Solid–Electrolyte Interphase Formation and Electrolyte Reduction at Li

Oct 29, 2012 - ABSTRACT: Understanding the nature and formation of the solid−electrolyte interphase (SEI) formed in electrochemical storage devices,...
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Solid−Electrolyte Interphase Formation and Electrolyte Reduction at Li-Ion Battery Graphite Anodes: Insights from First-Principles Molecular Dynamics P. Ganesh,*,† P. R. C. Kent,†,‡ and De-en Jiang§ †

Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States § Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ‡

S Supporting Information *

ABSTRACT: Understanding the nature and formation of the solid−electrolyte interphase (SEI) formed in electrochemical storage devices, such as Li-ion batteries, is most important for improving functionality. Few experiments exist that adequately probe the SEI, particularly in situ. We perform predictive ab initio molecular dynamics simulations of the anode−electrolyte interface for several electrolytes and interface functionalizations. These show strongly differing effects on the reducibility of the electrolyte. Electrolyte reduction occurs rapidly, on a picosecond time scale. Orientational ordering of electrolyte near the interface precedes reduction. The reduced species depend strongly on surface functionalization and presence of LiPF6 salt. While LiPF6 salt in ethylene carbonate is more stable at a hydrogen-terminated anode, oxygen/hydroxyl termination causes spontaneous dissociation to form LiF and other fluorophosphates. LiF migrates to the interface creating chainlike structures, consistent with experimental observations of LiF agglomeration. Inorganic products such as LiF and Li2CO3 migrate closer to the anode than purely organic components, consistent with their more ionic character. Significantly, we conclude that while the electrolyte reduction occurs at the molecular level near the interface, requiring specific alignments and proximity, the reducibility is governed by the average reduction potential barrier between the electrode (anode) and the electrolyte.



INTRODUCTION A fundamental understanding of interfacial phenomena in materials for energy storage and conversion is required to advance these technologies. For example, the performance of current Li-ion battery technology with liquid electrolytes is strongly dependent on the formation of a stable solid− electrolyte interphase (SEI) at the anode and also at the cathode in high-voltage systems.1,2 Formation of SEI is crucial to allow choice of anode materials, which operate at much lower voltages than the electrochemical stability window of electrolytes.2,3 This is because of its passivating nature, i.e., slower electron transport, while still maintaining a sufficiently high ionic transport. However, the SEI also has a large resistance, reducing the energy density of the cell and strongly affects the rate, cyclability, stability, and safety of the electrochemical cell. Continued growth of SEI due to continued electrolyte reduction with Li incorporation represents a source of capacity loss. Hence, understanding the formation and composition of SEI is crucial to designing interfaces that are more effective in blocking electron transport while maintaining high ion mobility.4−7 Despite many experiments, very little is conclusively known about the SEI’s atomic level structure, composition, and formation process. The present understanding from ex-situ © XXXX American Chemical Society

experiments is that a 10−50 nm thick anode SEI is formed by the reduction of the electrolyte, mainly in the first few charging cycles. The initial stages of SEI formation are unclear: For instance, do the reduction products first form8,9 and then grow into the SEI, or is a graphite-intercalated complex first formed,10 which subsequently reduces to form an SEI? While the exact composition of the SEI is unknown, spectroscopic studies11−15 have identified its chemical components: with ethylene carbonate (EC), the SEI is mainly composed of inorganic species such as LiF, Li2CO3, and polymers of lithium alkyl carbonate.15,16 While the popular notion was that longchained polymers blocked the anode surface, recent EELS study17 identified a predominance of LiF near the anode− electrolyte interface. Similar studies on other anodic systems have also identified LiF as the main component.5 However, the EELS studies have been unable to identify the organic species that are undoubtedly also present. As such, the exact composition and distribution of reductive species in the SEI are still unclear. Received: August 30, 2012 Revised: October 26, 2012

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Figure 1. Overlapping trajectories of Li-ion and carbonyl oxygen for (a) EC in H-terminated LiC6, (b) EC in OH-terminated edge on the left and O/OH terminated edge on the right of LiC6, (c) EC with 1 LiPF6 in H-terminated LiC6, (d) EC with 1 LiPF6 in OH-terminated edge on left and O/ OH-terminated edge on the right of LiC6, (e) PC in H-terminated LiC6, (f) DMC in OH-terminated edge on left and O/OH-terminated edge on the right of LiC6, and (g) static configurations of DMC, EC, PC, and PF6−. (h)−(l) show the reduced species for individual cases corresponding to the left column (i.e., (b)−(f)).

carbonate (PC)22 and dimethyl carbonate (DMC). Only recently has it been possible to give a full quantum-mechanical treatment of the solid−electrolyte interphase23,24 and bulk electrolyte.25,26 While a full quantum-mechanical description of the interphase is challenging, reactive classical simulations27,28,29 can be used to probe the greater time/length scales needed to know the SEI formation and composition. Such studies have also been undertaken recently29,30 with insightful results. Efforts at modeling Li-ion mobility across the

To model SEI formation, a quantum-mechanical description is required since the formation process involves redox reactions and electron transfer/transport. Electrolyte reduction has previously been studied by gas-phase quantum chemistry.16,18−22 The most probable EC reduction route was identified to be via cleavage of the OR−CR bond (Figure 1g) and requires 1e to finally reduce to stable inorganic salts with an additional electron. Similar reduction routes have been identified for other organic electrolytes, such as propylene B

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interphase have only been possible assuming ideal crystalline phases of inorganic species such as Li2CO3,31 LiF, or Li2O32 crystals. Further work in this direction is required to compare different organic solvents, reducibility changes with different surface terminations, and the role played by different salts. In this paper we perform an ab initio molecular dynamics of the initial chemistry at the interface between lithiated graphite and the electrolyte to shed light on the formation process of the SEI. The high lithium concentration in the prelithiated graphite maximizes the chance of observing reactions in our simulations. We interrogate the interfacial chemistry as a function of the electrolyte solvent (EC, PC, and DMC), the salt (with and without LiPF6), and different types of anode edge terminations (H, O, OH). We find that the band offset across the interface is strongly modified by all of the above and plays a significant role in governing the reducibility of the bulk electrolyte and the formation of reductive species. A key reaction found is the formation of LiF; once formed, LiF is found to most readily migrate to the interface, passivating it against further electrolyte reduction. Of the simulated scenarios, the limiting value of the electrochemical reduction potential barrier between the electrode and the electrolyte after the initial reduction to form SEI is significantly different when LiF is formed from other cases where LiF is not formed. This is a direct proof of the important role of LiF as a major SEI component in changing the electronic structure of the electrode and hence in changing the further reduction of the solvent molecules near the interphase.

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RESULTS AND DISCUSSION

Role of Functionalized Graphite Edges. As a baseline, we first explored the interface of LiG with pure EC (that is, with no salt present). We considered two scenarios of edge termination for LiG: all-H passivation as in Figure 1a and a mixture of O/OH groups as in Figure 1b (also see Figure S2 in the Supporting Information). These scenarios represent extremes of what might occur naturally. In the H termination case, no reaction products were seen during the 11 ps AIMD simulation. In the case of O/OH terminations, a few EC molecules underwent rapid reductive decomposition. The observed reduction products are shown in Figure 1h. The EC breakdown happens via the cleavage of the CR−OR bonds (Figure 1g), forming CO32− and C2H4. The reduction occurs first at the interface, and interfacial carbonate ions quickly form (LiCO3)−, followed by a stable Li2CO3, which is then seen to migrate closer to the anode interface. This is consistent with gas phase predictions at low EC concentrations,16 as would be expected near the interface. Another EC molecule dissociates to form C2H4 and CO2 + O*. We also find a C2H3O− nucleophilic species, formed from the substitution of one of the H atom of C2H4 with the free oxygen radical. The free proton steals a proton from another terminal hydroxyl to form a stable H2 molecule. Nucleophilic attack on EC is one of the proposed mechanism to form longer polymeric lithium alkyl carbonates.9 The presence of Li2CO3 and C2H3O− indicates that the 2e reduction routes39 may be predominant at the initial stages of EC decomposition at the interface. Upon inspection, the main reduction sites at the interface appeared to be those with oxygen termination. This is because oxygen-terminated sites are better at charge transfer than H-terminated sites40 and hence lead to electrolyte reduction. Figures 1a,b show the overlapping trajectories of lithium and carbonyl oxygen of EC in the two cases of all-H-termination and O/OH mixed termination. The localized motion of the carbonyl oxygens in the overlapped trajectory plots, where present, identifies the orientational ordering of the molecules. While the carbonyl oxygens of EC and lithium motion appear uncorrelated in the case of H-termination, they are strongly correlated, even in the bulklike center in the case of O/OHtermination. The correlated motion and subsequent orientational ordering of EC precede Li-ion diffusion into the solvent and subsequent EC reduction. Li-ion diffusion inside the graphite is high in H-terminated case, but the ions do not pass the terminal hydrogen atoms and do not enter the electrolyte easily. In contrast, with O/OH-termination, lithium anchors to terminal oxygens and diffuses more easily into solution, creating a reactive interface as seen in Figure 1b. This observation also suggests that availability of atomic lithium is crucial in solvent reduction at the interface. Without lithium at the interface, a distinct spatial gap is seen between the EC solvent and LiG. Role of Salt in Solution. In Li-ion batteries, usually ∼1 M Li salt such as LiPF6 is dissolved in the electrolyte. Hence, it is imperative to consider the effect of the salt on the interfacial chemistry. We found that inclusion of salt causes substantial changes in the observed chemistry. In the above case of the EC solvent interfacing with H-terminated carbon edges for LiG, a single EC molecule was substituted by a fully dissolvated LiPF6 salt (Li+ is surrounded by four EC molecules, while the PF6− anion is initially ∼8 Å away from Li+). In contrast to the case of the pure solvent, Li ions readily diffuse from LiG into the electrolyte, and EC reduction occurs as shown in Figure 1c.



COMPUTATIONAL DETAILS Ab initio molecular dynamics (AIMD) calculations were performed using the Vienna Ab Initio Simulation Package (VASP),33 with the PBE-GGA density functional and projectoraugmented wave potentials (PAW).34,35 The PBE-GGA was recently shown to give consistent results with the more accurate but time-consuming hybrid-functional HSE,36 which is not yet computationally affordable for molecular dynamics. A non-spinpolarized calculation was performed and should give a good description of the reduction.36 Calculations mainly used a 300 eV plane-wave cutoff, augmentation energy of 645 eV, and the Γ k-point. A few trajectories were checked at 400 eV (see Supporting Information). A 0.1 eV Gaussian smearing accelerated electronic convergence. The anode comprised of four layers of fully lithiated graphite (LiG) with an arm-chair edge (Figure 1). The composition was Li48C288, corresponding to stage 1 LiC6.37 Carbon arm-chair edges were functionalized with either all hydrogens (i.e., Htermination) or a mix of oxygens and hydroxyls (i.e., O/OHtermination on one edge and all OH-termination on the other). The simulation cell size was 29.95 Å × 12.78 Å × 14.824 Å. For pure solvents, a density of about 1.32 g/cm3 was used for EC (i.e., 20 molecules), 1.20 g/cm3 for PC (i.e., 16 molecules), and 1.07 g/cm3 for DMC (i.e., 15 molecules). To include a salt in the EC solvent, one EC molecule was substituted with LiPF6. Initial geometries of the electrolyte were created with Materials Studio and/or PACKMOL38 and then quenched using density functional forces. AIMD simulations were performed at an elevated temperature of 450 K using a Nose thermostat to allow fast equilibration. A tritium mass was used to allow a larger 1 fs time-steps. At least 11 ps of dynamic simulations was performed for each system studied (Figure 1). C

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Figure 2. Disintegration of PF6− to form LiF chains at the anode interface and PF3. A PF4 intermediate is seen to form in (d). The whole cycle takes about 3.3 ps. The presence of fluorine also increases the local lithium concentration in neighboring interfacial sites (color scheme follows Figure 1).

This could be because the dissolvated salt is not sufficiently screened by solvent, leading to attractive interactions with the Li ions in the anode. In addition to the usual EC decomposition route seen in the O/OH-termination, a new species pair, CO + LiO2C2H4, is seen to form at the interface at ∼2 ps (Figure 1i). The reaction occurs with the initial formation of CO + O(C2H4)O2−, which then combines with one Li+ to form CO + LiO2C2H4− and then combines with another Li+ to form the more stable and neutral Li2O2C2H4. CO produced remains stable for the remaining simulation time. Ethylene carbonate is an ester formed from ethylene glycol and CO2 in the presence of a catalyst. This reduction route suggests the reverse reaction where the intermediary forms a stable lithium glycol compound (Li2O2C2H4) with CO evolution. For this case of H-terminated carbon edges, the PF6− anion remains stable over the entire simulation time frame, and no fluorine related chemistry is observed. When the edges are terminated with a mixture of O/OH (Figure 1d), the PF6− anion, in contrast, is seen to decompose. It first decomposes to form PF 5 and LiF. 41 The PF 5 subsequently decomposes to another LiF and forms a Li fluorophosphate (Figure 1j). A PF3 is seen in this process. Decomposition of PF6− in EC-rich electrolytes to form LiF and PxFy compounds42 has been experimentally detected using XPS. Experiments also find Li2O, but we did not see this in our simulations. In the presence of water, experiments find that PF5 reacts to form PF3O. Our simulations show that the LiF molecules diffuse very quickly, migrating to the interface and remaining stable there. Within the small interface in the cell, LiFs are seen to form chains (Figures 1d and 2e−d). In reality, we would expect these LiF chains at the interface to agglomerate and grow to form nanoparticles/nanocrystals. This is consistent with in-situ results that predominantly find large regions of LiF in the SEI.5,17 The high diffusivity of LiF is due to its charge neutrality and low polarizability compared to the solvents in the solution. This further leads to its entrapment in regions with high LiF concentrations as would appear at the interface. As for the EC solvent, we found a different reduction species, HO(C2H4)CO2− (Figure 1j and Figure S3). This is formed via the following mechanism at the purely OHterminated interface:

C3H4O3 → 2CH 2 + CO32 − → CH 2O + CH 2CO2 → O(C2H4)CO2 2 − → HO(C2H4)CO2−

The resulting HO(C2H4)CO2− is seen to rotate and transiently form HO(C2H4)COOH within the length of our simulation. Terminal hydroxyls act as a source of protons to convert the aldehydes to an alcohol. Role of Electrochemistry. We repeated the calculation with H-termination and a LiPF6 salt with an additional background electron to mimic a uniform potential. The LiPF6 is found to be very stable as before. The excess electron localized on an EC molecule leading to the well-known OR−CR bond cleavage. This process occurs with no other subsequent reaction and leads to a large instantaneous drop in energy by ∼101 kcal/mol (4.4 eV), about 30 kcal/mol lower than gasphase enthalpies for the same process.18 A lower reaction enthalpy is consistent with increased screening in solution. Role of Solvent Choice (EC vs PC vs DMC). In addition to surface functionalization and salt addition, the solvent is another variable in the observed chemistry. To explore changes in the reduction chemistry due to different solvents, we simulated PC between a H-terminated graphite edge. While EC did not show any reduction, as discussed above, PC is readily reduced (Figure 1e). Two reduction pathways were observed. In one case, PC reduced to form CO32− and propylene. The carbonate anion then forms Li2CO3 as predicted by gas phase calculations.20 In the other case (Figure 1k), PC dissociated to CO2 + C2H3O− + CH3−. CH3− and C2H3O− subsequently form neutral LiCH3 and C2H3OLi species. The inorganic salts are seen to be very stable close to the interface for the remaining simulation time frame. Experiments find C2H3O to be a major component of the basal plane SEI.43 Like in the previous cases, the reduction was spontaneous and occurs with the diffusion of Li-ions into the solvent. Orientational ordering of molecules (Figure 1e) leads to formation of many PC−Li+ complexes at the interface. This is the main rate-limiting step for PC reduction and occurs with a 0.5 eV barrier in the gas phase.20 Li-ion diffusion is known to be higher in PC compared to EC at 450 K25 and could be one reason why PC reduces so readily compared to EC in our simulation. (Simulations of PC with a higher plane-wave cutoff are discussed in the Supporting Information.) D

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Department of Energy, Office of Science, Office of Basic Energy. Computations used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231.

Using DMC as a solvent in O/OH-terminated LiC6, no reductive decomposition was seen, similar to the EC case with H-terminated LiC6. While all the starting DMC molecules were in the cis−cis configuration (Figure 1g), two molecules at the interface underwent spontaneous transformation to cis−trans forming Li+ complexes with a Li−Oc distance of ∼1.91 Å (Figure 1l).





(1) Marom, R.; Amalraj, S. F.; Leifer, N.; Jacob, D.; Aurbach, D. J. Mater. Chem. 2011, 21, 9938. (2) Goodenough, J. B.; Kim, Y. Chem. Mater. 2010, 22, 587. (3) Xu, K. Energies 2010, 3, 135. (4) Xu, K. Chem. Rev. 2004, 104, 4303. (5) Wang, F.; Robert, R.; Chernova, N. A.; Pereira, N.; Omenya, F.; Badway, F.; Hua, X.; Ruotolo, M.; Zhang, R.; Wu, L.; Volkov, V.; Su, D.; Key, B.; Whittingham, M. S.; Grey, C. P.; Amatucci, G. G.; Zhu, Y.; Graetz, J. J. Am. Chem. Soc. 2011, 110925155717005. (6) Ota, H.; Sakata, Y.; Inoue, A.; Yamaguchi, S. J. Electrochem. Soc. 2004, 151, A1659. (7) Peled, E.; Menachem, C.; BarTow, D.; Melman, A. J. Electrochem. Soc. 1996, 143, L4. (8) Peled, E.; Golodnitsky, D.; Menachem, C.; Bar-Tow, D. J. Electrochem. Soc. 1998, 145, 3482. (9) Aurbach, D.; Levi, M. D.; Levi, E.; Schechter, A. J. Phys. Chem. B 1997, 101, 2195. (10) Besenhard, J. O.; Winter, M.; Yang, J.; Biberacher, W. J. Power Sources 1995, 54, 228. (11) Chusid, O.; Ely, Y. E.; Aurbach, D.; Babai, M.; Carmeli, Y. J. Power Sources 1993, 43, 47. (12) Choi, H. C.; Lee, S. Y.; Kim, S. B.; Kim, M. G.; Lee, M. K.; Shin, H. J.; Lee, J. S. J. Phys. Chem. B 2002, 106, 9252. (13) Baranchugov, V.; Markevich, E.; Salitra, G.; Aurbach, D.; Semrau, G.; Schmidt, M. A. J. Electrochem. Soc. 2008, 155, A217. (14) Markevich, E.; Baranchugov, V.; Salitra, G.; Aurbach, D.; Schmidt, M. A. J. Electrochem. Soc. 2008, 155, A132. (15) Aurbach, D.; Markovsky, B.; Weissman, I.; Levi, E.; Ein-Eli, Y. Electrochim. Acta 1999, 45, 67. (16) Wang, Y. X.; Nakamura, S.; Ue, M.; Balbuena, P. B. J. Am. Chem. Soc. 2001, 123, 11708. (17) Wang, F.; Graetz, J.; Moreno, M. S.; Ma, C.; Wu, L. J.; Volkov, V.; Zhu, Y. M. ACS Nano 2011, 5, 1190. (18) Tasaki, K.; Kanda, K.; Kobayashi, T.; Nakamura, S.; Ue, M. J. Electrochem. Soc. 2006, 153, A2192. (19) Han, Y. K.; Lee, S. U. Theor. Chem. Acc. 2004, 112, 106. (20) Vollmer, J. M.; Curtiss, L. A.; Vissers, D. R.; Amine, K. J. Electrochem. Soc. 2004, 151, A178. (21) Wang, Y. X.; Nakamura, S.; Tasaki, K.; Balbuena, P. B. J. Am. Chem. Soc. 2002, 124, 4408. (22) Xing, L. D.; Wang, C. Y.; Li, W. S.; Xu, M. Q.; Meng, X. L.; Zhao, S. F. J. Phys. Chem. B 2009, 113, 5181. (23) Leung, K.; Budzien, J. L. Phys. Chem. Chem. Phys. 2010, 12, 6583. (24) Leung, K.; Qi, Y.; Zavadil, K. R.; Jung, Y. S.; Dillon, A. C.; Cavanagh, A. S.; Lee, S.-H.; George, S. M. J. Am. Chem. Soc. 2011, 133, 14741. (25) Ganesh, P.; Jiang, D. E.; Kent, P. R. C. J. Phys. Chem. B 2011, 115, 3085. (26) Del Popolo, M. G.; Lynden-Bell, R. M.; Kohanoff, J. J. Phys. Chem. B 2005, 109, 5895. (27) Han, S. S.; van Duin, A. C. T.; Goddard, W. A.; Lee, H. M. J. Phys. Chem. A 2005, 109, 4575. (28) Nielson, K. D.; van Duin, A. C. T.; Oxgaard, J.; Deng, W. Q.; Goddard, W. A. J. Phys. Chem. A 2005, 109, 493. (29) Kim, S. P.; van Duin, A. C. T.; Shenoy, V. B. J. Power Sources 2011, 196, 8590. (30) Bedrov, D.; Smith, G. D.; van Duin, A. C. T. J. Phys. Chem. A. 2012, 116, 2978−2985. (31) Iddir, H.; Curtiss, L. A. J. Phys. Chem. C 2010, 114, 20903.

CONCLUSION To conclude, we have performed ab initio molecular dynamics to investigate the reduction of electrolytes forming solid− electrolyte interphase. Our simulations are restricted to short time scales and length scales, but we find multiple accessible reduction pathways. The reduction products are consistent with existing literature but are not deterministic; i.e., small changes in our simulation parameters lead to different pathways, possibly due to the large driving force for electrolyte reduction in our simulations. Our results suggest that reduction of cyclic carbonate electrolytes occur via a 2e process, and Li2CO3 should be expected to form a vital SEI component near the anode surface. LiF forms via salt decomposition and agglomerates at the anode interface, forming an important component of the SEI. This result highlights the importance of reducing fluorine chemistry, e.g., via non-fluorinated salts, for Li-ion battery applications. Given the importance of inorganic species such as LiF and Li2CO3 naturally formed near the electrode upon electrolyte reduction, engineering thin layers of similar inorganic materials, either crystalline or amorphous, to act as an electronically insulating barrier while allowing ionic transport proves to be an interesting pathway to design artificial SEI. In addition to finding new electrolyte reduction pathways, we also find that the electrolyte reduction is strongly influenced by anode surface functionalization and presence of reduced species. While a H-terminated surface does not reduce EC or DMC, an O/OH terminated surface quickly reduces EC. PC by itself is seen to be able to cause more mechanical damage to the graphene layer than EC. With Li present, PC decomposes quickly via an initial formation of Li+ complexes. The ease of formation of Li+−PC complexes in solution and the instability of graphite layers (Supporting Information) at low lithium concentrations corroborate the possibility of PC intercalation into graphite.



ASSOCIATED CONTENT

S Supporting Information *

Sliding and mechanical instability of graphene sheets, formation of high-energy products in our simulation, electrochemical reduction barrier, and interfacial electrochemical potential. This material is available free of charge via the Internet at http:// pubs.acs.org.



REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was supported as part of the Fluid Interface Reactions, Structures and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. E

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(32) Chen, Y. C.; Ouyang, C. Y.; Song, L. J.; Sun, Z. L. J. Phys. Chem. C 2011, 115, 7044. (33) Kresse, G.; Furthmuller, J. Phys. Rev. B 1996, 54, 11169. (34) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758. (35) Blochl, P. E. Phys. Rev. B 1994, 50, 17953. (36) Yu, J. M.; Balbuena, P. B.; Budzien, J.; Leung, K. J. Electrochem. Soc. 2011, 158, A400. (37) Persson, K.; Hinuma, Y.; Meng, Y. S.; Van der Ven, A.; Ceder, G. Phys. Rev. B 2010, 82, 125416. (38) Martinez, L.; Andrade, R.; Birgin, E. G.; Martinez, J. M. J. Comput. Chem. 2009, 30, 2157. (39) Li, T.; Balbuena, P. B. Chem. Phys. Lett. 2000, 317, 421. (40) Girard, H.; Simon, N.; Ballutaud, D.; Herlern, M.; Etcheberry, A. Diamond Relat. Mater. 2007, 16, 316. (41) Gachot, G.; Ribiere, P.; Mathiron, D.; Grugeon, S.; Armand, M.; Leriche, J. B.; Pilard, S.; Laruelle, S. Anal. Chem. 2011, 83, 478. (42) Bar-Tow, D.; Peled, E.; Burstein, L. J. Electrochem. Soc. 1999, 146, 824. (43) Peled, E.; Towa, D. B.; Merson, A.; Burstein, L. J. New Mater. Electrochem. Syst. 2000, 3, 319.

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