Quantitative Analysis of Large Voltage Hysteresis of Lithium Excess Materials by Backstitch Charge and Discharge Method

Lithium-excess (LEX) materials (LiMO2 · Li2MnO3; M = Co, Ni, etc.) are attractive as potential positive electrodes of high-capacity lithium-ion batteries, however, large voltage hysteresis of LEX materials in charge and discharge disturbs real application. Thus, the large voltage hysteresis was investigated by a novel electrochemical method termed as a “backstitch charge and discharge” (backstitch CD) method, in which unsymmetrical charge and discharge with a small capacity were continuously repeated. The backstitch CD method was applied to Li[Li1/5Co2/5Mn2/5]O2 (0.5LCoO2 · 0.5Li2MnO3) known as an LEX material for the first time. Li[Li1/5Co2/5Mn2/5]O2 showed different reversible potentials during the backstitch CD processes in spite of symmetrical polarization behavior at each process. The voltage hysteresis in Li[Li1/5Co2/5Mn2/5]O2 resulted from electrochemically reversible but different reactions occurring during charging and discharging processes. Contributions of overpotential and difference in reversible potential to the voltage hysteresis can be evaluated quantitatively by the backstitch CD method. © The Author(s) 2018. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. [DOI: 10.1149/2.0701811jes]

Lithium-ion batteries with high energy density have been strongly demanded in accordance with the expansion of their applications including automobiles, stationary use, etc. A class of lithium insertion materials known as lithium excess (LEX) materials has a reversible capacity larger than 300 mAh g −1 beneficial to increase energy density of lithium-ion batteries. [1][2][3] Typical LEX materials are the solid solutions of Li 2 MnO 3 and LiMO 2 (M = Cr, 4 Fe, 5 Co, 6 Ni, 7 Ni 1/2 Mn 1/2 8 and Co 1/3 Ni 1/3 Mn 1/3 9 ). The capacities of LEX materials are usually larger than those expected from solid-state redox reactions between M 3+ /M 4+ or M 2+ /M 4+ during charge and discharge. Additionally, LEX materials have a large voltage difference during charge and discharge with significant change in a voltage profile during cycling, although conventional lithium insertion materials such as LiCoO 2 , LiNiO 2 , LiMn 2 O 4 have insignificant voltage difference. In recent years, LEX materials based on Li 2 SnO 3 , Li 3 NbO 4 , and Li 4 MoO 5 have been reported to exhibit high capacity. [10][11][12][13][14] These materials having cation-disordered rock-salt structure exhibit more than 300 mAh g −1 of reversible capacity without significant deterioration of voltage profiles. Much effort has been devoted to structural analysis of LEX materials as well as the identification of solid-state redox species. [15][16][17][18][19][20][21][22][23][24][25] For example, X-ray spectroscopic analysis, including XANES, EXAFS, etc. revealed that oxygen anion plays a crucial role upon electrochemical reactions of LEX materials. 10,14,22,23 In LEX materials, oxygen anions oxidized to a further oxidation state are stabilized by Li and transition metal cations. 14 Such a charge compensation mechanism seems to be significant in solid-sate redox reactions. Thus, reaction mechanisms of these materials have been studied, however, the origin of large voltage hysteresis has yet to be fully clarified.
In recent years, electrochemical measurements, such as Galvanostatic intermittent titration technique (GITT), electrochemical impedance spectroscopy, etc., have been performed to investigate voltage hysteresis in LEX materials. Difference has been reported in open-circuit voltages during charging and discharging processes with increasing the charge-end voltage of LEX materials. 20,21 LEX materials were examined by electrochemical measurements combined with hard X-ray photoelectron spectroscopy (HAXPES) for O 1s to confirm the behavior of oxygen anion in detail. 19 Electrochemical characterization of LEX materials is useful to analyze voltage hysteresis, however, new electrochemical methods should be developed for simultaneous observation of reversible potential and overpotential of LEX materials. These two electrochemical parameters are crucial to investigate reaction mechanism inducing voltage hysteresis, because the reversible electrode potentials and overpotential provide insights into thermodynamics and electrochemical kinetics of the reactions, respectively.
We report herein a novel electrochemical method termed as a "backstitch charge and discharge" method, in which unsymmetrical charge and discharge operations with small capacities are repeated to determine reversible potentials at various states of charge, to investigate the anomalous hysteresis of LEX materials in charge and discharge curves. In general, the voltage hysteresis of LEX materials can be observed after cycling for long time. 22,23 However, a solid solution of LiCoO 2 and Li 2 MnO 3 , Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 , 6,26,27 known as an LEX material shows the voltage hysteresis after a few tens of cycles, enabling to validate the backstitch charge and discharge method in short time. The charge and discharge curves obtained for Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 by the backstitch charge and discharge method suggested that the large voltage hysteresis resulted from the different reversible electrode potentials between charging and discharging processes in addition to overpotential. The contributions of reversible potential difference and overpotential to voltage hysteresis were also evaluated by analyzing the charge and discharge curves. 1/5 Co 2/5 Mn 2/5 ]O 2 as solid-solution of 0.5LiCoO 2 · 0.5Li 2 MnO 3 was prepared by a solidstate synthesis. LiOH · H 2 O, Co(OH) 2 and MnOOH mixed with a mortar and a pestle were heated at 1000 • C for 24 hours in the air using a tubular electric furnace. The synthesized Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 was used as a positive electrode to construct a lithium-ion battery using Li[Li 1/3 Ti 5/3 ]O 4 (LTO) (LT 855-17c, Ishihara Sangyo Lot. 0042) as the negative electrode. The electrode materials were characterized by powder X-ray diffraction. The measurements were performed with an X-ray diffractometer (XRD-6100, Shimadzu Co. Ltd. Japan) equipped with graphite monochromator, using Fe Kα radiation (40 kV and 15 mA) at a scan rate of 0.5 • per minute from 9 to 104 • .

Material synthesis and characterization.-Li[Li
Electrochemical measurements.-The structure of electrochemical cell used for material testing was reported elsewhere. 28 Positive and negative electrodes were prepared as follows: black viscous slurry consisting of 88 wt% of Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 or LTO, 6 wt% of acetylene black, and 6 wt% of polyvinylidene fluoride dispersed in N-methyl-2-pyrrolidone (NMP) was cast onto an aluminum foil. An aluminum foil was heated to evaporate NMP at 80 • C for 1 h under vacuum, and then dried under vacuum at 150 • C overnight. Finally, the aluminum foil was punched out to form a disk electrode (16.0 mm dia.). Electrochemical cells were constructed with disk electrodes supporting Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 and LTO were used as a positive and negative electrodes, respectively, and 1 M LiPF 6 dissolved in ethylene carbonate/dimethyl carbonate (3/7 by volume) solution (Kishida Chemical Co. Ltd., Japan) as an electrolyte. The LTO/Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 cell was constructed with an LTO negative electrode, which was pre-cycled and stopped at a partially reduced state, and a fresh Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 electrode. Employment of the partially reduced LTO electrode as a negative electrode is beneficial to avoid capacity fading due to deterioration of lithium-metal electrode and imbalance in state of charges 29 even for a long-term cycling. Electrochemical tests for the cells were carried out with a battery cycler (Battery Laboratory System, Keisokuki Center Co. Ltd., Japan).

Results and Discussion
Electrochemical behavior of Li [ 31 Very weak superlattice lines observed in the 2θ range from 25 to 35 degrees resulted from cation ordering of Li and transition metal ions (Co and Mn ions) in transition layers. 26,27 The increase of cobalt contents resulted in weaker superlattice lines, suggesting that the crystal symmetry changes from monoclinic to hexagonal lattice. These structural features evidenced that Li  Figure 1 indicates the electrode potential of Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 against a lithium metal electrode calculated from the electrode potential of LTO against lithium metal electrode (+1.55 V). 32 The electrochemical behavior of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 showed unique features of LEX materials, i.e., the long voltage plateau at 4.5 V at the initial charge, the large voltage difference between charge and discharge, and the sudden decrease in capacities for both charge and discharge at later cycles. The large ca- pacity, ca. 300 mAh g −1 , at the first charge is larger than the expected value accompanied by the oxidation of Co 3+ to Co 4+ observed for conventional lithium insertion materials. Capacities gradually decreased for both charge and discharge at subsequent cycles from 200 mAh g −1 at the 2nd cycle to 180 mAh g −1 at 30th cycle. Charge capacity above 4.0 V and discharge capacity above 3.5 V decreased at later cycles, where the voltage difference between charge and discharge was larger than 0.5 V. The operating voltage on charge linearly increases from 3.5 to 4.5 V while discharge curves consist of two sigmoidal curves around 4.0 and 3.3 V. Discharge voltage went down to lower than 3 V at 30th cycle from 3.5 V at the 1st cycle. The large voltage hysteresis observed in charge and discharge curves of Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 is characteristic for LEX materials. Such large voltage hysteresis has never been reported for conventional lithium insertion materials, i.e., LiMO 2 having a layered structure, LiM 2 O 4 having a spinel structure and LiMPO 4 having a forsterite structure (M = 3d transition metals). However, the capacity of Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 retained with high coulombic efficiency during the cycles indicates that the lithium-insertion reaction could proceed in spite of the large voltage hysteresis.

Polarization measurements of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2
electrode.-Open-circuit voltage (OCV) measurements were carried out for an LTO/Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 cell to scrutinize the voltage hysteresis ( Figure 2). OCVs of the cell after charged or discharged to a desired capacity were determined by leaving under open-circuit conditions for 10 h. OCVs of the cell were low and high compared with operating voltages (closed-circuit voltage; CCV) during charge and discharge, respectively. Polarization defined as a voltage difference between OCV and CCV during charge was smaller than that during discharge. The polarization of 100 to 300 mV during charge depends on state of charge, which was smaller than that during discharge, ca. 400 mV. OCVs measured during charge was not the same as those during discharge over the entire range. The maximum difference in OCVs between charge and discharge was ca. 300 mV at a certain capacity ranged from 50 to 130 mAh g −1 . The OCVs during charge were always smaller than that during discharge even when the cell was kept under the open-circuit condition for 1 month. Thus, the difference in OCVs during charge and discharge induced the large voltage hysteresis of Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 as well as other LEX materials. [23][24][25] Polarization measurements carried out at the same state of charge for both charge and discharge can elucidate the difference of OCVs during charge and discharge ( Figure 3). Polarization curves measured for the LTO/Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 cell are also shown in Figures 3a and 3b. The chemical composition or the lithium content of Li 1-x [Li 1/5 Co 2/5 Mn 2/5 ]O 2 was expected to be the same in both of the states although large voltage plateau associated with oxygen evolution at the first charge disturbs rigorous determination of the lithium content of the material. Polarization measurements were performed for the cell charged (oxidized) or discharged (reduced) with applied at several current densities for a short period (10 s). The polarization measurements at charge (Figure 3a) indicated that the applying current to the cell induced the sudden change of cell voltage owing to the activation and resistance overvoltage. The slight change in the cell voltage during oxidation or reduction reaction results from time-dependent processes, such as lithium-ion diffusion in solid matrix and/or liquid electrolyte. The cell voltage went back to 4.0 V quickly by turning off the current. Larger polarization was observed on discharging process (Figure 3b) although the polarization behavior was similar to those on charging process. Polarization voltages during oxidation and reduction were symmetric about the OCVs. Polarization voltages at 10 s after applying a certain current were plotted against the current density to depict polarization curves of the reaction on both charging and discharging processes (Figure 4). The positive and negative current densities indicate anodic (oxidation reaction) and cathodic (reduction reaction) currents, respectively. The polarization curve for charging process was almost linear (Figure 4a), while that for discharging process was not a straight line (Figure 4b). The resistance of the cell was determined to be ca. 70 cm 2 from the slope of the polarization curve for charging process. The larger slope of the polarization curve for discharging process suggests that the resistance of the electrode was larger than that for charging process. This agrees well with the polarization during charging and discharging processes evaluated from OCV measurements shown in Figure 2. Both polarization curves on charging and discharging processes are symmetric around the OCVs but not the same, suggesting that the electrochemically reversible reaction during charging process differs from that during discharging process. Consequently, OCVs on charging and discharging processes can be defined as reversible electrode potentials of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 , hence the difference between polarization voltage and OCV can be defined as overpotential. The polarization measurements revealed large voltage hysteresis of Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 consisting of two kinds of voltage difference; one is overpotential determined by a slope of polarization curves and the other is a reversible potential difference. The former is related to kinetics of the electrochemical reaction of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 electrode, because overpotential depends on current density. The latter is related to thermodynamics of electrochemical reaction of Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 , because reversible electrode potentials correspond to the free energy change of the reactions. These results indicate that minimizing the difference in reversible potentials in addition to reducing the overpotential is important to reduce or diminish voltage hysteresis in LEX materials.

Backstitch charge and discharge measurements of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 electrode.-
The reversible potential of Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 at a certain state of charge depends on how to control the state of charge. The varied reversible potentials together with overpotential induced large voltage hysteresis observed in charge and discharge curves even when a cell was operated at low current density. Therefore, reversible potential and overpotential as a function of state of charge are useful electrochemical parameters to investigate the voltage hysteresis of Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 . Polarization measurements at every state of charges shown in Figure 4 provide these two electrochemical parameters over the entire range, however, the method is too complicated and time-consuming. Therefore, a novel charge and discharge method, termed as "backstitch charge and discharge (backstitch CD)" method, was developed to measure two electrochemical parameters of reversible potentials and overpotential simultaneously. A typical time course of applied current and specific capacity during the "backstitch CD" method is depicted in Figure 5. An electrode material changes in its state of charge by repeating the cycles associated with measuring overpotential in a small capacity range, because capacity in an oxidation segment is larger than that in a reduction  corresponds to oxidation (anodic) and reduction (cathodic) currents, respectively, and (c) specific capacity based on the active material. On charging process, capacity at oxidation segments is larger than that at reduction segments, resulting in gradual increase of the state of charge. The backstitch charge and discharge method can evaluate electrochemical parameters of the lithium insertion electrode at each state of charge; reversible potential from midpoint of oxidation and reduction potentials and overpotential from the difference between oxidation and reduction potentials.
segment. Charge and discharge curves obtained by this method will be box-shaped form connected by anodic and cathodic polarization curves as shown in Figure 3. Therefore, the backstitch CD method provides reversible potentials and overpotential of electrode materials simultaneously during charge and discharge.
Charge and discharge curves obtained by the backstitch method (backstitch CD curve) of an LTO/Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 cell during charging and discharging processes were shown in Figures 6a and  6b, respectively. The cell was cycled for 20 times before recording the curves for stabilization. Red and blue lines indicate operating voltage at oxidation and reduction segments, respectively, during charging and discharging processes. Overpotential of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 electrode at every state of charge can be estimated from the voltage difference between oxidation and reduction segments, or from vertical separation in the backstitch CD curves. Reversible electrode potentials of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 electrode can be expected to be almost midpoint between oxidation and reduction voltages, because overpotential is the same on oxidation and reduction reactions evidenced by the polarization curves shown in Figure 4. The backstitch CD curves showed that the relatively large overpotential (ca. 500 mV) in lower charge capacity region on charging process (Figure 6a) decreased to ca. 100 mV by increasing charge capacity around 100 mAh g −1 . The overpotential increased again to ca. 300 mV at the end of charging process. Overpotential of 250 mV in the early stage of discharging process increase to ca. 600 mV on discharging process in the region of voltage plateau at 3 V (Figure 6b).
Two backstitch CD curves on charging and discharging processes are depicted in Figure 7. The two curves (red for charging process and blue for discharging process) were not the same over the entire range, indicating that different kinds of electrochemical reactions of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 material proceeded on charging and discharging processes in terms of thermodynamic and kinetic viewpoints. The backstitch CD curves on charging process appeared at high voltage with narrow vertical separation compared with those on discharging process, suggesting that the electrochemical reaction on charging process had a larger free energy change with faster kinetics than that on discharging process. Reversible potentials of the reaction can be estimated from the vertical position (voltage) and overpotential from the vertical separation of the backstitch CD curves without additional electrochemical measurements. Galvanostatic or potentiostatic intermittent titration techniques (GITT or PITT) can also provide the OCV and overpotential, however, only the backstitch method can provide voltage profiles during charging and discharging processes, separately, clearly indicating that the large voltage hysteresis of LEX materials results from different electrochemical reactions during charging and discharging processes.
Backstitch CD curves of Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 electrodes are quite different from continuous charge and discharge curves at low current density. The gap between the two voltage profiles is caused by a period of time on oxidation and reduction segments, i.e., repeated charge and discharge cycling with a small capacity range for the backstitch method versus continuous charge and discharge cycling with full capacity. Backstitch CD tests with changing oxidation and  reduction capacity on each segment were carried out to fill the gap (Figure 8). The capacities in oxidation and reduction segments were varied as follows: (a) 4 and 2 mAh g −1 , (b) 10 and 5 mAh g −1 , (c) 30 and 25 mAh g −1 , and (d) 60 and 55 mAh g −1 . Differences in capacity between oxidation and reduction segments are 5 mAh g −1 (b-d), except (a) 2 mAh g −1 . The increase of segment capacities dramatically changed voltage profiles. Similar backstitch CD curves obtained for the segment capacities less than 10 mAh g −1 (Figures 8a  and 8b) suggest that segment capacity of 10 mAh g −1 is enough to roughly estimate overpotentials and reversible potentials for studying the reaction mechanism of Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 . The backstitch CD curves obtained by the segment capacities greater than 10 mAh g −1 showed broad vertical separation of the curves on both charging and discharging processes. Backstitch CD curves almost the same for the largest segment capacities (Figure 8d) suggest that a segment capacity of more than 60 mAh g −1 provides almost the same electrochemical information as a continuous charge and discharge method.
Differential chronopotentiograms (dQ/dE plots) calculated from the backstitch CD curves measured for large segment capacities can clarify correspondence between oxidation and reduction peaks during charging and discharging processes independently (Figure 9). The broad oxidation peak from 3.3 to 3.8 V was observed for both charging and discharging processes. The oxidation peak above 4.0 V during charging process was larger than that during discharging process. The large reduction peak at 3.4 V was observed during discharging process, while the small broad peak at the same voltage was observed during charging process. As can be seen in Figure 9, electrochemical reactions during charging and discharging processes can be distinguished and analyzed independently by applying the backstitch method. This is one of the advantages of the backstitch CD method compared with other electrochemical method of GITT and PITT.  Figure 10 shows the four characteristic potentials obtained from the backstitch CD curves with various segment capacities in Figure 8. E Red,Cha (close red circles) and E Ox,Dis (open blue circles) shifted toward higher and lower voltages, respectively, with increasing the segment capacities, on the other hand, E Ox,Cha (open red circles) and E Red,Dis (close blue circles) showed no significant change regardless of segment capacities. Average values of four characteristic potentials were plotted as a function of the segment capacities ( Figure 11). Oxidation potentials, E Ox,Cha and E Ox,Dis (open circles), increased with increasing the segment capacities, on the other hand, reduction potentials, E Red,Cha and E Red,Dis (closed circles), decreased. The change in the potentials was partially due to a limitation of capacity range measured for the potentials, i.e, E Ox at lower capacity region and E Red at higher capacity region cannot be measured due to large segment capacities. As shown in Figure 11, average potentials extrapolated to 0 mAh g −1 of segment capacity correspond to oxidation and reduction potentials obtained from polarization measurements with very small capacity. Therefore, reversible potentials and overpotential of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 electrode can be obtained by basic arithmetic operation of four characteristic voltages when segment capacity approaches to be 0 mAh g −1 . Overpotential on both oxidation and reduction reaction corresponds to the subtraction of a reduction   The difference in average reversible potentials between charging and discharging processes as a function of segment capacity, E Rev = E Rev,Cha -E Rev,Dis . The average reversible potentials during charging and discharging processes are calculated by the following equations, E Rev,Cha = (E Ox,Cha + E Red,Cha )/2 for charging process and E Rev,Dis = (E Ox,Dis + E Red,Dis )/2 for discharging process. potential from oxidation potential for charging processes, E Cha = E Ox,Cha -E Red , Cha and discharging process, E Dis = E Ox,Dis -E Red , Dis . Figure 12a shows two overpotentials, E Cha and E Dis , were plotted against segment capacities. E Cha and E Dis were estimated to be 200 mV and 400 mV, respectively, by extrapolating the lines to 0 mAh g −1 of segment capacity. Overpotential during discharging process was two times larger than that during charging process, which agrees with the results obtained from polarization measurements shown in Figure 4. Reversible potentials can be assumed to be the midpoint between oxidation and reduction potentials, because the overpotentials on oxidation and reduction reactions were the same for the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 electrode. Therefore, average reversible potentials of the electrode during charging and discharging processes can be calculated from the following equations; E Rev , Cha = (E Ox,Cha + E Red , Cha )/2 and E Rev,Dis = (E Ox,Dis + E Red , Dis )/2, respectively. The difference between the two reversible potentials, E Rev ( = E Rev,Cha -E Rev , Dis ), of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 electrode increased with decreasing the segment capacity reached to ca. 400 mV at 0 mAh g −1 of segment capacity (Figure 12b), indicating that electrochemical reactions of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 electrode between charging and discharging processes were thermodynamically not the same although both reactions were kinetically reversible. The large voltage hysteresis of the Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 electrode resulted from two potential differences, reversible electrode potential differences and overpotential. Thus, the analysis on the backstitch CD curves allows to evaluate the contributions of the reversible electrode potential difference ( E Rev = 400 mV) and the overpotentials (200 mV and 400 mV for charging and discharging processes, respectively) to voltage hysteresis quantitatively.

Conclusions
Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 known as a lithium-excess material showed large voltage hysteresis in its charge and discharge curves, more than 500 mV, without significant capacity fading during 30 cycles. The polarization measurements revealed that Li[Li 1/5 Co 2/5 Mn 2/5 ]O 2 exhibited that electrochemical reactions of the material were not the same between charging and discharging processes, causing two different reversible electrode potentials at the same state of charges. The backstitch charge and discharge method, in which unsymmetrical charge and discharge cycles with small capacity were continuously repeated, was able to provide two important electrochemical parameters, i.e., reversible potential and overpotential, simultaneously. The difference in reversible potentials between charging and discharging processes was as large as 400 mV, consequently, electrochemical reaction of the electrode materials showing large voltage hysteresis is necessary to progress thermodynamically rather than kinetically in order to reduce or diminish voltage hysteresis. Thus, it is manifested that the large voltage hysteresis is caused by the difference in reversible electrode potentials during charging and discharging process and polarization.
The backstitch charge and discharge method disclosed here would be a powerful tool to investigate electrochemical reactions of electrode materials with large voltage hysteresis in their charge and discharge curves, because difference in reversible electrode potentials during charging and discharging processes is thought to be the main reason for large voltage hysteresis. This method is applicable to some other electrode materials for high-capacity lithium-ion batteries with large voltage hysteresis, such as anionic redox materials, 10,25 the lithiumalloy electrodes, 33 the conversion electrode, 34,35 etc. Reversible electrode potentials corresponding to free energy and overpotential corresponding to kinetics of an electrochemical reaction will provide useful insights to understand reaction mechanism.