has increased and the ahex lattice parameters has decreased compared to their initial values (Table IV

V ≈ 4 V 4 V 3.8 V 3.5 V

Table IV-6: Lattice parameters calculated from refinements on the last XRD patterns data and the voltage and x values corresponding to the reach of the maximal chex value for each system.

Figure IV-23: Evolution of chex lattice parameter as a function of x for the four systems

Chapter IV 154

Conclusion

In this chapter, we studied the electrochemical performances and the evolution of the average structures of four systems NaxCoyMn1-yO2 for y = 2/3, 1/2, 1/3 and 1 by operando high-resolution XRD. The recent addition of FEC in electrolyte formulation allows to reach higher voltages on these systems than in the previous studies. The operando measurements showed the remaining of the P2 structure for each system in the studied voltage ranges at C/10. The presence of sheets glidings was also highlighted on relaxed NaxCoO2 phases for x < 1/3. Concerning the P2-NaxCoO2 system, previously, 9 monophasic domains were determined for x between 0.5 and 1. For x < 0.5, the system remains complex and one obvious peculiar phase can be highlighted for x = 1/3. The CoyMn1-y systems have a solid solution behavior during all the Na + deintercalation despite an important heterogeneity in the electrodes before the oxidation of Co 3+ into Co 4+ . For specific compositions, peculiar phases were also observed. These new peculiar phases were evidenced for Na1/3CoO2, Na1/3Co1/2Mn1/2O2 and Na1/2Co2/3Mn1/3O2 by voltage jumps on the galvanostatic curves and by the appearance of superstructures peaks on the XRD patterns. The refinements need to be performed again on relaxed phases to have a better insight of the real structure of these phases but it seems that the x = 1/2 phases crystallize in an orthorhombic cell in the Pnmm space group.

Na1/3CoO2 was also successfully refined in the P61 space group.

After focusing on the average structures, we will study the local structure evolution, in the next chapter, thanks to 23 Na MAS NMR, of the P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 systems.

Introduction

The previous chapter proposed a study of the average structural evolution of NaxCoyMn1-yO2 systems upon cycling. In this chapter, we focus on the study of the local structure and electronic structure evolution of P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 systems upon charging.

MAS NMR has been shown to be a key tool to investigate the deintercalation mechanisms in many battery materials [START_REF] Grey | NMR Studies of Cathode Materials for Lithium-Ion Rechargeable Batteries[END_REF][START_REF] Pecher | Materials' methods: NMR in battery research[END_REF][START_REF] Kitada | Unraveling the Reaction Mechanisms of SiO Anodes for Li-Ion Batteries by Combining in Situ 7 Li and ex Situ 7 Li/ 29 Si Solid-State NMR Spectroscopy[END_REF][START_REF] Clément | Short-range order and unusual modes of nickel redox in a fluorine-substituted disordered rocksalt oxide lithium-ion cathode[END_REF][131][132][133][134][135][136] . In 1999, Ménétrier et al. [START_REF] Ménétrier | The insulator-metal transition upon lithium deintercalation from LiCoO2: electronic properties and 7 Li NMR study[END_REF] in our group, proposed a deep investigation of the LixCoO2 system by [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR (Figure V-1). They assigned the signal at 0 ppm of O3-LiCoO2 to Li + surrounded by diamagnetic Co 3+ (t2g 6 eg 0 ) in their low spin configuration. They synthesized the different LixCoO2 phases in the 0.5 ≤ x < 1 by electrochemical deintercalation in order to perform ex-situ [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR. They showed that the 0 ppm signal remains the only one in the 0.94 ≤ x < 1 range despite the oxidation of the Co 3+ into paramagnetic Co 4+ (t2g 5 eg 0 ). However, its intensity strongly decreases when x decreases in this particular range.

The single electron in the electronic configuration of Co 4+ is in one of the t2g orbital pointing directly in the direction of the 2s orbital of the first Li + ions neighbor through a common edge of the LiO6 and CoO6 octahedra (Figure V-1c). In this case, the strong hyperfine interaction leads to the loss of the signal on the NMR spectra. Therefore, [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR showed, that in the 0.94 ≤ x ≤ 1 composition range, the electrons have a localized behavior. Moreover, an additional signal can be observed at 57 ppm on the x = 0.94 spectra. In the 0.75 < x < 0.94 range, the intensity of the 0 ppm and 57 ppm signals, respectively, decreases and increases when x decreases indicating the presence of a two-phase region. This biphasic behavior is also visible on the LixCoO2 galvanostatic curve by the presence of a voltage plateau in this particular range. For x < 0.75, the signal at 0 ppm disappears and the 57 ppm signal is shifted to higher values when x decreases indicating the presence, in the material, of delocalized electrons with an increasing participation of the Li 2s orbital to the Knight shift. [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR highlighted in this study the modification of the hyperfine interaction nature from a paramagnetic contact shift to a Knight shift upon Li + deintercalation. Note that [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR has been successfully applied to study the deintercalation mechanisms in many other systems [START_REF] Levasseur | Evidence for structural defects in non-stoichiometric HT-LiCoO2: electrochemical, electronic properties and 7 Li NMR studies[END_REF]137 .

Chapter V

157

(c) Representation of the direct overlap between a single electron from the t2g orbital of Co 4+ and the 2s Li orbital

Chapter V 158 23 Na MAS NMR can be also used to probe the local structure and electronic structure in battery materials eventhough the resolution of the spectra is not as good as obtained for [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li due to the strong quadrupolar moment of 23 Na compared to [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li (Table I- The 23 Na NMR MAS spectra of P2-Na2/3Co2/3Mn1/3O2 pristine material has been studied, in our group by Carlier et al. [START_REF] Carlier | The P2-Na2/3Co2/3Mn1/3O2 phase: structure, physical properties and electrochemical behavior as positive electrode in sodium battery[END_REF] , and compared to P2-Na2/3CoO2 (Figure V-3). As also observed on P2-Na2/3CoO2, the P2-Na2/3Co2/3Mn1/3O2 spectra has a broad lineshape because of the 2 nd order quadrupolar interaction. Moreover, the NMR shift value is higher as Mn 4+ ions (t2g 3 eg 0 ) carries 3 unpaired electrons vs 1 electron for Co 4+ .

Chapter V

159 Figure V-2: (a) 23 Na MAS NMR spectra of the P2-NaxCoO2 samples (b) Diffusion pathway of the Na + ions in the P2 stacking. From reference [START_REF] Carlier | Sodium Ion Mobility in NaxCoO2 (0.6 < x < 0.75) Cobaltites Studied by 23 Na MAS NMR[END_REF] . 23 Na MAS NMR spectra of both pristine phases recorded on a 7.05 T magnet with a spinning frequency of 30 kHz. * are the spinning side bands. From reference [START_REF] Carlier | The P2-Na2/3Co2/3Mn1/3O2 phase: structure, physical properties and electrochemical behavior as positive electrode in sodium battery[END_REF] .

Figure V-3:

Chapter V 160

More recently, Raphaële Clément and collaborators (C. Grey group) investigated different systems that can be used as positive electrode materials for Na-ion batteries. They studied different phases with various Na + content by ex-situ 23 Na MAS NMR in order to understand the mechanisms occurring during the Na + (de)intercalation and to have an insight of the local structure and electronic structure evolution of the different materials [START_REF] Clément | Direct evidence for high Na mobility and high voltage structural processes in P2-Nax[LiyNizMn1-y-z]O2 (0< x, y, z< 1) cathodes from solid-state NMR and DFT calculations[END_REF][138][139][140][141] . The particularity of their works is that the different phases were synthetized by electrochemical (de)intercalation for different Na + contents in order to characterize them. They studied, for example, different amounts of Mg 2+ ion doping in P2-NaxMnO2 by ex-situ MAS NMR in order to understand the mechanisms involved by this doping and why its leads to a significant enhancement of the electrochemical properties 140 .

Moreover, they also studied high voltage NaxMnO2 phases (x < 0.3) that underwent some sheet glidings: the signals are largely broadened due to the panel of new environments involved by the glidings. They investigated the role of the dopants on these high voltage phase transitions: Li as dopant in NaxNizMn1-zO2 systems [START_REF] Clément | Direct evidence for high Na mobility and high voltage structural processes in P2-Nax[LiyNizMn1-y-z]O2 (0< x, y, z< 1) cathodes from solid-state NMR and DFT calculations[END_REF] or Mg in NaxMnO2 140 . In this chapter, the P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 systems were investigated in the same vein. In fact, we synthetized different phases by electrochemical deintercalation and we analyzed them by ex-situ XRD and ex-situ 23 Na MAS NMR in order to investigate the mechanisms occurring during the charge of both systems.

Chapter V 161 2. P2-Na x CoO 2 and P2-Na x Co 2/3 Mn 1/3 O 2 systems 2.1 23 Na MAS NMR spectra of the pristine phases disconnected and entered in the glovebox where its voltage was measured to be assured that the synthetized phase didn't evolve after the battery disconnection. The cell was, then, opened and the positive electrode powder was washed with DiMethyl Carbonate. Note that, usually, the half of the 100 mg of initial powder was lost during the pelleting or in the separators. The remaining amount of powder was enough to fill, at least, a 0.3 mm diameter capillary for XRD acquisitions and a 2.5 mm diameter rotor for 23 Na MAS NMR acquisitions, so that the characterizations presented in this chapter have been done on a same electrode material for a given voltage. Note that for the NaxCo2/3Mn1/3O2 synthesis, the carbon additive was only composed of soot that's why the graphite impurities are only observed on the NaxCoO2 XRD patterns. In agreement with our in-situ XRD experiments, the P2 structure is maintained for x values up to 1/3 in both systems. Moreover, the low resolution of the patterns prevents from observing any superstructure peaks. Therefore, all the XRD patterns were refined using the P63/mmc space group with, first, the Le Bail method. Note that no splitting of the peaks due to the orthorhombic distortion highlighted in the previous chapter, can be observed for the x = 0.5 phases. It is possible that the targeted voltages were not exactly correct or that the phases slightly changed after the disconnection of the battery.

Table V-1: NMR parameters of both pristine phases calculated by two fits on the spectra shown in

As observed in the previous chapter, the chex and ahex lattice parameters, respectively, increase and decrease before reaching limit values around x = 0.4. The evolution of these values are plotted on voltage of sheets glidings beginning on the NaxCoO2 system. Note that the small shift between the peaks observed on Na0.25CoO2 and Na0.22Co2/3Mn1/3O2 XRD patterns is due to the slight difference in Na + content between the two materials. Table V-4 shows the repartition between the two different Na intercalation sites for the P2 phases determined with the Rietveld refinements. During the charge, the amount of Na + ions in the Naf sites stays constant while the amount of Na + ions in the Nae sites largely decreases until reaching the x = 0.5 composition. For x = 0.5, the amounts of Na + ions are almost the same in both sites for the two systems. In the 1/3 < x < 0.5 range, the Na + ions in Naf sites are mainly removed. Another interesting point is that the Na ions occupy almost only the Nae sites in the Na1/3CoO2 phase.

P2-domain

Chapter V

x

Magnetic properties on NaxCoO2 system

In order to better understand the NMR shift evolution discussed in the following paragraph, we also analyzed the magnetic properties of some of our NaxCoO2 phases, compared with literature.

The magnetic measurements were performed from 7 K to 300 K without an application of a magnetic field during the cooling and with the application of 1 T during the acquisitions on a Super Quantum Interference Device (SQUID) magnetometer MPMS5. As the powders were used for the XRD and NMR characterizations, we only get enough powder for the magnetic measurements of four samples: x = 0.67, x = 0.55, x = 0.4 and x = 0.33. Figure V-15a shows the evolution of the susceptibility as a function of temperature obtained on these samples. Igarashi et al. [START_REF] Igarashi | Precise Control of Na Content in the Layered Cobaltate γ-NaxCoO2[END_REF] already reported the susceptibility of some NaxCoO2 phases but only for 0.7 ≤ x ≤ 0.5 compositions

(Figure V-15b).
They highlighted that the NaxCoO2 samples have a Curie-Weiss behavior ("Curie-Weiss metal regime") in the 0.64-0.7 range in good agreement with our experimental magnetic measurement realized on the Na0.67CoO2 phase. In the 0.52 < x < 0.58 range, the magnetic properties turns to a Pauli paramagnetic regime due to the delocalized character of the electrons.

For our samples, the Pauli paramagnetic behavior can be observed, experimentally, on the phases synthetized with x ≤ 0.55. Note that the Na + content corresponding to transition from the "Curie- This change in behavior of the magnetic susceptibility vs the Na + content can be understood considering the specific band structure expected for the Co n+ ion in a distorted CoO6 octahedra flattened along the c direction as discussed in the first chapter. The t2g orbital degeneracy is lift in two groups: a1g and eg' orbitals, resulting from a recombination of the d orbitals (as described in the first chapter section 1.3.2). Figure V-17a proposes the band structure of the P2-NaxCoO2 phases expected in the "Curie-Weiss metal regime" and in the "Pauli regime". In the "Curie-Weiss metal regime", the phases also exhibit a metallic behavior [START_REF] Singh | Electronic structure of NaCo2O4[END_REF] , we thus expect some localized (heavy) electrons as well as some delocalized (light) electrons respectively occupying the a1g and eg bands.

In the Pauli paramagnetic regime, no localized electrons are expected in the localized a1g orbitals anymore: the Fermi level is thus located in the eg' orbitals below the a1g states (Figure V-17b).

The change in position of the Fermi level, can be understood by the oxidation of Co 3+ to Co 4+ ions and by the increase of the CoO6 distortion when the Na + content decreases, resulting in an increase in energy of the a1g band and decrease of the eg' one. We can define a θ angle between the z axis and an axis along a Co-O direction (Figure I-5). Due to the D3d distortion, this angle is supposed to become higher than 54.74° (value in the case of a regular octahedra). phase, is larger than the one reported previously [START_REF] Carlier | The P2-Na2/3Co2/3Mn1/3O2 phase: structure, physical properties and electrochemical behavior as positive electrode in sodium battery[END_REF] and would rather reflect a Na composition slightly higher for x ~0.68.

Chapter V 180

Lineshape evolution  NaxCoO2

The lineshape, as already mentioned, is due to the 2 nd order quadrupolar interaction in the 0.33 ≤ x ≤ 0.82 range. The software DMFit allows us to fit the signals using a quadrupolar simulated lineshape. Moreover, we decided to fit also the signal in the 0.33 ≤ x ≤ 0.55 with a 2 nd order quadrupolar lineshape signal in order to extract the isotropic position of the signals, the 𝜈 𝑄 quadrupolar constants and the anisotropy value η (Table V ) is due to the increase of the ionic mobility of the Na + ions in the interslab spaces. In order to fit the isotropic signal, we used a Gaussian-Lorentzian lineshape on DMFit. For x = 1/2, the lineshape is unclear for the moment, in fact, in the case of a peculiar phase, the ionic mobility would be low enough, due to the Na + /vacancy ordering, to allow to slightly distinguish the Nae and Naf sites. But in our case, no orthorhombic distortion of the peaks can be observed on Na0.5Co2/3Mn1/3O2 XRD pattern indicating that our phase is not ordered (Figure

V-9).

For the "OP" phases, a broadening of the signals is also observed due to the decrease of the ionic mobility in the phase. As discussed for Na0.25CoO2, the presence of many intercalation sites and stacking faults involved the presence of many contributions.

Signal shift evolution

For both systems, the shift position is mainly governed by the hyperfine interaction. But, for the NaxCoO2 phases (and especially for x > 0.5), the quadrupolar interaction contributes also to the isotropic position as seen in Table V-6.

In order to discuss the evolution of the shift in the P2 structure domain, we separated the spectra on Figure V-18 in three zones:

 in the zone 1, the NMR shift strongly increases  in the zone 2, the NMR shift decreases. For NaxCoO2, we decided to limit the zone 2 to x = 0.5 because of the magnetic transition reported by Foo et al. 108  in the zone 3, the NMR shift stays constant (or slightly decreases), with a much lower shift that observed in zone 2

Chapter V 184

The x ranges of these zones are not fixed but their introduction allows to simplify the discussion.

As already discussed in the chapters I and II, the hyperfine interaction in NMR depend on the nature of the unpaired electrons.

 Localized electrons leads to a Fermi contact shifts which represents the amount of electronic spin transferred from metal transition ions to the probed nucleus through the chemical bonds. This interaction, therefore, strongly depends of the number of single electrons in the electronic configuration of the metal transition ions. The Fermi contact shift 𝛿 𝐹𝑒𝑟𝑚𝑖 𝑖 is described with the following equation: V-4), but as one does not expect a strong shift difference for those two environments [START_REF] Clément | Direct evidence for high Na mobility and high voltage structural processes in P2-Nax[LiyNizMn1-y-z]O2 (0< x, y, z< 1) cathodes from solid-state NMR and DFT calculations[END_REF] , this effect won't be therefore discussed below. The shift evolution versus the Na + content is also plotted in "Curie-Weiss metal regime" and "Pauli paramagnetic regime" are separated by an orange dashed line (c) 23 Na MAS NMR isotropic shift evolution as a function of x.

𝛿 𝐹𝑒𝑟𝑚𝑖 𝑖 = 1 3𝑆𝑁 𝐴 𝜌 𝑖 (0)𝜒 𝑀
 For the NaxCo2/3Mn1/3O2 system The impossibility to refine the XRD patterns with the Rietveld method prevents from studying the geometry point of view with the Na-O distances. We can assume that the Na + layers evolution is following the chex lattice evolution since no severe modification of the CoO2 layer thickness is expected form the oxidation of Co 3+ to Co 4+ ions. Note the overall shifts are larger than observed for the NaxCoO2 phases due to the presence of Mn 4+ (t2g 3 eg 0 ) ions that leads to a higher Fermi contact shift contribution. This system is more complex than NaxCoO2 because we need to consider the contribution of the Mn 4+ ions to the total shift value. Moreover, a transition from a "Curie-Weiss metal" regime to a Pauli paramagnetism is not necessarily occurring at x = 0.5 on this system.

Cheng et al. 118 reported the partial DOS on Na2/3Co2/3Mn1/3O2 and highlighted the presence of the D3d distortion for the Mn 4+ ions. They also reported that the filled t2g orbitals of the Mn 4+ ions have a lower energy that the t2g orbitals of the Co ions. Figure V-22b displays the schematic band diagram of NaxCo2/3Mn1/3O2 in the "Curie-Weiss metal regime" considering the D3d distortion and the up and down populations. Regarding the energy of the Fermi level, we expect some localized electrons as well as some delocalized electrons respectively occupying the a1g and eg' bands of the Co 3+/4+ and some localized electrons in the levels of the Mn 4+ ions in the "Curie-Weiss metal regime". The total NMR shift can be expressed as:

𝛿 𝑡𝑜𝑡 = 𝛿 𝐹𝑒𝑟𝑚𝑖 𝑀𝑛 4+ + 𝛿 𝐹𝑒𝑟𝑚𝑖,𝑎 1𝑔 𝐶𝑜 4+ + 𝛿 𝐾𝑛𝑖𝑔ℎ𝑡,𝑒 𝑔 ′ 𝐶𝑜 𝑛+
𝛿 𝐹𝑒𝑟𝑚𝑖 𝑀𝑛 4+ is supposed to remain constant as only the Co 3+ /Co 4+ redox couple is involved in the redox process for x < 2/3 from an electronic point of view. However, from a geometric point of view, its contribution decreases when x decrease due to the Na + layer thickness increase.

Conclusion

In this chapter, we studied the local structure and electronic structure and the mechanisms occurring during the Na + deintercalation by ex-situ 23 Na MAS NMR in two different systems. Rietveld refinements on the NaxCoO2 phases patterns showed a global increase of the Na + ion layers thickness. Moreover, Le Bail refinements showed an increase of the c lattice parameter during the Na + deintercalation in NaxCo2/3Mn1/3O2. For the phases with compositions, x < 0.33, the XRD patterns suggested an important decrease of the c lattice parameters compared to the value in the P2 structures due to the sheets gliding and "OP" phase formation.

The 23 Na MAS NMR shift evolution can be interpreted considering different effects: the structural and electronic structure modifications occurring upon charging for x values corresponding to a "Curie-Weiss metal regime". During the Na + deintercalation, the consecutive predominance of both effects explains why the NMR shift, first, increases and then, decreases. For the lowest Na + contents, the localized electrons of the Co 4+ ions are no more involved in the total shift value. Therefore, NaxCoO2, for x < 0.5 has a metallic behavior with a constant Knight shift contribution of the delocalized electrons to the total NMR shift while the NMR shift in NaxCo2/3Mn1/3O2, for x < 0.45, is due to a "Knight shift" with a constant contribution of the localized electrons of the Mn 4+ ions.

Finally, for the two disordered "OP" phases formed at high voltage, the intercalation in octahedral or prismatic sites for the Na + ions leads to the observation of many contributions on both spectra.

Syntheses by electrochemical (de)intercalation is, therefore, an accurate technique in order to study the mechanisms involved during the Na + (de)intercalation by ex-situ MAS NMR and XRD.

Introduction

In this chapter, we report the 23 Na MAS NMR study of the O3-NaxRuO3 phases used as positive electrode in Na-ion batteries. The particularity of this layered oxide system is to propose an extra capacity due to the participation of the oxygen ions to the redox process and to propose a good stability in cycling. This work was done in collaboration with the Pr. Yamada group at the University of Tokyo. The main goal was to characterize the modification in the electronic structure upon Na + deintercalation in a system where O-redox is involved at high voltage. For this study, all the syntheses were realized in Tokyo by Benoit Mortemard de Boisse and sent in airtight containers to Bordeaux in order to perform the NMR acquisitions. The samples were directly entered in a glovebox before the powder packing in rotors.

In 2004, Mogare et al. 143 are the first to propose a synthesis of the pristine O3-Na2RuO3 (Figure VI-1) phase via a thermal decomposition of Na2RuO4. Rozier et al. 144 reported a capacity of almost 180 mA.h.g -1 which largely exceeds the value that the oxidation of Ru 4+ (t2g 4 eg 0 ) into Ru 5+ (t2g 3 eg 0 ) can deliver. Mortemard de Boisse et al. [START_REF] Mortemard De Boisse | Intermediate honeycomb ordering to trigger oxygen redox chemistry in layered battery electrode[END_REF] reinvestigated the material in the aim to understand this extra capacity. They showed that 1.5 electrons can be removed from the phase upon charging to 4.0 V. They reported that this extra capacity is due to the participation of the oxygen ions in the redox process in the 0.5 ≤ x < 1 range. In fact, the O-O distance (2.580(4) Å) is short enough, when the system reaches the O1-Na1RuO3 composition, to raise the antibonding 𝜎* orbitals of the O-O bonds at the Fermi level involving the oxygen redox reaction. The extra capacity allows the system to reach the Na1/2RuO3 compositions with an O1 structure (Figure VI-2). Note that this phenomenon is observed on other systems and involved extra capacity and for example in systems for Li-ion batteries [145][146][147][148] . The O3-Na2RuO3 formula can be rewritten as O3-Na[Na1/3Ru2/3]O2 in a more usual lamellar oxide nomenclature: the transition metal layers are composed of a honeycomb ordering with one Na + ion surrounded by 6 Ru 4+ ions as shown in Figure VI-1.

Figure VI-1:

Structure of O3-Na2RuO3 with the oxygen ions in red, the Na + ions in yellow and the Ru 4+ ions in grey. Extracted from reference [START_REF] Mortemard De Boisse | Intermediate honeycomb ordering to trigger oxygen redox chemistry in layered battery electrode[END_REF] .

In 2019, Mortemard de Boisse et al. [START_REF] Mortemard De Boisse | Coulombic self-ordering upon charging a large capacity layered cathode material for rechargeable batteries[END_REF] reinvestigated the O3-NaxRuO3 system. They showed that Na2RuO3 presents 40 % of stacking faults due to occasional shifts of the [Na1/3Ru2/3]O2 slabs perpendicularly to the stacking direction. Note that the amount of stacking faults strongly decreases during the Na + deintercalation (to 2%) but increases again to its initial value (40 %) at the end of each cycle. The O1-Na1RuO3 and O1'-Na1/2RuO3 phases have characteristic Ru 5+ /vacancy ordering in the transition metal layers and Na + /vacancy ordering in the interslab spaces meaning that the Na + ions from the transition metal layers are the first to be deintercalated during the charge of the Chapter VI 197 2. 23

Na MAS NMR results

Single pulse 23 Na MAS NMR spectra were recorded on a Bruker 500 Avance spectrometer at 132.302 MHz (B0= 11.75 T). A spinning frequency of 30 kHz was used. The sample were placed in zirconia rotors in a dry box and studied by NMR immediately after taking the rotors out of the glovebox. An XRD pattern taken after the RMN studies ensured that the samples did not evolved during the NMR acquisitions, indicating satisfactory air-tightness of the rotors. As 23 Na is a quadrupolar nucleus with I = 3/2, a short pulse length of 1 µs corresponding to a selective π/8 pulse determined using an aqueous 0.1 mol.l -1 NaCl solution was employed. In these conditions, we ensure that the main signal observed is due to the -½+½ central transitions. The spectral width was set to 1 MHz, and the recycle time D0 = 0.2 s, is long enough to avoid T1 saturation effects.

The baseline distortions resulting from the spectrometer dead time (8 µs) were computationally removed using a polynomial baseline correction routine. The external reference was a 0.1 mol.L -1 NaCl aqueous solution. 23 Na MAS NMR spectra of two O3-Na2RuO3 phases prepared in the same way as described in reference [START_REF] Mortemard De Boisse | Coulombic self-ordering upon charging a large capacity layered cathode material for rechargeable batteries[END_REF] . Both spectra of O3-Na2RuO3 clearly exhibits two isotropic shifts located at ~2400 and 877 ppm while one spectrum exhibits an additional signal at 750 ppm.

Pristine phase

Such large shift values are typically resulting from Fermi contact shift interactions expected between Ru 4+ (t2g 4 eg 0 ) ions and 23 Na nucleus. By analogy with the NMR spectra of Li2MnO3 that exhibits also a honeycomb ordering (Li/Mn in the layers) 149

Deintercalated phases and reversibility of the system

In order to check the reversibility of the cycling process of O3-Na2RuO3 depending on the upper cutoff voltage, we investigated the local structure by 23 Na MAS NMR of two phases recovered at the end of the discharge and synthetized by electrochemical reintercalation at 1.5 V. The first one was charged up to 3.07 V (Na1RuO3) and the second one up to 4 V (Na1/2RuO3). (remaining electrolyte salt, SEI). The acquisitions were performed in the same conditions than for the pristine phase. All the spectra were normalized to the number of scans. No significant differences are observed for the two materials recovered after a charge up to 3.07 V (Na1RuO3) or up to 4 V (Na1/2RuO3) followed by a discharge at 1.5 V: their spectra exhibit two signals (around 895 ppm and one around 2550 ppm), showing that the deintercalation process is overall reversible and the Na + ions can be reintercalated in the transition metal layers (signal at 2550 ppm). Those spectra are, however slightly different from the one of the pristine phase. The slight difference in the shift values is probably due to some slight differences in distances and angles due to the reformation of stacking faults and to the overall Na composition that might be slightly lower than 2, although no evidence of an extra signal possibly assigned to Na next to Ru 5+ (t2g 3 eg 0 ) ions is observed. No signal at 750 ppm is clearly observed in the discharged phases but the signal at 895 ppm is larger than the one of the pristine material, probably also due to the reformation of stacking faults that may differ from the pristine materials. As a conclusion, the cycling at 4 V that involves the O-redox mechanism is mostly reversible and do not imply Ru irreversible migration in the interslab space. This point confirms the previous results obtained by XRD for the same phases after cycling and the good reversibility of the electrochemical process.

O1-Na1RuO3 and O1'-Na1/2RuO3 were also studied by 23 Na MAS NMR. Figure VI-5 shows the Na site environments in both phases. Mortemard de Boisse et al. [START_REF] Mortemard De Boisse | Coulombic self-ordering upon charging a large capacity layered cathode material for rechargeable batteries[END_REF] reported that Na1RuO3 crystallizes in the R3 ̅ space group while Na1/2RuO3 crystallizes in the P3 ̅ :1m space group. Surprisingly, the O1-Na1RuO3, does not exhibit any shifted signal in our acquisition conditions Chapter VI 201 (Figure VI-6) suggesting a complex behavior of the Fermi contact shift (link to the structure and electronic structure) for this composition. From a geometric aspects, Mortemard de Boisse et al. [START_REF] Mortemard De Boisse | Coulombic self-ordering upon charging a large capacity layered cathode material for rechargeable batteries[END_REF] reported that the interlayer distance continuously decreases from x = 2 to x = 1. This can be explained by the presence of non-centered Na + ions in their octahedra as depicted on Figure VI-5, as Na + is located in an octahedron sharing a face with Ru V O6 on one side and with □O6 on the other side. These particular positions lead to Ru-O-Na angles different than the usual 90° and 180° for 1 st and 2 nd neighbors interactions. By only considering the distance between the Na + and the Ru 5+ , there are 6 Ru 5+ as 2 nd neighbor with ~126° Ru-O-Na interactions, 3 Ru 5+ interact as 3 rd neighbor at ~137° and only 1 Ru 5+ interacts at ~82° as 1 st cationic neighbor (Figure VI-5). The presence of these particular angles shows an uncommon and complex behavior of this system. The Ru 5+ as 1 st cationic neighbor (red arrow on Figure VI-5) shares one face of its RuO6 octahedron with one NaO6 octahedron. The distance between this Ru 5+ and the Na + ions, in this case, is 3.149 Å.

Moreover, the 𝜃 angle, defined in the first chapter (Figure I-6) between the z axis and a Ru-O direction, is equal to ~60° indicating a possible D3d distortion and lift of degeneracy of the t2g orbitals into the a1g and eg' orbitals. In this case, it is possible that the localized behavior of the electrons in 4d orbitals leads to a the loss of the observability of the signal due to a direct overlap mechanism in a similar way than for LixCoO2 in the 0.94 -1 range [START_REF] Ménétrier | The insulator-metal transition upon lithium deintercalation from LiCoO2: electronic properties and 7 Li NMR study[END_REF] . Moreover, another possibility is the that the Ru 5+ as first neighbors (126° interactions) are mainly involved in the spin transfer mechanism due to the short Na-O distance (2.129 Å) shown in Figure VI-5. Therefore, this short Na-O distance could lead to an important spin transfer from the Ru 5+ to the 3s Na orbital and the loss of observability of the NMR signal, which would be too shifted, too broad or associated with a very short T1 or T2 relaxing times.

For Na1/2RuO3, a 23 Na MAS NMR signal is observed around a major contribution located at 30 ppm. The presence of an additional signal at 100 ppm can be due to the 2 % of stacking faults highlighted in the previous work. Chapter VI 204

Conclusion

In this chapter, we studied the evolution of the local structure of O3-NaxRuO3 by ex-situ 23 Na MAS NMR on phases synthetized by electrochemical (de)intercalation and confirmed its good reversibility of the redox process even using an upper cutoff voltage involving O-redox. The participation of the oxygen ions to the redox process is very interesting for the development of new materials positive electrode materials with high energy densities. Nowadays, the number of studies concerning this kind of materials is drastically increasing. These systems are usually composed of Mg 2+ , Na + ions or □ in their transition metal layers. We can mention Nax(MgyMn1-y)O2 151 , Nax(□1/7Mn6/7)O2 152 , NaxRu0.75Sn0.25O3 144 or NaxIrO3 153 which are systems that were studied as positive electrode materials for Na-ion batteries where an anionic redox process participates to the global redox process at high voltages.

Concerning the NMR study of the deintercalated phases shows that the NMR evolution is more complex to understand without complementary magnetic properties or electrical conductivity measurements. A loss of signal observation is obtained for O1-Na1RuO3, while a 30 ppm signal is observed for Na1/2RuO3 suggesting a magnetic transition between x = 1/2 and x = 1. For the future, it would be interesting to study other compositions in order to have a better insight of the global evolution of the shift and the mechanisms involved during the Na + deintercalation.

General Conclusion/Perspectives

During this work, solid state NMR has been used as a key tool to characterize, as a complementary technique to XRD, the atomic structure of several lamellar oxides. In addition, thanks to the hyperfine coupling, solid state NMR allowed to investigate the local electronic structure of the materials and its modification upon cycling. We were also interested in the ionic dynamics of the Li + ions in the interslab spaces for two specific layered oxides.

The first part of this work concerned an OP4-(Li,Na)CoO2 phase which proposes a very unusual structure because of an 1:1 alternation of interslab spaces filled with Li + in octahedral sites and Na + in prismatic sites. As a misunderstanding existed between the chemical formula of the phase and its structure, we decided to investigate the local structure of the phase. [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR showed the presence of five different environments for the Li + ions in the material. Moreover, we highlighted that the NMR signal shifts are due to two contributions: a Knight shift and a Fermi contact shift due to the presence of, respectively, electrons with a localized behavior and electrons with a delocalized behavior in the electronic structure. This "Curie Weiss metallic regime" involves that the electronic structure is difficult to be modelled by DFT calculations. Based on the 23 Na MAS NMR results, we further considered the presence of Na + ions in the Li interslab spaces in our Rietveld refinement and we thus determined OP4-[Li0.42Na0.05]Na0.32CoO2 as chemical formula.

Finally, the Li + ions exhibited no obvious dynamics in the interslab spaces, for the probed timescale, as revealed by the selective inversion technique due to the almost 95 % filling of the Li interslab spaces with Li + and Na + ions in octahedral sites.

Note that also that during this PhD, we published, in collaboration with Romain Berthelot (ICGM, Montpellier), the study of a layered oxide Li3-xNaxNi2SbO6 with a honeycomb ordering in the Ni2SbO2 slabs 154 . Contrary to the OP4 phase, this phase proposes a random occupancy of the interslab spaces with the Na + and Li + ions in octahedral geometries. NMR was used as a local characterization technique to reach this conclusion and is a powerful technique to study the distribution and localization of the different ions in a material.

The dynamics of the Li + ions was evidenced by solid-state MAS NMR (selective inversion technique) in another phase synthetized during this work, O4-LixCoO2. In fact, vacancies are thus present in the Li interslab spaces making easier the Li + ions mobility. This material was obtained by a "in solution" ion-exchange technique from the OP4 phase. The idea was to synthetize a phase with [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li ions in the O3-type layers and [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li ions in the O2-type layers by considering a possible selective exchange. However, [START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li and [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR showed that the exchange isn't selective and both Li + ions types occupy, randomly, the two different crystallographic sites. Moreover, we showed that a small amount of Na + ions remains in the structure after the ion-exchange. We suggested that this Na + ions are located in octahedral sites in the Li interslab layers.

The mechanisms occurring upon cycling have been studied by in-situ Synchrotron XRD and 23 Na MAS NMR for different P2-NaxCoyMn1-yO2 (y = 1/3, 1/2, 2/3 and 1) phases used as positive electrode materials in Na batteries. We determined that P2-NaxCoO2 can be cycled at C/20 reversibly up to 4.3 V vs Na + /Na and shows a complex phases diagram with a succession of solid solution and two-phase reactions upon Na deintercalation. While the P2 structure is maintained for x > 1/3, for 1/3 < x < 1/2, we showed a solid-solution behavior despite that "in average" the presence of possible incommensurable structures associated to ion and charge ordering are observed. A new ordered phase Na1/3CoO2 was also evidenced and it was shown to crystallize in a hexagonal cell with a √3 ahex x √3 ahex x 3 chex superlattice. However, this phase needs further investigations to get a description of its actual structure. Moreover, we showed that sheets glidings occur for x < 1/3 with the transformation of the P2-type structure into an "OP"-like one with different intercalation sites for the Na + ions and many stacking faults. Sheets glidings are associated with a decrease of the c lattice parameter due to the formation of octahedral sites. For future works, it would be interesting to investigate more carefully the discharge following the charge up to 4.6 V in order to understand the reason of the strong polarization observed on the galvanostatic curve at C/20.

Concerning the Co,Mn systems, we highlighted that P2-NaxCo2/3Mn1/3O2 can be cycled reversibly at C/20 up to 4 V (vs Na + /Na) and that the two other studied systems (for y = 1/3 and 1/2) show an important polarization when cycled, respectively, up to 4 V and 4.3 V. Globally these systems reveal a solid solution behavior with one or two peculiar phases for specific compositions (x = 1/2 and/or x = 1/3). The presence of sheets glidings at high voltage was also highlighted on the NaxCo2/3Mn1/3O2 system. Additionally, we determined that Na1/2Co2/3Mn1/3O2 crystallizes in the Pnmm space group like the Na1/2CoO2 phase. The discharge following the charge up to 4.5 V would synthetized by electrochemical (de)intercalation. We showed a good reversibility of this system at the local scale and a reintercalation of the Na + ions in the transition metal layers after one cycle.

The electronic structure evolution of this system is relatively complex to understand while no sheets glidings occurs even for the lowest Na + contents. The evolution of the NMR shifts during the Na + deintercalation seems to be mainly correlated with the geometry of the structure and especially, the distance between the Na + and the Ru ions as first neighbors leading to a strongly shifted signal for Na1RuO3. However, for Na1/2RuO3, the shift can either be due to a Knight shift or a Fermi contact shift but without magnetic measurements, it is, for the moment, difficult to conclude about the magnetic state of these phases. Moreover, it would be interesting to synthetize more phases with different Na + compositions in order to have a better insight of the evolution of the local structure.

The systems with extra capacity due to the participation of the oxygen couple to the redox process are very interesting and promising for the future, in the battery field as no structural transition due to layers glidings seems to occur in these systems at high voltage allowing a better stability in cycling. These kinds of system would be interesting to be studied for different amounts of Na + ions in order to understand the different mechanisms occurring during the charge with [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li and/or 23 Na MAS NMR. For instance, Yang et al 155 . reported that the NaxLi0.18Fe0.12Mn0.7O2 system have an interesting capacity of 190 mAh.g -1 with a relatively good capacity retention.

A.3 Na4/7CoO2

This phase was described, previously, by Igarashi et al. 109 in the hexagonal cell with a different space group than P2 structure. They realized electron and neutron diffraction in order to exhibit the superstructure ordering and determined a P63/m space group with a √7𝑎 ℎ𝑒𝑥 x √7𝑎 ℎ𝑒𝑥 x 𝑐 ℎ𝑒𝑥 superlattice. In this manuscript, we show the refined XRD pattern of this phase ( une forte recrudescence depuis 10 ans à cause de la diminution drastique 9 de la quantité de ressources en Li. En particulier, le système P2-NaxCoO2 présente un intérêt tout particulier car certaines phases présentent des propriétés physiques intéressantes telles que des propriétés thermoélectrique ou encore supraconductrice [START_REF] Terasaki | Large thermoelectric power in NaCo2O4 single crystals[END_REF][START_REF] Takada | Superconductivity in two-diemnsional CoO2 layers[END_REF][START_REF] Chou | Thermodynamic and transport measurements of superconducting Na0.3CoO2• 1.3 H2O single crystals prepared by electrochemical deintercalation[END_REF][START_REF] Landron | Ab initio evaluation of the local effective interactions in the superconducting compound Na0.35CoO2•1.3 H2O[END_REF][START_REF] Lee | Large enhancement of the thermopower in NaxCoO2 at high Na doping[END_REF][START_REF] Lee | Enhancement of the thermopower in NaxCoO2 in the large-x regime (x>0.75)[END_REF] . Dans ce manuscrit, nous avons étudier la structure moyenne de différentes phases de différents systèmes, comme P2-NaxCoO2, par diffraction des rayons X (DRX). De plus, la Résonance Magnétique Nucléaire avec rotation à l'angle magique (MAS RMN) du 23 Na a été utilisée comme technique de caractérisation afin d'étudier la structure locale, électronique et la structure électronique locale des différentes phases synthétisées lors de ce travail de thèse. La RMN a déjà largement été utilisées dans le domaine des batteries [START_REF] Grey | NMR Studies of Cathode Materials for Lithium-Ion Rechargeable Batteries[END_REF][START_REF] Pecher | Materials' methods: NMR in battery research[END_REF] pour l'étude des matériaux d'électrodes, de l'électrolyte ou encore des interfaces. La RMN du 23 Na est sensible à la présence d'électrons célibataires dans l'environnement du noyau de 23 Na via les interactions hyperfines. Deux interactions sont, dans ce travail, principalement responsables des déplacements chimiques observés sur les différents spectres RMN obtenus : le contact de Fermi et le déplacement de Knight. Le contact de Fermi est proportionnel à la quantité de densité de spin transférée de l'ion M vers l'orbitale s du noyau de 23 Na à travers les liaisons chimiques et donc via l'orbitale 2p de l'ion oxygène. Cette interaction concerne ainsi les électrons de type localisées. Le déplacement chimique impliqué par cette interaction peut s'écrire [START_REF] Bertini | Magnetic susceptibility in paramagnetic NMR[END_REF] : Lors de cette thèse, différentes phases P2-NaxCoO2 ont été synthétisées et analysées par DRX exsitu et MAS RMN du 23 Na afin de comprendre les mécanismes impliqués lors de la charge et de la décharge d'une batterie Na-ion. Cette thèse fait suite aux travaux de thèse de Romain Berthelot qui a étudié le diagramme de phase du système P2-NaxCoO2 pour x > 0.5 par DRX in-situ mettant en évidence la présence de nombreux domaines selon la quantité d'ions Na + intercalés au sein du matériau [START_REF] Berthelot | Contribution à l'étude électrochimique du système P2-NaxCoO2. Synthèse et caractérisation de nouveaux oxydes lamellaires ordonnés (A/A')CoO2 (A[END_REF][START_REF] Berthelot | Electrochemical investigation of the P2-NaxCoO2 phase diagram[END_REF] .

𝛿 𝐹𝑒𝑟𝑚𝑖 𝑖 = 1 3𝑆𝑁 𝐴 𝜌 𝑖 (

Electrochimie

Des mesures en cyclage ont été réalisées en batterie Na(s) / NaPF6 dans 1 M de Propylène Cependant, ce comportement n'est pour le moment pas totalement clair et pourrait être dû à une différence de cinétique pendant la décharge par rapport à la charge.

Synthèse par voie électrochimique de différentes phases

Afin d'étudier les mécanismes impliqués pendant la désintercalation des ions Na + par DRX et RMN du 23 Na ex-situ mais aussi de comprendre les phénomènes se produisant entre 4. A noter que le paramètre de maille ahex diminue faiblement lorsque x diminue car l'ion Co 3+ (0 .545 Å de rayon) est légèrement plus grand que l'ion Co 4+ (0.53 Å de rayon) 3 . Les deux paramètres de maille atteignent une valeur limite pour x = 0.4 en charge.

Conclusion générale

List of Figures

Figure GI- 1 :

 1 Figure GI-1: Representation of the AxMO2 structure. The M ions are in grey, the A ions are in green and the O ions are in red. The A, B and C letters corresponds to the oxygen positions in order to have a compact stacking.

  described the lamellar oxides AxMO2 (A = alkali ion(s), M = transition metal ion(s)) as a stacking derived from the structure of 𝛼-NaFeO2 50 or O3-NaFeO2 1 . O3-NaFeO2 derived from the NaCl lattice, as shown on Figure I-1a, by switching the chloride ions by oxygen ions and filling the cationic sites by iron and sodium ions. A deformation along the [1 1 1] direction (Figure I-1b) due to the Na + (1.02 Å) and Fe 3+ (0.645 Å) 3 ions dimension difference occurs and leads to a rhombohedral lattice. A hexagonal description, as shown in general introduction, is also possible in the R3 ̅ m (number 166) space group by considering the [1 1 1] direction as the c axis.

Figure I- 1 :Figure I- 2 :

 12 Figure I-1: a) Representation of O3-NaFeO2 structure in NaCl rock salt type structure. The dashed line in the cell represents the (111) direction b) Representation of O3-NaFeO2 structure considering the distortion along the (111) direction 50 .

Figure I- 3

 3 depicts a representation of the O3, P2 and P3 structures and shows the geometry of the intercalation sites in each case.

Figure I- 3 :

 3 Figure I-3: Representation of the O3, P2 and P3 structures and representation of the corresponding Na + intercalation sites

Chapter I 16 1. 3 Figure I- 4

 1634 Figure I-4 depicts the representation of the 3d orbitals of the M transition metal ions in an octahedral environment. In the lamellar oxides, the metal transition ions are surrounded by six O ions. The crystal field theory shows that the interaction between the 3d orbitals and the electrostatic potential due to the oxygen ions negatively charged leads to a breaking of degeneracies of the dz² and dx²-y² orbitals. They are, therefore, located at a higher energy level than the free M ion. The three orbitals dxy, dyz and dxy which point between the O ligands are stabilized due to a lower energy level compared to the free Co ion. These three orbitals are called t2g. The eg orbitals represent the two remaining orbitals, dx²-y² and dz².

Figure I- 4 :

 4 Figure I-4 : Representation of the 3d orbitals in an octahedral environment. The dz² and dx²-y² orbitals point to the ligands while the dxy orbitals point between the O ligands. dxy and dxz are not represented but are symmetrically equivalent to dxy

Figure I- 5 :

 5 Figure I-5 : (a) Electronic configurations of the Co ions in Oh symmetry

  close but different energy levels for both eg' orbitals (FigureI-7).

Figure I- 6 :

 6 Figure I-6 : (a) Electronic configurations in Oh and D3d symmetry for Co 3+ ions. (b) Representation of the compression due to the D3d symmetry occurring on CoO6 octahedra.

Figure I- 7 :

 7 Figure I-7 : Representation of Co t2g orbital after trigonal distortion for Na1/2CoO2. Landron et al. 58 model considers two Co sites with different energy gaps between the levels.

Figure I- 8 :

 8 Figure I-8 : Schematic representation of the band structure of P2-NaxCoO2 after the splitting of the t2g orbitals with the D3d distortion.

the

  Na interslab spaces (Figure I-9c).

Figure I- 9 : 22 2. 2 Figure I- 10 :

 922210 Figure I-9 : (a) Initial state of the Na battery with NaxMO2 as positive electrode material. Metal sodium is used as negative electrode and the electrolyte is liquid. Representation of a Na battery during (b) the charge with the Na + deintercalation from NaxMO2 and (c) the discharge with the intercalation of Na + in NaxMO2. The Na + ions are represented by the green circle.

Q

  : capacity (A.h) I: applied current (A) Chapter I t: duration of (dis)charge (h) F: Faraday constant (C.mol -1 )

Figure I- 11

 11 shows the stacking realized in a coin cell: the positive electrode is directly in contact with the positive current collector and separated from the negative electrode (metal sodium) by three glass fiber separators. The metal sodium negative electrode is flattened in the glovebox before being cut to obtain a 12 mm diameter electrode. The solid sodium is finally deposited on a stainless steel support and put directly in contact with the separators soaked of electrolyte. A stainless steel spring is put between the negative electrode and the negative current collector to converse a constant pressure during the sealing and a good electrical contact during the cycling. Finally, a joint allows to prevent the contacts between both Chapter I 26 current collectors and therefore to avoid short circuits. The joint also ensures the airtightness of the coin cell after sealing in the glovebox with a press.

Figure I- 11 :

 11 Figure I-11 : (a) Representation of the stacking used to assemble of the battery in a coin cell (b) Sealed coin cell after assembly

  ) a potentiostatic step. Once the targeted voltage is reached by the battery, the voltage is maintained while the current is relaxing until a negligible value (Figure I-12). A negligible current value means that the battery can be disconnect without any risk of a structural evolution. This technique will be used to synthetize the samples studied in the chapter V for ex-situ characterization techniques. More information about the experimental set-up of the cell will be discussed at that time.

Figure I- 12 :

 12 Figure I-12 : Evolution of the voltage and the current as a function of time during the two steps necessary to synthetize a phase by electrochemical (de)intercalation.

3. 1 . 1 . 1

 111 Airtight sample holder (Co K𝛼 1,2 radiations) Before the acquisitions, the powders were ground and placed in an airtight sample holder with an Al base. A polyimide (Kapton) window which is transparent to the X-Rays was used to let the beam pass as shown on Figure I-13. This technique allows to get acquisitions with a good quality. In fact, a fluorescence of the NaxMO2 (M with Co) phases is observed when using Cu K𝛼 1,2 radiations and leads to lower quality XRD patterns. The limitation of this technique is the necessity to fill completely the sample holder to avoid the presence of aluminum diffraction peaks on the XRD patterns. Therefore, a relatively high amount of powder was necessary. The acquisitions could be carried from 6° to 150° in the 2θ range. Le Bail and Rietveld refinements 59 allowed to determine information about the average structure of the analyzed powders. The refinements were performed on the software FullProf 60 .

Figure I- 13 : 29 3. 1 . 1 . 2

 1329112 Figure I-13: Pictures of the airtight sample holder used for XRD acquisitions

Figure I- 14 :

 14 Figure I-14 : (a) Coin cell drilled with 3 mm diameter holes on both current collectors. (b) Current collector holes covered with a polyimide 7 mm diameter film.

Figure I- 15 ). 32 Figure I- 15 :

 153215 Figure I-15 :Zeeman effect with the splitting in two magnetic levels when a magnetic field is applied for I = ½ and 𝛾> 0

  to 𝐵 0 ⃗⃗⃗⃗ , a maximal electric signal at 𝜔 0 frequency is detected by the same coil that generates 𝐵 1 ⃗⃗⃗⃗ magnetic field (Figure I-16).

Figure I- 16 :

 16 Figure I-16 : Representation of a NMR experiment. At equilibrium, 𝑀 0 ⃗⃗⃗⃗⃗ is parallel to 𝐵 0 ⃗⃗⃗⃗ . 𝐵 1 ⃗⃗⃗⃗ perturbation leads to the magnetization flip in the (x,y) plane. (0, x', y', z' (=z)) is the new system considering the rotation of the magnetization around 𝐵 0 ⃗⃗⃗⃗ .

Figure I- 17 :

 17 Figure I-17 : Representation of the rotors in the NMR probe at the Magic Angle for MAS experiments. The picture is extracted from 61 .

  𝜒 𝑀 : magnetic molar susceptibility 𝜇 0 : magnetic constant Chapter I 36 𝜇 𝐵 : Bohr magneton 𝐴 𝑖 is the only parameter able to change the shift sign to negative or positive values. This constant depends of the electronic spin density on the i nucleus called 𝜌 𝑖 (0). 𝐴 𝑖 = 𝜇 0 3𝑆 𝛾 𝑖 𝑔 𝑒 𝜇 𝐵 ħ𝜌 𝑖 (0) S: spin quantum number 𝜌 𝑖 (0) = ∑ ( |𝜓 𝑗 ↑ (0)| 2 -|𝜓 𝑗 ↓ (0)| 2 ) 𝑗 with |𝜓 𝑗 ↑ (0)| 2 the probability of presence of positive polarized spin and |𝜓 𝑗 ↓ (0)| 2 the probability of presence of a negative polarized spin.

  EFG tensor Q: nuclear quadrupole moment The EFG increases with the anisotropy of the charge distribution of the crystal environment (Figure I-19)

Figure I- 19 :

 19 Figure I-19 : Repartition of the quadrupolar moments created for I > 1/2 spin

Figure I- 20 :

 20 Figure I-20: Energy level diagram for the I = 3/2 nuclei after application of a magnetic field. Extracted from 66 .

section 3. 2 . 1 . 2 )

 212 . The 𝐵 1 ⃗⃗⃗⃗ pulse duration allows the magnetization to move from its equilibrium position. For the simple pulse experiments, it is not mandatory to flip the magnetization in the (x,y) plane because only the projection in the plane is measured. However by flipping the magnetization in the (x,y) plane, higher magnitudes are measured. A time out is also added between the pulse end and the beginning of the measurement due to the double use of the coil which generates the B1 magnetic field and receives the signal. This double use involves perturbations at the beginning of the FID. The time out prevents from recording the first points of an already short FID (Figure I-21). Two consequences are that the broad signals can't be correctly observed and the use of a first order phasing of the NMR spectrum which involves a baselines distortion in sin(x)/x. The impulsion times ans times out are around few µs for while the recycle delays are around 1 s for paramagnetic compounds and around 10 s for diamagnetic compounds.

Figure I- 21 :

 21 Figure I-21 : Recording of the FID and Fourier transformation for a simple pulse sequence

Figure I- 22 :

 22 Figure I-22 : Hahn Echo sequence

Figure I- 23 :

 23 Figure I-23: Basic form of a 2D exchange experiment. Both pulses are 90°. Excitation label corresponds to the first pulse to transverse magnetization in (x,y) plane. Second pulse allows to restore the magnetization along 𝐵 0 ⃗⃗⃗⃗ direction. Third pulse reconverts the magnetization in (x,y) plane. Extracted from 61 .

Figure I- 24 :

 24 Figure I-24 : Schematic representation of a 2D EXSY spectrum. 𝛺 represents the peaks frequency. Extracted from 61 .

  (Figure I-3).

Figure II- 1 :

 1 Figure II-1 : Perspective representation of OP4-(Li/Na)CoO2. Na + ions occupy prismatic sites which can either share faces (Naf, in red) or edges (Nae, in purple) with the surrounding CoO6 octahedra (in blue). The Li + ions occupy octahedral sites (in yellow). The oxygen ions positions are labelled with the letters A, B and C.

Figure II- 2 .

 2 One can distinguish the layered structure of the OP4 phase. It is also possible to observe the hexagonal shape of the crystals. The bigger particles measure almost 200 µm while the smaller particles are 3 µm long. Nanometric particles can also be observed on the particles which either can be trace of Co3O4 or the result of a reaction to air.

Figure II- 2 :

 2 Figure II-2 : SEM pictures of the sample A at different magnifications. Dashed lines represent the hexagonal shape of a OP4 crystal.

Figure II- 3 : 56 2. 2

 3562 Figure II-3 : Representation of the different structures introduced in this chapter.

Figure II- 5 :

 5 Figure II-5: Electrical conductivity of an OP4 phase as a function of temperature (from 6K to 300 K).

Figure II- 6 Figure II- 6 :

 66 Figure II-6 displays the evolution of the magnetic susceptibility of the sample A as a function of temperature from 7 K to 300 K with a constant magnetic field of 1 T. The measurements were performed on a Super Quantum Interference Device (SQUID) magnetometer MPMS5 The sample A was cooled without any application of a magnetic field (ZFC). The fit of the experimental data was realized taking into account a paramagnetic contribution 𝜒 0 , following a Curie-Weiss law:

The 1D 7 4 .

 74 Li MAS NMR spectra of the three samples are shown in Figure II-8 under a 2.35 magnetic field and a 30 kHz spinning frequency. The three samples exhibit 5 signals located after fitting at 32, 18 ppm, 0, -84 and -203 ppm and respectively labelled 1 to 5 (Figure II-9). The presence of many signals suggests a repartition of different Co ions environments in the layers. The signal 3 can be assigned to Li + ions in diamagnetic LS-Co 3+ (t2g 6 ) environments similar to the one in O3-LiCoO2 90,91 , whereas all the other signals are clearly due to the Fermi contact interaction observed for Li + in octahedral environments surrounded by paramagnetic ions. After fitting the signals of the spectra (Figure II-9) including the spinning side bands, the resulting signal intensities were extracted and summarized in Table II-The signal 5 was not considered because of its very low intensity. The intensity values obtained for the signal 2 are similar for all the samples and are therefore not affected by the nature of the impurities in the samples. Contrary to the signal 2, the signal 3 (0 ppm) intensity is slightly larger for the sample A in agreement with the presence of O3-LiCoO2 as impurity.

Figure II- 7 :

 7 Figure II-7 : Comparison of the 7 Li MAS NMR spectra recorded on the sample C at two different magnetic fields (2.35 and 7.05 T) using the same spinning frequency (30 kHz) with a Hahn Echo sequence. Insert: Zoom in order to highlight the presence of the signal at -203 ppm.

Figure II- 8 :

 8 Figure II-8 : Experimental 7 Li MAS NMR spectra of the samples A, B and C (2.35 T magnet, spinning frequency = 30 kHz, Hahn echo sequence).

Figure II- 9 :

 9 Figure II-9 : Fits of the signals 1, 2, 3 and 4 compared to the experimental spectra (in red) recorded on samples (a) A (b) B (c) C.

Figure II- 6 ).

 6 Calculations were also realized by considering the theoretical Curie constant value Cth.

Figure II- 10

 10 Figure II-10 : a) Representation of the hypothetical cell Li1/2Na1/3CoO2 used as model for DFT calculations. This model considers full Li layers and 67% filled Na layers. b) Highlighting of the Na + /vacancy ordering in the Na interslab spaces.

  5 ) and 5/6 LS-Co 3+ (t2g 6 ) (Figure II-11).

Figure II- 11 :

 11 Figure II-11: (a) Calculated spin DOS of the model presented in Figure II-10. (a) total. (b) partial on the Co 3d orbitals.

3 . 2 ) 67 Figure II- 12 :

 326712 Figure II-12 : Comparison between the experimental[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR spectrum of the OP4 phase and the calculated spectra considering the theoretical Curie constant and the experimental one.

Figure II- 13 :

 13 Figure II-13 : Calculated 3D spin density map plotted using a 10 -3 e -/A² isosurface value. a1g orbital is mainly carrying the spins. The yellow color represents the positive spin density.

Figure II- 14 :

 14 Figure II-14: Band structure of the Co 3+ ions in the case of NaxCoO2 (a) before and (b) after the octahedra distortion.

4. 3

 3 Variable temperature (VT) VT-MAS NMR experiments were performed at a 13 kHz spinning frequency in a 265 K ≤ T ≤ 450 K temperature on the 7.05 T magnet equipped of a 4 mm WVT MAS probe (Figure II-15). Hahn echo sequences were used. Note that at 450 K, one can also distinguish a new component labelled 3'. A coalescence phenomenon seems to occur when T increases indicating a slow chemical exchange between the Li sites. The signals narrowing when T increases is also due to a low increase of the mobility. The mobility of the Li + ions will be investigated by NMR later in the next section of this chapter. Nevertheless, the variation of the signals position reveals the complexity of the origin of the shifts. Indeed, for Fermi contact shifted signals observed in paramagnetic compounds, the shifts are following the same trend versus T as does the magnetic susceptibility, i.e a 𝑪 𝑻-𝜽 for a Curie-Weiss law and should tend to 0 ppm for T  +∞.

Figure II- 15 : 2 (

 152 Figure II-15 : Experimental 7 Li MAS NMR spectra recorded on a 7.05 T magnet at different temperatures in the 265 K -450 K. The NMR sequences were Hahn echoes and the spinning frequency was 13 kHz.

Figure II- 16 : 4 )

 164 Figure II-16: Experimental 7 Li MAS NMR spectra recorded on a 7.05 T magnetic field with a spinning frequency of 30 kHz for T = 250 K, 300 K and 320 K.

Figure II- 17 : 1 Table II- 5 :

 1715 Figure II-17: Fitted lines of the NMR shifts evolution of the signals 1, 2 and 3 as a function of temperature.

Figure II- 18

 18 Figure II-18 represents the pulse sequence of the inversion-recovery technique.

Figure II- 19 : 7 :

 197 Figure II-19 : Evolution of the signals intensities for each signal as a function of 𝜏 𝑚 delays

  (Figure II-20). A range of mixing times is also used to allow different chemical exchange times.

Figure II- 20 :

 20 Figure II-20 : Selective Inversion pulse sequence

Figure II- 21 :

 21 Figure II-21 : Experimental 7 Li MAS NMR spectra of the sample B performed with the selective inversion technique at 340 K with mixing times from 0.05 ms to 6 s. The acquisitions were realized on a 7.05 T magnet with a spinning frequency of 65 kHz. (a) The signal 1 was selectively inverted. (b) The signal 2 was selectively inverted. (c) The signal 3 was selectively inverted.

23

  Na MAS NMR was performed on a Bruker Avance spectrometer at 79.4 MHz (7.05 T magnet) and 132.3 MHz (11.75 T magnet). As23 Na is a strong quadrupolar nucleus with I = 3/2, a short pulse length of 1 µs corresponding to a π/8 pulse determined using an aqueous 1 M NaCl solution was employed. In these conditions, the main signal observed is due to the -½  +½ central transition. The spectral width was set to 1 MHz, and the recycle time D0 = 0.5 s, is long enough to avoid T1 saturation effects. Using a 7.05 T magnetic field increases, a second order quadrupolar broadening of the signal at 203 ppm is observed and preventing the resolution of the different signals. Nevertheless, under a 11.75 T magnetic field a second order quadrupolar lineshape is still observed for all the lines but allow the resolution of the Na signal in the structure.

Figure II- 22 :

 22 Figure II-22: Comparison of the 23 Na MAS NMR spectra recorded of the sample A for two different magnetic fields (7.05 T and 11.75 T). The spinning frequency was 30 kHz and the sequence was a single pulse.

Figure II-23a shows the 23

 23 Figure II-23a shows the 23 Na MAS NMR spectra recorded on the three (Li,Na)CoO2 compounds under a 11.75 T magnetic field. Figure II-23b shows the presence of two signals which can be further fitted using a 2 nd quadrupolar lineshape (Figure II-23b and TableII-8). Here, the fitted parameters are the signals positions, intensities but also the quadrupolar-coupling constant and the asymmetry of the electric field gradient tensor.

Figure II- 23 :

 23 Figure II-23 : (a) Experimental 23 Na MAS NMR spectrum of the three studied samples with performed on a 11.75 T magnet at a spinning frequency of 30 kHz. (b) Fits of the signals 1 and 2 recorded by NMR on sample A compared to the experimental spectrum. * represents the spinning side bands

Figure II- 24 :

 24 Figure II-24 : VT-23 Na MAS NMR recorded on a 7.05 T magnet at a spinning frequency of 13 kHz in the 265 K < T < 450K range. * are the spinning side bands.

9 .

 9 ). Our23 Na MAS NMR study indicates that some Na + ions might be located in the Li layer in the OP4 phase. Such a possibility was therefore further considered in the structural model used for the Rietveld refinement of the structure of the sample A using the SXRD data. A good agreement between the calculated pattern and the experimental one could be thus achieved (Figure II-25). The resulting fitted parameters are given in Table II-Note that the refinement allows to determine that the sample A is composed of 3 % of LiCoO2 and 97 % of OP4 phase. A slight peak asymmetry confirms the presence of a low amount of stacking faults in the structure. For the refinement, we fixed the Co and O sites to be fully occupied. The occupancy of Li sites was also fixed at 0.42 by considering that 97 % of the refined powder is composed of the OP4 phase. The Biso values of the alkali ions were also fixed. Therefore, only the z position of the oxygen ions, the Biso values of the Co and O ions and the occupancy of the Na sites were refined considering the possibility of having Na + ions in the Li layers. As a results, we found 0.10(1) Na + in addition to the 0.84 Li + ions in the O-type interslab spaces involving a global occupation of ~ 95 % in agreement with the absence of observed lithium mobility by selective inversion. The P-type interslab spaces have more vacancies, since they are filled at 64(1) % by Na + ions, in agreement with the mobility of Na + ions observed by 1D MAS NMR. The resulting chemical formula is OP4-Li0.42Na0.37CoO2 in good agreement with the literature (Table II-1) but can be more specifically written as OP4-[Li0.42Na0.05]Na0.32CoO2. The calculated distances are shown in Figure II-26. The Co-OLi-Na distance for the Na + ions in the O-type interslab spaces is shorter than the Co-ONa-Na distance for Na + ions in the P-type interslab spaces, leading to a stronger hyperfine interaction and thus confirming the signal 1 assignment.

Figure II- 25 :

 25 Figure II-25: Synchrotron XRD pattern as a function of 2𝜃 position of the sample A with λ = 0.8261 Å. Red bars and black bars correspond, respectively, to the Bragg positions of O3-LiCoO2 and OP4-(Li/Na)CoO2. Red points correspond to experimental XRD pattern while black line is the calculated one obtained by Rietveld refinement. The blue line is the difference between the experimental and the calculated lines.

Figure II- 26 :

 26 Figure II-26: Bonds distances calculated after Rietveld refinement of OP4 phase.

89 1 . 2 . 3 . 3 . 3 4 . 6 / 7

 12333467 The different LiCoO2 polytypes .................................................................................... Synthesis conditions ................................................................................................... Average structures and chemical compositions characterization ................................. 3.1 OP4 phase average structure ............................................................................... 3.2 O4 samples average structures ............................................................................ Chemical compositions ........................................................................................ Li and 23 Na MAS NMR.............................................................................................. 4.1 Standard sample .................................................................................................. 4.2 A selective exchange? ........................................................................................ 4.3 Evidence of Na + ions in the structure .................................................................. 5. Li + ions mobility in the interslab spaces ........................................................................ 6. Conclusion ................................................................................................................

  O2 layers with the (2/3, 1/3, 0) translation, as shown on Figure III-2.

Figure III- 2 :

 2 Figure III-2:Representation of one layer gliding allowing the formation of the O4 phase from the OP4 one. From[START_REF] Berthelot | Contribution à l'étude électrochimique du système P2-NaxCoO2. Synthèse et caractérisation de nouveaux oxydes lamellaires ordonnés (A/A')CoO2 (A[END_REF]

Figure III- 3 ).

 3 The structure crystallizes in the P63mc space group with lattice parameters ahex. ~ 2.8 Å and chex. ~ 18.8 Å, two positions for the Co ions, two positions for the Li + ions and four positions for the O ions[START_REF] Berthelot | Synthesis and Investigations on an O4-LiCoO2 Polytype[END_REF][START_REF] Yabuuchi | A comparative study of LiCoO2 polymorphs: structural and electrochemical characterization of O2-, O3-, and O4-type phases[END_REF]100 . Note that in a previous study in the group, simulations showed that the formation of stacking faults during the ion-exchange involves the broadening of the (00l) and (hk0) peaks on the XRD patterns.

Figure III- 3 :

 3 Figure III-3 : Representation of the O4-LiCoO2 structure. From reference 43 .

  The XRD pattern (FigureIII-5) of the OP4 phase is similar to the patterns introduced in the previous chapter. However, the phase contains a small amount of OPP9 impurity and the cell parameters of the OP4 phase enriched with[START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li ions are ahex = 2.822(1) Å and chex = 20.26(1) Å in good agreement with the values obtained previously. This phase was, then, used as precursor in order to realize the ion-exchange.

Figure III- 5 :

 5 Figure III-5: Refined XRD pattern of OP4-( 6 Li/Na)CoO2 phase used for the ion-exchanges.

Figure III- 7

 7 Figure III-7 shows the[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR spectrum of this sample.[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR was realized on this sample and performed on a 7.05 T magnet with a Hahn Echo sequence. The spectral width was set to 1 MHz, and the recycle time D0 = 10 s, is long enough to avoid T1 saturation effects. The NMR spectrum exhibits three signals at -4, +32 and +66 ppm. The presence of such strongly shifted signals denote the presence of Co 4+ ions. The signal located at -4 ppm could be assigned to diamagnetic domains: Li + ions surrounded by LS-Co 3+ as 1 st and 2 nd neighbors, although influences by further paramagnetic neighbors as rather broad and not located at -0.4 ppm as observed for Li in O3-LiCoO2 (FigureIII-7)[START_REF] Ménétrier | The insulator-metal transition upon lithium deintercalation from LiCoO2: electronic properties and 7 Li NMR study[END_REF] . The presence of paramagnetic signals confirms the presence of a Li + ions amount different from 1 and therefore vacancies in the interslab spaces. For localized LS-Co 4+ ions with unpaired electron in the t2g orbitals one would have expected positive shift for 90° Co-O-Li interactions and negative shifts for 180° Co-O-Li by analogy with the study of Cr-doped LiCoO2 samples[START_REF] Carlier | Understanding the NMR shifts in paramagnetic transition metal oxides using density functional theory calculations[END_REF] . However here only positive shifts are observed. A hypothesis to explain the presence of both positively shifted paramagnetic signals is the presence of delocalized electrons in the electronic structure of the phase (Knight shift contribution) leading to a "Curie-Weiss metallic" regime with the presence of both localized and delocalized electrons. For instance, Knight shift contributions are reported on the O3-LixCoO2 system for x < 0.74[START_REF] Ménétrier | The insulator-metal transition upon lithium deintercalation from LiCoO2: electronic properties and 7 Li NMR study[END_REF] and on O2-LixCoO2 for x < 0.75104 . The origin of the different signals needs, however, further investigations.

Figure III- 7 :

 7 Figure III-7: Experimental 7 Li MAS NMR spectrum obtained with a Hahn Echo sequence of the standard sample on a 7.05 T magnet with a spinning frequency of 30 kHz. * are the spinning side bands.

Figure III- 8

 8 allows to compare the MAS NMR spectra of the standard sample, the EIE sample and the SIE sample. Note that the spectra were normalized to the number of scans and to the mass of powder in each rotor on Figure III-8b. The comparison on the spectra of the standard sample and the EIE sample shows that the exchange isn't selective, in fact, the 7 Li and 6 Li ions are randomly distributed between the different Li sites. We are, therefore, not in presence of the expected structure proposed on Figure III-4. Moreover, the small difference between the shift values in the two samples, SIE and EIE is the consequence of the slight difference in the alkali ions composition regarding the compositions determined by ICP-OES. Finally, another interesting point is the intensities of the signals depending of the probed Li nucleusand the analyzed sample. The lower intensity of the[START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li signals on the EIE sample spectrum compared to those observed on the SIE sample spectrum suggests that a higher amount of the[START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li ions are removed from the structure during the exchange in the case of the EIE sample. It is possible that an increase of the reflux duration would lead to a removal of the[START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li ions to the amount corresponding to natural abundance. Moreover, the relative intensity between the three signals observed on the[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR spectra is different. In the case of the EIE sample, the intensity of the -4 ppm signal is relatively low compared to the intensities of this signal recorded on the standard sample and EIE sample. That could indicate that the exchange is not complete for the SIE sample because of the different Li + /Na + ratio used to synthetize this sample. Therefore, it is possible that the Li sites which involve the two paramagnetic signals are the first to be filled during the exchange followed by the O3-LiCoO2-like sites. As both[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li and[START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li ions occupy the same sites, only dynamic MAS NMR for the[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li nucleus was performed in McMaster University, Hamilton, Canada.

Figure III- 8 :

 8 Figure III-8: (a) Experimental[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR spectra of the standard sample (b) Experimental[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li and[START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li MAS NMR spectra of EIE and SIE samples normalized by the number of scans and the mass in the rotor. All the spectra were realized on a 7.05 T magnet with a spinning frequency of 30 kHz.

Figure III- 9 :

 9 Figure III-9:Experimental23 Na MAS NMR spectra of both O4-phases compared to the OP4 phase. Only the spectra of the O4 materials were normalized to the number of scans and to the mass of powder in the rotor. NMR was performed on 7.05 T magnet with a spinning frequency of 30 kHz.

106 Figure III- 11 :

 10611 Figure III-11: Experimental 7 Li MAS NMR selective inversion on EIE sample on a 4.7 T with a spinning frequency of 60 kHz. (a) -4 ppm signal is probed (b) 30 ppm site is probed (c) 68 ppm site is probed by the soft pulse

Figure III- 12 :

 12 Figure III-12: Experimental[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR selective inversion on a 2.35 T magnet with a spinning frequency of 30 kHz of SIE sample. We only probed the diamagnetic signal with the soft pulse.

  (Figure GI-2). The investigation of the electrochemical performances of the different NaxCoO2 polytypes as positive electrode material for Na batteries highlighted the complexity of the different systems in the 2 V -3.5 V voltage range 76 . By cycling the P'3, O'3 and O3 polytypes, the systems undergo a succession of structural changes involving for instance Na + /vacancy ordering at specific Na + content highlighted by voltage jumps and drops during the charge and discharge (Figure IV-1a). Note that the Na + content in Figure IV-1a was incorrect. The P2-NaxCoO2 cycling curve (Figure IV-1b) exhibits also many voltage jumps or drops due to the existence of Na + /vacancy ordering in the Na interslabs 47 . The phases diagram of the P2 polytype was investigated by in-situ XRD, recently by Berthelot et al. for x > 0.6 47 (Figure IV-1b). They monitored the evolution of the (008) diffraction line position which provides an insight of the chex lattice parameter change during the discharge.

113 Figure IV- 1 :

 1131 Figure IV-1: a) Electrochemical cycling in the 2 V -3.5 V range of the P3, O3 and O'3 NaxCoO2 polytypes. Reproduced from reference 76 . b) In-situ XRD patterns with the corresponding discharge from 3.1 V to 2.1 V of the P2 polytype. From reference 47 .

Figure IV- 2 :

 2 Figure IV-2: Representation, in the (a, b) plane, of the Na + /vacancy ordering for Na1/2CoO2(reference: 110 ), Na4/7CoO2 (reference: 109 ) and Na2/3CoO2 (reference:[START_REF] Platova | Nuclear quadrupole resonance and X-ray investigation of the structure of Na2/3CoO2[END_REF] ). The purple dashed lines represent the initial hexagonal cell while the solid purple lines represent the superstructure cells. Extracted from reference[START_REF] Berthelot | Contribution à l'étude électrochimique du système P2-NaxCoO2. Synthèse et caractérisation de nouveaux oxydes lamellaires ordonnés (A/A')CoO2 (A[END_REF] .

  . Contrary to P2-NaxCoO2, Carlier et al. highlighted the presence of only one voltage jump on its galvanostatic curve for x = 1/2 when charging to 4.0 V vs Na + /Na. Cheng et al.118 reported by X-Ray Absorption the redox couples involved during the charge and discharge of the system. They expected that the pristine phase, Na2/3Co2/3Mn1/3O2 contains only Co 3+ and Mn 4+ ions. During the discharge for x > 2/3, the Co 3+ and Mn 4+ ions are reduced into Co 2+ and Mn 3+ ions while during the charge for x < 2/3, only the Co 3+ ions are oxidized into Co 4+ ions. The change of the couple at x = 2/3 is associated with a change of the slope on the galvanostatic curve. Note that the electrochemical performances of other CoyMn1-y systems were reported in the literature (

3 Table IV- 3 :Figure IV- 3 : 20 Chapter IV 119 2 . 1 .Figure IV- 4 :

 33320214 Figure IV-3: a) Cycling curves of a Na/NaClO4 in 1M PC/P2-NaxCoO2 cell in the 1.35 -3.9 V vs Na + /Na range at C/20 b) Cycling curves of a Na/NaPF6 in 1M PC + 2% FEC/P2-NaxCoO2 cell in the 1.4 -4.3 V vs Na + /Na range at C/20

Figure IV- 5 :

 5 Figure IV-5: Thermal treatment for the P2-𝑁𝑎 𝑥0 CoyMn1-yO2 phases synthesis

Figure IV- 6

 6 Figure IV-6 shows the Scanning Electron Microscopy (SEM) of P2-𝑁𝑎 ~0.7 𝐶𝑜𝑂 2 phase. It shows the hexagonal shape of the structure with particles of 15 µm average diameter and 10 µm thickness.

Figure IV- 6 :

 6 Figure IV-6: SEM images of P2-𝑁𝑎 ~0.7 𝐶𝑜𝑂 2 phase at two different magnifications.

4 )

 4 are in good agreement with literature (NaxCoO2 127 , NaxCoyMn1-yO2 120 ). Note that ahex is almost constant whatever the composition because of the slight difference between the Co 3+ (0.545 Å),Co 4+ (0.53 Å) and Mn 4+ (0.53 Å) ions radii.

Figure IV- 7 :

 7 Figure IV-7: SXRD patterns of the a) NaxCoO2 b) NaxCo2/3Mn1/3O2 c) NaxCo1/2Mn1/2O2 d) NaxCo1/3Mn2/3O2 pristine phases. Red points: experimental data, black lines: calculated curves, blue lines: difference between experimental and calculated data, black bars: Bragg positions. The two inserts are zooms on the (002) peak and in the 15°-23° range to evidence the presence of superstructure peaks.

3 .Table IV- 5 : 3 . 1 Figure IV- 8

 35318 Figure IV-8 shows the evolutions of the cell voltage as a function of Na + content (x) in the material for the four systems cycled in their low voltage range. The NaxCoO2 and NaxCo2/3Mn1/3O2 systems exhibit a low polarization (Figure IV-8a and b) and a good capacity retention upon cycling (Figure IV-9). Note that the NaxCoO2 pristine phase was not the same than the refined one and it

  worse (FigureIV-8c, 8d and 9). Among all the systems, P2-NaxCoO2 exhibits the best capacity retention (97 % in 40 cycles) compared to the Co-Mn systems (95 % in 35 cycles for NaxCo2/3Mn1/3O2 and 90 % in 13 cycles for NaxCo1/2Mn1/2O2). Concerning the redox couples involved during the NaxCo1/2Mn1/2O2 and NaxCo1/3Mn2/3O2 systems charges, one can expect that all Mn 3+ (and Co 2+ ions possibly) are first oxidized into Mn 4+ (and Co 3+ ) for x = 1/2 and 1/3, respectively, before the oxidation of Co 3+ into Co 4+ as observed for the NaxCo2/3Mn1/3O2 system at x = 2/3 118 . A tiny slope change can be observed on both NaxCo1/2Mn1/2O2 and NaxCo1/3Mn2/3O2 galvanostatic curves and could be due to this redox couple change. The larger polarization observed for those two phases can be due to a lower electrical conductivity due to the lower amount of Co 4+ ions during the electrochemical cycling compared to the amount in the NaxCoO2 and NaxCo2/3Mn1/3O2 systems.

Figure IV- 8 : 129 Figure IV- 9 :

 81299 Figure IV-8: Galvanostatic curves of the Na(s)/P2-NaxMO2 cell at C/20 in their low voltage range for a) NaxCoO2 b) NaxCo2/3Mn1/3O2 c) NaxCo1/2Mn1/2O2 d) NaxCo1/3Mn2/3O2

Figure IV- 10 :

 10 Figure IV-10: Comparison between the first and the 40 th cycle realized on the same Na(s) / P2-NaxCoO2 cell at C/20 in the low voltage range.

  -12a and b). The evolutions of their specific capacities are plotted in Figure IV-11 and compared to the capacities obtained in the low voltage ranges. Figure IV-11 shows a very fast decrease after only 2 cycles of the NaxCoO2 specific capacity (black crosses). The capacity retention is only 78 % after 40 cycles and the capacity becomes after few cycles lower than in the low voltage range (black square).For the NaxCo2/3Mn1/3O2 system, a relatively fast capacity decrease is also observed (87 % capacity loss in 7 cycles). A cycling to 4.6 V involves, thus, irreversible phenomena for both systems which, significantly, reduces the capacity and the performances of both batteries upon cycling.The two other systems were cycled to 4.6 V, in order to check the eventual presence of voltage jumps at high voltage, voltage plateau or solid solution domains (FigureIV-12c and d). Two new peculiar phases for x = 1/3 on the NaxCo2/3Mn1/3O2 and NaxCo1/2Mn1/2O2 systems are highlighted by the presence of voltage jumps. No obvious ordered phases can be identified on the NaxCo1/3Mn2/3O2 system. Except for the specific compositions which correspond to these peculiar phases, the curve shape suggests the presence of solid solution domains for the three systems (Co,Mn) during charge and discharge in their "high" voltage ranges.For NaxCoO2, a peculiar phase for x = 1/3 is observed when cycling to 4.6 V due to the presence of a voltage jump at this specific composition. The first discharge after a charge to 4.6 V involves a smoothing of the discharge galvanostatic curve without any voltage drops at the expected peculiar phases compositions as observed when cycled to 4.3 V (Figure IV-8a). However, the voltage jumps reappear during the next charge, mainly, for x = 2/3, 1/2 and 1/3 but globally disappear from the 3 rd charge. The origin of this behavior is still unclear and could be due to a strong difference in kinetics during the discharge compared to the charge. For NaxCo2/3Mn1/3O2, the voltage drops/jumps are still observed during the following discharges/charges despite the decrease of the specific capacity when cycling to 4.5 V (FigureIV-12b). Note that the voltage drop at x = 1/2 remains over almost 20 cycles.

Figure IV- 11 :

 11 Figure IV-11: Capacity as a function of cycle number for NaxCoO2 and NaxCo2/3Mn1/3O2 system in both voltage ranges at C/20.

Figure IV- 12 :

 12 Figure IV-12: Galvanostatic curves of the Na(s)/P2-NaxMO2 cell at C/20 in their high voltage range for a) NaxCoO2 b) NaxCo2/3Mn1/3O2 c) NaxCo1/2Mn1/2O2 d) NaxCo1/3Mn2/3O2

Figure IV- 13 Figure IV- 13 :

 1313 Figure IV-13: XRD patterns obtained by operando XRD on the NaxCoO2 system on the first charge from 1.5 V to 4.6 V at C/10 (a) in the 5 -30° range (b) in the 16.3 -18.5° range. The colored lines represent the XRD patterns of the peculiar phases Na2/3CoO2, Na0.57CoO2 and Na1/2CoO2.

from 4 . 1 V

 41 to 4.8 V with a step of 0.05 V were applied. The reported XRD patterns are the last one recorded at each voltage corresponding to a maximal relaxed phase (FigureIV-14). Note that the used cell was not the same than for the operando acquisitions introduced before.

Figure IV- 14 :

 14 Figure IV-14: Voltage (in black) and current (in red) evolution during the PITT measurements on NaxCoO2 as a function of time

  From

4. 1 V

 1 to 4.55 V (black lines), the average structure remains in the P2 structure as shown by the presence of a thin P2 peak at a constant 2θ position. Note the presence of two contributions to the (002) peak from 4.3 V to 4.55 V. At 4.6 V, the P2 structure is still maintained but the (002) lines starts to broaden probably due to some "O"-type stacking faults formation. In fact, the XRD pattern Chapter IV 140 traced in blue is the first to show a strong broadening of its (00l) and (10l) peaks. For voltages from 4.65 to 4.8 V (in red), (00l) peaks almost disappear and (10l) peaks are broadened and become asymmetric. Moreover, the (002) peak is largely broadened and shifted to larger angle values characteristic of a decrease of the chex lattice parameter. The peaks asymmetry and the decrease of the chex lattice parameter highlight the presence of sheets glidings leading to a strong disorder. The sheets glidings were already reported by Komaba and coworkers 128 and more recently by Billaud130 et al. on other P2-systems by ex-situ XRD. Note that in these papers, these phases were determined in an OP4 structure considering that the Na + ions are intercalated in prismatic and octahedral sites after the P2-OP4 phase transition. In our study, the phase obtained at high voltage is called "OP" phase and not OP4 due to the absence of a good ordering along the c axis contrary to the phase studied in the chapter II. Figure IV-15 shows the transition between the ideal P2 structure and the faulted "OP" one involving the formation of O-type intercalation sites. Moreover, the decrease of the c lattice parameter of the "OP" phase suggests that the thickness of the O-type interslab spaces is smaller than the thickness of the P-type interslab spaces.

Figure IV- 15 :

 15 Figure IV-15: Representation of the CoO2 stacking in ideal P2 structure and P2 structure with an O-type stacking fault after sheets glidings.

Figure IV- 16 :Figure IV- 17 :

 1617 Figure IV-16: XRD patterns of stabilized NaxCoO2 phases by PITT at different voltages from 4.1 V to 4.8 V for a) 7 < 2𝜃 < 30° and b) 7 < 2𝜃 < 11°. $ = Al, * = Na.

Figure IV- 18 :

 18 Figure IV-18: Representation in the (a,b) plane of the initial hexagonal cell (solid line) and the superstructure hexagonal cell (dashed line)

Figure IV- 20

 20 shows the refinement of the SXRD data recorded on this phase. The calculated lattice parameters with the Pnmm space group are as = 4.8848(6) Å, bs = 5.6171(9) Å and cs = 11.257(2) Å. All the diffraction peaks are indexed with this supercell except one tiny additional peak on the right of (123) and (203) peaks corresponding probably to the formation of another phase. It is the first time, that an XRD pattern of an ordered phase on this system is reported.Note that no obvious superstructure peak appears for x = 1/3 in our conditions while the voltage jump is well-defined on the galvanostatic curve. The blue arrow represents the appearance of an additional peak at 2𝜃 = 9.2°. This peak indicates probably the formation of a defected "OP" phase due to the CoO2 sheet glidings as also observed on Figure IV-16. The discharge of the cell following the experiment presented is given in the Appendix part (A-5).

Figure IV- 19 : 10 Figure IV- 20 :

 191020 Figure IV-19: XRD patterns obtained during the operando measurements on the NaxCo2/3Mn1/3O2 system on the first charge from 1.25 V to 4.5 V at C/10

Figure V- 1 :

 1 Figure V-1: (a) 7 Li MAS NMR spectra of the LixCoO2 phases for 0.5 ≤ x ≤ 1. * represents the spinning side bands. (b) 7 Li MAS NMR spectra from x = 0.94 to x = 1 in the -40 -40 ppm range. Reported from reference 91 . (c) Representation of the direct overlap between a single electron from the t2g orbital of Co 4+ and the 2s Li orbital

2 ).

 2 In 2009, Carlier et al.[START_REF] Carlier | Sodium Ion Mobility in NaxCoO2 (0.6 < x < 0.75) Cobaltites Studied by 23 Na MAS NMR[END_REF] reported a NMR study of the P2-NaxCoO2 system for 0.55 ≤ x ≤ 0.75. All the phases were obtained by direct powder synthesis. The shape of the signal is governed by the 2 nd order quadrupolar interaction whereas the position is governed by the hyperfine interaction. Moreover, the P2structure is characterized by the presence of two signals for Na + intercalation: Nae and Naf (FigureI-3). As depicted onFigure V-2b, each site has its own Electric Field Gradient value with the main contribution (Vzz) along the c axis. When moving from a site to another, the Na + ions are surrounded by three other sites. Therefore, the presence of this 3-fold axial symmetry with the same direction than Vzz leads to an average chemical shift between both Vzz contributions. Note that the phase for x0 = 0.88 is out of range of the P2 existence. Therefore, the diamagnetic signal is due to an important amount of remaining precursors. The real composition of this phase is, however, unclear. They showed that the NMR shift values increase when x decreases in good agreement with the oxidation of diamagnetic Co 3+ into paramagnetic Co 4+ considering the phases in a Curie-Weiss regime with localized electrons and delocalized electrons at the Fermi level. (Figure V-2a).

Figure V- 4

 4 Figure V-4 displays the23 Na MAS NMR spectra of both pristine phases discussed in the previous chapter. The measurements were performed using a single pulse sequence on a 7.05 T magnet with a spinning frequency of 30 kHz in the conditions than in reference[START_REF] Carlier | The P2-Na2/3Co2/3Mn1/3O2 phase: structure, physical properties and electrochemical behavior as positive electrode in sodium battery[END_REF] . The spectral width was set to 1 MHz, and the recycle time D0 = 0.5 s, is long enough to avoid T1 saturation effects. The same lineshape due to the 2 nd order quadrupolar interaction are observed for the 𝑁𝑎 ~0.7 𝐶𝑜𝑂 2 spectrum than in the previous work. Table V-1 summarizes the shift position, the quadrupolar constant and the anisotropy value for our 𝑁𝑎 ~0.7 𝐶𝑜𝑂 2 sample, fitted on the experimental spectrum using the software DMFit[START_REF] Massiot | Modelling one-and two-dimensional solid-state NMR spectra[END_REF] . Figure V-5 shows a relative good match between the experimental and the fitted spectrum with a quadrupolar lineshape. η reaches a non-negligible value meaning that the sites exhibit a low axial dissymmetry: the Na + ions are not exactly in the center of the prismatic sites in average. Moreover, the position of the signal at 351 ppm is in agreement with the previous data (around 350 ppm at RT 94 ) (Figure V-3). Concerning the P2-𝑁𝑎 ~2/3 𝐶𝑜 2/3 𝑀𝑛 2/3 𝑂 2 phase, the signal is broader and the lineshape is different than in Figure V-3, possibly due a highest distribution of the Na + environments in our phase due to less random distribution of the Co 3+ and Mn 4+ ions in the transition metal layers. Moreover, on the synchrotron XRD pattern of this phase (Figure IV-7b), the (002) peak exhibits a shoulder on its right indicting a heterogeneity in the pristine material or a composition slightly different from 2/3 in a biphasic domain. The lineshape observed on the NMR spectrum (Figure V-4) is therefore, due to a more important number of environments than on spectrum showed in Figure V-3.

Figure V- 4 Chapter V 162 Figure V- 4 :

 41624 Figure V-4:23 Na MAS NMR spectra of P2-𝑁𝑎 ~0.7 𝐶𝑜𝑂 2 and P2-𝑁𝑎 ~2/3 𝐶𝑜 2/3 𝑀𝑛 2/3 𝑂 2 on a 7.05 T magnet at a spinning frequency of 30 kHz with a single pulse sequence.

Figure V- 5 :163 2 . 2 6 .

 5226 Figure V-5: Experimental and fitted NMR signal using a 2 nd order quadrupolar lineshape realized on the NaxCoO2 pristine phase spectrum

Figure V- 7

 7 Figure V-7 displays an example of typical curves obtained on the P2-NaxCoO2 system. In this example, the new phase was synthetized at 4.2 V from 𝑁𝑎 ~0.7 𝐶𝑜𝑂 2 to reach the x = 1/3 composition. The black curve represents the voltage evolution as a function of time with a similar shape than the galvanostatic curve introduced in the previous chapter. In fact, the same voltage jumps and domains than on Figure IV-8a are seen. The red curve shows the current evolution and its relaxation during the potentiostatic step. Once this second step finished, the cell was

Figure V- 6 :Figure V- 7 : 165 :Figure V- 8 :166 2 . 3

 67165823 Figure V-6: Representation of the electrochemical cell used for the synthesis of (de)intercalated phases

Figure V- 10

 10 Figure V-10 as a function of x and is in good agreement with the values determined in the previous chapter for ahex and chex limit values (TableIV-6).

- 9 :

 9 Figure V-9: Experimental XRD patterns of the (a) NaxCoO2 (b) NaxCo2/3Mn1/3O2 phases. * represents the graphite peak used in the electrode formulation.

Figure V- 10 :Figure V- 11 : 3 .

 10113 Figure V-10: Evolution of the (a) a lattice parameter (b) c lattice parameter for P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 phases studied in this chapter

Figure V-13a showsTable V- 3 :

 3 Figure V-13a shows the structure of a P2 material and defines clearly what will be called the Na + ions layers and the MO2 layers in Figure V-13b. Globally, the Na + ions layers thickness increases during the charge up to a maximal value reached around x = 0.4 while the CoO2 slabs thickness slightly decreases to the same x values. The increase of the Na + ion layers thickness is in agreement with the Na + deintercalation and the increase of the O-O repulsions between the layers. The decrease of the CoO2 slabs thickness is coherent with the oxidation of Co 3+ to Co 4+ that increases the Co-O covalency. Note that the Na0.82CoO2 phase layers thickness is not shown on the Figure V-13b due to the impossibility to perform a proper Rietveld refinement of its XRD pattern. As the chex lattice parameters evolution is rather similar for the two systems (Figure V-10), and as the ionic radii of Co 3+ (0.545 Å), Co 4+ (0.53 Å) and Mn 4+ (0.53 Å)3 are also rather similar, we expect a similar evolution of the slabs thickness for the P2-NaxCo2/3Mn1/3O2 phases.

Figure V- 12 :

 12 Figure V-12: Refined XRD pattern as a function of 2𝜃 position of Na0.4CoO2. Black bars correspond to the Bragg positions of the phase. Red points correspond to experimental XRD pattern while black line is the calculated one obtained by Rietveld refinement. The blue line is the difference between experimental and calculated lines. * is a peak due to the graphite present in the mixture.

Figure V- 13 :

 13 Figure V-13: (a) Schematic representation of the P2-stacking (b) Evolution of the layers thicknesses in the P2-structure for P2-NaxCoO2

Figure V- 14 176 Figure V- 14 :

 1417614 Figure V-14 compares the different bonds distances in the NaO6 and CoO6 octahedra for P2-Na0.33CoO2 and P2-Na0.67CoO2. As expected the Co-O distance decreases because of the distortion of the CoO6 octahedra during Na + deintercalation. Moreover, the Na-O distance increases during Na + deintercalation which is coherent with the global increase of the Na + layer thickness.

Chapter V 177 Figure V- 15 :

 17715 Figure V-15: (a) Magnetic measurements of some NaxCoO2 phase as a function of temperature from 7 K to 300 K (a) synthetized in this work under a 1T magnetic field (b) from reference 75 under a 0.8 T magnetic field.

Figure V- 16 :

 16 Figure V-16: Magnetic phases diagram of P2-NaxCoO2. Data are extracted from 108 .

Figure V- 17 :

 17 Figure V-17: Representation of the band structure of the P2-NaxCoO2 phases with the D3d symmetry in the (a) "Curie-Weiss metal regime" (b) in the Pauli paramagnetic regime

Chapter V 181 .Figure V- 18 : 182 Figure V- 19 :The 2

 18118182192 Figure V-18: Evolution of the 23 Na MAS NMR shifts for (a) NaxCoO2 and (b) NaxCo2/3Mn1/3O2 systems. The acquisitions were realized on a 7.05 T magnet with a spinning frequency of 30 kHz and a simple pulse sequence. * = spinning side bands.



  𝜒 𝑀 : magnetic molar susceptibility S: spin quantum number 𝜌 𝑖 (0): spin density on the probed nucleus  Delocalized electrons lead to Knight shifts. Similarly, to the Fermi contact shift, it involves the presence of electronic spin density on the s orbitals of the probed nucleus. However, in that case, the spin density comes from the participation of the s electrons at the Fermi level. Here, then the Knight shift depends on the contribution of the Na 3s orbital at the Fermi level. The Knight shift (𝛿 𝐾𝑛𝑖𝑔ℎ𝑡 ) equation is the following: susceptibility of conduction electrons at Fermi level 〈|𝜓 𝑟=0 |²〉: contribution of "s" orbitals at Fermi level of probed nucleus Chapter V For the NaxCoO2 system In order to interpret the NMR shift evolution and to make the link with the mechanisms involved during the Na + deintercalation, we need to consider two factors: the local geometric evolution represented by the evolution of the Na-O distance and the chex lattice parameter in Figure V-20a and the local electronic structure evolution considering the oxidation of diamagnetic Co 3+ (t2g 6 eg 0 ) into paramagnetic Co 4+ (t2g 5 eg 0 ) and the Curie-Weiss metal -Pauli paramagnetic transition for x = 0.5 (Figure V-20b). Note that a change in the average position for Na + ions is also linked to the Nae and Naf site occupancy (Table

186 

 186 Figure V-20c and each zone introduced previously is depicted with a specific blue contrast color.  In zone 1 (0.67 ≤ x ≤ 0.82), the NMR shift increase can be explained by the oxidation of diamagnetic Co 3+ (LS, t2g 6 eg 0 ) into paramagnetic Co 4+ (LS, t2g 5 eg 0 ) while a majority of the electrons have a localized behavior. The more paramagnetic species are formed the more shifted is the signal. The position of the signal in this composition domain probably results from a sum of a Fermi contact shift and a Knight shift as discussed already in the chapter II for the OP4 phase. Therefore, the shift can be expressed as: 𝛿 𝑡𝑜𝑡 = 𝛿 𝐹𝑒𝑟𝑚𝑖,𝑎 1𝑔 𝐶𝑜 4+ + 𝛿 𝐾𝑛𝑖𝑔ℎ𝑡,𝑒 𝑔 ′ 𝐶𝑜 𝑛+  In zone 2 (0.5 ≤ x ≤ 0.67), the NMR shift significantly decreases when x decreases despite the oxidation of Co 3+ to Co 4+ ions (still in a "Curie-Weiss metal domain" x > 0.5). As shown on Figure V-13b and Figure V-20a, the thickness of the Na + layers and the Na-O distance increase when x decreases. This increase leads to a weaker overlap between the Na 3s and the O 2p orbitals and thus to a weaker overall spin transfer from the Co 4+ ions to the Na 3s orbital, reducing the Fermi contact shift. Thus, for 𝛿 𝐹𝑒𝑟𝑚𝑖,𝑎 1𝑔 𝐶𝑜 4+ , two antagonist effects occurring as x decreasing: an increase of the amount of unpaired electrons and a decrease of the efficiency of the spin transfer mechanisms. It seems that in this composition domain, the modification of the local geometry is predominant. Chapter V In zone 3 (0.33 ≤ x ≤ 0.5), an important decrease of the NMR shifts, compared to the values in the zone 2, is observed and is due to the change of regime which probably occurs in the 0.4 -0.5 x range. In this zone, the NMR shift evolution is mostly governed by the Knight shift contribution due to the establishment of the Pauli paramagnetic regime with only delocalized electrons in the electronic structure and no significant evolution of the Na-O distance (Figure V-20a). Therefore, 𝛿 𝐹𝑒𝑟𝑚𝑖,𝑎 1𝑔 𝐶𝑜 4+ ~ 0 ppm and the Na 3s orbital participation to the Knight shift seems to be almost constant during the Na + deintercalation.

Figure V- 20 :

 20 Figure V-20: For the P2-NaxCoO2 system: (a) Evolution of the Na-O distance and c lattice parameter as a function of x. (b) Evolution of the amount of formal Co 4+ ions as a function of x."Curie-Weiss metal regime" and "Pauli paramagnetic regime" are separated by an orange dashed line (c)23 Na MAS NMR isotropic shift evolution as a function of x.

.

  of the Na 3s orbital participation to the Knight shift is almost constant The evolution of 𝛿 𝐹𝑒𝑟𝑚𝑖,𝑎 1𝑔 𝐶𝑜 4+ depends if we consider the electronic structure or the geometric point of view as already discussed for NaxCoO2. Note that from a geometric point of view 𝛿 𝐹𝑒𝑟𝑚𝑖,𝑎 1𝑔 𝐶𝑜 4+ evolves in the same way than 𝛿 𝐹𝑒𝑟𝑚𝑖,𝑎 1𝑔 𝑀𝑛 4+ In zone 1 (0.57 ≤ x ≤ 0.68), the shift increases is due to the change in the electronic structure due to the formation of Co 4+ ions (t2g 5 eg 0 ) as x decreases (Figure V-21b) involving an increase of 𝛿 𝐹𝑒𝑟𝑚𝑖,𝑎 1𝑔 𝐶𝑜 4+ not compensated by the probable slight decrease of 𝛿 𝐹𝑒𝑟𝑚𝑖, 𝑀𝑛 4+ due to increase of the chex lattice parameter in this zone (Figure V-21a). As observed for NaxCoO2, the shift decreases in the zone 2 (0.45 ≤ x ≤ 0.57) (Figure V-21c). Therefore, the geometric point of view is also predominant for this system in the zone 2. This point is strengthened by the important increase of chex lattice parameter in the zone 2 (Figure V-21a). In this zone, both 𝛿 𝐹𝑒𝑟𝑚𝑖,𝑎 1𝑔 𝐶𝑜 4+ and 𝛿 𝐹𝑒𝑟𝑚𝑖,𝑎 1𝑔 𝑀𝑛 4+ contributions increase due to the D3d distortion of the MO6 octahedra. Then, a change in position of the Fermi level, as x decreases, is expected and can be understood by the oxidation of Co 3+ to Co 4+ ions in a same way than for NaxCoO2, resulting in an increase in energy of the a1g band of the Co and Mn ions when the system reaches the zone 3 (Figure V-22b). In this system, a magnetic transition probably occurs between 0.4 ≤ x ≤ 0.45. However, this magnetic state can't be completely considered as metallic due to the participation of the localized electrons of the Mn 4+ ions to the total shift. That's why we called this magnetic state, "Pauli regime".  In the zone 3 (0.33 ≤ x ≤ 0.4), as the shift is almost constant, the 𝛿 𝐹𝑒𝑟𝑚𝑖,𝑎 1𝑔 𝐶𝑜 4+ should be null due to empty a1g band as depicted on Figure V-21c. Moreover, the low evolution of the chex lattice parameter in this zone (Figure V-21a) suggests that 𝛿 𝐹𝑒𝑟𝑚𝑖 𝑀𝑛 4+ should stay almost constant in the zone 3. Therefore, the participation of the 3s Na orbital to the "Knight shift" should be almost constant in good agreement with the shift evolution of the NaxCoO2 phases in the same zone.

Figure V- 21 : 191 Figure V- 22 :

 2119122 Figure V-21: (a) Evolution of the c lattice parameters as a function of x for NaxCo2/3Mn1/3O2 phases (b) Evolution of the amount of formal Co 4+ ions as a function of x. (c) Isotropic shift evolution obtained after the fit of the spectra as a function of x. The Zone 1, 2 and 3 are separated by black dashed lines.

1 . 2 . 1 2 . 2

 12122 Introduction ............................................................................................................. 2. 23 Na MAS NMR results .............................................................................................. Pristine phase .................................................................................................... Deintercalated phases and reversibility of the system ........................................ 3. Conclusion ................................................................................................................ VI.

  battery (Figure VI-2b).

Figure VI- 2 :

 2 Figure VI-2: (a) Electrochemical performances between 1.5 and 4 V of the O3-NaxRuO3 system at C/10 (b) Representation of the O1-Na1RuO3 and O1'-Na1/2RuO3 structures and the corresponding Ru ions, Na ions and vacancies repartition in the layers. From reference 48 .

Figure VI- 3

 3 Figure VI-3 represents the three Na sites environments in O3-Na2RuO3. O3-Na2RuO3 crystalizes in the C2/m space group leading to two Na sites in the interslab space which are relatively similar and label Na2 and Na3 in this work. They only differ because of the monoclinic distortion of the cell. Figure VI-4a shows the 23 Na MAS NMR spectra of two O3-Na2RuO3 phases prepared in the

  , we can assign the most shifted signals to Na1 (site: 2a) in the Ru plane, interacting with 6 Ru 4+ as 1 st neighbors (90° Ru-O-Na) and the less shifted ones to Na2 and Na3 (Figure VI-3). Both Na2 (site: 4h) and Na3 (site: 2d) sites have 4 Ru 4+ as first neighbors (90° Ru-O-Na) and 4 Ru 4+ as second neighbors (180° Ru-O-Na interactions). They result in really similar Fermi contact shifts around ~877 ppm. This signal

Figure VI- 4 :

 4 Figure VI-4: (a) 23 Na MAS NMR spectra of two O3-Na2RuO3 phases. The measurements were realized on a 11.75 T magnet with a spinning frequency of 30 kHz and a single pulse sequence. (b) Fits realized on DMFit of the signal at 877 ppm using two Na contributions corresponding to Na2 and Na3 using fixed widths and fixed Gaussian/Lorentzian proportions. (c) Fits realized on DMFit of the signal at 877 ppm using two Na contributions corresponding to Na2 and Na3 and free parameters. * represents the spinning side bands

Figure VI- 6

 6 displays the NMR spectra of these two phases. Additionally, Figure VI-6 shows the NMR spectra of the NaxRuO3 materials recovered after the Na + electrochemical deintercalation at 3.07 V (O1-Na1RuO3) and at 4 V (O1'-Na1/2RuO3) compared to the one of the pristine O3-Na2RuO3. In Figure VI-6, the signal located around 0 ppm is assigned to Na carbonates, or other Na diamagnetic species

Figure VI- 2

 2 exhibits the Na + /vacancy ordering in the interslab spaces and Figure VI-5 depicts the environment of the unique Na site in this phase. No Na + ions is located in octahedral sites with a common face with RuO6 anymore. Therefore, no direct overlap between the a1g Ru orbitals and 3s Na orbital is possible anymore, what would prevent the loss of observability of the NMR shift. The Na + ions occupy the center of one octahedra site as depicted in Figure VI-5 sharing only edges or corner with RuO6. Mortemard de Boisse et al 48 . showed that the interslab spaces thickness still decreases from x = 1 to x = 1/2 but the Na-O distance increasesChapter VI202 by considering the oxygen ions involved in the 126° interactions for Na1RuO3. Moreover by using the calculated parameters obtained by a Rietveld refinement and reported in reference[START_REF] Mortemard De Boisse | Coulombic self-ordering upon charging a large capacity layered cathode material for rechargeable batteries[END_REF] for Na1/2RuO3, we determined that 𝜃 ~ 57° which indicates that the RuO6 octahedra are less distorted than in the case of Na1RuO3. For this specific composition, O-redox has occurred and is associated to the formation of relatively short O-O bonds. If paramagnetic O were formed, one could have expected a large Fermi contact shift for the adjacent Na + ions. As the shift observed is relatively small, it more likely corresponds to either a Knight shift or a Fermi contact shift with small spin transfer from Ru to Na. As no magnetic measurements were performed for the Na1RuO3 and Na1/2RuO3 phases, it is, for the moment, difficult to understand their electronic structure. Magnetic measurements could inform about the presence of localized or delocalized electrons. Note that the magnetic properties of LixRuO3 had been investigated by Kobayashi et al.150 . They reported that Li1RuO3 has a temperature independent susceptibility evolution suggesting the presence of only delocalized electrons which is not in agreement with the behavior of Na1RuO3 observed with23 Na MAS NMR.

Figure VI- 5 :

 5 Figure VI-5: Representation of the different Na sites environments in Na1RuO3 and Na1/2RuO3.

Figure VI- 6 :

 6 Figure VI-6:23 Na MAS NMR spectra of the pristine Na2RuO3 (black line), Na2RuO3 after one cycle (magenta and blue lines), Na1RuO3 (red line) and Na1/2RuO3 (green line). The spectra were recorded on a 11.75 T magnet with a spinning frequency of 30kHz and using a single pulse sequence. * are the spinning side bands.

Figure A- 1 :

 1 Figure A-1: SXRD pattern of Na2/3CoO2 in the R3 ̅ c space group. Red points = Yobs, black line = Ycalc, blue line = Yobs -Ycalc, black ticks = Bragg positions. Insert highlights the presence of the superstructure peaks.

Figure A- 2 :

 2 Figure A-2: SXRD pattern of Na1/2CoO2 in the Pnmm space group. Red points = Yobs, black line = Ycalc, blue line = Yobs -Ycalc, black ticks = Bragg positions. Insert highlights the presence of the superstructure peaks.

  Figure A-3). The calculated lattice parameters are in good agreement with the superstructure determined by Igarashi et al. 109 (as = 7.459(1) Å and cs = 11.04(1) Å).

Figure A- 3 :

 3 Figure A-3: SXRD pattern of Na4/7CoO2 in P63/m space group. Red points = Yobs, black line = Ycalc, blue line = Yobs -Ycalc, black ticks = Bragg positions. Insert highlights the presence of superstructure peaks.

Figure RE- 1 :

 1 Figure RE-1: Représentation des structures O3, P2 et P3 et environnements locaux respectifs des ions Na +

  0)𝜒 𝑀 (𝑇) S: nombre de spin 𝜒 𝑀 (𝑇): susceptibilité magnétique molaire 𝜌 𝑖 (0) = ∑ ( |𝜓 𝑗 ↑ (0)| 2 -|𝜓 𝑗 ↓ (0)| 2 ) 𝑗 avec |𝜓 𝑗 ↑ (0)| 2 la probabilité de présence de spin positif sur l'orbitale s et |𝜓 𝑗 ↓ (0)| 2 la probabilité de présence de spin négative sur l'orbitale s. Le déplacement de Knight implique la présence d'une densité électronique de spin sur le noyau s sondé, cependant pour cette interaction, la densité de spin provient de la participation des électrons s au niveau de Fermi et implique ainsi les électrons de type délocalisés. Le déplacement chimique total correspond ainsi à la somme des contributions des électrons localisés et des électrons délocalisés. 𝛿 𝑡𝑜𝑡 = 𝛿 𝐹𝑒𝑟𝑚𝑖 𝑀 𝑛+ + 𝛿 𝐾𝑛𝑖𝑔ℎ𝑡 𝑀 𝑛+ La présence d'électrons localisés et délocalisés provient d'une distorsion trigonale D3d des octaèdres CoO6 dans le cas des cobaltates. Cette distorsion implique une compression des octaèdres suivant l'axe z comme représenté sur la Figure RE-2a. Cette distorsion implique la levée de dégénérescence des orbitales t2g en une orbitale a1g et deux orbitales eg' 54 . La Figure RE-2b représente la structure de bande du système P2-NaxCoO2 après la distorsion D3d et montrant le niveau de Fermi à la fois dans une bande étroite a1g et une bande large eg' impliquant respectivement la présence des électrons localisés et délocalisés.

Figure RE- 2 :

 2 Figure RE-2: (a) Représentation de l'octaèdre CoO6. Les flèches bleues indiquent la direction de la distorsion D3d impliquant la compression des octaèdres suivant z. (b) Représentation de la levée de dégénérescence des orbitales t2g en 2 orbitales eg' et 1 orbitale a1g. Représentation schématique du diagramme de bandes de P2-NaxCoO2 après distorsion D3d.

Figure RE- 3 :

 3 Figure RE-3: Diffractogramme RX enregistré sur P2-Na0.7CoO2. Points rouges : données expérimentales, trait noir : données affinées, trait bleu : différence entre le profil expérimental et affinée, traits noirs : positions de Bragg. Les zooms ont été réalisés sur la raie (002) et entre 15° et 23° afin de mettre en évidence les pics de surstructure.

  Carbonate (PC) + 2% FluoroEthyl Carbonate (FEC) / P2-NaxCoO2 à un régime de C/20. Deux fenêtres de potentiel ont alors été étudiées : 1.5 -4.3 V et 1.5 -4.6 V vs Na + /Na (Figures RE-4).

Figure RE- 4 :

 4 Figure RE-4: Courbe de cyclage galvanostatique à C/20 entre (a) 1.5 et 4.3 V (b) 1.5 V et 4.6 V

  3 et 4.6 V, différentes phases P2-NaxCoO2 ont été synthétisées par une technique électrochimique pour différents potentiels entre 1.5 et 4.6 V. Ces synthèses ont été réalisées dans des cellules électrochimiques étanches et assemblées en boîte à gants. Le matériau d'électrode positif est un mélange de 90 % massique de matériau actif et 10 % massique de noir de carbone. A noter que nous ne pouvions pas utiliser de liants (PTFE) pour ces synthèses car il aurait alors été impossible de remplir un capillaire pour les acquisitions DRX. C'est pour cette raison que nous avons pastillé le mélange utilisé comme matériau d'électrode positive afin d'obtenir une électrode dense. Une fois la cellule assemblée, la synthèse par voie électrochimique se fait en deux étapes : une étape galvanostatique à C/20 jusqu'au potentiel cible puis une étape potentiostatique où le potentiel cible est maintenu alors que l'intensité diminue jusqu'à une valeur faible voire nulle. Une fois la batterie relaxée, elle peut être débranchée puis entrée en boîte à gants. Les potentiels cibles sont représentés sur la Figure RE-5a. La Figure RE-5b montre l'évolution du courant et du potentiel en fonction du temps dans le cas de la synthèse de Na0.33CoO2 pour à un potentiel cible de 4.2 V.

Figure RE- 5 :

 5 Figure RE-5: (a) Charge entre 1.5 et 4.6 V (trait noir) et décharge entre 4.3 et 1.5 V (trait rouge) à C/20. Les traits en pointillés indiquent les potentiels cibles pour les synthèses par voie électrochimique des phases NaxCoO2. (b) Evolution du potentiel (en noir) et du courant (en rouge) afin de réaliser la synthèse de Na0.33CoO2 par voie électrochimique.

Figure RE- 6 :

 6 Figure RE-6: Diffractogrammes enregistrés sur les phases synthétisée par voie électrochimique. Cadre bleu : zoom sur la raie (002). Cadre rouge : zoom sur la zone 30° -55°. * représente le pic dû au graphite présent dans la formulation du matériau d'électrode positif.

Figure RE- 7 :

 7 Figure RE-7: (a) Evolution du paramètre de maille chex en fonction de x. Ces valeurs sont obtenues par affinement de type Le Bail. (b) Evolution des épaisseurs de feuillets en fonction de x. Ces valeurs ont été déterminées par affinement de type Rietveld.

Figure RE- 8 :

 8 Figure RE-8: Représentation de la structure de bande des phases NaxCoO2 (a) dans un régime de type « Curie-Weiss métallique » pour x > 0.5 (b) dans un régime métallique pour x < 0.5.

Figure RE- 9 :

 9 Figure RE-9: Représentation de la modification structurale due aux glissement de feuillets

Figure RE- 10 :

 10 Figure RE-10: Evolution des spectres RMN enregistrés sur les phases synthétisées par voie électrochimique.

Figure RE- 11 :

 11 Figure RE-11: Pour le système NaxCoO2 (a) Evolution de chex et de la distance Na-O en fonction de x. (b) Evolution du nombre formel d'ion Co 4+ paramagnétique en fonction de x. (c) Evolution du déplacement chimique en fonction de x. La nuance de couleur délimite les zones 1, 2 et 3. La ligne en pointillés orange correspond à la transition entre les deux régimes magnétiques.

Figure RE- 12 :

 12 Figure RE-12: Pour le système NaxCo2/3Mn1/3O2 (a) Evolution de chex en fonction de x. (b) Evolution du nombre formel d'ion Co 4+ paramagnétique en fonction de x. (c) Evolution du déplacement chimique en fonction de x. La nuance de couleur délimite les zones 1, 2 et 3. La ligne en pointillés orange correspond à la transition entre les deux régimes magnétiques.

Figure GI- 1 :Figure GI- 2 :

 12 Figure GI-1: Representation of the AxMO2 structure. The M ions are in grey, the A ions are in green and the O ions are in red. The A, B and C letters corresponds to the oxygen positions in order to have a compact stacking. .......................................................................................................................................... Figure GI-2: Phases diagram of NaxCoO2. The grey zones represent the single phase synthesis zones while the white zones are the multiple phases synthesis zones. Extracted from 7 ................................................

Figure I- 1 :

 1 Figure I-1: a) Representation of O3-NaFeO2 structure in NaCl rock salt type structure. The dashed line in the cell represents the [1 1 1] direction b) Representation of O3-NaFeO2 structure considering the distortion along the [1 1 1] direction 50 . ....................................................................................................... Figure I-2: Representation of the hexagonal, monoclinic and rhombohedral cells from the O3 structure. The equations introduced before allow to switch from one cell to another. ............................................. Figure I-3: Representation of the O3, P2 and P3 structures and representation of the corresponding Na + intercalation sites ........................................................................................................................................Figure I-4 : Representation of the 3d orbitals in an octahedral environment. The dz² and dx²-y² orbitals point to the ligands while the dxy orbitals point between the O ligands. dxy and dxz are not represented but are symmetrically equivalent to dxy ...................................................................................................... Figure I-5 : (a) Electronic configurations of the Co ions in Oh symmetry .................................................... Figure I-6 : (a) Electronic configurations in Oh and D3d symmetry for Co 3+ ions. (b) Representation of the compression due to the D3d symmetry occurring on CoO6 octahedra. .......................................................Figure I-7 : Representation of Co t2g orbital after trigonal distortion for Na1/2CoO2. Landron et al. 58 model considers two Co sites with different energy gaps between the levels. ..................................................... Figure I-8 : Schematic representation of the band structure of NaxCoO2 after the splitting of the t2g orbitals with the D3d distortion.................................................................................................................... Figure I-9 : (a) Initial state of the Na battery with NaxMO2 as positive electrode material. Metal sodium is used as negative electrode and the electrolyte is liquid. Representation of a Na battery during (b) the charge with the Na + deintercalation from NaxMO2 and (c) the discharge with the intercalation of Na + in NaxMO2. The Na + ions are represented by the green circle. ....................................................................... Figure I-10 : Representation of the different slopes that can be observed on a galvanostatic cycling. ..... Figure I-11 : (a) Representation of the stacking used to assemble of the battery in a coin cell (b) Sealed coin cell after assembly ............................................................................................................................... Figure I-12 : Evolution of the voltage and the current as a function of the time during the two steps necessary to synthetize a phase by electrochemical (de)intercalation. ..................................................... Figure I-13: Pictures of the airtight sample holder used for XRD acquisitions ...........................................Figure I-14 : (a) Coin cell drilled with 3 mm diameter holes on both current collectors. (b) Current collector holes covered with a polyimide 7 mm diameter film. .................................................................Figure I-15 : Zeeman effect with the splitting in two magnetic levels when a magnetic field is applied for I = ½ and 𝛾> 0 ................................................................................................................................................ Figure I-16 : Representation of a NMR experiment. At equilibrium, 𝑀0 is parallel to 𝐵0. 𝐵1 perturbation leads to the magnetization flip in the (x,y) plane. (0, x', y', z' (=z)) is the new system considering the rotation of the magnetization around 𝐵0. ..................................................................................................

Figure I- 5 :Figure I- 7 :Figure I- 8 :Figure I- 13 :

 57813 Figure I-1: a) Representation of O3-NaFeO2 structure in NaCl rock salt type structure. The dashed line in the cell represents the [1 1 1] direction b) Representation of O3-NaFeO2 structure considering the distortion along the [1 1 1] direction 50 . ....................................................................................................... Figure I-2: Representation of the hexagonal, monoclinic and rhombohedral cells from the O3 structure. The equations introduced before allow to switch from one cell to another. ............................................. Figure I-3: Representation of the O3, P2 and P3 structures and representation of the corresponding Na + intercalation sites ........................................................................................................................................Figure I-4 : Representation of the 3d orbitals in an octahedral environment. The dz² and dx²-y² orbitals point to the ligands while the dxy orbitals point between the O ligands. dxy and dxz are not represented but are symmetrically equivalent to dxy ...................................................................................................... Figure I-5 : (a) Electronic configurations of the Co ions in Oh symmetry .................................................... Figure I-6 : (a) Electronic configurations in Oh and D3d symmetry for Co 3+ ions. (b) Representation of the compression due to the D3d symmetry occurring on CoO6 octahedra. .......................................................Figure I-7 : Representation of Co t2g orbital after trigonal distortion for Na1/2CoO2. Landron et al. 58 model considers two Co sites with different energy gaps between the levels. ..................................................... Figure I-8 : Schematic representation of the band structure of NaxCoO2 after the splitting of the t2g orbitals with the D3d distortion.................................................................................................................... Figure I-9 : (a) Initial state of the Na battery with NaxMO2 as positive electrode material. Metal sodium is used as negative electrode and the electrolyte is liquid. Representation of a Na battery during (b) the charge with the Na + deintercalation from NaxMO2 and (c) the discharge with the intercalation of Na + in NaxMO2. The Na + ions are represented by the green circle. ....................................................................... Figure I-10 : Representation of the different slopes that can be observed on a galvanostatic cycling. ..... Figure I-11 : (a) Representation of the stacking used to assemble of the battery in a coin cell (b) Sealed coin cell after assembly ............................................................................................................................... Figure I-12 : Evolution of the voltage and the current as a function of the time during the two steps necessary to synthetize a phase by electrochemical (de)intercalation. ..................................................... Figure I-13: Pictures of the airtight sample holder used for XRD acquisitions ...........................................Figure I-14 : (a) Coin cell drilled with 3 mm diameter holes on both current collectors. (b) Current collector holes covered with a polyimide 7 mm diameter film. .................................................................Figure I-15 : Zeeman effect with the splitting in two magnetic levels when a magnetic field is applied for I = ½ and 𝛾> 0 ................................................................................................................................................ Figure I-16 : Representation of a NMR experiment. At equilibrium, 𝑀0 is parallel to 𝐵0. 𝐵1 perturbation leads to the magnetization flip in the (x,y) plane. (0, x', y', z' (=z)) is the new system considering the rotation of the magnetization around 𝐵0. ..................................................................................................

Figure

  Figure I-17 : Representation of the rotors in the NMR probe at the Magic Angle for MAS experiments. The picture is extracted from 61 . ................................................................................................................. Figure I-18: Representation of the Fermi contact shift for a 90° interaction between a half-filled t2g orbital of a M ion and a Na nucleus via an 2p orbital of the oxygen ion. ............................................................... Figure I-19 : Repartition of the quadrupolar moments created for I > 1/2 spin ........................................ Figure I-20: Energy level diagram for the I = 3/2 nuclei after application of a magnetic field. Extracted from 66 . ........................................................................................................................................................ Figure I-21 : Recording of the FID and Fourier transformation for a simple pulse sequence.....................Figure I-22 : Hahn Echo sequence ............................................................................................................... Figure I-23: Basic form of a 2D exchange experiment. Both pulses are 90°. Excitation label corresponds to the first pulse to transverse magnetization in (x,y) plane. Second pulse allows to restore the magnetization along 𝐵0 direction. Third pulse reconverts the magnetization in (x,y) plane. Extracted from 61 . ........................................................................................................................................................ Figure I-24 : Schematic representation of a 2D EXSY spectrum. 𝛺 represents the peaks frequency. Extracted from 61 . ........................................................................................................................................

Figure II- 9 :

 9 Figure II-1 : Perspective representation of OP4-(Li/Na)CoO2. Na + ions occupy prismatic sites which can either share faces (Naf, in red) or edges (Nae, in purple) with the surrounding CoO6 octahedra (in blue). The Li + ions occupy octahedral sites (in yellow). The oxygen ions positions are labelled with the letters A, B and C. ........................................................................................................................................................ Figure II-2 : SEM pictures of the sample A at different magnifications. Dashed lines represent the hexagonal shape of a OP4 crystal. ...............................................................................................................Figure II-3 : Representation of the different structures introduced in this chapter. .................................. Figure II-4 : Experimental XRD patterns of the samples A, B and C plotted as a function of the d spacing. Insert: Zoom in the 5.75 Å-4.50 Å region in order to focus on the impurities peaks. * are the Al peaks due to the sample holder used for the XRD acquisition. ................................................................................... Figure II-5: Electrical conductivity of an OP4 phase as a function of the temperature (from 6K to 300 K). ..................................................................................................................................................................... Figure II-6: Magnetic susceptibility and inverse magnetic susceptibility (in the insert) of the sample A as a function of the temperature (6 K to 300 K) realized under a 1T magnetic field. ........................................ Figure II-7 : Comparison of the 7 Li MAS NMR spectra recorded on the sample C at two different magnetic fields (2.35 and 7.05 T) using the same spinning frequency (30 kHz) with a Hahn Echo sequence. Insert: Zoom in order to highlight the presence of the signal at -203 ppm. .......................................................... Figure II-8 : Experimental 7 Li MAS NMR spectra of the samples A, B and C (2.35 T magnet, spinning frequency = 30 kHz, Hahn echo sequence). ................................................................................................ Figure II-9 : Fits of the signals 1, 2, 3 and 4 compared to the experimental spectra (in red) recorded on samples (a) A (b) B (c) C. ..............................................................................................................................Figure II-10 : a) Representation of the hypothetical cell Li1/2Na1/3CoO2 used as model for DFT calculations. This model considers full Li layers and 67% filled Na layers. b) Highlighting of the Na + /vacancy ordering in the Na interslab spaces. ..............................................................................................................................Figure II-11: (a) Calculated spin DOS of the model presented in Figure II-10. (a) total. (b) partial on the Co 3d orbitals. ...................................................................................................................................................Figure II-12 : Comparison between the experimental 23 Na MAS NMR spectrum of the OP4 phase and the calculated spectra considering the theoretical Curie constant and the experimental one. .......................

Figure II- 13 :

 13 Figure II-13 : Calculated 3D spin density map plotted using a 10 -3 e -/A² isosurface value. a1g orbital is mainly carrying the spins. The yellow color represents the positive spin density. ..................................... Figure II-14: Band structure of the Co 3+ ions in the case of NaxCoO2 (a) before and (b) after the octahedra distortion. .................................................................................................................................................... Figure II-15 : Experimental 7 Li MAS NMR spectra recorded on a 7.05 T magnet at different temperatures in the 265 K -450 K. The NMR sequences were Hahn echoes and the spinning frequency was 13 kHz. ..Figure II-16: Experimental 7 Li MAS NMR spectra recorded on a 7.05 T magnetic field with a spinning frequency of 30 kHz for T = 250 K, 300 K and 320 K. .................................................................................. Figure II-17: Fitted lines of the NMR shifts evolution of the signals 1, 2 and 3 as a function of the temperature. ............................................................................................................................................... Figure II-18 : Pulse sequence of the inversion recovery. Extracted from reference 61 ............................... Figure II-19 : Evolution of the signals intensities for each signal as a function of the mixing time ............ Figure II-20 : Selective Inversion pulse sequence ....................................................................................... Figure II-21 : Experimental 7 Li MAS NMR spectra of the sample B performed with the selective inversion technique at 340 K with mixing times from 0.05 ms to 6 s. The acquisitions were realized on a 7.05 T magnet with a spinning frequency of 65 kHz. (a) The signal 1 was selectively inverted. (b) The signal 2 was selectively inverted. (c) The signal 3 was selectively inverted. ................................................................... Figure II-22: Comparison of the 23 Na MAS NMR spectra recorded of the sample A for two different magnetic fields (7.05 T and 11.75 T). The spinning frequency was 30 kHz and the sequence was a single pulse. ........................................................................................................................................................... Figure II-23 : (a) Experimental 23 Na MAS NMR spectrum of the three studied samples with performed on a 11.75 T magnet at a spinning frequency of 30 kHz. (b) Fits of the signals 1 and 2 recorded by NMR on sample A compared to the experimental spectrum. * represents the spinning side bands ...................... Figure II-24 : VT-23 Na MAS NMR recorded on a 7.05 T magnet at a spinning frequency of 13 kHz in the 265 K < T < 450K range. * are the spinning side bands. .............................................................................. Figure II-25: Synchrotron XRD pattern as a function of the 2𝜃 position of the sample A with λ = 0.8261 Å. Red bars and black bars correspond, respectively, to the Bragg positions of O3-LiCoO2 and OP4-(Li/Na)CoO2. Red points correspond to experimental XRD pattern while black line is the calculated one obtained by Rietveld refinement. The blue line is the difference between the experimental and the calculated lines. ........................................................................................................................................... Figure II-26: Bonds distances calculated after Rietveld refinement of OP4 phase. ....................................

Figure II- 16 :Figure II- 17 :Figure II- 19 :

 161719 Figure II-13 : Calculated 3D spin density map plotted using a 10 -3 e -/A² isosurface value. a1g orbital is mainly carrying the spins. The yellow color represents the positive spin density. ..................................... Figure II-14: Band structure of the Co 3+ ions in the case of NaxCoO2 (a) before and (b) after the octahedra distortion. .................................................................................................................................................... Figure II-15 : Experimental 7 Li MAS NMR spectra recorded on a 7.05 T magnet at different temperatures in the 265 K -450 K. The NMR sequences were Hahn echoes and the spinning frequency was 13 kHz. ..Figure II-16: Experimental 7 Li MAS NMR spectra recorded on a 7.05 T magnetic field with a spinning frequency of 30 kHz for T = 250 K, 300 K and 320 K. .................................................................................. Figure II-17: Fitted lines of the NMR shifts evolution of the signals 1, 2 and 3 as a function of the temperature. ............................................................................................................................................... Figure II-18 : Pulse sequence of the inversion recovery. Extracted from reference 61 ............................... Figure II-19 : Evolution of the signals intensities for each signal as a function of the mixing time ............ Figure II-20 : Selective Inversion pulse sequence ....................................................................................... Figure II-21 : Experimental 7 Li MAS NMR spectra of the sample B performed with the selective inversion technique at 340 K with mixing times from 0.05 ms to 6 s. The acquisitions were realized on a 7.05 T magnet with a spinning frequency of 65 kHz. (a) The signal 1 was selectively inverted. (b) The signal 2 was selectively inverted. (c) The signal 3 was selectively inverted. ................................................................... Figure II-22: Comparison of the 23 Na MAS NMR spectra recorded of the sample A for two different magnetic fields (7.05 T and 11.75 T). The spinning frequency was 30 kHz and the sequence was a single pulse. ........................................................................................................................................................... Figure II-23 : (a) Experimental 23 Na MAS NMR spectrum of the three studied samples with performed on a 11.75 T magnet at a spinning frequency of 30 kHz. (b) Fits of the signals 1 and 2 recorded by NMR on sample A compared to the experimental spectrum. * represents the spinning side bands ...................... Figure II-24 : VT-23 Na MAS NMR recorded on a 7.05 T magnet at a spinning frequency of 13 kHz in the 265 K < T < 450K range. * are the spinning side bands. .............................................................................. Figure II-25: Synchrotron XRD pattern as a function of the 2𝜃 position of the sample A with λ = 0.8261 Å. Red bars and black bars correspond, respectively, to the Bragg positions of O3-LiCoO2 and OP4-(Li/Na)CoO2. Red points correspond to experimental XRD pattern while black line is the calculated one obtained by Rietveld refinement. The blue line is the difference between the experimental and the calculated lines. ........................................................................................................................................... Figure II-26: Bonds distances calculated after Rietveld refinement of OP4 phase. ....................................

Figure III- 1 :Figure III- 2 :Figure III- 3 :Figure III- 4 :Figure III- 5 :Figure III- 6 :

 123456 Figure III-1 : Representation of the CoO2 gliding to generate octahedra sites and form the O2 polytype. From 43 .........................................................................................................................................................Figure III-2: Representation of one layer gliding allowing the formation of the O4 phase from the OP4 one. From 43 .................................................................................................................................................Figure III-3 : Representation of the O4-LiCoO2 structure. From reference 43 . ............................................ Figure III-4: Representation of the expected O4 structure after ion-exchange from the OP4 phase enriched with 6 Li ions ..................................................................................................................................Figure III-5: Refined XRD pattern of OP4-( 6 Li/Na)CoO2 phase used for the ion-exchanges. ......................Figure III-6: Experimental XRD patterns of both samples compared to the theoretical one using Berthelot et al. data 43 .................................................................................................................................................. Figure III-7: Experimental 7 Li MAS NMR spectrum obtained with a Hahn Echo sequence of the standard sample on a 7.05 T magnet with a spinning frequency of 30 kHz. * are the spinning side bands..............

Figure III- 8 :Figure III- 9 :Figure III- 11 :Figure III- 12 :

 891112 Figure III-8:(a) Experimental[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li MAS NMR spectra of the standard sample (b) Experimental[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li and[START_REF] Reddy | High performance Na x CoO 2 as a cathode material for rechargeable sodium batteries[END_REF] Li MAS NMR spectra of EIE and SIE samples normalized by the number of scans and the mass in the rotor. All the spectra were realized on a 7.05 T magnet with a spinning frequency of 30 kHz. ......................... Figure III-9: Experimental 23 Na MAS NMR spectra of both O4-phases compared to the OP4 phase. Only the spectra of the O4 materials were normalized to the number of scans and to the mass of powder in the rotor. NMR was performed on 7.05 T magnet with a spinning frequency of 30 kHz. ........................ Figure III-10: 23 Na MAS NMR spectrum performed on sample B using an EXSY measurements of EIE at room temperature with a mixing time of 0.3 s (4.7 T magnet, spinning frequency of 60 kHz) ................ Figure III-11: Experimental 7 Li MAS NMR selective inversion on EIE sample on a 4.7 T with a spinning frequency of 60 kHz. (a) -4 ppm signal is probed (b) 30 ppm site is probed (c) 68 ppm site is probed by the soft pulse ............................................................................................................................................. Figure III-12: Experimental 7 Li MAS NMR selective inversion on a 2.35 T magnet with a spinning frequency of 30 kHz of SIE sample. We only probed the diamagnetic signal with the soft pulse. ...........

Figure IV- 1 :

 1 Figure IV-1: a) Electrochemical cycling in the 2 V -3.5 V range of the P3, O3 and O'3 NaxCoO2 polytypes. Reproduced from reference 76 . b) In-situ XRD patterns with the corresponding discharge from 3.1 V to 2.1 V of the P2 polytype. From reference 47 . ................................................................................................... Figure IV-2: Representation, in the (a, b) plane, of the Na + /vacancy ordering for Na1/2CoO2 (reference: 110 ), Na4/7CoO2 (reference: 109 ) and Na2/3CoO2 (reference: 92 ). The purple dashed lines represent the initial hexagonal cell while the solid purple lines represent the superstructure cells. Extracted from reference 43 . ...................................................................................................................................................................Figure IV-3: a) Cycling curves of a Na/NaClO4 in 1M PC/P2-NaxCoO2 cell in the 1.35 -3.9 V vs Na + /Na range at C/20 b) Cycling curves of a Na/NaPF6 in 1M PC + 2% FEC/P2-NaxCoO2 cell in the 1.4 -4.3 V vs Na + /Na range at C/20 ................................................................................................................................ Figure IV-4: Thermal treatment for the P2-𝑁𝑎~0.7CoO2 synthesis ......................................................... Figure IV-5: Thermal treatment for the P2-𝑁𝑎𝑥0CoyMn1-yO2 phases synthesis ....................................... Figure IV-6: SEM images of P2-𝑁𝑎~0.7𝐶𝑜𝑂2 phase at two different magnifications. ............................ Figure IV-7: SXRD patterns of the a) NaxCoO2 b) NaxCo2/3Mn1/3O2 c) NaxCo1/2Mn1/2O2 d) NaxCo1/3Mn2/3O2 pristine phases. Red points: experimental data, black lines: calculated curves, blue lines: difference between experimental and calculated data, black bars: Bragg positions. The two inserts are zooms on the (002) peak and in the 15°-23° range to evidence the presence of superstructure peaks. ....................... Figure IV-8: Galvanostatic curves of the Na(s)/P2-NaxMO2 cell at C/20 in their low voltage range for a) NaxCoO2 b) NaxCo2/3Mn1/3O2 c) NaxCo1/2Mn1/2O2 d) NaxCo1/3Mn2/3O2 ....................................................... Figure IV-9: Evolution of the specific capacities in their low voltage window when cycling in their low voltage range at C/20 ................................................................................................................................ Figure IV-10: Comparison between the first and the 40 th cycle realized on the same Na(s) / P2-NaxCoO2 cell at C/20 in the low voltage range. ........................................................................................................Figure IV-11: Capacity as a function of cycle number for NaxCoO2 and NaxCo2/3Mn1/3O2 system in both voltage ranges at C/20. .............................................................................................................................Figure IV-12: Galvanostatic curves of the Na(s)/P2-NaxMO2 cell at C/20 in their high voltage range for a) NaxCoO2 b) NaxCo2/3Mn1/3O2 c) NaxCo1/2Mn1/2O2 d) NaxCo1/3Mn2/3O2 ....................................................... Figure IV-13: XRD patterns obtained by operando XRD on the NaxCoO2 system on the first charge from 1.5 V to 4.6 V at C/10 (a) in the 5 -30° range (b) in the 16.3 -18.5° range. The colored lines represent the XRD patterns of the peculiar phases Na2/3CoO2, Na0.57CoO2 and Na1/2CoO2.......................................

Figure IV- 3 :Figure IV- 4 :Figure IV- 5 :

 345 a) Cycling curves of a Na/NaClO4 in 1M PC/P2-NaxCoO2 cell in the 1.35 -3.9 V vs Na + /Na range at C/20 b) Cycling curves of a Na/NaPF6 in 1M PC + 2% FEC/P2-NaxCoO2 cell in the 1.4 -4.3 V vs Na + /Na range at C/20 ................................................................................................................................ Thermal treatment for the P2-𝑁𝑎~0.7CoO2 synthesis ......................................................... Thermal treatment for the P2-𝑁𝑎𝑥0CoyMn1-yO2 phases synthesis ....................................... Figure IV-6: SEM images of P2-𝑁𝑎~0.7𝐶𝑜𝑂2 phase at two different magnifications. ............................ Figure IV-7: SXRD patterns of the a) NaxCoO2 b) NaxCo2/3Mn1/3O2 c) NaxCo1/2Mn1/2O2 d) NaxCo1/3Mn2/3O2 pristine phases. Red points: experimental data, black lines: calculated curves, blue lines: difference between experimental and calculated data, black bars: Bragg positions. The two inserts are zooms on the (002) peak and in the 15°-23° range to evidence the presence of superstructure peaks. .......................

Figure IV- 8 :

 8 Galvanostatic curves of the Na(s)/P2-NaxMO2 cell at C/20 in their low voltage range for a) NaxCoO2 b) NaxCo2/3Mn1/3O2 c) NaxCo1/2Mn1/2O2 d) NaxCo1/3Mn2/3O2 .......................................................

Figure IV- 9 :

 9 Evolution of the specific capacities in their low voltage window when cycling in their low voltage range at C/20 ................................................................................................................................ Figure IV-10: Comparison between the first and the 40 th cycle realized on the same Na(s) / P2-NaxCoO2 cell at C/20 in the low voltage range. ........................................................................................................

Figure IV- 11 :

 11 Capacity as a function of cycle number for NaxCoO2 and NaxCo2/3Mn1/3O2 system in both voltage ranges at C/20. .............................................................................................................................

Figure IV- 12 :

 12 Galvanostatic curves of the Na(s)/P2-NaxMO2 cell at C/20 in their high voltage range for a) NaxCoO2 b) NaxCo2/3Mn1/3O2 c) NaxCo1/2Mn1/2O2 d) NaxCo1/3Mn2/3O2 ....................................................... Figure IV-13: XRD patterns obtained by operando XRD on the NaxCoO2 system on the first charge from 1.5 V to 4.6 V at C/10 (a) in the 5 -30° range (b) in the 16.3 -18.5° range. The colored lines represent the XRD patterns of the peculiar phases Na2/3CoO2, Na0.57CoO2 and Na1/2CoO2.......................................

Figure IV- 14 :Figure V- 1 :Figure V- 5 :Figure V- 6 :Figure V- 7 :Figure V- 8 :Figure V- 10 :

 141567810 Figure IV-14: Voltage (in black) and current (in red) evolution during the PITT measurements on NaxCoO2 as a function of time .................................................................................................................................. 139 Figure IV-15: Representation of the CoO2 stacking in ideal P2 structure and P2 structure with an O-type stacking fault after sheets glidings. ........................................................................................................... 140 Figure IV-16: XRD patterns of stabilized NaxCoO2 phases by PITT at different voltages from 4.1 V to 4.8 V for a) 7 < 2𝜃 < 30° and b) 7 < 2𝜃 < 11°. $ = Al, * = Na. .............................................................................. 141 Figure IV-17: SXRD pattern of Na1/3CoO2 in the (a) P63/mmc space group (b) P61 space group. Red points = Yobs, black line = Ycalc, blue line = Yobs -Ycalc, black ticks = Bragg positions. Insert highlights the presence of superstructure peaks. $ = Al, * = Na, ^ = C. ........................................................................... 143 Figure IV-18: Representation in the (a,b) plane of the initial hexagonal cell (solid line) and the superstructure hexagonal cell (dashed line) ............................................................................................. 144 Figure IV-19: XRD patterns obtained during the operando measurements on the NaxCo2/3Mn1/3O2 system on the first charge from 1.25 V to 4.5 V at C/10 ....................................................................................... 146 Figure IV-20: SXRD pattern of Na1/2Co2/3Mn1/3O2 in the Pnmm space group. Red points = Yobs, black line = Ycalc, blue line = Yobs -Ycalc, black ticks = Bragg positions. Insert highlights the the presence of superstructure peaks. ................................................................................................................................ 147 Figure IV-21: XRD patterns obtained by operando measurements on NaxCo1/2Mn1/2O2 system on first charge from 1.25 V to 4.5 V at C/10. ......................................................................................................... 149 Figure IV-22: XRD patterns obtained by operando measurements on NaxCo1/3Mn2/3O2 system on first charge from 1.25 V to 4.5 V at C/10. ......................................................................................................... 151 Figure IV-23: Evolution of chex lattice parameter as a function of x for the four systems ........................ 153

Figure V- 13 :

 13 Figure V-10: Evolution of the (a) a lattice parameter (b) c lattice parameter for P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 phases studied in this chapter ....................................................................................... Figure V-11: XRD patterns of the "OP" phases: Na0.25CoO2 and Na0.22Co2/3Mn1/3O2 stabilized at, respectively, 4.6 and 4.5 V vs Na + /Na ........................................................................................................ Figure V-12: Refined XRD pattern as a function of the 2θ position of Na0.4CoO2. Black bars correspond to the Bragg positions of the phase. Red points correspond to experimental XRD pattern while black line is the calculated one obtained by Rietveld refinement. The blue line is the difference between experimental and calculated lines. * is a peak due to the graphite present in the mixture. ...................Figure V-13: (a) Schematic representation of the P2-stacking (b) Evolution of the layers thicknesses in the P2-structure for P2-NaxCoO2 ..................................................................................................................... Figure V-14: Comparison of the different distances in (a) P2-Na0.33CoO2 and (b) P2-Na0.67CoO2 ............. Figure V-15: (a) Magnetic measurements of some NaxCoO2 phase as a function of the temperature from 7 K to 300 K (a) synthetized in this work under a 1T magnetic field (b) from reference 75 under a 0.8 T magnetic field. ........................................................................................................................................... Figure V-16: Magnetic phase diagram of P2-NaxCoO2. Data are extracted from 108 . ............................... Figure V-17: Representation of the band structure of the P2-NaxCoO2 phases with the D3d symmetry in the (a) "Curie-Weiss metal regime" (b) in the Pauli paramagnetic regime .............................................. Figure V-18: Evolution of the 23 Na MAS NMR shifts for (a) NaxCoO2 and (b) NaxCo2/3Mn1/3O2 systems. The acquisitions were realized on a 7.05 T magnet with a spinning frequency of 30 kHz and a simple pulse sequence. * = spinning side bands. ...........................................................................................................Figure V-19: Experimental and fitted using a 2 nd order quadrupolar lineshape NMR signals realized on the Na0.67CoO2 spectrum.................................................................................................................................. Figure V-20: For the P2-NaxCoO2 system: (a) Evolution of the Na-O distance and c lattice parameter as a function of x. (b) Evolution of the amount of formal Co 4+ ions as a function of x. "Curie-Weiss metal regime" and "Pauli paramagnetic regime" are separated by an orange dashed line (c) 23 Na isotropic shift evolution as a function of x. ...................................................................................................................... Figure V-21: (a) Evolution of the c lattice parameters as a function of x for NaxCo2/3Mn1/3O2 phases (b) Evolution of the amount of formal Co 4+ ions as a function of x. (c) Isotropic shift evolution obtained after the fit of the spectra as a function of x. The Zone 1, 2 and 3 are separated by black dashed lines. ........ Figure V-22: Schematic representation of the band structure of the t2g levels of the (a) P2-NaxCoO2 and (b) P2-NaxCo2/3Mn1/3O2 phases with the D3d symmetry in the "Curie-Weiss metal regime" considering up and down DOS. .................................................................................................................................................

Figure V- 16 :

 16 Figure V-10: Evolution of the (a) a lattice parameter (b) c lattice parameter for P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 phases studied in this chapter ....................................................................................... Figure V-11: XRD patterns of the "OP" phases: Na0.25CoO2 and Na0.22Co2/3Mn1/3O2 stabilized at, respectively, 4.6 and 4.5 V vs Na + /Na ........................................................................................................ Figure V-12: Refined XRD pattern as a function of the 2θ position of Na0.4CoO2. Black bars correspond to the Bragg positions of the phase. Red points correspond to experimental XRD pattern while black line is the calculated one obtained by Rietveld refinement. The blue line is the difference between experimental and calculated lines. * is a peak due to the graphite present in the mixture. ...................Figure V-13: (a) Schematic representation of the P2-stacking (b) Evolution of the layers thicknesses in the P2-structure for P2-NaxCoO2 ..................................................................................................................... Figure V-14: Comparison of the different distances in (a) P2-Na0.33CoO2 and (b) P2-Na0.67CoO2 ............. Figure V-15: (a) Magnetic measurements of some NaxCoO2 phase as a function of the temperature from 7 K to 300 K (a) synthetized in this work under a 1T magnetic field (b) from reference 75 under a 0.8 T magnetic field. ........................................................................................................................................... Figure V-16: Magnetic phase diagram of P2-NaxCoO2. Data are extracted from 108 . ............................... Figure V-17: Representation of the band structure of the P2-NaxCoO2 phases with the D3d symmetry in the (a) "Curie-Weiss metal regime" (b) in the Pauli paramagnetic regime .............................................. Figure V-18: Evolution of the 23 Na MAS NMR shifts for (a) NaxCoO2 and (b) NaxCo2/3Mn1/3O2 systems. The acquisitions were realized on a 7.05 T magnet with a spinning frequency of 30 kHz and a simple pulse sequence. * = spinning side bands. ...........................................................................................................Figure V-19: Experimental and fitted using a 2 nd order quadrupolar lineshape NMR signals realized on the Na0.67CoO2 spectrum.................................................................................................................................. Figure V-20: For the P2-NaxCoO2 system: (a) Evolution of the Na-O distance and c lattice parameter as a function of x. (b) Evolution of the amount of formal Co 4+ ions as a function of x. "Curie-Weiss metal regime" and "Pauli paramagnetic regime" are separated by an orange dashed line (c) 23 Na isotropic shift evolution as a function of x. ...................................................................................................................... Figure V-21: (a) Evolution of the c lattice parameters as a function of x for NaxCo2/3Mn1/3O2 phases (b) Evolution of the amount of formal Co 4+ ions as a function of x. (c) Isotropic shift evolution obtained after the fit of the spectra as a function of x. The Zone 1, 2 and 3 are separated by black dashed lines. ........ Figure V-22: Schematic representation of the band structure of the t2g levels of the (a) P2-NaxCoO2 and (b) P2-NaxCo2/3Mn1/3O2 phases with the D3d symmetry in the "Curie-Weiss metal regime" considering up and down DOS. .................................................................................................................................................

Figure V- 17 :

 17 Figure V-10: Evolution of the (a) a lattice parameter (b) c lattice parameter for P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 phases studied in this chapter ....................................................................................... Figure V-11: XRD patterns of the "OP" phases: Na0.25CoO2 and Na0.22Co2/3Mn1/3O2 stabilized at, respectively, 4.6 and 4.5 V vs Na + /Na ........................................................................................................ Figure V-12: Refined XRD pattern as a function of the 2θ position of Na0.4CoO2. Black bars correspond to the Bragg positions of the phase. Red points correspond to experimental XRD pattern while black line is the calculated one obtained by Rietveld refinement. The blue line is the difference between experimental and calculated lines. * is a peak due to the graphite present in the mixture. ...................Figure V-13: (a) Schematic representation of the P2-stacking (b) Evolution of the layers thicknesses in the P2-structure for P2-NaxCoO2 ..................................................................................................................... Figure V-14: Comparison of the different distances in (a) P2-Na0.33CoO2 and (b) P2-Na0.67CoO2 ............. Figure V-15: (a) Magnetic measurements of some NaxCoO2 phase as a function of the temperature from 7 K to 300 K (a) synthetized in this work under a 1T magnetic field (b) from reference 75 under a 0.8 T magnetic field. ........................................................................................................................................... Figure V-16: Magnetic phase diagram of P2-NaxCoO2. Data are extracted from 108 . ............................... Figure V-17: Representation of the band structure of the P2-NaxCoO2 phases with the D3d symmetry in the (a) "Curie-Weiss metal regime" (b) in the Pauli paramagnetic regime .............................................. Figure V-18: Evolution of the 23 Na MAS NMR shifts for (a) NaxCoO2 and (b) NaxCo2/3Mn1/3O2 systems. The acquisitions were realized on a 7.05 T magnet with a spinning frequency of 30 kHz and a simple pulse sequence. * = spinning side bands. ...........................................................................................................Figure V-19: Experimental and fitted using a 2 nd order quadrupolar lineshape NMR signals realized on the Na0.67CoO2 spectrum.................................................................................................................................. Figure V-20: For the P2-NaxCoO2 system: (a) Evolution of the Na-O distance and c lattice parameter as a function of x. (b) Evolution of the amount of formal Co 4+ ions as a function of x. "Curie-Weiss metal regime" and "Pauli paramagnetic regime" are separated by an orange dashed line (c) 23 Na isotropic shift evolution as a function of x. ...................................................................................................................... Figure V-21: (a) Evolution of the c lattice parameters as a function of x for NaxCo2/3Mn1/3O2 phases (b) Evolution of the amount of formal Co 4+ ions as a function of x. (c) Isotropic shift evolution obtained after the fit of the spectra as a function of x. The Zone 1, 2 and 3 are separated by black dashed lines. ........ Figure V-22: Schematic representation of the band structure of the t2g levels of the (a) P2-NaxCoO2 and (b) P2-NaxCo2/3Mn1/3O2 phases with the D3d symmetry in the "Curie-Weiss metal regime" considering up and down DOS. .................................................................................................................................................

Figure V- 18 :

 18 Figure V-10: Evolution of the (a) a lattice parameter (b) c lattice parameter for P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 phases studied in this chapter ....................................................................................... Figure V-11: XRD patterns of the "OP" phases: Na0.25CoO2 and Na0.22Co2/3Mn1/3O2 stabilized at, respectively, 4.6 and 4.5 V vs Na + /Na ........................................................................................................ Figure V-12: Refined XRD pattern as a function of the 2θ position of Na0.4CoO2. Black bars correspond to the Bragg positions of the phase. Red points correspond to experimental XRD pattern while black line is the calculated one obtained by Rietveld refinement. The blue line is the difference between experimental and calculated lines. * is a peak due to the graphite present in the mixture. ...................Figure V-13: (a) Schematic representation of the P2-stacking (b) Evolution of the layers thicknesses in the P2-structure for P2-NaxCoO2 ..................................................................................................................... Figure V-14: Comparison of the different distances in (a) P2-Na0.33CoO2 and (b) P2-Na0.67CoO2 ............. Figure V-15: (a) Magnetic measurements of some NaxCoO2 phase as a function of the temperature from 7 K to 300 K (a) synthetized in this work under a 1T magnetic field (b) from reference 75 under a 0.8 T magnetic field. ........................................................................................................................................... Figure V-16: Magnetic phase diagram of P2-NaxCoO2. Data are extracted from 108 . ............................... Figure V-17: Representation of the band structure of the P2-NaxCoO2 phases with the D3d symmetry in the (a) "Curie-Weiss metal regime" (b) in the Pauli paramagnetic regime .............................................. Figure V-18: Evolution of the 23 Na MAS NMR shifts for (a) NaxCoO2 and (b) NaxCo2/3Mn1/3O2 systems. The acquisitions were realized on a 7.05 T magnet with a spinning frequency of 30 kHz and a simple pulse sequence. * = spinning side bands. ...........................................................................................................Figure V-19: Experimental and fitted using a 2 nd order quadrupolar lineshape NMR signals realized on the Na0.67CoO2 spectrum.................................................................................................................................. Figure V-20: For the P2-NaxCoO2 system: (a) Evolution of the Na-O distance and c lattice parameter as a function of x. (b) Evolution of the amount of formal Co 4+ ions as a function of x. "Curie-Weiss metal regime" and "Pauli paramagnetic regime" are separated by an orange dashed line (c) 23 Na isotropic shift evolution as a function of x. ...................................................................................................................... Figure V-21: (a) Evolution of the c lattice parameters as a function of x for NaxCo2/3Mn1/3O2 phases (b) Evolution of the amount of formal Co 4+ ions as a function of x. (c) Isotropic shift evolution obtained after the fit of the spectra as a function of x. The Zone 1, 2 and 3 are separated by black dashed lines. ........ Figure V-22: Schematic representation of the band structure of the t2g levels of the (a) P2-NaxCoO2 and (b) P2-NaxCo2/3Mn1/3O2 phases with the D3d symmetry in the "Curie-Weiss metal regime" considering up and down DOS. .................................................................................................................................................

Figure V- 19 :

 19 Figure V-10: Evolution of the (a) a lattice parameter (b) c lattice parameter for P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 phases studied in this chapter ....................................................................................... Figure V-11: XRD patterns of the "OP" phases: Na0.25CoO2 and Na0.22Co2/3Mn1/3O2 stabilized at, respectively, 4.6 and 4.5 V vs Na + /Na ........................................................................................................ Figure V-12: Refined XRD pattern as a function of the 2θ position of Na0.4CoO2. Black bars correspond to the Bragg positions of the phase. Red points correspond to experimental XRD pattern while black line is the calculated one obtained by Rietveld refinement. The blue line is the difference between experimental and calculated lines. * is a peak due to the graphite present in the mixture. ...................Figure V-13: (a) Schematic representation of the P2-stacking (b) Evolution of the layers thicknesses in the P2-structure for P2-NaxCoO2 ..................................................................................................................... Figure V-14: Comparison of the different distances in (a) P2-Na0.33CoO2 and (b) P2-Na0.67CoO2 ............. Figure V-15: (a) Magnetic measurements of some NaxCoO2 phase as a function of the temperature from 7 K to 300 K (a) synthetized in this work under a 1T magnetic field (b) from reference 75 under a 0.8 T magnetic field. ........................................................................................................................................... Figure V-16: Magnetic phase diagram of P2-NaxCoO2. Data are extracted from 108 . ............................... Figure V-17: Representation of the band structure of the P2-NaxCoO2 phases with the D3d symmetry in the (a) "Curie-Weiss metal regime" (b) in the Pauli paramagnetic regime .............................................. Figure V-18: Evolution of the 23 Na MAS NMR shifts for (a) NaxCoO2 and (b) NaxCo2/3Mn1/3O2 systems. The acquisitions were realized on a 7.05 T magnet with a spinning frequency of 30 kHz and a simple pulse sequence. * = spinning side bands. ...........................................................................................................Figure V-19: Experimental and fitted using a 2 nd order quadrupolar lineshape NMR signals realized on the Na0.67CoO2 spectrum.................................................................................................................................. Figure V-20: For the P2-NaxCoO2 system: (a) Evolution of the Na-O distance and c lattice parameter as a function of x. (b) Evolution of the amount of formal Co 4+ ions as a function of x. "Curie-Weiss metal regime" and "Pauli paramagnetic regime" are separated by an orange dashed line (c) 23 Na isotropic shift evolution as a function of x. ...................................................................................................................... Figure V-21: (a) Evolution of the c lattice parameters as a function of x for NaxCo2/3Mn1/3O2 phases (b) Evolution of the amount of formal Co 4+ ions as a function of x. (c) Isotropic shift evolution obtained after the fit of the spectra as a function of x. The Zone 1, 2 and 3 are separated by black dashed lines. ........ Figure V-22: Schematic representation of the band structure of the t2g levels of the (a) P2-NaxCoO2 and (b) P2-NaxCo2/3Mn1/3O2 phases with the D3d symmetry in the "Curie-Weiss metal regime" considering up and down DOS. .................................................................................................................................................

Figure V- 20 :

 20 Figure V-10: Evolution of the (a) a lattice parameter (b) c lattice parameter for P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 phases studied in this chapter ....................................................................................... Figure V-11: XRD patterns of the "OP" phases: Na0.25CoO2 and Na0.22Co2/3Mn1/3O2 stabilized at, respectively, 4.6 and 4.5 V vs Na + /Na ........................................................................................................ Figure V-12: Refined XRD pattern as a function of the 2θ position of Na0.4CoO2. Black bars correspond to the Bragg positions of the phase. Red points correspond to experimental XRD pattern while black line is the calculated one obtained by Rietveld refinement. The blue line is the difference between experimental and calculated lines. * is a peak due to the graphite present in the mixture. ...................Figure V-13: (a) Schematic representation of the P2-stacking (b) Evolution of the layers thicknesses in the P2-structure for P2-NaxCoO2 ..................................................................................................................... Figure V-14: Comparison of the different distances in (a) P2-Na0.33CoO2 and (b) P2-Na0.67CoO2 ............. Figure V-15: (a) Magnetic measurements of some NaxCoO2 phase as a function of the temperature from 7 K to 300 K (a) synthetized in this work under a 1T magnetic field (b) from reference 75 under a 0.8 T magnetic field. ........................................................................................................................................... Figure V-16: Magnetic phase diagram of P2-NaxCoO2. Data are extracted from 108 . ............................... Figure V-17: Representation of the band structure of the P2-NaxCoO2 phases with the D3d symmetry in the (a) "Curie-Weiss metal regime" (b) in the Pauli paramagnetic regime .............................................. Figure V-18: Evolution of the 23 Na MAS NMR shifts for (a) NaxCoO2 and (b) NaxCo2/3Mn1/3O2 systems. The acquisitions were realized on a 7.05 T magnet with a spinning frequency of 30 kHz and a simple pulse sequence. * = spinning side bands. ...........................................................................................................Figure V-19: Experimental and fitted using a 2 nd order quadrupolar lineshape NMR signals realized on the Na0.67CoO2 spectrum.................................................................................................................................. Figure V-20: For the P2-NaxCoO2 system: (a) Evolution of the Na-O distance and c lattice parameter as a function of x. (b) Evolution of the amount of formal Co 4+ ions as a function of x. "Curie-Weiss metal regime" and "Pauli paramagnetic regime" are separated by an orange dashed line (c) 23 Na isotropic shift evolution as a function of x. ...................................................................................................................... Figure V-21: (a) Evolution of the c lattice parameters as a function of x for NaxCo2/3Mn1/3O2 phases (b) Evolution of the amount of formal Co 4+ ions as a function of x. (c) Isotropic shift evolution obtained after the fit of the spectra as a function of x. The Zone 1, 2 and 3 are separated by black dashed lines. ........ Figure V-22: Schematic representation of the band structure of the t2g levels of the (a) P2-NaxCoO2 and (b) P2-NaxCo2/3Mn1/3O2 phases with the D3d symmetry in the "Curie-Weiss metal regime" considering up and down DOS. .................................................................................................................................................

Figure VI- 1 :

 1 Figure VI-1: Structure of O3-Na2RuO3 with the oxygen ions in red, the Na + ions in yellow and the Ru 4+ ions in grey. Extracted from reference 46 . .........................................................................................................Figure VI-2: (a) Electrochemical performances between 1.5 and 4 V of the O3-NaxRuO3 system at C/10 (b) Representation of the O1-Na1RuO3 and O1'-Na1/2RuO3 structures and the corresponding Ru ions, Na ions and vacancies repartition in the layers. From reference 48 . ......................................................................Figure VI-3: Representation of the different Na site environments in O3-Na2RuO3. ................................Figure VI-4: (a) 23 Na MAS NMR spectra of two O3-Na2RuO3 phases. The measurements were realized on a 11.75 T magnet with a spinning frequency of 30 kHz and a single pulse sequence. (b) Fits realized on DMFit of the signal at 877 ppm using two Na contributions corresponding to Na2 and Na3 using fixed widths and fixed Gaussian/Lorentzian proportions. (c) Fits realized on DMFit of the signal at 877 ppm

Figure VI- 2 :

 2 Figure VI-1: Structure of O3-Na2RuO3 with the oxygen ions in red, the Na + ions in yellow and the Ru 4+ ions in grey. Extracted from reference 46 . .........................................................................................................Figure VI-2: (a) Electrochemical performances between 1.5 and 4 V of the O3-NaxRuO3 system at C/10 (b) Representation of the O1-Na1RuO3 and O1'-Na1/2RuO3 structures and the corresponding Ru ions, Na ions and vacancies repartition in the layers. From reference 48 . ......................................................................Figure VI-3: Representation of the different Na site environments in O3-Na2RuO3. ................................Figure VI-4: (a) 23 Na MAS NMR spectra of two O3-Na2RuO3 phases. The measurements were realized on a 11.75 T magnet with a spinning frequency of 30 kHz and a single pulse sequence. (b) Fits realized on DMFit of the signal at 877 ppm using two Na contributions corresponding to Na2 and Na3 using fixed widths and fixed Gaussian/Lorentzian proportions. (c) Fits realized on DMFit of the signal at 877 ppm

Figure VI- 3 :

 3 Figure VI-1: Structure of O3-Na2RuO3 with the oxygen ions in red, the Na + ions in yellow and the Ru 4+ ions in grey. Extracted from reference 46 . .........................................................................................................Figure VI-2: (a) Electrochemical performances between 1.5 and 4 V of the O3-NaxRuO3 system at C/10 (b) Representation of the O1-Na1RuO3 and O1'-Na1/2RuO3 structures and the corresponding Ru ions, Na ions and vacancies repartition in the layers. From reference 48 . ......................................................................Figure VI-3: Representation of the different Na site environments in O3-Na2RuO3. ................................Figure VI-4: (a) 23 Na MAS NMR spectra of two O3-Na2RuO3 phases. The measurements were realized on a 11.75 T magnet with a spinning frequency of 30 kHz and a single pulse sequence. (b) Fits realized on DMFit of the signal at 877 ppm using two Na contributions corresponding to Na2 and Na3 using fixed widths and fixed Gaussian/Lorentzian proportions. (c) Fits realized on DMFit of the signal at 877 ppm

Figure VI- 4 :Figure VI- 5 :

 45 Figure VI-1: Structure of O3-Na2RuO3 with the oxygen ions in red, the Na + ions in yellow and the Ru 4+ ions in grey. Extracted from reference 46 . .........................................................................................................Figure VI-2: (a) Electrochemical performances between 1.5 and 4 V of the O3-NaxRuO3 system at C/10 (b) Representation of the O1-Na1RuO3 and O1'-Na1/2RuO3 structures and the corresponding Ru ions, Na ions and vacancies repartition in the layers. From reference 48 . ......................................................................Figure VI-3: Representation of the different Na site environments in O3-Na2RuO3. ................................Figure VI-4: (a) 23 Na MAS NMR spectra of two O3-Na2RuO3 phases. The measurements were realized on a 11.75 T magnet with a spinning frequency of 30 kHz and a single pulse sequence. (b) Fits realized on DMFit of the signal at 877 ppm using two Na contributions corresponding to Na2 and Na3 using fixed widths and fixed Gaussian/Lorentzian proportions. (c) Fits realized on DMFit of the signal at 877 ppm

Figure RE- 1 :

 1 Figure RE-1: Représentation des structures O3, P2 et P3 et environnements locaux des ions Na + ......... Figure RE-2: (a) Représentation de l'octaèdre CoO6. Les flèches bleues indiquent la direction de la distorsion D3d impliquant la compression des octaèdres. (b) Représentation de la levée de dégénérescence des orbitales t2g en 2 orbitales eg' et 1 orbitale a1g. Représentation schématique du diagramme de bandes de P2-NaxCoO2 après distorsion D3d. .................................................................... Figure RE-3: Diffractogramme RX de Na0.7CoO2. Points rouges : données expérimentales, trait noir : données affinées, trait bleu : différence entre le profil expérimental et affinée, traits noirs : positions de Bragg. Les zooms ont été réalisés sur la raie (002) et entre 15° et 23° afin de mettre en évidence les pics de surstructure. ......................................................................................................................................... Figure RE-4: Courbe de cyclage galvanostatique à C/20 entre (a) 1.5 et 4.3 V (b) 1.5 V et 4.6 V ............. Figure RE-5: (a) Charge entre 1.5 et 4.6 V (trait noir) et décharge entre 4.3 et 1.5 V (trait rouge) à C/20. Les traits en pointillés indiquent les potentiels cibles pour les synthèses par voie électrochimique des phases NaxCoO2. (b) Evolution du potentiel (en noir) et du courant (en rouge) afin de réaliser la synthèse de Na0.33CoO2 par voie électrochimique.................................................................................................... Figure RE-6: Diffractogrammes enregistrés sur les phases synthétisée par voie électrochimique. Cadre bleu : zoom sur la raie (002). Cadre rouge : zoom sur la zone 30° -55°. * représente le pic dû au graphite présent dans la formulation du matériau d'électrode positif. .................................................................. Figure RE-7: (a) Evolution du paramètre de maille chex en fonction de x. Ces valeurs sont obtenues par affinement de type Le Bail. (b) Evolution des épaisseurs de feuillets en fonction de x. Ces valeurs ont été déterminées par affinement de type Rietveld. ......................................................................................... Figure RE-8: Représentation de la structure de bande des phases NaxCoO2 (a) dans un régime de type « Curie-Weiss métallique » pour x > 0.5 (b) dans un régime métallique pour x < 0.5. ............................. Figure RE-9: Représentation de la modification structurale due aux glissement de feuillets .................. Figure RE-10: Evolution des spectres RMN enregistrés sur les phases synthétisées par voie électrochimique......................................................................................................................................... Figure RE-11: Pour le système NaxCoO2 (a) Evolution de chex et de la distance Na-O en fonction de x. (b) Evolution du nombre formel d'ion Co 4+ paramagnétique en fonction de x. (c) Evolution du déplacement chimique en fonction de x. La nuance de couleur délimite les zones 1, 2 et 3. La ligne en pointillés orange correspond à la transition entre les deux régimes magnétiques. .............................................................Figure RE-12: Pour le système NaxCo2/3Mn1/3O2 (a) Evolution de chex en fonction de x. (b) Evolution du nombre formel d'ion Co 4+ paramagnétique en fonction de x. (c) Evolution du déplacement chimique en fonction de x. La nuance de couleur délimite les zones 1, 2 et 3. La ligne en pointillés orange correspond à la transition entre les deux régimes magnétiques. ................................................................................

Figure RE- 6 :

 6 Figure RE-1: Représentation des structures O3, P2 et P3 et environnements locaux des ions Na + ......... Figure RE-2: (a) Représentation de l'octaèdre CoO6. Les flèches bleues indiquent la direction de la distorsion D3d impliquant la compression des octaèdres. (b) Représentation de la levée de dégénérescence des orbitales t2g en 2 orbitales eg' et 1 orbitale a1g. Représentation schématique du diagramme de bandes de P2-NaxCoO2 après distorsion D3d. .................................................................... Figure RE-3: Diffractogramme RX de Na0.7CoO2. Points rouges : données expérimentales, trait noir : données affinées, trait bleu : différence entre le profil expérimental et affinée, traits noirs : positions de Bragg. Les zooms ont été réalisés sur la raie (002) et entre 15° et 23° afin de mettre en évidence les pics de surstructure. ......................................................................................................................................... Figure RE-4: Courbe de cyclage galvanostatique à C/20 entre (a) 1.5 et 4.3 V (b) 1.5 V et 4.6 V ............. Figure RE-5: (a) Charge entre 1.5 et 4.6 V (trait noir) et décharge entre 4.3 et 1.5 V (trait rouge) à C/20. Les traits en pointillés indiquent les potentiels cibles pour les synthèses par voie électrochimique des phases NaxCoO2. (b) Evolution du potentiel (en noir) et du courant (en rouge) afin de réaliser la synthèse de Na0.33CoO2 par voie électrochimique.................................................................................................... Figure RE-6: Diffractogrammes enregistrés sur les phases synthétisée par voie électrochimique. Cadre bleu : zoom sur la raie (002). Cadre rouge : zoom sur la zone 30° -55°. * représente le pic dû au graphite présent dans la formulation du matériau d'électrode positif. .................................................................. Figure RE-7: (a) Evolution du paramètre de maille chex en fonction de x. Ces valeurs sont obtenues par affinement de type Le Bail. (b) Evolution des épaisseurs de feuillets en fonction de x. Ces valeurs ont été déterminées par affinement de type Rietveld. ......................................................................................... Figure RE-8: Représentation de la structure de bande des phases NaxCoO2 (a) dans un régime de type « Curie-Weiss métallique » pour x > 0.5 (b) dans un régime métallique pour x < 0.5. ............................. Figure RE-9: Représentation de la modification structurale due aux glissement de feuillets .................. Figure RE-10: Evolution des spectres RMN enregistrés sur les phases synthétisées par voie électrochimique......................................................................................................................................... Figure RE-11: Pour le système NaxCoO2 (a) Evolution de chex et de la distance Na-O en fonction de x. (b) Evolution du nombre formel d'ion Co 4+ paramagnétique en fonction de x. (c) Evolution du déplacement chimique en fonction de x. La nuance de couleur délimite les zones 1, 2 et 3. La ligne en pointillés orange correspond à la transition entre les deux régimes magnétiques. .............................................................Figure RE-12: Pour le système NaxCo2/3Mn1/3O2 (a) Evolution de chex en fonction de x. (b) Evolution du nombre formel d'ion Co 4+ paramagnétique en fonction de x. (c) Evolution du déplacement chimique en fonction de x. La nuance de couleur délimite les zones 1, 2 et 3. La ligne en pointillés orange correspond à la transition entre les deux régimes magnétiques. ................................................................................

Figure RE- 11 :

 11 Figure RE-1: Représentation des structures O3, P2 et P3 et environnements locaux des ions Na + ......... Figure RE-2: (a) Représentation de l'octaèdre CoO6. Les flèches bleues indiquent la direction de la distorsion D3d impliquant la compression des octaèdres. (b) Représentation de la levée de dégénérescence des orbitales t2g en 2 orbitales eg' et 1 orbitale a1g. Représentation schématique du diagramme de bandes de P2-NaxCoO2 après distorsion D3d. .................................................................... Figure RE-3: Diffractogramme RX de Na0.7CoO2. Points rouges : données expérimentales, trait noir : données affinées, trait bleu : différence entre le profil expérimental et affinée, traits noirs : positions de Bragg. Les zooms ont été réalisés sur la raie (002) et entre 15° et 23° afin de mettre en évidence les pics de surstructure. ......................................................................................................................................... Figure RE-4: Courbe de cyclage galvanostatique à C/20 entre (a) 1.5 et 4.3 V (b) 1.5 V et 4.6 V ............. Figure RE-5: (a) Charge entre 1.5 et 4.6 V (trait noir) et décharge entre 4.3 et 1.5 V (trait rouge) à C/20. Les traits en pointillés indiquent les potentiels cibles pour les synthèses par voie électrochimique des phases NaxCoO2. (b) Evolution du potentiel (en noir) et du courant (en rouge) afin de réaliser la synthèse de Na0.33CoO2 par voie électrochimique.................................................................................................... Figure RE-6: Diffractogrammes enregistrés sur les phases synthétisée par voie électrochimique. Cadre bleu : zoom sur la raie (002). Cadre rouge : zoom sur la zone 30° -55°. * représente le pic dû au graphite présent dans la formulation du matériau d'électrode positif. .................................................................. Figure RE-7: (a) Evolution du paramètre de maille chex en fonction de x. Ces valeurs sont obtenues par affinement de type Le Bail. (b) Evolution des épaisseurs de feuillets en fonction de x. Ces valeurs ont été déterminées par affinement de type Rietveld. ......................................................................................... Figure RE-8: Représentation de la structure de bande des phases NaxCoO2 (a) dans un régime de type « Curie-Weiss métallique » pour x > 0.5 (b) dans un régime métallique pour x < 0.5. ............................. Figure RE-9: Représentation de la modification structurale due aux glissement de feuillets .................. Figure RE-10: Evolution des spectres RMN enregistrés sur les phases synthétisées par voie électrochimique......................................................................................................................................... Figure RE-11: Pour le système NaxCoO2 (a) Evolution de chex et de la distance Na-O en fonction de x. (b) Evolution du nombre formel d'ion Co 4+ paramagnétique en fonction de x. (c) Evolution du déplacement chimique en fonction de x. La nuance de couleur délimite les zones 1, 2 et 3. La ligne en pointillés orange correspond à la transition entre les deux régimes magnétiques. .............................................................Figure RE-12: Pour le système NaxCo2/3Mn1/3O2 (a) Evolution de chex en fonction de x. (b) Evolution du nombre formel d'ion Co 4+ paramagnétique en fonction de x. (c) Evolution du déplacement chimique en fonction de x. La nuance de couleur délimite les zones 1, 2 et 3. La ligne en pointillés orange correspond à la transition entre les deux régimes magnétiques. ................................................................................

Figure RE- 12 :

 12 Figure RE-1: Représentation des structures O3, P2 et P3 et environnements locaux des ions Na + ......... Figure RE-2: (a) Représentation de l'octaèdre CoO6. Les flèches bleues indiquent la direction de la distorsion D3d impliquant la compression des octaèdres. (b) Représentation de la levée de dégénérescence des orbitales t2g en 2 orbitales eg' et 1 orbitale a1g. Représentation schématique du diagramme de bandes de P2-NaxCoO2 après distorsion D3d. .................................................................... Figure RE-3: Diffractogramme RX de Na0.7CoO2. Points rouges : données expérimentales, trait noir : données affinées, trait bleu : différence entre le profil expérimental et affinée, traits noirs : positions de Bragg. Les zooms ont été réalisés sur la raie (002) et entre 15° et 23° afin de mettre en évidence les pics de surstructure. ......................................................................................................................................... Figure RE-4: Courbe de cyclage galvanostatique à C/20 entre (a) 1.5 et 4.3 V (b) 1.5 V et 4.6 V ............. Figure RE-5: (a) Charge entre 1.5 et 4.6 V (trait noir) et décharge entre 4.3 et 1.5 V (trait rouge) à C/20. Les traits en pointillés indiquent les potentiels cibles pour les synthèses par voie électrochimique des phases NaxCoO2. (b) Evolution du potentiel (en noir) et du courant (en rouge) afin de réaliser la synthèse de Na0.33CoO2 par voie électrochimique.................................................................................................... Figure RE-6: Diffractogrammes enregistrés sur les phases synthétisée par voie électrochimique. Cadre bleu : zoom sur la raie (002). Cadre rouge : zoom sur la zone 30° -55°. * représente le pic dû au graphite présent dans la formulation du matériau d'électrode positif. .................................................................. Figure RE-7: (a) Evolution du paramètre de maille chex en fonction de x. Ces valeurs sont obtenues par affinement de type Le Bail. (b) Evolution des épaisseurs de feuillets en fonction de x. Ces valeurs ont été déterminées par affinement de type Rietveld. ......................................................................................... Figure RE-8: Représentation de la structure de bande des phases NaxCoO2 (a) dans un régime de type « Curie-Weiss métallique » pour x > 0.5 (b) dans un régime métallique pour x < 0.5. ............................. Figure RE-9: Représentation de la modification structurale due aux glissement de feuillets .................. Figure RE-10: Evolution des spectres RMN enregistrés sur les phases synthétisées par voie électrochimique......................................................................................................................................... Figure RE-11: Pour le système NaxCoO2 (a) Evolution de chex et de la distance Na-O en fonction de x. (b) Evolution du nombre formel d'ion Co 4+ paramagnétique en fonction de x. (c) Evolution du déplacement chimique en fonction de x. La nuance de couleur délimite les zones 1, 2 et 3. La ligne en pointillés orange correspond à la transition entre les deux régimes magnétiques. .............................................................Figure RE-12: Pour le système NaxCo2/3Mn1/3O2 (a) Evolution de chex en fonction de x. (b) Evolution du nombre formel d'ion Co 4+ paramagnétique en fonction de x. (c) Evolution du déplacement chimique en fonction de x. La nuance de couleur délimite les zones 1, 2 et 3. La ligne en pointillés orange correspond à la transition entre les deux régimes magnétiques. ................................................................................

Table I -

 I

1 : Usual space groups and atomic positions for the O3, P3 and P2 structures.

Table I -

 I

	6 Li	1	-0.083	7.6	44.17
	7 Li	3/2	-4.01	92.4	116.6
	23 Na	3/2	10.40	100	79.39

2: NMR properties of

Table II

 II

	-1 : Comparison of the crystallographic data and precursors used for the syntheses of the
	different OP4 phases reported in the literature.

Ref Chemical formula Space group a hex (Å) c hex (Å) Precursors

	All the proposed chemical formulas are slightly different from the ideal Li0.5Na0.35CoO2 one, but
	the presence of traces of O3-LiCoO2 and P2-Na0.7CoO2 may alter the composition that was
	determined by Inductively Coupled Plasma (ICP) measurements. An air quench is also used in
	some publications whereas others used a slow cooling. Berthelot et al. 44 , for the first time, studied
	the formation of the OP4-(Li,Na)CoO2 phase by in-situ variable temperature XRD: the phase is
	formed at around 855°C but decomposes into O3-LiCoO2 and P2-Na0.7CoO2 if slowly cooled. The
	lattice parameters are relatively close in each publication, although different space groups are used:
	P63mc or P63/mmc that only differ by one symmetry operation. In this manuscript, the P63/mmc
	41 space group was used in fact, the two positions of the oxygen ions (labelled OLi and ONa on Figure Li 0.43 Na 0.36 CoO 1.96 P6 3 mc 2.839(4) 20.36(3) P2-Na 0.7 CoO 2 + O3-LiCoO
	II-1) can be adjusted in order to refine the eventual slight dissymmetry of the Co ions in their
	78 octahedra. Moreover, a structure labelled OPP9-(Li,Na,Na)CoO2 was evidenced (Figure II-3) as Li 0.48 Na 0.35 CoO 2 P6 3 /mmc 2.824 20.293 Na 2 CO 3 + Li 2 CO 3 + Co 3 O 4
	competitor of OP4-(Li,Na)CoO2 formation by varying the ratios between the O3-LiCoO2 and P2-
	79 Na0.7CoO2 precursors Li 0.41 Na 0.31 CoO 2	P6 3 mc	2.8266(3)	20.265(2) Na 2 CO 3 + Li 2 CO 3 + Co 3 O 4
	80	Li 0.42 Na 0.36 CoO 2	P6 3 mc	2.839(4)	20.36(3)	Na 2 CO 3 + Li 2 CO 3 + Co 3 O 4
	44	Li 0.42 Na 0.37 CoO 2	P6 3 /mmc	2.8301(2)	20.286(2) P2-Na 0.7 CoO 2 + O3-LiCoO
	81	Li 0.48 Na 0.35 CoO 2	P6 3 mc	2.821(3)	20.163(2) P2-Na 0.7 CoO 2 + O3-LiCoO
	82	Li 0.42 Na 0.36 CoO 2	P6 3 mc	2.831	20.26	P2-Na 0.7 CoO 2 + O3-LiCoO
	83	Li 0.37 Na 0.31 CoO 2	P6 3 /mmc	2.8208(2)	20.277(1) Na 2 CO 3 + Li 2 CO 3 + Co 3 O 4

Table II-2. Initial alkaline content for LixNayCoO2 x y

	The powders were then pressed into pellets under a controlled argon atmosphere and were heated
	in a furnace under air at 870 °C for 48 h with a 2°C/min heating rate. After the heat treatment, all
	the pellets were rapidly quenched to room temperature and entered in the Ar-filled glovebox. The
	expected reaction for the Li0.42Na0.38CoO2 synthesis in stoichiometric proportions is:
	0.21 𝐿𝑖 2 𝐶𝑂 3 + 0.19 𝑁𝑎 2 𝐶𝑂 3 +	1 3	𝐶𝑜 3 𝑂 4 → 𝐿𝑖 0.42 𝑁𝑎 0.38 𝐶𝑜𝑂 2 + 𝑦 𝐶𝑂 2
	Co3O4, or O3-LiCoO2 and P2-𝑁𝑎 ~0.7 CoO2 as precursors. As less impurities were observed by XRD
	in the first case, we report only syntheses carried on using Li2CO3 (Sigma-Aldrich, 99.9%, dried at
	350°C), Na2CO3 (Sigma Aldrich, 99.9%, dried at 200°C) and Co3O4 (home-made from cobalt
	nitrate, heat treated under air at 450°C). Those precursors were initially mixed and ground together
	in a Ar-filled glovebox targeting slightly different chemical compositions around Li0.42Na0.38CoO2
	in order to compensate possible alkaline ion loss by evaporation 44 . The initial alkali compositions
	are summarized in Sample C		0.42	0.40
	Sample B		0.42	0.41
	Sample A		0.44	0.38
	Table II-2: Initial alkaline compositions of the three samples A, B and C

Signal 4 (-83.6 ppm)

	Sample C	47%	19%	12%	22%
	Sample B	52%	18%	11%	19%
	Sample A	41%	19%	18%	22%
	Table II-4 : Repartition of the fitted areas of each Li + signal for the three studied samples. The
	signal 5 was neglected because of its low intensity.

Table II -

 II For each measurement, 16 mixing times were applied.

	RT	310 K	320 K / 340 K
	50 ns	50 ns	50 ns
	1 ms	10 ms	10 ms
	5 ms	50 ms	50 ms
	10 ms	100 ms	100 ms
	15 ms	150 ms	150 ms
	25 ms	200 ms	200 ms
	50 ms	250 ms	250 ms
	75 ms	300 ms	300 ms
	100 ms	350 ms	350 ms
	200 ms	400 ms	400 ms
	300 ms	500 ms	500 ms
	400 ms	750 ms	750 ms
	500 ms	1 s	1 s
	1 s	5 s	4 s
	5 s	10 s	5 s
	10 s	15 s	6 s

[START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF]

Li MAS NMR inversion-recovery was performed on a probe for 1.3 mm-diameter zirconia rotors (spinning frequency = 65 kHz) with a 7.05 T magnet at McMaster University, Canada. The measurements were performed on the sample B with different mixing times depending of the temperature (Table

II

-6). 6 : 𝜏 𝑚 delays used at the different temperatures for 7 Li MAS NMR inversion recovery Only the intensities as a function of 𝜏 𝑚 delays at RT are plotted in this manuscript (Figure II-19).

  The O2-LiCoO2 polytype is characterized by LiO6 octahedra sharing edges with three adjacent CoO6 octahedra of one CoO2 slab and an adjacent face with a CoO6 octahedra of the opposite CoO2 slab.The oxygen stacking is AB-CB and the phase crystallizes in the P63mc space group. The thickness of one CoO2 and one LiO2 slabs is slightly higher than for O3-LiCoO2 because the Li + -Co 3+

(Figure III-1).

  2,102 . An O6 polytype was introduced by Mendiboure et al. 103 . It is formed during the O2-LixCoO2 Li + deintercalation 103,104 . Another polytype was reported by Paulsen et al. 101 . Thereafter, this stacking was labelled T # 2

Table III - 1 :

 III1 -1. The Li + /Na + ratio corresponds to the molar amount of Li + ions in the LiCl solution over the molar amount of Na + ions present in the OP4 structure. After the reflux, the powders were Synthesis conditions of the two O4-LiCoO2 sample(EIE and SIE)

		Chapter III
	3. Average structures and chemical compositions characterization
	3.1 OP4 enriched with 6 Li phase XRD pattern
	XRD was performed on the PANalytical X'Pert Pro diffractometer equipped with a Co anticathode
	from 12° to 90°. The Le Bail method was used to refine the XRD pattern.
		Temperature	Reflux duration	Li	+ /Na + ratio
	EIE sample	105 °C	4 h		20
	SIE sample	105 °C	4 h		1
			95

cooled, washed in distilled water and filtered under vacuum many times. The powders were finally dried for 12 h at 110 °C. The two synthetized samples are labelled EIE (for Excess Ion-Exchange) and SIE (for Stoichiometric Ion-Exchange) and their synthesis conditions only differ from the use of different Li + /Na + ratio. The expected structure after ion-exchange is represented on Figure III-4.

Table IV -2). Na x Mn 1-y Co y O 2 material

 IV

		E range	Capacity (mA.h.g -1 )	C-rate	Capacity retention	Electrolyte	Ref
	P2-Na x Mn 0.89 Co 0.11 O 1.5 -3.8 V	138	C/3	67 % (20 cycles)	NaClO 4 in PC	119
	P2-Na x Mn 1/2 Co 1/2 O 2	1.5 -4 V	123	C/8	69 % (30 cycles)	NaClO 4 in PC	120
	P2-Na x Mn 0.3 Co 0.7 O 2	2.0 -3.8 V	60	C/2	87 % (60 cycles)	EC/DEC NaClO 4 in	121
	P2-Na x Co 0.1 Mn 0.9 O 2	1.5 -3.8 V	160	C/3	68 % (150 cycles)	PC/EC NaClO 4 in	4
	P2-Na x Mn 0.25 Co 0.75 O 1.5 -4.2 V	120	C/10	87 % (100 cycles)	NaPF 6 in PC/EC	122
	P2-Na x Mn 1/2 Co 1/2 O 2	1.5 -4.2 V	140	C/10	85 % (100 cycles)	NaPF 6 in PC/EC	122
	P2-NaxMn 0.75 Co 0.25 O 1.5 -4.2 V	160	C/10	78% (100 cycles)	NaPF6 in PC/EC	122
	P2-NaxMn0.2Co0.802	2.0 -4.0 V	80	C/20	?	NaClO 4 in PC	123
	P2-NaxMn0.3Co0.7O2	2.0 -4.0 V	85	C/20	?	NaClO 4 in PC	123
	P2-NaxMn0.6Co0.4O2	2.0 -4.0 V	70	C/20	?	NaClO 4 in PC	123

Table IV - 4 :

 IV4 Lattice parameters calculated by Le Bail refinements for each pristine phase. The exact Na + composition

	Chapter IV
	Space group : P6 3 /mmc	a hex (Å)	c hex(Å)
	𝑵𝒂 ~𝟎.𝟕 𝑪𝒐𝑶 𝟐	2.8363(2)	10.876(1)
	𝑵𝒂 ~𝟐/𝟑 𝑪𝒐 𝟐/𝟑 𝑴𝒏 𝟏/𝟑 𝑶 𝟐	2.8304(2)	11.052(3)
	𝑵𝒂 ~𝟎.𝟔 𝑪𝒐 𝟏/𝟐 𝑴𝒏 𝟏/𝟐 𝑶 𝟐	2.8291(1)	11.203(2)
	𝑵𝒂 ~𝟎.𝟔 𝑪𝒐 𝟏/𝟑 𝑴𝒏 𝟐/𝟑 𝑶 𝟐	2.8467(3)	11.304(4)
	125

Na x CoO 2 Na x Co 2/3 Mn 1/3 O 2 Na x Co 1/2 Mn 1/2 O 2 Na x Co 1/3 Mn 2/3 O 2

	Studied voltage range	1.5 V -4.6 V	1.25 V -4.5 V	1.25 V -4.5 V	1.25 V -4.5 V
	Minimal a hex (Å)	2.810(1)	2.818(1)	2.822(1)	2.828(1)
	Maximal c hex (Å)	11.20(1)	11.30(1)	11.33(1)	11.35(1)
	Maximal c hex
	value reached	0.4	0.4	0.4	0.4
	for x ≈
	Maximal c hex
	value reached
	for

-4

). In Figure IV-23, the evolution of the chex lattice parameters is plotted as a function of x for the four systems. Concerning the Co,Mn phases, the evolution of chex confirms the presence a solid solution behavior while for NaxCoO2, many breaks in the Vegard law can be observed due to the presence of different kinds of domains. Moreover, the NaxCoO2, NaxCo1/2Mn1/2O2 and NaxCo1/3Mn2/3O2 XRD patterns don't exhibit any obvious sheets glidings during the operando measurements even at high voltage. However, for NaxCo2/3Mn1/3O2, the additional peak observed at 9.2° shows that sheets glidings occur for x ≈ 0.2.

Table V -

 V

		𝒂 𝒉𝒆𝒙 (Å)	𝒄 𝒉𝒆𝒙 (Å)
	Na 0.82 CoO 2	2.845(1)	10.90(1)
	Na 0.33 CoO 2	2.809(1)	11.20(1)
	Na 0.67 Co 2/3 Mn 1/3 O 2	2.829(1)	11.05(1)
	Na 0.33 Co 2/3 Mn 1/3 O 2	2.817(1)	11.29(1)

2: Lattice parameters of the P2-phases synthetized at the lowest and highest voltages for the two systems. The lattice parameters of the other phases are plotted on Figure V-10.

Table V -4: Repartition

 V

		Na e	Na f
	0.82	-	-
	0.67	0.44(1)	0.23(1)
	0.55	0.34(1)	0.23(1)
	0.50	0.27(1)	0.23(1)
	0.40	0.24(1)	0.16(1)
	0.35	0.31(1)	0.04(1)
	0.33	0.31(1)	0.02(1)

of the Na + ions in the interslab spaces between both intercalation sites for the P2-NaxCoO2 phases

Table V -

 V

	x	𝜣(°)
	0.67	59.3(1)
	0.55	59.3(1)
	0.50	60.1(1)
	0.40	60.1(1)
	0.35	60.3(1)
	0.33	60.5(1)

Table V-5 summarizes the

θ values calculated in our phases. As expected, the θ value increases with decreasing x involving that the octahedra are flattened during the Na + deintercalation involving the expected increase of the a1g band. 5: Evolution of the 𝜃 angle in the different P2-NaxCoO2 phases

  En effet, des pics caractéristiques de cette structure ne sont plus visibles sur le diffractogramme alors que d'autres sont élargis et asymétriques. Par exemple la raie (002) est élargie et décalée vers les plus grands angles en accord avec la présence de glissement de feuillets. Ce phénomène peut s'expliquer par la présence des répulsions O-O devenues trop importantes pour stabiliser uniquement des feuillets de type P 128,130 .

	Certains feuillets glissent alors afin de stabiliser la les ions oxygènes menant à la présence de
	feuillets de type O (octaédrique) (Figure RE-9). Cependant, l'allure du diffractogramme suggère
	que l'alternance entre les feuillets de type O et P n'est pas régulière et semble aléatoire. C'est pour

Enfin, le diffractogramme enregistré sur la phase synthétisée à 4.6 V vs Na + /Na souligne que la structure du matériau Na0.25CoO2 est désordonnée et n'est plus de P2 puisque le diffractogramme ne peut pas être affiné dans le groupe d'espace P63/mmc. cela que par la suite de ce résumé, cette phase est nommée « OP ». A noter que ces glissements de feuillets ont déjà été mise en évidence sur d'autres systèmes par d'autres groupes de recherche sur des matériaux différents

128,140

.

  Ce travail de thèse a montré que la RMN du solide est une technique de caractérisation puissance et est complémentaire à la DRX. La RMN permet l'étude des structures électronique et locale des matériaux mais également d'étudier les modifications structurales lors de cyclage électrochimique. Concernant la structure locale des matériaux la RMN informe sur le nombre pour les ions Na + ou Li + , les environnements locaux de ces derniers ou encore les distances et angles des liaisons M-O-A. Concernant la structure électronique, la RMN permet de renseigner sur les régimes magnétiques des phases étudiées et par

	Les études des phases OP4-(Li,Na)CoO2 et O4-LiCoO2 (non présentés dans ce résumé étendu) ont
	également permis de montrer l'intérêt de la RMN pour l'étude de la mobilité ionique au sein des
	matériaux.
	Concernant les systèmes NaxCoO2 et NaxCo2/3Mn1/3O2, la RMN et la DRX ont permis de mettre en
	évidence la formation d'une phase fautée à haut potentiel en raison de glissement de feuillets pour
	des matériaux ayant un faible taux de Na conséquent sur la présence d'électrons localisés et/ou délocalisés. Enfin, l'étude de la mobilité
	ionique peut renseigner sur les constantes de vitesse k ou encore les énergies d'activation si les
	mesures sont réalisées à différentes températures.

+ dans les espaces interfeuillets. Les différentes phases ont été obtenues par voie électrochimique. Cette étude confirme également la véracité de cette technique pour l'étude de l'influence du taux de N + dans les matériaux. La RMN a mis en évidence un comportement complexe du système puisque le déplacement chimique évolue d'une manière inattendue, en effet, il croît d'abord, puis décroît fortement avant de devenir presque constant. Cette évolution dépend si le facteur géométrique (représenté par l'évolution des distances Na-O) ou électronique (représenté par le quantité d'ion Co 4+ au sein du matériau) est prédominant dans le régime magnétique de type Curie-Weiss métallique. Dans le régime métallique, le déplacement chimique reste quasiment constant signifiant que la participation des orbitales 3s Na est constante.

Pour conclure la RMN nous a permis, de suivre l'évolution de différents paramètres pendant la charge des deux systèmes cités précédemment comme la mobilité ionique, l'asymétrie des sites, les contributions quadripolaires ou encore les déplacements chimiques.

  [START_REF] Takeda | Sodium deintercalation from sodium iron oxide[END_REF] . ....................................................................................................... Representation of the hexagonal, monoclinic and rhombohedral cells from the O3 structure. The equations introduced before allow to switch from one cell to another. ............................................. Representation of the O3, P2 and P3 structures and representation of the corresponding Na + intercalation sites ........................................................................................................................................

	Figure I-2: Figure I-3:

Figure I-4 : Representation of the 3d orbitals in an octahedral environment. The dz² and dx²-y² orbitals point to the ligands while the dxy orbitals point between the O ligands. dxy and dxz are not represented but are symmetrically equivalent to dxy ......................................................................................................

  I-17 : Representation of the rotors in the NMR probe at the Magic Angle for MAS experiments. The picture is extracted from 61 . ................................................................................................................. Figure I-18: Representation of the Fermi contact shift for a 90° interaction between a half-filled t2g orbital of a M ion and a Na nucleus via an 2p orbital of the oxygen ion. ............................................................... Figure I-19 : Repartition of the quadrupolar moments created for I > 1/2 spin ........................................ Energy level diagram for the I = 3/2 nuclei after application of a magnetic field. Extracted from 66 . ........................................................................................................................................................ Figure I-21 : Recording of the FID and Fourier transformation for a simple pulse sequence.....................Figure I-22 : Hahn Echo sequence ............................................................................................................... Figure I-23: Basic form of a 2D exchange experiment. Both pulses are 90°. Excitation label corresponds to the first pulse to transverse magnetization in (x,y) plane. Second pulse allows to restore the magnetization along 𝐵0 direction. Third pulse reconverts the magnetization in (x,y) plane. Extracted from 61 . ........................................................................................................................................................ Figure I-24 : Schematic representation of a 2D EXSY spectrum. 𝛺 represents the peaks frequency. Extracted from 61 . ........................................................................................................................................ : Perspective representation of OP4-(Li/Na)CoO2. Na + ions occupy prismatic sites which can either share faces (Naf, in red) or edges (Nae, in purple) with the surrounding CoO6 octahedra (in blue). Comparison of the 7 Li MAS NMR spectra recorded on the sample C at two different magnetic fields (2.35 and 7.05 T) using the same spinning frequency (30 kHz) with a Hahn Echo sequence. Insert: Zoom in order to highlight the presence of the signal at -203 ppm. .......................................................... Figure II-8 : Experimental 7 Li MAS NMR spectra of the samples A, B and C (2.35 T magnet, spinning frequency = 30 kHz, Hahn echo sequence). ................................................................................................

	Figure I-20: Figure II-1

The Li + ions occupy octahedral sites (in yellow). The oxygen ions positions are labelled with the letters A, B and C. ........................................................................................................................................................

Figure II-2 : SEM pictures of the sample A at different magnifications. Dashed lines represent the hexagonal shape of a OP4 crystal. ............................................................................................................... Figure II-3 : Representation of the different structures introduced in this chapter. .................................. Figure II-4 : Experimental XRD patterns of the samples A, B and C plotted as a function of the d spacing. Insert: Zoom in the 5.75 Å-4.50 Å region in order to focus on the impurities peaks. * are the Al peaks due to the sample holder used for the XRD acquisition. ................................................................................... Figure II-5: Electrical conductivity of an OP4 phase as a function of the temperature (from 6K to 300 K). ..................................................................................................................................................................... Figure II-6: Magnetic susceptibility and inverse magnetic susceptibility (in the insert) of the sample A as a function of the temperature (6 K to 300 K) realized under a 1T magnetic field. ........................................ Figure II-7 :

  -3 e -/A² isosurface value. a1g orbital is mainly carrying the spins. The yellow color represents the positive spin density. ..................................... Figure II-14: Band structure of the Co 3+ ions in the case of NaxCoO2 (a) before and (b) after the octahedra distortion. .................................................................................................................................................... Figure II-15 : Experimental 7 Li MAS NMR spectra recorded on a 7.05 T magnet at different temperatures in the 265 K -450 K. The NMR sequences were Hahn echoes and the spinning frequency was 13 kHz. ..

Figure IV-21: XRD patterns obtained by operando measurements on NaxCo1/2Mn1/2O2 system on first charge from 1.25 V to 4.5 V at C/10.

Figure IV-22: XRD patterns obtained by operando measurements on NaxCo1/3Mn2/3O2 system on first charge from 1.25 V to 4.5 V at C/10.

Remerciements

displays the XRD patterns obtained operando. As expected, the chex lattice parameters globally increases until a limit value reached for x ≈ 0.4 (11.35(1) Å). The (004) peak evolution suggests that this system has a solid solution behavior during all the charge. The presence of many contributions on the XRD patterns suggests an important heterogeneity as observed on the previously studied Co,Mn systems. This heterogeneity can be observed in the 0.71 < x < 0.36 range.

For x < 0.36, a well-defined (004) peak is visible on the XRD patterns, probably to the appearance of Co 4+ ions. As expected, regarding the galvanostatic charge, no superstructure peak appears during the charge on any pattern.

Chapter V: 23 for Na in Na2 (site 2d) and Na3 (site 4h) [START_REF] Mortemard De Boisse | Coulombic self-ordering upon charging a large capacity layered cathode material for rechargeable batteries[END_REF] . By releasing all the parameters (Figure VI-4c), we obtained the expected two for one proportion between Na3 and Na2. However, the signals have different widths (40 and 77 ppm) and different Gaussian/Lorentzian proportions (0.72 for the less shifted signal and 0.67 for the other) which is surprising for Na nucleus in really similar environments. Consequently, this slight asymmetry could be due to some different Na environments because of the stacking faults. The 750 ppm one may also be assigned to the presence of some stacking faults evidenced in this material that may modify slightly locally the bond distances and angles [START_REF] Mortemard De Boisse | Coulombic self-ordering upon charging a large capacity layered cathode material for rechargeable batteries[END_REF] . be also interesting to be investigated in order to understand the mechanisms involved even if the polarization is weaker than in the case of NaxCoO2.

As just mentioned, the mechanisms involved during the Na + deintercalation were studied in the P2-NaxCoO2 and P2-NaxCo2/3Mn1/3O2 systems. For each system, the formation of intermediate phases was identified. They were thus synthesized by electrochemical deintercalation at specific voltages. in order to be analyzed ex-situ by XRD and 23 Na MAS NMR. Rietveld refinements of the XRD patterns showed that the Na layers' thickness increases during the battery charge for P2-NaxCoO2 until reaching a limit value for x = 0.4. 23 Na MAS NMR exhibited a complex behavior for both systems during the Na + deintercalation in fact, the shift values first increase and then decrease before reaching an almost constant value for the lower x values. It is, therefore, impossible to only consider the Co 3+ (t2g 6 eg 0 ) ions oxidation into paramagnetic Co 4+ ions (t2g 5 eg 0 ) to explain the shift evolution, two effects have to be considered: the evolution of the structure geometry (increase of the Na-O distance when x decreases) and the evolution of the electronic structure (increase of the amount of formal Co 4+ ions when x decreases). We showed that both effects are consecutively predominant when the Na + content in both systems decreases and we highlighted the presence of a "Curie-Weiss metallic regime" for x > 0.5 with localized and delocalized electrons. Finally, for the lowest x values (x < 0.5), the presence of only delocalized electrons (Pauli paramagnetic regime) in the electronic structure of P2-NaxCoO2 and the constant NMR shift suggest that the participation of the Na 3s orbital to the Knight shift is almost constant. For P2-NaxCo2/3Mn1/3O2, the evolution of the NMR shift is due to a "Knight shift" with an additional constant participation of the localized electrons of the Mn 4+ (t2g 3 eg 0 ) ions for the lowest x compositions. It should be interesting to study both NaxCo1/2Mn1/2O2 and NaxCo1/3Mn2/3O2 systems in the same vein in order to confirm the presence of a magnetic transition occurring for x < 0.5 in the Co,Mn systems. Concerning the "OP" phases resulting from sheets glidings and obtained at high voltage, 23 Na MAS NMR confirmed the presence of a panel of different environments for both systems.

In the last chapter, O3-NaxRuO3 was instigated by ex-situ 23 The most intense diffraction peaks are those indexed with the P63/mmc space group, only the superstructure peaks allow to determine the superstructure lattice for the peculiar phase. Platova et al. [START_REF] Platova | Nuclear quadrupole resonance and X-ray investigation of the structure of Na2/3CoO2[END_REF] suggests a cationic order in an orthorhombic cell with the R3 ̅ c space group and cell parameters bigger than in the corresponding hexagonal cell (√12𝑎 ℎ𝑒𝑥 x √12𝑎 ℎ𝑒𝑥 x 3𝑐 ℎ𝑒𝑥 ). Berthelot et al. [START_REF] Berthelot | Electrochemical investigation of the P2-NaxCoO2 phase diagram[END_REF] managed to index each peak with the cell described by Platova et al. We will only check if a Le Bail refinement is possible with the patterns obtained during the operando measurements (Figure A-1). Note that peaks impurities (Na, Al or graphite) were manually removed from the XRD pattern for the refinements. The lattice parameters (as = 9.797(1) Å and cs = 32.81(1) Å) calculated are in good agreement with those determined by theoretically by Platova et al. [START_REF] Platova | Nuclear quadrupole resonance and X-ray investigation of the structure of Na2/3CoO2[END_REF] and experimentally by Berthelot et al. [START_REF] Berthelot | Electrochemical investigation of the P2-NaxCoO2 phase diagram[END_REF] .

A.2 Na1/2CoO2

The XRD pattern is shown in Figure A-2 and most of the peaks are the same than for the P2 structure phase with the P63/mmc space group. Additional peaks appear (in insert) and can be refined in an orthorhombic cell as proposed by Huang et al. [START_REF] Huang | Low temperature phase transitions and crystal structure of Na0. 5CoO2[END_REF] with an order (√3𝑎 ℎ𝑒𝑥 x 2𝑎 ℎ𝑒𝑥 x 𝑐 ℎ𝑒𝑥 ) in the Na interslab spaces. This phase, as Na2/3CoO2, was already refined by Berthelot et al. in the Pnmm space group. In this manuscript, calculated lattice parameters are as = 4.865(1) Å, bs = 5.626(1) Å and cs = 11.12(1) Å, in good agreement with those determined in former studies. A.5 First discharge on the NaxCo2/3Mn1/3O2 system

A.4 First discharge on the NaxCoO2 system

Table IV-1:

The peculiar phases already reported on the NaxCoO2 system for x ≥ 0.5 with the associated voltages of formation, space groups and superlattices ..

Table V-1: NMR parameters of both pristine phases calculated by two fits on the spectra shown in

Titre : Étude de la structure, structure électronique et de la dynamique dans des oxydes lamellaires pour batteries Na-ion

Résumé : Les oxydes lamellaires de type AxMO2 (A = alcalin, M = métal de transition) sont largement étudiés comme matériaux d'électrode positive dans des batteries Li-ion ou Na-ion. Par ailleurs, ils peuvent présenter également de propriétés physiques originales. Une première partie de ce travail de thèse vise à étudier par RMN du 23 Na et [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li, la structure moyenne, locale et électronique ainsi que la mobilité des ions Li + dans les espaces interfeuillets de deux oxydes lamellaires originaux : OP4-(Li,Na)CoO2 et O4-LixCoO2. Des mesures en température ont mis en évidence la présence à la fois d'électrons localisés et délocalisés au sein de la structure. De plus, La RMN 2D du [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li a montré l'absence de mobilité des ions Li + dans la phase OP4 à cause d'interfeuillets partiellement remplis d'ions Na + . Concernant la phase O4, une mobilité des ions Li + au sein de la structure est mise en évidence. P2-NaxCoO2 est un matériau modèle comme matériau d'électrode positive pour batteries Na-ion. Lors de cette thèse, les diagrammes de phase de P2-NaxCoO2 ainsi que de trois autres systèmes P2-NaxCoyMn1-yO2 (y = 1/3, 1/2 et 2/3) ont été étudiés par DRX in-situ, avec une attention particulière sur les phénomènes se déroulant à hauts potentiels (> 4.3 V vs Na + /Na). De nombreux changements structuraux sont reportés et des sur-structures inédites ont été observées. Par la suite, des glissements de feuillets ont été mis en évidence pour des compositions en Na + inférieures à 1/3 à la fois par DRX in-situ et ex-situ. Enfin, des phases des systèmes NaxCoO2, NaxCo2/3Mn1/3O2 et O3-NaxRuO3 avec différentes teneurs en ions Na + ont été stabilisées et analysées ex-situ par DRX et RMN du 23 Na afin de comprendre les mécanismes se produisant lors de la charge et la décharge de ces matériaux d'électrode. La RMN a permis de suivre les processus redox et les modifications parfois complexe, des liaisons chimiques.

Mots clés : RMN, batteries Na-ion, structure, dynamique, structure électronique Title: Structure, electronic structure and dynamics in layered transition metal oxides for Na-ion batteries Abstract: The lamellar oxides AxMO2 (A = alkali ions, M = transition metal) are largely studied as positive electrode materials for Li-ion or Na-ion batteries. They can also propose interesting and none-common physical properties. The first part of this work concerns the study of the average, local and electronic structure besides the Li + ions mobility in the interslab spaces of two unusual phases: OP4-(Li,Na)CoO2 et O4-LixCoO2 by [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li and 23 Na MAS NMR. Concerning the OP4 phase, variable temperature measurements highlight the presence of localized and delocalized electrons in the structure. Moreover, [START_REF] Lei | Synthesis and Stoichiometry of Different Layered Sodium Cobalt Oxides[END_REF] Li 2D NMR suggests that the Li + ions are not mobile in the structure because of a partial filling of interslabs by Na + ions while in the O4 phase, a mobility of Li + ions can be observed. P2-NaxCoO2 is a model material as positive electrode material for Na-ion batteries. In this work, the phase diagrams of this system and of three others systems P2-NaxCoyMn1-yO2 (y = 1/3, 1/2 and 2/3) were studied by in-situ XRD with a specific attention to the phenomena occurring at high voltages (> 4.3 V vs Na + /Na). Many structural changes are reported and new super-structures are shown. Layers' glidings were also highlighted for compositions in Na + ions below 1/3 by in-situ and ex-situ XRD. Finally, phases of NaxCoO2, NaxCo2/3Mn1/3O2 and O3-NaxRuO3 with various x values were stabilized and analyzed ex-situ by XRD and 23 Na NMR in order to understand the mechanisms occurring during the charge and the discharge of these electrode materials. NMR shows a complex behavior of the different systems et especially a modification in the chemical bonds nature.

Keywords : NMR, Na-ion batteries, structure, dynamics, electronic structure Unité de recherche ICMCB, UMR 5026, 87 Avenue du Dr Albert Schweitzer, 33600 Pessac