Biao Li

Gaurav Assat

Paul Pearce

Victoria Nikitina

Antonella Iadecola

Charles Delacourt

Jean-Marie Tarascon
email: jean-marie.tarascon@college-de-france.fr

Exploring the Kinetic Limitations Causing Unusual Low-Voltage Li Reinsertion in either Layered or Tri-Dimensional Li2IrO3 Cathode Materials

The and -Li2IrO3 polymorphs were recently studied in view of their anionic redox capabilities that were triggered by full Li removal. Herein, we solely focused on the reacting mechanism involved during the first reversible Li removal (Li2IrO3 LiIrO3). We found that the charge and discharge processes show significant deviations from the equilibrium potential, with especially the appearance of a peculiar low-voltage feature during discharge with increasing the discharge current. Through detailed electrochemical experiments, such as rate dependence and relaxation, we show that this feature is associated to a kinetically limited phase transition behavior. Moreover, we demonstrated that the large voltage hysteresis pertaining to the removal and uptake of one Li from Li2IrO3 is nested in the different way that the biphasic transition proceeds between charge and discharge, as deduced by operando X-ray diffraction. Additionally, electroanalytical measurements coupled with scanning electron microscopy unveils that the sluggish biphasic transition is rooted in the slow diffusion of Li + ion together with the existence of high nucleation barrier of the biphasic reaction. Lastly, the similarities and differences between the kinetics limitations in both Li2IrO3 polymorphs are then discussed with respect to similar type of limitations occasionally encountered in conventional layered oxides and other cathodes. Voltage (V) d C/25 Voltage (V) e C/10 Voltage (V) f C/5 Voltage (V) dQ/dV g C/2.5 Voltage (V) h 1C Voltage (V) * * Voltage vs Li (V) Capacity (mAh g -1 ) a Voltage (V) Time (h) Time (h) Voltage (V) Ratio Cutoff SoC

Introduction

Li-ion batteries have become about four-times cheaper over the last decade and can now store up to three-times more energy within the same size (volume), hence the reason why we have witnessed the transfer of know-how from the portable electronic sector to the sectors of transportation and stationary storage. However, the long lasting success of Li-ion batteries will depend on whether we can continue to improve their energy density while lowering their cost and enhancing their sustainability. Li-rich Mn-based layered oxide cathodes, e.g. Li1.2Ni0.13Mn0.54Co0.13O2 (Li-rich NMC) that is an archetypical composition, have been demonstrated to hold the highest promise regarding practical energy density at the cell level. [START_REF] Thackeray | Li2MnO3-stabilized LiMO2 (M = Mn, Ni, Co) electrodes for lithium-ion batteries[END_REF][START_REF] Rozier | Review-Li-Rich Layered Oxide Cathodes for Next-Generation Li-Ion Batteries: Chances and Challenges[END_REF] Indeed, it was shown that such Li-rich NMC phases can deliver capacities reaching 300 mA h g - 1 , as compared to 200 mA h g -1 for classical Li-stoichiometric NMC materials. [START_REF] Zheng | Li-and Mn-Rich Cathode Materials: Challenges to Commercialization[END_REF][START_REF] Yu | High-Energy Cathode Materials (Li2MnO3-LiMO2) for Lithium-Ion Batteries[END_REF] Such an enhanced capacity was demonstrated to be nested in combined anionic and cationic redox processes [START_REF] Koga | Reversible Oxygen Participation to the Redox Processes Revealed for Li1.20Mn0.54Co0.13Ni0.13O2[END_REF][START_REF] Luo | Charge-compensation in 3d-transition-metal-oxide intercalation cathodes through the generation of localized electron holes on oxygen[END_REF] a new paradigm now worldwide studied to design high capacity electrode materials. [START_REF] Yabuuchi | High-capacity electrode materials for rechargeable lithium batteries: Li3NbO4-based system with cation-disordered rocksalt structure[END_REF][START_REF] Seo | The structural and chemical origin of the oxygen redox activity in layered and cation-disordered Li-excess cathode materials[END_REF][START_REF] Zhan | Enabling the high capacity of lithium-rich anti-fluorite lithium iron oxide by simultaneous anionic and cationic redox[END_REF][START_REF] Maitra | Oxygen redox chemistry without excess alkali-metal ions in Na2/3[Mg0.28Mn0.72]O2[END_REF][START_REF] Li | Thermodynamic Activation of Charge Transfer in Anionic Redox Process for Li-Ion Batteries[END_REF] Despite the promise of large capacity, unfortunately, a decade-long research effort in commercializing Li-rich NMC cathodes (Li1.2Ni0.13Mn0.54Co0.13O2) has remained unsuccessful. This is because the extra capacity comes with undesirable practical drawbacks, such as voltage fade, voltage hysteresis leading to low round-trip energy efficiency and thermal dissipation, and poor rate capability. [START_REF] Erickson | Review-Recent Advances and Remaining Challenges for Lithium Ion Battery Cathodes[END_REF][START_REF] Assat | Editors' Choice-Practical Assessment of Anionic Redox in Li-Rich Layered Oxide Cathodes: A Mixed Blessing for High Energy Li-Ion Batteries[END_REF][START_REF] Li | Anionic Redox in Rechargeable Lithium Batteries[END_REF] Strategies for mitigation of these issues have early on targeted their fundamental origins, but this turns out to be quite difficult using Li-rich NMC since it is complicated by interweaved electrochemical activity of three transition metals (TMs) and oxygen. [START_REF] Assat | Fundamental interplay between anionic/cationic redox governing the kinetics and thermodynamics of lithiumrich cathodes[END_REF] Aware of the aforementioned complexity, our group designed simplified (or 'model') Li-rich layered oxide based on the solid solution Li2M1-xM'xO3 (M= Ru, M'=Sn, Mn, Ti) within which the cationic and anionic redox processes were nicely decoupled. [START_REF] Sathiya | High Performance Li2Ru1-yMnyO3(0.2 ≤y≤ 0.8) Cathode Materials for Rechargeable Lithium-Ion Batteries: Their Understanding[END_REF][START_REF] Sathiya | Reversible anionic redox chemistry in high-capacity layered-oxide electrodes[END_REF][START_REF] Sathiya | Origin of voltage decay in high-capacity layered oxide electrodes[END_REF] Moreover, we show the feasibility to partially solve the voltage fade via well-selected chemical substitutions to prevent trapping of cations in tetrahedral sites. [START_REF] Sathiya | Origin of voltage decay in high-capacity layered oxide electrodes[END_REF] Equally, specific surface treatments or the design of coreshell and concentration-gradient particles were shown to be beneficial to partially mitigate voltage changes. [START_REF] Liu | Surface Doping to Enhance Structural Integrity and Performance of Li-Rich Layered Oxide[END_REF][START_REF] Li | Synthesis and Characterization of the Lithium-Rich Core-Shell Cathodes with Low Irreversible Capacity and Mitigated Voltage Fade[END_REF][START_REF] Pajot | Synthesis of Li and Mn-Rich Layered Oxides as Concentration-Gradients for Lithium-Ion Batteries[END_REF] On the other hand, solving the issues of voltage hysteresis and sluggish anionic kinetics is more challenging. To address them, we decided to study materials within which cationic and anionic redox processes are not decoupled but occur at the same potential so that cationic redox with fast kinetics can serve as a redox-mediator for the sluggish anionic processa situation offered by the model and -Li2IrO3 polymorphs, studied in our group, which adopts a 2D and 3D structure, respectively. [START_REF] Mccalla | Visualization of O-O peroxo-like dimers in high-capacity layered oxides for Li-ion batteries[END_REF][START_REF] Pearce | Evidence for anionic redox activity in a tridimensional-ordered Li-rich positive electrode beta-Li2IrO3[END_REF] The voltage-composition curves for such compounds display a low voltage (3.5 V) and high voltage (4.5 V) plateau reminiscent of coexisting anionic-cationic redox processes and of anionic solely, respectively, as deduced by XPS analysis. Since we have started this work, it is worth mentioning that the existence of anionic redox activity on this plateau has been quite controversial with RIXS measurements claiming no oxygen activity [START_REF] Hong | Metal-oxygen decoordination stabilizes anion redox in Li-rich oxides[END_REF] and XAS the opposite [START_REF] Li | Probing Electrochemically Induced Structural Evolution and Oxygen Redox Reactions in Layered Lithium Iridate[END_REF] .

Whatever, independently of such a debate, we studied the kinetic aspects of this 3.5 V combined cationic-anionic redox plateau in both and -polymorphs. Although we could not decouple cationic and anionic redox processes, we unravel in contrast an unusual phenomenon that is the passage of a single voltage plateau to a two-step voltage profile by increasing the cycling rates. Additionally we found a low-voltage feature that forms large hysteresis in both and polymorphs. The absence of this anomaly in the GITT measurements suggests specific kinetic limitations alike those found in other insertion compounds. Through combined electrochemical and operando X-ray diffraction (XRD) measurements we could determine that the origin of such voltage anomaly is due to subtle phase changes, and differs from those observed in conventional layered compounds for sluggish lithium "monovacancy hopping" and high-voltage spinel phase that is ascribed to cation disorder.

Experimental Section

Materials synthesis and electrochemical tests. The synthesis for and -Li2IrO3 was done by solid-state methods, as reported elsewhere. [START_REF] Mccalla | Visualization of O-O peroxo-like dimers in high-capacity layered oxides for Li-ion batteries[END_REF][START_REF] Pearce | Evidence for anionic redox activity in a tridimensional-ordered Li-rich positive electrode beta-Li2IrO3[END_REF] Bellcore-type method was applied to prepare highporosity free-standing electrodes that are composed of 73 wt% active material (without ballmilling), 9% Carbon Super P and 18% binder-Poly(vinylidene fluoride-co-hexafluoropropylene) (Arkema). The as-prepared Bellcore film was cut into discs of ~1 cm 2 to obtain the positive electrodes. By using Li metal foil as the anode, two layers Whatman GF/D borosilicate glass microfibre sheet (GE Healthcare Life Sciences) as the separator, and a LP100 (Merck) electrolyte with the composition of 1 M LiPF6 in ethylene carbonate:propylene carbonate:dimethyl carbonate in a 1:1:3 volume ratio, the 2032-type test coin cells were fabricated in an argon-filled glovebox. Cyclic voltammetry, chronoamperometry and impedance spectroscopy measurements were performed in three-electrode cells using working electrodes with active material loading of 0.5 mg per cm 2 of Al foil with Li reference and Li counter electrodes. All the electrochemical tests were performed with BioLogic potentiostats.

XRD and XAS.

Operando XRD was conducted by an airtight electrochemical cell equipped with a Beryllium window in a BRUKER D8 Advance diffractometer with Cu K radiation (λKα1 = 1.54056 Å, λKα2 = 1.54439 Å). The cell was charging and discharging with the XRD scans being collected simultaneously. Ir LIII-edge XAS spectra were acquired in transmission mode at the ROCK beamline of SOLEIL synchrotron (France). A Si(111) channel-cut quick-XAS monochromator with an energy resolution of 2 eV at 11 keV was used. The intensity of the monochromatic X-ray beam was measured by three consecutive ionization detectors. Measurements were performed on bellcore electrodes cycled to desired Li content. The energy calibration was established with simultaneous absorption measurements on an Ir metal foil placed between the second and the third ionization chamber. The obtained data were then processed by Athena software for energy calibration and normalization. Fourier transforms of extended X-ray absorption fine-structure (EXAFS) oscillations were further carried out within a k-range between 3.5 Å -1 to 16 Å -1 .

(Å -3 ) k (Å) -Li 2 IrO 3 -Li 2 IrO 3 -Li 2 IrO 3 -Li 2 IrO 3 -Li 2 IrO 3 -Li 2 IrO 3 c b b a |X(R)|Å -4 R (Å)

Results and Discussions

Brief introduction of and -Li2IrO3

The synthesis of and -Li2IrO3 was performed by a solid-state method as we reported previously [START_REF] Mccalla | Visualization of O-O peroxo-like dimers in high-capacity layered oxides for Li-ion batteries[END_REF][START_REF] Pearce | Evidence for anionic redox activity in a tridimensional-ordered Li-rich positive electrode beta-Li2IrO3[END_REF] . and -Li2IrO3 adopt different long-range structures as illustrated by Figure 1a-1b, which is also reflected by the different XRD patterns shown in Figure 1c, and the full-range electrochemistry can be found in Figure 1d. -Li2IrO3 crystalizes into a typical 2D layered rocksalt oxides with a honeycomb superstructure in a C2/m symmetry, while -Li2IrO3 forms a 3D framework constructed by edge-sharing IrO6 octahedra. Although being different in long-range order, they have surprisingly identical local structures as suggested by the perfectly superimposed Ir LIII-edge X-ray absorption near-edge structure (XANES) (Figure 1e) and the corresponding EXFAS spectra (Figure 1f) as well as the R space magnitudes (inset of Figure 1f). The local atomic arrangement around Ir atoms in both two phases were extracted (schematic in Figure 1f), showing exactly the same coordination environments extended from 1 st shell to 3 rd shell (Li atoms are excluded due to negligible scattering factors with X-rays). Hence, these identical local structures produce very similar electronic structures that lead to their similar electrochemical behavior, as we will show later.

Unusual electrochemistry of and -LixIrO3

(2 ≥ x ≥ 1)
The whole electrochemistry of these two Li2IrO3 polymorphs upon delithiation has been well studied for their anionic redox capabilities [START_REF] Mccalla | Visualization of O-O peroxo-like dimers in high-capacity layered oxides for Li-ion batteries[END_REF][START_REF] Pearce | Evidence for anionic redox activity in a tridimensional-ordered Li-rich positive electrode beta-Li2IrO3[END_REF] , while here we just focus on the first lithium removal from Li2IrO3 to Li1IrO3 that takes place around the equilibrium potential (Ueq) of ~3.45 V. Figure 2 shows the unusual electrochemical behavior of -Li2IrO3 such that after one lithium extraction, there is a large portion of lithium (about 0.5 Li) that cannot be reinserted back using a cutoff of 2.4 V. By holding the voltage at the end of the discharging with very small cutoff current of C/50, about 0.2 Li can further be recovered, but this remains far from the initial state of x = 2 (Figure 2a and2b). This "irreversibility" is further structurally supported by the ex situ XRD patterns, which shows incomplete phase transformation from Li1IrO3 back to Li2IrO3 when discharged to 2.4V and even after 2.4 V potentiostatic holding (Figure S1). In the subsequent cycle, we even imposed an extremely small cutoff current of C/100 for the current decay during the 2.4 V potentiostatic hold (Figure 2c and2d), but still could only reach x = ~1.85. Noting the sluggish nature of the current decay during the 2.4 V potentiostatic hold (panels b and d), such a large "irreversibility" cannot simply be ascribed to the irreversible phase change or side reactions caused by electrolyte decomposition, especially under shallow delithiation (only half of structural Li extracted) and the voltage cutoff (3.9 V) being well within the electrolyte stability window. To further understand these kinetic limitations in -Li2IrO3, we next studied the effect of gradually varying the current rates from a low-rate of C/100 to a high rate of 1C using a CCCV protocol (C/100 cutoff) within 3.9 V to 2.4 V leading to cycling in the range from x = 1 to x = ~1.85 (Figure 3a). At the slowest rate of C/100, the electrochemical reaction takes place very close to the Ueq of 3.45 V as a flat plateau, typical for biphasic processes. On discharge, gradually increasing the C rate leads to an earlier polarization of the process, such that at 1C, less than half of the capacity is delivered during the CC step. On the other hand, on charge, this effect is less drastic but still a significant polarization is observed at 1C with the appearance of two voltage features. This implies that there is overall an asymmetrical response of the charge and discharge processes. To assess the polarization response to the current rate, we plotted dQ/dV figures listed from Figure 3b to 3h, where they show increasing asymmetry of the oxidative and reductive peaks along with the increasing current rates. Most notably, the oxidative peak splits into two, with the gap between peaks that increases with the C-rate. This uncovers that as the charge process is pushed faster, it leads to a non-equilibrium situation with seemingly two separate electrochemical )

x in Li x IrO 3 c d C/5 C/50 cutoff Voltage vs Li (V) x in Li x IrO 3
Current density (mA g -1

)

x in Li x IrO 3 C/5
C/100 cutoff processes possibly differing in terms of their kinetics, whereas the discharge process is apparently a single electrochemical behavior near Ueq. However, bearing in mind that the discharge terminates at a much lower capacity, it is possible that there are other processes, similar to the one observed on charge, but that are triggered below the 2.4 V cutoff. So next, we decided to lower the discharge cutoff voltage. We first performed CCCV procedures for the first two cycles with a 2.4 V cutoff, as shown in Figure 4a-4b. Similar to Figure 2, it is apparent that the constant voltage step helps in Li reinsertion, but never leads to a full recovery to x = 2. However, by lowering the discharging cutoff voltage down to 1.65 V in the 3 rd cycle, a low-voltage sloped feature at about 1.8 V emerges, which completely recovers the initial state of x = 2 (Figure 4c). Further cycling showing the same 1.8 V feature during discharge with closed charge-discharge curves (Figure 4d) demonstrates that this is a reversible lithium insertion-extraction behavior, but with a large voltage asymmetry during the charge and discharge processes. Thus, it is now clear that the two different kinetic regimes observed in the charging process in Figure 3 also exist during discharge and with higher severity, as thoroughly unveiled by the two well separated staircase-like voltage steps. We further performed the kinetic analysis with different current rates and GITT experiments in this whole range from x = 2 to 1 (3.9 V to 1.65 V). As shown in Figure 5a, the discharge capacity at the 3.45 V plateau decreases gradually with increasing the C rate from C/50 to 2C (CCCV protocol), as the remaining capacity is transferred to the low 1.8 V step, thus highlighting the large kinetic limitation. Note that the 1.8 V feature is visible even at the lowest rate of C/50. This kinetic limitation is apparently not due to electronic conductivity which causes capacity loss that can never been recovered by lowering the voltage limit, as further supported by the minor contribution of IR drop in the GITT profiles (Figure 5e inset). Correspondingly, the charge voltage also shows larger polarization with larger C rates (Figure 5b, note the different scale than panel a), with the electrochemical curves changing from a flat plateau to multiple voltage features. However, the responses of charge and discharge are also asymmetrical such that the latter is predominated by capacity rearrangement at well-separated voltages rather than the more convoluted features observed in charge. Voltage window opening Voltage vs Li (V)

x in Li x IrO 3 2 nd Voltage vs Li (V) x in Li x IrO 3 3 rd Voltage vs Li (V) x in Li x IrO 3 a b c d
experiments were also employed to inspect this path-dependent character, which is a method used to understand hysteresis by previous studies. [START_REF] Croy | Examining Hysteresis in Composite xLi2MnO3•(1-x)LiMO2 Cathode Structures[END_REF] As shown in Figure 5c and5d, by opening the charging voltage, the low voltage feature increases as a function of the charge capacity. The inset of Figure 5c further demonstrates that, with increasing cutoff state of charge (SoC), the ratio of the length of low-voltage plateau to that of high-voltage plateau at discharge increases acceleratingly, implying more severity of the kinetic limitation with deep delithiation. This might suggest that with deep delithiation from Li2IrO3 to Li1IrO3, the electrode follows different path during discharge from that of reinsertion in partially delithiated electrode. This behavior is reversed in case of discharging-voltage opening experiment, where the charging curve follows the same one almost all the way (a little discrepancy for the full cycle). This actually again manifests the asymmetrical charge-discharge behavior, with respect to the reaction kinetics, as further demonstrated via the GITT results in Figure 5e and 5f. Upon 1C pulse and 4h relaxation, the high voltage polarization is totally eliminated by GITT, with both charge and discharge voltage reaching the same equilibrium potential of about 3.45 V. The huge voltage polarization shown during the low 1.8 V feature really stands out against the charge process, implying great asymmetry as well as the high limitation of kinetics. In addition, the relaxation takes place fast within less than two hour in reaching the Ueq (insets in Figure 5e-5f), which is a typical lithium-diffusion or phase-redistribution behavior. While comparatively, the charge shows more rapid relaxation (~10 minutes) than discharge, again reflecting the asymmetry of severer sluggishness for discharge kinetics. Before gaining further insight into the origin of the large hysteresis, we replicated our study from layered -Li2IrO3 to -Li2IrO3, which is known to have a tri-dimensional framework and thus higher robustness of the structure against anionic redox, to see if the structural dimensionality will play a role. Figure 6 presents the CCCV cycle results of -Li2IrO3, which displays two slightly separated plateaus around 3.4 V during discharge as opposed to a single one for -Li2IrO3. Moreover, it surprisingly shows the similar inability to get back to x = 2 Li stoichiometry on discharge as in -Li2IrO3 due to the sluggishness of Li reinsertion, despite a long 2.0 V potentiostatic hold. Here again, by further lowering the cutoff voltage to 1.65 V, the lithium can be fully reinserted back at the 1.8 V sloped feature leading to a large voltage hysteresis (Figure 6b). Note that the  phase allows further lowering of the cutoff voltage to 1.3 V as it can reversibly uptake about 0.5 extra Li per formula at the potential of about 1.45 V without any hysteresis (Figure 6c and6d), with two faintly distinguishable plateaus corresponding to two biphasic processes according to our previous study. [START_REF] Pearce | Evidence for anionic redox activity in a tridimensional-ordered Li-rich positive electrode beta-Li2IrO3[END_REF] Regardless of this 1.45 V plateau for extra Li insertion, the behavior of -Li2IrO3 bears remarkable similarity with that of -Li2IrO3 in terms of the hysteresis feature, implying its independence with regard to the long-range structural dimensionality. Furthermore, the rate analysis and voltage relaxation test (Figure 7) provides clear evidence of sluggish kinetics of the low-voltage plateau as well as the asymmetry of the charge and discharge responses, fully consistent with the -Li2IrO3 phase.

Although these two polymorphs have different long-range dimensionalities, the similar Ir-O electronic structure resulted from their identical local structures (even applicable for Li1IrO3, as shown in Figure S2), which defines the electrochemical property, makes it not surprising for the existence of similar hysteresis behavior in both two phases. Given that the relaxation of the voltage back to Ueq is very fast at the low-voltage feature, we reasonably attribute this kinetic limitation to the lithium-diffusion or phase-redistribution problem, which is a very short time scale. To decipher between them, we next used operando XRD to track the evolution of long ranger order in order to pursue an answer.

Operando XRD study of -Li2IrO3 and -Li2IrO3

Operando XRD measurements were carried out by cycling the -Li2IrO3 electrode in an operando cell for 5 cycles in the whole 3.9 -1.65 V range, meanwhile simultaneously collecting XRD scans. The following discussion excludes the first cycle because it is just a formation cycle that leads to some electrochemical grinding followed by stabilized subsequent cycles. Figure 8 shows the operando XRD results of -Li2IrO3 at a low current rate of C/15, with the evolution of selected peaks shown by the contour plots. Initially, upon charging the first peak at 18.6 slightly shifts indicative of a solid solution prior to reach a biphasic domain (Figure 8b). During the subsequent discharge, we observe nearly the reverse phase sequence except for a strong solidsolution-like behavior of the biphasic transition that is a result of deviation from equilibrium path. Interestingly, when looking at the range of 20-24 degree, there is partial appearance (white dashed circles in Figure 8c) of an intermediate phase that is possibly related to a -Li1.5IrO3 phase in analogy to the well crystallized -Li1.5IrO3 phase that we have reported previously. [START_REF] Pearce | Evidence for anionic redox activity in a tridimensional-ordered Li-rich positive electrode beta-Li2IrO3[END_REF] The reaction can hence be viewed as a triphasic reaction where the charged phase forms at the expense of the pristine O3 phase via an kinetically stable intermediate transition state, and vice-versa on discharge. The schematic of the phase transition at C/15 shows quite a symmetrical phase evolution upon charging and discharging (Figure 8d). However, this evolution is not perfectly symmetric as there are strong hints of solid-solution behavior.

Figure 8e-8g show the operando XRD results of the same cell cycled at a faster rate of C/2. The 18.3-19.2 region in 2q remains the same as at C/15 (Figure 8f). In contrast, the second 2q region (Figure 8g) reveals a drastic difference, namely the disappearance of the intermediate phase in charge but not on discharge while this intermediate phase is present both on charge and discharge at C/15 as better illustrated in the schematic (Figure 8h). This does not come as a surprise since it is well known that increasing high rate cycling leads to a greater departure from the equilibrium regime and more so when the system is kinetically limited. Moreover, the disappearance of intermediate in charge and not in discharge suggests slightly different reacting paths that could have an impact on the kinetics of the system.

A further analysis of this room temperature phase evolution for -LixIrO3 at C/2 reveals an additional difference in the way the -Li2IrO3 ↔ -Li1IrO3 transformation proceeds during charge versus discharge (see shaded areas in Figure 8 bottom). In charge, it shows only a single -Li2IrO3 phase and the accumulation of the intermediate phase appears to be skipped, highlighting the rapidity of the -intermediate → -Li1IrO3. However, for discharge the intermediate phase accumulates significantly, highlighting the sluggishness of -intermediate → -Li2IrO3. This retarded phase transition in discharge suggests that the kinetics of the reacting path of the discharge process is more sluggish than the charge one, hence needing a higher overpotential.

A similar operando XRD study was also done on 3D -Li2IrO3 to check the effect of structural dimensionality 2D () vs. 3D () on the phase transformation kinetics. Alike previously, after initial formation cycles the X-ray data collected at a current rate of C/10 and then at C/2 is shown as contour plots in Figure 9 top and bottom, respectively, along with the schematics of phase evolution. The results indicate the presence of two consecutive well-defined biphasic reactions parted by an intermediate phase (-Li1.5IrO3) during charge and discharge at C/10 (Figure 9b-9d). Such difference is however more dimmed at C/2, namely in discharge (see dashed rectangle in Figure 9h) and further highlighted in Figure 9j top (shaded area C) by the large domain of coexistence of the -Li2IrO3 and -intermediate phase as contrasted by the charge process (shaded area D). This, to some extent, mirrors in a less dramatic behavior of -Li2IrO3, which shows a pronounced asymmetrical phase evolution. Altogether, these results indicate that to a few differences, both 2D and 3D Li2IrO3 behave alike and show sluggish phase conversion in discharge. This is not a total surprise since these two polymorphs nearly adopt the same local structure as we have demonstrated initially in Figure 1 and Figure S2.

Cyclic voltammetry analysis

Being aware of the phase transition problem, as deduced by XRD, we further applied cyclic voltammetry (CV) to understand the kinetics of phase transformation. We first examined the CVs of α-Li2IrO3 with different cathodic limits and the results are shown in Figure 10a. After the first formation cycle between 2.7 V-3.9 V, we could observe two separated processes (anodic peaks 1 and 2), but with only single-behavior-like cathodic peak in discharge (blue line in Figure 10a). Afterwards, there is the appearance of a new additional peak (peak 3 in Figure 10b) by extending the cathodic limit to 2.0 V, with some capacity redistribution between the processes 1 and 2 (orange line in Figure 10a). Further decreasing the cathodic limit to 1.65 V triggers an onset of a new reduction peak, which corresponds to the aforementioned low-voltage feature where finally the stoichiometry of -Li2IrO3 is reached. An additional peak 4 (Figure 10b) in further charge reminds us that there is possibly a little overlithiation during discharge to 1.65 V. Moreover, once Li2IrO3 is restored, the reversed charge scan shows a more severe capacity redistribution at 3.4-3.9 V, with the anodic peak 1 almost invisible and peak 2 getting broadened (black line in Figure 10a). Nevertheless, there are still two distinct processes on both charge and discharge, as shown by CVs with different anodic limits (Figure 10c), where we could see a sharp cathodic peak 2 grows based on a broad peak 1 upon widening the voltage window. At this stage it become difficult to further exploit from the CV scan the mechanism involved in the 1.65 V3.9 V voltage range, since the anodic peaks are not well defined and capacity is redistributed at high scan rates. Instead, we concentrated on the CV scan between 2.43.9 V, namely the reversible process of extraction (-Li1.85IrO3 → -Li1IrO3) and insertion (-Li1IrO3 → -Li1.85IrO3) corresponding to the galvanostatic cycle in Figure 4b. In Figure 11a, CVs at different (relatively low) scan rates show two distinct processes (peak 1 and 2) on charge, which can be assigned to -Li1.85IrO3→-intermediate and -intermediate → -Li1IrO3 phase transition, respectively, while we could only observe a single-behavior-like cathodic peak in discharge. However, upon further increasing the scan rate an additional peak 1 is decoupled from peak 2 (Figure 11b) since at low scan rates they are overlapped and therefore cannot differentiated. The large shifting of peak 1 under high scan rates implies a very kinetic-limited reaction, namely -intermediate → -Li1.85IrO3, in accordance with what we have observed from operando XRD. Besides, when increasing scan rates, there is a single-phase region (Figure 11b) instead of a sharp exponential rise in current, indicative of a nucleation-controlled phase transformations [START_REF] Vassiliev | Electrochemical Patterns of Phase Transforming Intercalation Materials: Diagnostic Criteria for the Case of Slow Nucleation Rate Control[END_REF] . This suggests the reaction 1 (-Li1.85IrO3 → -intermediate) prefers a solid-solution path rather than a nucleation-controlled two-phase reaction at high scan rates. This is in agreement with the disappearance of the -intermediate phase previously observed by operando XRD when -Li2IrO3 was charged at C/2 (Figure 7g). In contrast, the persistency of the -intermediate phase during the discharge at C/2 reflects a higher nucleation energy barrier for the reversed reaction process (intermediate → -Li1.85IrO3), which is the origin of the low-voltage feature. Noted that during discharge there is a very slow current decay (inset of Figure 11a), which could be related with slow Li diffusion. To better understand Li diffusivity, we used Montella approach [START_REF] Montella | Discussion of the potential step method for the determination of the diffusion coefficients of guest species in host materials: Part I. Influence of charge transfer kinetics and ohmic potential drop[END_REF][START_REF] Montella | Apparent diffusion coefficient of intercalated species measured with PITT: A simple formulation[END_REF] to determine the diffusion time constants (τD) for Li-rich phase (-Li1.85IrO3) and Lipoor phase (-Li1IrO3), as shown in Figure 11c-d. Since it's hard to estimate the τD in extremely large particles in the samples (see SEM images in Figure S3a-3b), we solely exploited the narrow single-phase regions, just before the phase transformation starts to estimate diffusivities. The evaluated diffusion time constants are believed to correlate with the differences in the phase boundary propagation rates during the phase transformation, while large strain energies should contribute further in the slowness of the phase boundary migration. On discharge, the diffusion occurs in the Li-rich phase, -Li1.85IrO3 (Figure 11c), with a τD of 13 000 -15 000 s. On charge, the phase boundary and Li + ions move in the Li-poor phase(s), -Li1IrO3, with τD of 5000 -6000 s (Figure 11d). This big difference of the diffusion time constants for charge and discharge well explains the asymmetry of the charge-discharge kinetics and the long current decay in Figure 11a (inset) as well.

E (V) I (mA) 1' 2' I (mA) first charging 2.7 V 2.0 V 1.65 V a 1 2 2.7 V 2.0 V 1.65 V b 3 3' 4 c I (mA) E (V) E (V)
Since slow Li diffusion dominates the response of -Li2IrO3, it becomes impossible to determine the nucleation rate constants or the nucleation barriers, but we could deduce that a large nucleation energy barrier associated with high strain exists according to the exfoliation layers observed in SEM images (Figure S3c-3d). Therefore, it is possible that both slow Li diffusion and high nucleation energy barrier of -intermediate → -Li1.85IrO3 contribute to the whole hysteresis or the low-voltage feature.

For the β-Li2IrO3 electrodes, the CVs show similar features, with only minor differences from the  phase electrochemical behavior. Anodic peaks 1 and 2 are now poorly resolved even in the 2.4 -3.8 V potential range (Figure S4a) and the cathodic peak appears as a single process even at very high scan rates: 0.4 -0.5 mV/s (Figure S4b). This is indicative of somewhat lower nucleation barriers for the β phase compared to the α-Li2IrO3 sample. Correspondingly, the singlephase region on charge, which appears at high scan rates for the  phase, is less pronounced (though clearly observed in Figure S4b at 3.4 -3.5 V) for the β-Li2IrO3 sample. Additionally, at 3.7 -3.8 V further delithiation of β-Li1IrO3 starts as a single-phase process, which manifests itself in the appearance of two small cathodic peaks at 3.65 and 3.78 V in the reverse scan. The diffusivities near the phase transformation potentials again show the pronounced asymmetry for the Li-poor and Li-rich phases (3 500 and 11 500 s, Figure S4c), which explains the differences in the charge and discharge kinetics alike for the α-Li2IrO3 electrodes. Extending the cathodic potential limit to 1.65 V also results in quite similar trends, with the additional Li-ions being inserted in the low-voltage region (Figure S4d). However, unlike the observed changes in the CVs of α-Li2IrO3 electrodes, the restoration of the β-Li2IrO3 stoichiometry results in the diminution of the nucleation barriers, as evidenced by the sharper rises in current in the ascending branches of the peaks (Figure S4d). These minor dissimilarities in the behavior of the two polymorphs should originate from the structural differences between the layered and tri-dimensional material.

The existence of a single-phase region is the very close proximity of the two-phase process for the β-Li2IrO3 material (Figure S5a) allows probing the Li-ion diffusivity at β-Li2-δIrO3 composition. The diffusion time constant evaluated from impedance spectroscopy data equals to ~70 s -1 at 3.7 V (Figure S5b), where single-phase Li + insertion/extraction takes place. This value is two orders of magnitude higher than the diffusion time constants near the phase-transformation potentials for the Li1.85IrO3 → intermediate and Li1IrO3 → intermediate processes. This shows that the low Li diffusivities account for the processes involving deep lithiation of the LiIrO3 structures.

Discussion

Prior to confront our results with previous studies on this topic, it is imperative to recall some aspects regarding the thermodynamics and kinetics of voltage hysteresis as well as some examples. For tens of years, the voltage hysteresis problem has been found in a variety of electrodes for not only Li-ion batteries, but also other systems like nickel-based alkaline batteries. [START_REF] Bardé | Situ Neutron Powder Diffraction of a Nickel Hydroxide Electrode[END_REF] Although great efforts were contributed to exploring the underlying origin of these hysteresis problems, some of them still remain elusive and controversial. This dilemma arises from the confusion between the thermodynamic origin of the hysteresis and the kinetic polarization due to their different time-scales of relaxation. For a typical kinetic polarization, the relaxation has a very short time-scale so that the voltage can reach the equilibrium potential very fast. These polarizations are supposed to be rooted in either low electronic or ionic conductivity, and can be referred as electron diffusion or ion (Li etc.) diffusion problem. Normally a high surface current density, generated by high charge-discharge rate or large particle size, will aggravate such polarizations.

However, for some electrodes, it turns that the equilibrium potential is hard to reach even after weeks of relaxation. Such systems possess a prominent quasi-static hysteresis that originates from some thermodynamic origins. Among them are the conversion reaction type electrodes which show large voltage hysteresis owing to thermodynamic limitations associated to either bond breaking/re-formation [START_REF] Bruce | Nanomaterials for rechargeable lithium batteries[END_REF] , different charge-discharge reacting paths [START_REF] Doe | First-Principles Investigation of the Li-Fe-F Phase Diagram and Equilibrium and Nonequilibrium Conversion Reactions of Iron Fluorides with Lithium[END_REF][START_REF] Li | Origins of Large Voltage Hysteresis in High-Energy-Density Metal Fluoride Lithium-Ion Battery Conversion Electrodes[END_REF][START_REF] Meggiolaro | Origin of the Voltage Hysteresis of MgH2 Electrodes in Lithium Batteries[END_REF][START_REF] Khatib | Origin of the Voltage Hysteresis in the CoP Conversion Material for Li-Ion Batteries[END_REF] or surface/interface energy penalty caused by particle electrochemical nanosizing [START_REF] Cabana | Beyond intercalation-based Li-ion batteries: the state of the art and challenges of electrode materials reacting through conversion reactions[END_REF] . Similar quasi OCV hysteresis caused by sp 2 to sp 3 bond changes was also reported in hydrogen-containing carbons by T. Zheng et al. [START_REF] Zheng | Hysteresis during Lithium Insertion in Hydrogen-Containing Carbons[END_REF] Besides, a totally different thermodynamic-origin explanation to account for the "zero-current" hysteresis of LiFePO4 was proposed by W. Dreyer et al. based on a so-called "rubber balloon" model, which is nested in the non-monotonic shape of the "single particle" equilibrium potential curve. [START_REF] Dreyer | The thermodynamic origin of hysteresis in insertion batteries[END_REF] In this case, the "thermodynamic" hysteresis between the charge and discharge plateaus can be attributed to the supersaturation required to form a critical nucleus of another phase inside the pristine phase-transforming material. These thermodynamic origins are apparently different from the one rooted in conventional kinetic polarizations.

Anionic redox further complicates these hysteretic issues by providing a variety of Li-rich electrodes with diverse magnitudes of quasi-static hysteresis. Initially, the origin of the anionicredox-induced hysteresis was simply believed to be nested in the reversible cation migration. [START_REF] Croy | Examining Hysteresis in Composite xLi2MnO3•(1-x)LiMO2 Cathode Structures[END_REF][START_REF] Dogan | Re-entrant lithium local environments and defect driven electrochemistry of Li-and Mn-rich Li-ion battery cathodes[END_REF] This simple picture has been challenged by recent studies which correlate hysteresis to a chargetransfer bandgap effect [START_REF] Jacquet | Charge Transfer Band Gap as an Indicator of Hysteresis in Li-Disordered Rock Salt Cathodes for Li-Ion Batteries[END_REF] and O-O bond stabilization 41 in d 0 cation-disorder compounds. Lastly, micro-calorimetry studies of the LRSO compound conclusively demonstrated that hysteresis is present as long as a deviation from the equilibrium path is triggered by some sluggish structural reorganizations, including cation migration, O-O dimerization, layered gliding etc. [START_REF] Assat | Probing the thermal effects of voltage hysteresis in anionic redox-based lithium-rich cathodes using isothermal calorimetry[END_REF] Now coming back to our study of the Li2IrO3 polymorphs, we have demonstrated a sluggish phase transition appearing in discharge that causes the low-voltage 1.8 V feature associated with the hysteresis. Thus a legitimate question deals with the origin of the sluggish (intermediateα or -Li2IrO3) phase transition. Bearing in mind the coexistence of both cationic and anionic processes on the 3.4 V plateau in these compounds, it was at first tempting to correlate this phase transition to anionic redox process, which is now well known to show slow kinetics as compared to the fast cationic process. This was consistent with the path-dependent feature of -Li2IrO3 which resembles lithium-rich NMC compound for which a gradual opening of the charging voltage window leads to larger hysteresis in discharge as more contribution of anionic redox is released. [START_REF] Assat | Fundamental interplay between anionic/cationic redox governing the kinetics and thermodynamics of lithiumrich cathodes[END_REF][START_REF] Croy | Examining Hysteresis in Composite xLi2MnO3•(1-x)LiMO2 Cathode Structures[END_REF] However, operando XAS measurements were unsuccessful in establishing phase transitionanionic redox correlation due to the requirement of high energy beam that cannot be access to anions. Moreover, GITT analysis has revealed a short-time scale of relaxation, that is quite different from what we have observed in Li-rich NMC and LRSO unless the cationic redox (Ir 5+/4+ ) can accelerate the relaxation which is quite unlikely, hence the need to look for an alternative explanation.

On the other hand, as shown by the electrochemical analysis, the sluggishness of phase transition could be attributed to very slow Li diffusion and high nucleation energy barrier. It needs to be mentioned that the spinel LiMn1.5Ni0.5O4 ↔ Li2Mn1.5Ni0.5O4 also shows a very similar overpotential features as the Li1IrO3 ↔ Li2IrO3 reported herein. [START_REF] Lee | Influence of Cation Ordering and Lattice Distortion on the Charge-Discharge Behavior of LiMn1.5Ni0.5O4 Spinel between 5.0 and 2.0 V[END_REF] Within this spinel, the transitionmetal ions disordering incurs a smaller space for lithium accommodation into the 16c octahedral sites, hence leading to sluggish kinetics for lithium diffusion whose consequence is the appearance of an hysteresis. This kinetic limitation in LiMn1.5Ni0.5O4 was also found to be accompanied with a sluggish phase transition from T2 to T1 phase, with the former transforming to equilibrium T1 phase by a fast relaxation process alike in our iridates. This hypothesis is further strengthened by the fact that Li occupies tetrahedral sites in the Li1IrO3 polymorphs as well as Li1Mn1.5Ni0.5O4, while it moves upon Li insertion to octahedral sites in the Li2IrO3 polymorphs as well as in overlithiated Li2Mn1.5Ni0.5O4 spinel, thus possibly explaining the very similar overpotential features in the two families of compounds.

There are also several reports about kinetic limitations pertaining to Ni-containing conventional O3-type layered compounds showing similar sluggish phase transitions, as exemplified by LiNi1/3Co1/3Mn1/3O2 (NCM) and LiNi0.80Co0.15Al0.05O2 (NCA). [START_REF] Kang | Investigating the firstcycle irreversibility of lithium metal oxide cathodes for Li batteries[END_REF][START_REF] Kasnatscheew | The truth about the 1st cycle Coulombic efficiency of LiNi1/3Co1/3Mn1/3O2 (NCM) cathodes[END_REF][START_REF] Robert | Switch of the Charge Storage Mechanism of LixNi0.80Co0.15Al0.05O2 at Overdischarge Conditions[END_REF][START_REF] Mueller-Neuhaus | Understanding Irreversible Capacity in LixNi1-yFeyO2 Cathode Materials[END_REF] For these compounds, the lithium diffusion was considered to be worsened for a low threshold of lithiumvacancy concentration based on the "monovacancy hopping" model proposed by Van der Ven et al.  lithium hopping via monovacancy path having higher kinetic energy barrier [START_REF] Van Der Ven | Lithium Diffusion in Layered LixCoO2[END_REF] . Experimentally, this is manifested as a substantial "irreversibility" during the first cycle that can nevertheless be recovered via a low voltage plateau by lowering the cutoff discharge voltage. This led to the well-known over-lithiation of, for instance, LiNiO2 into a Li2NiO2 at the particle surface with the latter having Li in tetrahedral instead of octahedral sites for the former. [START_REF] Kang | Investigating the firstcycle irreversibility of lithium metal oxide cathodes for Li batteries[END_REF] Could this surface scenario apply to LixIrO3 with the formation of Li2[Li1/3Ir2/3]O2 hence explaining the drastic voltage drop at 3.4 V for both α and  polymorphs? Several observations do not support this scenario. First, the over-lithiation plateau of -Li2IrO3 can be observed clearly at lower voltage for both polymorphs (Figure 12a-12b and Figure 6d), and it is also highly reversible with small hysteresis unlike in LiNiO2. Second, the formation of Li2MO2 phase cannot explain the path-dependent behavior of the low-voltage feature. Finally, we could not observe any Li2MO2 phase formation for layered -Li2IrO3 at 1.8 V as one previously did in conventional compounds (Figure 12c), while when the cell was over-discharged to 1.35 V a distinct peak at 18.2 shows up indicating the transformation to Li2MO2 phase (Figure 12d).

Overall, having excluded the Li2MO2 surface scenario as well as the interplay between phase transition and anionic redox we are falling short of other structural/transport phenomena that could account for lithium-diffusion or nucleation problems. A certainty is that the hysteresis spotted for both Li2IrO3 polymorphs possesses specific signatures that cannot be found in other insertion compounds presenting hysteresis phenomena. Thus, Li2IrO3 polymorphs broaden the diversity and complexity of hysteresis problems in insertion compounds that are too hastily ascribed to cation migration.

Conclusion

In summary, we have studied the electrochemical delithiation/lithiation of both and -Li2IrO3 to Li1IrO3 and found the lithiation process is kinetically limited with the appearance of a 1.8 V low-voltage feature associated to a large voltage hysteresis. From GITT measurements we could totally eliminate the hysteresis as the materials display fast relaxation. Moreover, via the opening-voltage-window experiment we could evidence that the low-voltage feature shows a pathdependent behavior and changes as a function of the charge depth. By means of operando XRD Finally, the sluggishness of phase transition was ascribed to the slow Li diffusion and its high nucleation barrier as deduced from the CV analysis coupled with Montella approach and from both the exfoliated layers as observed from SEM results and the phase evolution analysis by operando XRD, respectively. Overall, we believe this low-voltage feature and hysteresis observed in Li2IrO3 polymorphs are caused by the kinetically limited reaction of intermediate (Li1.5IrO3)  Li2IrO3 rooted in sluggish Li diffusivity and the high nucleation barrier of this biphasic transition. In a broad sense, this finding will fertilize the diversity of the hysteresis in insertion compounds of Li-ion batteries. It also exemplifies that the hysteretic behavior is more complex than expected, especially in Lirich compounds involving anionic redox where cation migration was widely considered to be responsible for hysteresis. This kinetic limitation in Li2IrO3 will also enrich our understanding of the analogous phenomena in other electrodes.

ASSOCIATED CONTENT

Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org. It includes XANES of Ir collected on both  and  Li1IrO3, SEM images for -LixIrO3 and electrochemical analysis data of -Li2IrO3.

Figure 1 .

 1 Figure 1. Schematic crystal structures of (a) and (b) -Li2IrO3. (c) The XRD patterns of and -Li2IrO3, showing different long range order. (d) Full range electrochemical curves of and -Li2IrO3 between 0<x<2. Note that about 0.5 lithium cannot be extracted from -Li2IrO3 due to some structural reason, unlike the  phase. (e) Ir LIII-edge XANES spectra and (f) the corresponding k 3 -weighted EXAFS oscillations of and -Li2IrO3. The inset shows the magnitude of Fourier Transform of k 3 -weighted EXAFS of and -Li2IrO3. The similar local structures around every Ir center atom in both the two phases are shown at bottom left (dark blue and red atoms correspond to Ir and O, respectively).

Figure 2 .

 2 Figure 2. (a) Constant-current and constant-voltage (CCCV) charge-discharge profiles of -Li2IrO3 at first cycle with the evolution of specific current shown in (b). A constant current was first applied at C/5 (22 mA g -1 ), and the cutoff current was set to C/50. (c) CCCV chargedischarge profiles of -Li2IrO3 over the second cycle, with the evolution of specific current shown in (d), where the cutoff current was set to C/100.

Figure 3 .

 3 Figure 3. (a) CCCV charge-discharge profiles of -Li2IrO3 at C/100, C/5 and 1C rates (intermediate rates not shown for the sake of clarity). Note that the longer than usual charge capacity at C/100 is due to side reactions whose effect is accentuated at such low rates. (b)-(h) dQ/dV plots of different current rates (y-axis scales differ across panels).

Figure 4 .

 4 Figure 4. (a) 1 st cycle of -Li2IrO3 to Li1IrO3 cutting off at 2.4V at discharging, followed by constant voltage method with the cutoff current as C/100. (b) Second cycle following the first cycle in (a) in the same voltage range. (c) 3 rd cycle of the same cell but with lowered cutoff voltage of 1.65V at the discharge process. (d) 4 th cycle following the 3 rd cycle in (c) discharging to 1.65V.

Figure 5 .Figure 6 .

 56 Figure 5. (a) Charge and (b) discharge profiles of -Li2IrO3 to Li1IrO3 at different current rates increasing from C/50 to 2C (CCCV protocol with C/100 cutoff). (c) Charge and (d) discharge voltage window opening results at C/5. The inset of c shows the ratio of the length of low-voltage plateau to that of high-voltage plateau of discharge as a function of the cutoff SoC in the voltagewindow-opening experiment. GITT curve of (e) charge and (f) discharge process with a 1C pulse and 4 hours rest. The insets show the representative relaxation process of the * marked GITT unit.

Figure 7 . 3 VoltageFigure 8 .

 738 Figure 7. Cycling curve of -Li2IrO3 at different rates of (a) C/5, (b) 1C, and (c) 3C with CCCV protocols (C/100 current cutoff). (d) The 4h relaxation during the low-voltage feature while cycling at 1C. The inset shows the relaxation along with time, which is similar to  phase that it almost reaches Ueq within less than 1 hour.

Figure 9 .

 9 Figure 9. (a) Electrochemical cycling curve of -Li2IrO3 at C/10 within an operando XRD cell. Contour plots of the evolution of operando XRD scan between (b) 22.2-23.8 degree, (c) 32.2-33.8 degree and (d) 34.2-36 degree for -Li2IrO3 at C/10. (e) Schematic illustration of the phase change in -Li2IrO3 at C/10. (f) Electrochemical cycling curve of -Li2IrO3 at C/2 in the subsequent cycle within an operando XRD cell. Contour plots of the evolution of operando XRD scan between (g) 22.2-23.8 degree, (h) 32.2-33.8 degree and (i) 34.2-36 degree for -Li2IrO3 at C/2. (j) Schematic illustration of the phase change in -Li2IrO3 under C/2. The bands shaded in grey marked by A, B, C, and D highlight the equivalent processes during charge and discharge in the hysteretic range for both current rates.

Figure 10 .

 10 Figure 10. (a) CVs (0.1 mV/s) of -Li2IrO3 electrodes with cathodic potential limits 2.7, 2.0, and 1.65 V. (b) Enlarged part of the CVs in the 1.65 -3.0 V region. (c) CVs of -Li2IrO3 electrodes (with 1.65 V cathodic limit) registered with different anodic limits (3.50 V, 3.60 V, 3.90 V).

Figure 11 .

 11 Figure 11. CVs of α-Li2IrO3 electrode in the 2.4 -3.9 V range at different scan rates: (a) low to intermediate scan rates (inset marks out the slow current decay region at scan rate of 0.05 mV/s); (b) high scan rates. (c) Current transients registered upon delithiation for the potential steps from 3.380 to 3.390 V, 3.390 to 3.400 V (diffusion in the α-Li1.85IrO3 phase). (d) Current transients registered upon lithiation for the potential steps from 3.460 to 3.470 V, 3.470 to 3.380 V (diffusion in the LiIrO3 phase).

Figure 12 .

 12 Figure 12. (a)The first three cycles of -Li2IrO3 charged and discharged between 1.35V and 2.5V at C/5, with overlithiation/delithiation of one lithium. (b) The 4 th cycle reacted between 1.35V and 3.75V at C/5, with differentiated plateaus from kinetic limitation of the phase change and formation of Li2MO2 phase. (c) Selected XRD patterns from -Li2IrO3 at C/2 between 17-19.6 degree. There is no new phase formation in the range of 17.2-18.2 degree at the end of 1.8V plateau and the end of constant-voltage discharge at 1.65V. (d) XRD patterns for -Li2IrO3 at the end of discharge at C/2 and the one further discharged to 1.35V. The peak at 18.2 corresponds to the Li2MO2 phase (M=Li1/3Ir2/3).

  unraveled asymmetrical phase changes between charge and discharge for both polymorphsthe biphasic reaction intermediate (Li1.5IrO3)  Li2IrO3 is hindered kinetically.

h relax Voltage (V) Time (h)

ACKNOWLEDGMENT

The authors thank the ROCK beamline (financed by the French National Research Agency (ANR) as a part of the "Investissements d'Avenir" program, reference: ANR-10-EQPX-45;), SOLEIL synchrotron, for the X-ray absorption spectroscopy experiment (proposal 20171299). B.L, G.A, P.P, and J.-M.T. acknowledge funding from the European Research Council (ERC) (FP/2014)/ERC, Grant-Project 670116-ARPEMA. Use of the 11-BM mail service of the APS at Argonne National Laboratory was supported by the US Department of Energy under contract No. DE-AC02-06CH11357 and is gratefully acknowledged.

AUTHOR INFORMATION

Corresponding Author *Jean-Marie Tarascon: jean-marie.tarascon@college-de-france.fr


Wilfried Uhring
email: wilfried.uhring@unistra.fr

Jean-Baptiste Schell
email: jbschell@unistra.fr

Luc Hébrard
email: luc.hebrard@unistra.fr

Integrated Streak Camera With on Chip Averaging for Signal to Noise Ratio Improvement

Keywords: High-speed imaging, CMOS, N-path filter, noise. I

A technique to reject the noise of the Trans-Impedance Amplifiers (TIAs) of an integrated streak camera in the case of a repeatable input signal is proposed. The modifications of the sensor architecture are marginal with only one additional power supply connected to the column buffer of the sampling cell. The noise rejection can be adjusted independently of the effective bandwidth of the system. The simulation results show that the TIA noise can be reduced from 3.5mV to 0.31mV, which is the limit of the used sampling cells due to the thermal noise on capacitor (kTC). The resulting signal-to-noise ratio is more than 10 times better with an acquisition time of only 20 µs thanks to the on-chip analog averaging feature.

INTRODUCTION

High-speed imaging using Complementary Metal-Oxide Semiconductor (CMOS) or Charged Coupled Device (CCD) sensors has seen a sharp increase with the apparition of commercial products able to achieve a frame rate of 20 Mega frames per second (Mfps) [START_REF]High-speed video camera, Shimadzu model Hyper Vision HPV-X2[END_REF] [START_REF]Ultra_High speed Video, Specialised Imaging, Model Kirana[END_REF]. Thanks to the concept of burst imaging introduced in 1993 by Pr. Etoh Goji [START_REF] Etoh | Trahigh-speed multiframing camera with an automatic trigger[END_REF], this sensor can generate a pixel rate in the range of 1 Tera pixels per second by storing the images within the sensor during the acquisition. Recently, the 3D microelectronic technology allowed to push the state of the art of the 2D high speed burst video sensors with some new functionalities such as an onthe-fly digitalization [START_REF] Millet | A 5 Million Frames Per Second 3D Stacked Image Sensor With In-Pixel Digital Storage[END_REF] and an enhanced frame rate of 100 Mfps [START_REF] Kuroda | Over 100 million frames per second high speed global shutter CMOS image sensor[END_REF] [START_REF] Uhring | A Scalable Architecture for Multi Millions Frames per Second CMOS Sensor With Digital Storage[END_REF]. Nevertheless, in order to reach a higher frame rate, the 2D acquisition paradigm has to be abandoned to the benefit of the streak imaging paradigm. The streak imaging approach is the sampling of just a single spatial line of the scene per unit of time. As a consequence, a spatial dimension is lost and the video is no longer a pile of spatial images I(x,y) where x and y are the spatial dimensions, but a pile of lines which can be represented as a spatiotemporal image I(x,t), where t is the time. Indeed, the fastest frame rate achieved with a CMOS sensor has been realized thanks to a streak imaging sensor, such as the one shown in Fig. 1 [START_REF] Zlatanski | Sub-500 ps Temporal Resolution Streak-mode Optical Sensor[END_REF]. By releasing the silicon area constraints of the 2D imagers, one single pixel (the grayed line of Fig. 1) can set in a front end with a large sampling and storage unit beside the photodiode, with almost no spatial limit except the sensor width. Thus, a wideband front end and sampling unit can be embedded, and a line rate of 8 Giga lines per second with a temporal resolution better than 500 ps has been demonstrated [START_REF] Zlatanski | Sub-500 ps Temporal Resolution Streak-mode Optical Sensor[END_REF].

The drawback of such a high bandwidth performance is the noise of the system that increases with the cut-off frequency. Although a high bandwidth is required for single shot measurements, there are some other approaches to measure a repetitive event. Time correlated single photon counting is obviously a very good technique to measure the temporal evolution of a light pulse with a very high signalto-noise ratio, but the acquisition time can be quite long and these sensors are intrinsically unable to achieve a single shot measurement [START_REF] Becker | Advanced Time-Correlated Single Photon Counting Techniques[END_REF]. In this paper, we propose a technique to reduce the noise of a single shot integrated streak camera with very few modifications of the architecture.

Temporal Sweep Unit

The overall system architecture and theory of operation are detailed in Section II. The approach functionality and efficiency are then assessed with simulation results depicted in Section III. Section IV concludes on the work.

II. SYSTEM ARCHITECTURE AND OPERATION

A. System architecture

A pixel of the integrated streak camera is composed of a photodiode, a wideband Trans-Impedance amplifier (TIA) and a sampling and storage line, which is a bank of capacitors switched with NMOS (N-type Metal Oxide Semiconductor) transistors, as described in Fig. 2. Each NMOS switch is driven by the Si signal generated by the temporal sweep unit with i [1;N] and N the number of images of the line stored in the sensor. The Si signals are set on and off sequentially in order to sample the signal applied on the common line by the TIA A, which gives an image of the light intensity on the photodiode. After the sampling of the signal, the voltage Ci on each holding capacitor CHi is then readout by a source follower. Both the photodiode and the readout unit are not presented in Fig. 2 for clarity reason, but they are detailed in [START_REF] Zlatanski | Sub-500 ps Temporal Resolution Streak-mode Optical Sensor[END_REF]. The bandwidth of the sampling cell can be well above the bandwidth of the TIA which is about 1 GHz. Thus, each time the NMOS is switched on, we can assume that the voltage on the node Ci follows instantaneously the TIA output. This is the operation in the single shot mode. Nevertheless, the noise at the output of the TIA is also sampled and affects the signal-to-noise ratio.

B. Theory of operation of the on chip averaging

It is well known that averaging a signal reduces the temporal noise and, if the signal can be repeated, multiple acquisitions of a single shot can be readout and averaged on a computer. However, the repetition rate of the event is then limited by the readout time, i.e., about a few Hz. This bottleneck can be circumvented by a high repetition rate on chip averaging. By reducing the voltage of the gate of the NMOS transistor, the "on resistance" R of the transistor can be increased and the behavior of the sampling cell is equivalent to an ideal switch followed by a resistor and the holding capacitance, as depicted in Fig. 2.

If the RCHi time constant of the sampling cell is higher than the switch on duration T of the Si signal, the voltage on the node Ci does not have time to follow the output of the TIA. At the same time, the TIA noise is also filtered by the RCHi filter. When the camera is synchronously triggered by the laser source or vice versa, each time the signal is repeated, the node voltage Ci trends to reach the signal during the switch on duration T. In the meantime, the temporal noise is still filtered and is randomly positive or negative. As a consequence, a high noise rejection can be achieved by reducing the sampling cell bandwidth. The system behaves like an N-Path filter and the transfer function can be written as [START_REF] Jones | Theory and Performanc of N-Path Filters[END_REF]:

      2 0 sinc , K out K in Vs K G s jK K V s N             (1)
where Vin(s) is the signal at the output of the TIA, Vout(s) is the signal reconstructed with the readout of the Ci node voltage and G(s)=1/(1+RCHs) is the transfer function of the RCH filter. Equation ( 1) is equivalent to a comb Dirac modulated by a sinc due to the gate function of the Si signal and convolved to the elementary filter G(s).

The complete transfer function from (1) is illustrated in Fig. 3 for sampling cell bandwidths of 100 kHz and 10 kHz for N=200 cells and a sampling rate of 1 GHz, i.e., a period T of 1 ns. As the signal is periodically repeated, it can be decomposed in a Fourier series with fundamental frequency at 1 GHz/200, i.e., 5 MHz and its harmonics. Thus, the complete transfer function for the measured signal is almost equal to 1 for its fundamental and is slightly modulated by the sinc function for its harmonics. Indeed, each sample trends to be the mean voltage of the TIA signal along the gate duration T of the sampling signal which is the reason of the low pass behavior of the sinc function.

C. Noise rejection Fig. 4 is a close-up view of the complete transfer function at the frequency of 5 MHz for sampling cell bandwidths of 100 kHz and 10 kHz. Its magnitude at 5 MHz is actually 0 dB in order for the signal fundamental to fully pass through the filter. The other spectral peaks of the complete transfer function look similar, except for their magnitude modulated by the sinc function. If we assume that the temporal noise at the output of the TIA is a white noise, this noise is rejected between two spectral peaks thanks to the low pass filter G(s). The narrower are the peaks, the higher is the rejection. Nevertheless, the overlap of the response of two peaks limits the maximal rejection. Indeed, the transfer functions given in Fig. 3 and Fig. 4 indicate a rejection of about 15 and 30 dB for a filter bandwidth of respectively 100 kHz and 10 kHz. With an ideal brickwall filter, the noise rejection should be increased by n where n is the ratio of the filter bandwidth, i.e., the rejection should be 10 higher with a filter bandwidth of 10 kHz with respect of the one at 100 kHz. 1) with a first order filter G(s) = 1/(1+RCs) and a bandwidth of 100 kHz, 10 kHz and 1 kHz respectively. The noise rejection is close to 10=3.16 for a decade of bandwidth.

D. Practical limitations

Lowering the filter bandwidth rejects the noise but, as a drawback, a higher number of signal repetition is required. Indeed, a sampling cell is switched on only during the sampling duration T, i.e., the duty cycle is nominally 1/N. As a consequence, the apparent constant time a of the cell is about N times the constant time of the RCH filter, i.e., a=NRCH. Moreover, the sampling cell suffers from a leakage current that makes it unable to operate with a too long time constant. In a conventional CMOS technology, the leakage time constant is in the range of 100 ms. Thus, the minimal usable filter bandwidth is in the range of 1 kHz.

The noise rejection is also limited by kTC noise which is the thermal noise of the resistance R integrated on the capacitance and is given by [START_REF]Ultra_High speed Video, Specialised Imaging, Model Kirana[END_REF].

ktc H kT V C   (2)

III. SIMULATION RESULTS

A. Bandwidth tunning

The bandwidth of cell filter G(s) can be adjusted by adjusting the gate to source voltage VGS of the NMOS transistor in order to obtain an on resistance R that matches f=1/(2RCH) where f is the required bandwidth and CH is the value of the holding capacitance. The on resistance follows a strongly nonlinear response according to VGS that allows generating a large dynamic of resistance value R and thus, a large dynamic of bandwidth. The Gate voltage is generated thanks to buffers with an adjustable power supply. Though the source of the transistor is following the TIA output and consequently, the VGS is signal dependent. Fig. 5 gives the small signal bandwidth of the sampling cell filter versus the buffer power supply voltage for different TIA output voltages for the designed sampling cell. More than 3 decades can easily be covered thanks to this technique which does not require any additional transistors within the sampling cell. The only modification relies on the tuning of the supply voltage of the buffer that drives the Si voltage. These buffers are common for a whole column of the sensor and each column buffer is powered by the same power supply. As a consequence, the only modification of the system architecture is to add a specific power supply for these buffers.

B. Sinusoidal signal acquisition

The noise rejection has been evaluated with a SPICE simulation for two sinusoidal signals of 5 and 50 MHz at the input of the TIA. The total added rms noise at the output of the TIA integrate from 10 Hz to 10 GHz is 3.5mV rms. The results are shown in Fig. 6 for several filter bandwidth of 1 GHz down to 1 MHz. The displayed curves are the concatenation of the voltage Ci from the sampling cells i=1 to 200 after 100 accumulations of the same signal. The simulated time is then 200 cells×1 ns×550 accumulations = 110 µs.

With a filter bandwidth of 1 GHz (pink curve of Fig. 6), the sampled signal with 100 accumulations is almost the image of the last one. Indeed, during the 1 ns long aperture of the switches, the voltage at the nodes Ci has enough time to reach the TIA output. In this case, the results are very close to a classical sampling and we can see that the noise added by the TIA is present on the sampled signal. With a filter bandwidth of respectively 100 MHz (green), 10 MHz (blue) and 1 MHz (red), the noise is less and less present on the sinusoids. We can also see that the shape and amplitude of the sinusoids are not affected by the filter bandwidth reduction and that the 50 MHz signal can be measured even with a filter bandwidth of only 1 MHz. This simulation demonstrates that the white noise can be efficiently rejected without altering the periodic signal.

C. Noise rejection assessment

In order to characterize the noise rejection, the same simulation as the previous one was made without any signal at the input. The observed signal should be the operating point of the TIA output, i.e., a static voltage of about 1 V. The result is shown in Fig. 7.

Once again, we can clearly see that the noise is rejected and that the reconstructed signal becomes less noisy. The equivalent power spectral densities of the measured noises are plotted in Fig. 7. We can see that the rejection is applied on the whole spectrum of the white noise and especially also for the low frequencies. The statistical distributions of theses samples are also depicted in Fig. 8. The assessed noise with a bandwidth of 1 GHz is 1.75 mV rms and is reduced down to 0.769 mV rms for a bandwidth of 100 MHz, i.e., a

IV. CONCLUSION

A technique to reject the noise of the TIAs of an integrated streak camera in the case of a repeatable input signal is proposed. The modifications of the sensor architecture are marginal with only one additional power supply connected to the column buffer of the sampling cell. The noise rejection can be adjusted independently of the effective bandwidth of the system. The simulation results show that the TIA noise can be reduced from 3.5mV to 0.31mV which is the limit of the used sampling cells due to the kTC noise. The resulting signal-to-noise ratio is more than 10 times better with an acquisition time of only 20 µs thanks to the on-chip analog averaging features.

Fig. 1 .

 1 Fig. 1. A streak camera sensor architecture

Fig. 2 .

 2 Fig. 2. Simplified architecture of a single pixel and its equivalent model

Fig. 3 .

 3 Fig. 3. Complete transfer function of the on-chip averaging system for sampling cell bandwidths of 100 kHz (top) and 10 kHz (bottom)

Fig. 4 .

 4 Fig. 4. Close-up view of the fundamental at 5 MHz of the complete transfer function of the one chip averaging system for sampling cell bandwidths of 100 kHz (top) and 10 kHz (bottom)

Fig. 5 .

 5 Fig. 5. Small signal bandwidth of the sampling cell filter versus the buffer power supply voltage for different TIA output voltage

Fig. 6 .

 6 Fig. 6. Simulation of the noise rejection on a sinusoidal input signal of 50 MHz (top) and 5 MHz (bottom) for a filter bandwidth of 1 GHz down to 1 MHz. A cell is equivalent to 1 ns

Fig. 8 .

 8 Fig. 8. Noise distribution (mV) of the simulated sample for noise rejection assessment for different filter cell bandwidths

TABLE I

 I

	.	NOISE REJECTION IMPROVEMENT FOR SEVERAL FILTER
		BANDWIDTH
	100 kHz  10 kHz 10 kHz1 kHz	1 kHz100 Hz
	4.25	3.36	3.1
	TABLE I. gives the computed white noise rejection for
	the transfer function (

  For a bandwidth of 10 Mhz, the noise is reduced again down to 0.383 mV rms, i.e., the rejection from 100 to 10 MHz is about 2. Finally, the rejection over the decade from 10 to 1 MHz is only 1.2 with a noise at 1 MHz of 0.31 mVrms. This last simulated rejection ratio is less than expected because it is limited by the kTC noise of the sampling cell which integrates a holding capacitance of 40 fF, i.e., VkTC = 0.32 mV. The proposed noise rejection technique makes the TIA noise negligible with respect to the kTC noise level.

		1						10 -6
		0.995
	Amplitude (V)	0.98 0.985 0.99		BW 1MHz BW 100MHz BW 1GHz BW 10MHz		Amplitude (V 2 )	10 -8 10 -7
									BW 1MHz
		0.975							BW 10MHz BW 100MHz
									BW 1GHz
		0.97	0	50	100	150	200	10 6 10 -9	10 7	10 8	10 9
				Sample cell				Frequence (Hz)
		Fig. 7. Simulation of the TIA white noise rejection for different filter
	bandwidth. Acquired Samples (left) and equivalent power spectral density
							(right)
	rejection of 2.3.