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Review Article

Electrochemomechanics of Electrodes in Li-Ion Batteries: A Review

[+] Author and Article Information
Rong Xu

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47906

Kejie Zhao

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47906
e-mail: kjzhao@purdue.edu

1Corresponding author.

Manuscript received June 11, 2016; final manuscript received November 16, 2016; published online December 12, 2016. Assoc. Editor: George Nelson.

J. Electrochem. En. Conv. Stor. 13(3), 030803 (Dec 12, 2016) (9 pages) Paper No: JEECS-16-1079; doi: 10.1115/1.4035310 History: Received June 11, 2016; Revised November 16, 2016

A Li-ion battery is a system that dynamically couples electrochemistry and mechanics. The electrochemical processes of Li insertion and extraction in the electrodes lead to a wealth of phenomena of mechanics, such as large deformation, plasticity, cavitation, fracture, and fatigue. Likewise, mechanics influences the thermodynamics and kinetics of interfacial reactions, ionic transport, and phase transformation of the electrodes. The emergence of high-capacity batteries particularly enriches the field of electrochemomechanics. This paper reviews recent observations on the intimate coupling between stresses and electrochemical processes, including diffusion-induced stresses, stress-regulated surface charge transfer, interfacial reactions, inhomogeneous growth of lithiated phases, instability of solid-state reaction front (SSRF), as well as lithiation-modulated plasticity and fracture in the electrodes. Most of the coupling effects are at the early stage of study and are to be better understood. We focus on the elaboration of these phenomena using schematic illustration. A deep understanding of the interactions between mechanics and electrochemistry and bridging these interdisciplinary fields can be truly rewarding in the development of resilient high-capacity batteries.

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References

Armand, M. , and Tarascon, J. M. , 2008, “ Building Better Batteries,” Nature, 451(7179), pp. 652–657. [CrossRef] [PubMed]
Whittingham, M. S. , 2008, “ Materials Challenges Facing Electrical Energy Storage,” MRS Bull., 33(4), pp. 411–419. [CrossRef]
Scrosati, B. , and Garche, J. , 2010, “ Lithium Batteries: Status, Prospects and Future,” J. Power Sources, 195(9), pp. 2419–2430. [CrossRef]
Nitta, N. , Wu, F. , Lee, J. T. , and Yushin, G. , 2015, “ Li-Ion Battery Materials: Present and Future,” Mater. Today, 18(5), pp. 252–264. [CrossRef]
Kasavajjula, U. , Wang, C. , and Appleby, A. J. , 2007, “ Nano- and Bulk-Silicon-Based Insertion Anodes for Lithium-Ion Secondary Cells,” J. Power Sources, 163(2), pp. 1003–1039. [CrossRef]
Zhang, W. J. , 2011, “ A Review of the Electrochemical Performance of Alloy Anodes for Lithium-Ion Batteries,” J. Power Sources, 196(1), pp. 13–24. [CrossRef]
McDowell, M. T. , Xia, S. , and Zhu, T. , 2016, “ The Mechanics of Large-Volume-Change Transformations in High-Capacity Battery Materials,” Extreme Mech. Lett., 9(Pt. 3), pp. 480–494. [CrossRef]
Cannarella, J. , and Arnold, C. B. , 2014, “ Stress Evolution and Capacity Fade in Constrained Lithium-Ion Pouch Cells,” J. Power Sources, 245, pp. 745–751. [CrossRef]
Sun, H. , Xin, G. , Hu, T. , Yu, M. , Shao, D. , Sun, X. , and Lian, J. , 2014, “ High-Rate Lithiation-Induced Reactivation of Mesoporous Hollow Spheres for Long-Lived Lithium-Ion Batteries,” Nat. Commun., 5, p. 4526. [PubMed]
Baggetto, L. , Danilov, D. , and Notten, P. H. L. , 2011, “ Honeycomb-Structured Silicon: Remarkable Morphological Changes Induced by Electrochemical (De)Lithiation,” Adv. Mater., 23(13), pp. 1563–1566. [CrossRef] [PubMed]
Chan, C. K. , Peng, H. , Liu, G. , McIlwrath, K. , Zhang, X. F. , Huggins, R. A. , and Cui, Y. , 2008, “ High-Performance Lithium Battery Anodes Using Silicon Nanowires,” Nat. Nanotechnol., 3(1), pp. 31–35. [CrossRef] [PubMed]
Kim, H. , Han, B. , Choo, J. , and Cho, J. , 2008, “ Three-Dimensional Porous Silicon Particles for Use in High-Performance Li Secondary Batteries,” Angew. Chem., 120(52), pp. 10305–10308. [CrossRef]
Liu, N. , Wu, H. , McDowell, M. T. , Yao, Y. , Wang, C. M. , and Cui, Y. , 2012, “ A Yolk-Shell Design for Stabilized and Scalable Li-Ion Battery Alloy Anodes,” Nano Lett., 12(6), pp. 3315–3321. [CrossRef] [PubMed]
Wu, H. , Zheng, G. Y. , Liu, N. A. , Carney, T. J. , Yang, Y. , and Cui, Y. , 2012, “ Engineering Empty Space Between Si Nanoparticles for Li-Ion Battery Anodes,” Nano Lett., 12(2), pp. 904–909. [CrossRef] [PubMed]
Yao, Y. , McDowell, M. T. , Ryu, I. , Wu, H. , Liu, N. , Hu, L. , Nix, W. D. , and Cui, Y. , 2011, “ Interconnected Silicon Hollow Nanospheres for Lithium-Ion Battery Anodes With Long Cycle Life,” Nano Lett., 11(7), pp. 2949–2954. [CrossRef] [PubMed]
Cui, L. F. , Hu, L. B. , Choi, J. W. , and Cui, Y. , 2010, “ Light-Weight Free-Standing Carbon Nanotube-Silicon Films for Anodes of Li-Ion Batteries,” ACS Nano, 4(7), pp. 3671–3678. [CrossRef] [PubMed]
Wang, C. M. , Li, X. L. , Wang, Z. G. , Xu, W. , Liu, J. , Gao, F. , Kovarik, L. , Zhang, J. G. , Howe, J. , Burton, D. J. , Liu, Z. Y. , Xiao, X. C. , Thevuthasan, S. , and Baer, D. R. , 2012, “ In Situ TEM Investigation of Congruent Phase Transition and Structural Evolution of Nanostructured Silicon/Carbon Anode for Li Ion Batteries,” Nano Lett., 12(3), pp. 1624–1632. [CrossRef] [PubMed]
Yamada, M. , Ueda, A. , Matsumoto, K. , and Ohzuku, T. , 2011, “ Silicon-Based Negative Electrode for High-Capacity Li-Ion Batteries: “SiO”-Carbon Composite,” J. Electrochem. Soc., 158(4), pp. A417–A421. [CrossRef]
Sandu, G. , Brassart, L. , Gohy, J. F. , Pardoen, T. , Melinte, S. , and Vlad, A. , 2014, “ Surface Coating Mediated Swelling and Fracture of Silicon Nanowires During Lithiation,” ACS Nano, 8(9), pp. 9427–9436. [CrossRef] [PubMed]
Wang, J. W. , Liu, X. H. , Zhao, K. J. , Palmer, A. , Patten, E. , Burton, D. , Mao, S. X. , Suo, Z. G. , and Huang, J. Y. , 2012, “ Sandwich-Lithiation and Longitudinal Crack in Amorphous Silicon Coated on Carbon Nanofibers,” ACS Nano, 6(10), pp. 9158–9167. [CrossRef] [PubMed]
Nowack, L. V. , Bunjaku, T. , Wegner, K. , Pratsinis, S. E. , Luisier, M. , and Wood, V. , 2015, “ Design and Fabrication of Microspheres With Hierarchical Internal Structure for Tuning Battery Performance,” Adv. Sci., 2(6), p. 1500078.
Magasinski, A. , Dixon, P. , Hertzberg, B. , Kvit, A. , Ayala, J. , and Yushin, G. , 2010, “ High-Performance Li-Ion Nodes Using a Hierarchical Bottom-Up Approach,” Nat. Mater., 9(4), pp. 353–358. [CrossRef] [PubMed]
Chen, X. L. , Gerasopoulos, K. , Guo, J. C. , Brown, A. , Wang, C. S. , Ghodssi, R. , and Culver, J. N. , 2011, “ A Patterned 3D Silicon Anode Fabricated by Electrodeposition on a Virus-Structured Current Collector,” Adv. Funct. Mater., 21(2), pp. 380–387. [CrossRef]
Haftbaradaran, H. , Xiao, X. C. , Verbrugge, M. W. , and Gao, H. J. , 2012, “ Method to Deduce the Critical Size for Interfacial Delamination of Patterned Electrode Structures and Application to Lithiation of Thin-Film Silicon Islands,” J. Power Sources, 206, pp. 357–366. [CrossRef]
Soni, S. K. , Sheldon, B. W. , Xiao, X. C. , Verbrugge, M. W. , Ahn, D. , Haftbaradaran, H. , and Gao, H. J. , 2012, “ Stress Mitigation During the Lithiation of Patterned Amorphous Si Islands,” J. Electrochem. Soc., 159(1), pp. A38–A43. [CrossRef]
Beaulieu, L. Y. , Eberman, K. W. , Turner, R. L. , Krause, L. J. , and Dahn, J. R. , 2001, “ Colossal Reversible Volume Changes in Lithium Alloys,” Solid State Lett., 4(9), pp. A137–A140. [CrossRef]
Zhao, K. , Pharr, M. , Vlassak, J. J. , and Suo, Z. , 2010, “ Fracture of Electrodes in Lithium-Ion Batteries Caused by Fast Charging,” J. Appl. Phys., 108(7), p. 073517. [CrossRef]
Mukhopadhyay, A. , and Sheldon, B. W. , 2014, “ Deformation and Stress in Electrode Materials for Li-Ion Batteries,” Prog. Mater. Sci., 63, pp. 58–116. [CrossRef]
Zhao, K. , Pharr, M. , Wan, Q. , Wang, W. L. , Kaxiras, E. , Vlassak, J. J. , and Suo, Z. , 2012, “ Concurrent Reaction and Plasticity During Initial Lithiation of Crystalline Silicon in Lithium-Ion Batteries,” J. Electrochem. Soc., 159(3), pp. A238–A243. [CrossRef]
Choi, J. W. , McDonough, J. , Jeong, S. , Yoo, J. S. , Chan, C. K. , and Cui, Y. , 2010, “ Stepwise Nanopore Evolution in One-Dimensional Nanostructures,” Nano Lett., 10(4), pp. 1409–1413. [CrossRef] [PubMed]
Liu, X. H. , Huang, S. , Picraux, S. T. , Li, J. , Zhu, T. , and Huang, J. Y. , 2011, “ Reversible Nanopore Formation in Ge Nanowires During Lithiation–Delithiation Cycling: An In Situ Transmission Electron Microscopy Study,” Nano Lett., 11(9), pp. 3991–3997. [CrossRef] [PubMed]
Zhao, K. , Wang, W. L. , Gregoire, J. , Pharr, M. , Suo, Z. , Vlassak, J. J. , and Kaxiras, E. , 2011, “ Lithium-Assisted Plastic Deformation of Silicon Electrodes in Lithium-Ion Batteries: A First-Principles Theoretical Study,” Nano Lett., 11(7), pp. 2962–2967. [CrossRef] [PubMed]
Zhao, K. , Tritsaris, G. A. , Pharr, M. , Wang, W. L. , Okeke, O. , Suo, Z. , Vlassak, J. J. , and Kaxiras, E. , 2012, “ Reactive Flow in Silicon Electrodes Assisted by the Insertion of Lithium,” Nano Lett., 12(8), pp. 4397–4403. [CrossRef] [PubMed]
Brassart, L. , and Suo, Z. , 2013, “ Reactive Flow in Solids,” J. Mech. Phys. Solids, 61(1), pp. 61–77. [CrossRef]
Huang, X. , Yang, H. , Liang, W. , Raju, M. , Terrones, M. , Crespi, V . H. , van Duin, A. C. , and Zhang, S. , 2013, “ Lithiation Induced Corrosive Fracture in Defective Carbon Nanotubes,” Appl. Phys. Lett., 103(15), p. 153901. [CrossRef]
Xu, R. , Vasconcelos, L. S. , and Zhao, K. , 2016, “ Computational Analysis of Chemomechanical Behaviors of Composite Electrodes in Li-Ion Batteries,” J. Mater. Res., 31(18), pp. 2715–2727. [CrossRef]
Yang, H. , Liang, W. , Guo, X. , Wang, C. M. , and Zhang, S. , 2015, “ Strong Kinetics-Stress Coupling in Lithiation of Si and Ge Anodes,” Extreme Mech. Lett., 2, pp. 1–6. [CrossRef]
Sheldon, B. W. , Soni, S. K. , Xiao, X. , and Qi, Y. , 2011, “ Stress Contributions to Solution Thermodynamics in Li-Si Alloys,” Electrochem. Solid-State Lett., 15(1), pp. A9–A11. [CrossRef]
Sethuraman, V. A. , Chon, M. J. , Shimshak, M. , Srinivasan, V. , and Guduru, P. R. , 2010, “ In Situ Measurements of Stress Evolution in Silicon Thin Films During Electrochemical Lithiation and Delithiation,” J. Power Sources, 195(15), pp. 5062–5066. [CrossRef]
Pharr, M. , Suo, Z. , and Vlassak, J. J. , 2014, “ Variation of Stress With Charging Rate Due to Strain-Rate Sensitivity of Silicon Electrodes of Li-Ion Batteries,” J. Power Sources, 270, pp. 569–575. [CrossRef]
Spaepen, F. , 2005, “ A Survey of Energies in Materials Science,” Philos. Mag., 85(26), pp. 2979–2987. [CrossRef]
Zhao, K. , Pharr, M. , Cai, S. , Vlassak, J. J. , and Suo, Z. , 2011, “ Large Plastic Deformation in High-Capacity Lithium-Ion Batteries Caused by Charge and Discharge,” J. Am. Ceram. Soc., 94(s1), pp. s226–s235. [CrossRef]
Soni, S. K. , Sheldon, B. W. , Xiao, X. , Bower, A. F. , and Verbrugge, M. W. , 2012, “ Diffusion Mediated Lithiation Stresses in Si Thin Film Electrodes,” J. Electrochem. Soc., 159(9), pp. A1520–A1527. [CrossRef]
Gao, Y. F. , and Zhou, M. , 2011, “ Strong Stress-Enhanced Diffusion in Amorphous Lithium Alloy Nanowire Electrodes,” J. Appl. Phys., 109(1), p. 014310. [CrossRef]
Gao, Y. F. , and Zhou, M. , 2013, “ Coupled Mechano-Diffusional Driving Forces for Fracture in Electrode Materials,” J. Power Sources, 230, pp. 176–193. [CrossRef]
Pan, J. , Zhang, Q. , Li, J. , Beck, M. J. , Xiao, X. , and Cheng, Y. T. , 2015, “ Effects of Stress on Lithium Transport in Amorphous Silicon Electrodes for Lithium-Ion Batteries,” Nano Energy, 13, pp. 192–199. [CrossRef]
Choi, Y. M. , and Pyun, S. I. , 1997, “ Effects of Intercalation-Induced Stress on Li Transport Through Porous LiCoO2 Electrode,” Solid State Ionics, 99(3), pp. 173–183. [CrossRef]
Prussin, S. , 1961, “ The Generation and Distribution of Dislocations by Solute Diffusion,” J. Appl. Phys., 32(10), p. 1876. [CrossRef]
Larche, F. , and Cahn, J. W. , 1973, “ Linear Theory of Thermochemical Equilibrium of Solids Under Stress,” Acta Metall., 21(8), pp. 1051–1063. [CrossRef]
Larche, F. , and Cahn, J. W. , 1978, “ Non-Linear Theory of Thermochemical Equilibrium of Solids Under Stress,” Acta Metall., 26(1), pp. 53–60. [CrossRef]
Li, J. C. M. , 1978, “ Physical-Chemistry of Some Microstructural Phenomena,” Metall. Mater. Trans. A, 9(10), pp. 1353–1380. [CrossRef]
Stephenson, G. B. , 1988, “ Deformation During Interdiffusion,” Acta Metall., 36(10), pp. 2663–2683. [CrossRef]
Christensen, J. , and Newman, J. , 2006, “ Stress Generation and Fracture in Li Insertion Materials,” J. Solid State Electrochem., 10(5), pp. 293–319. [CrossRef]
Christensen, J. , and Newman, J. , 2006, “ A Mathematical Model of Stress Generation and Fracture in Li Manganese Oxide,” J. Electrochem. Soc., 153(6), pp. A1019–A1030. [CrossRef]
Zhang, X. C. , Shyy, W. , and Sastry, A. M. , 2007, “ Numerical Simulation of Intercalation-Induced Stress in Li-Ion Battery Electrode Particles,” J. Electrochem. Soc., 154(10), pp. A910–A916. [CrossRef]
Zhang, X. C. , Sastry, A. M. , and Shyy, W. , 2008, “ Intercalation-Induced Stress and Heat Generation Within Single Li-Ion Battery Cathode Particles,” J. Electrochem. Soc., 155(7), pp. A542–A552. [CrossRef]
Golmon, S. , Maute, K. , Lee, S. H. , and Dunn, M. L. , 2010, “ Stress Generation in Silicon Particles During Li Insertion,” Appl. Phys. Lett., 97(3), p. 033111. [CrossRef]
Cheng, Y. T. , and Verbrugge, M. W. , 2009, “ Evolution of Stress Within a Spherical Insertion Electrode Particle Under Potentiostatic and Galvanostatic Operation,” J. Power Sources, 190(2), pp. 453–460. [CrossRef]
Cheng, Y. T. , and Verbrugge, M. W. , 2010, “ Diffusion-Induced Stress, Interfacial Charge Transfer, and Criteria for Avoiding Crack Initiation of Electrode Particles,” J. Electrochem. Soc., 157(4), pp. A508–A516. [CrossRef]
Haftbaradaran, H. , Gao, H. J. , and Curtin, W. A. , 2010, “ A Surface Locking Instability for Atomic Intercalation Into a Solid Electrode,” Appl. Phys. Lett., 96(9), p. 091909. [CrossRef]
Haftbaradaran, H. , Song, J. , Curtin, W. A. , and Gao, H. J. , 2011, “ Continuum and Atomistic Models of Strongly Coupled Diffusion, Stress, and Solute Concentration,” J. Power Sources, 196(1), pp. 361–370. [CrossRef]
Gao, Y. F. , and Zhou, M. , 2012, “ Strong Dependency of Li Diffusion on Mechanical Constraints in High-Capacity Li-Ion Battery Electrodes,” Acta Mech. Sin., 28(4), pp. 1068–1077. [CrossRef]
Cheng, Y. T. , and Verbrugge, M. W. , 2008, “ The Influence of Surface Mechanics on Diffusion Induced Stresses Within Spherical Nanoparticles,” J. Appl. Phys., 104(8), p. 083521. [CrossRef]
DeLuca, C. M. , Maute, K. , and Dunn, M. L. , 2011, “ Effects of Electrode Particle Morphology on Stress Generation in Silicon During Li Insertion,” J. Power Sources, 196(22), pp. 9672–9681. [CrossRef]
Deshpande, R. , Cheng, Y. T. , and Verbrugge, M. W. , 2010, “ Modeling Diffusion-Induced Stress in Nanowire Electrode Structures,” J. Power Sources, 195(15), pp. 5081–5088. [CrossRef]
Garcia, R. E. , Chiang, Y. M. , Carter, W. C. , Limthongkul, P. , and Bishop, C. M. , 2005, “ Microstructural Modeling and Design of Rechargeable Li-Ion Batteries,” J. Electrochem. Soc., 152(1), pp. A255–A263. [CrossRef]
Purkayastha, R. T. , and McMeeking, R. M. , 2012, “ An Integrated 2-D Model of a Li Ion Battery: The Effect of Material Parameters and Morphology on Storage Particle Stress,” Comput. Mech., 50(2), pp. 209–227. [CrossRef]
Zhang, J. Q. , Lu, B. , Song, Y. C. , and Ji, X. , 2012, “ Diffusion Induced Stress in Layered Li-Ion Battery Electrode Plates,” J. Power Sources, 209, pp. 220–227. [CrossRef]
Yang, B. , He, Y. P. , Irsa, J. , Lundgren, C. A. , Ratchford, J. B. , and Zhao, Y. P. , 2012, “ Effects of Composition-Dependent Modulus, Finite Concentration and Boundary Constraint on Li-Ion Diffusion and Stresses in a Bilayer Cu-Coated Si Nano-Anode,” J. Power Sources, 204, pp. 168–176. [CrossRef]
Lim, C. , Yan, B. , Yin, L. L. , and Zhu, L. K. , 2012, “ Simulation of Diffusion-Induced Stress Using Reconstructed Electrodes Particle Structures Generated by Micro/Nano-CT,” Electrochim. Acta, 75, pp. 279–287. [CrossRef]
Huang, H. Y. S. , and Wang, Y. X. , 2012, “ Dislocation Based Stress Developments in Li-Ion Batteries,” J. Electrochem. Soc., 159(6), pp. A815–A821. [CrossRef]
Bhandakkar, T. K. , and Johnson, H. T. , 2012, “ Diffusion Induced Stresses in Buckling Battery Electrodes,” J. Mech. Phys. Solids, 60(6), pp. 1103–1121. [CrossRef]
Barai, P. , and Mukherjee, P. P. , 2013, “ Stochastic Analysis of Diffusion Induced Damage in Lithium-Ion Battery Electrodes,” J. Electrochem. Soc., 160(6), pp. A955–A967. [CrossRef]
Chen, C. F. , Barai, P. , and Mukherjee, P. P. , 2014, “ Diffusion Induced Damage and Impedance Response in Lithium-Ion Battery Electrodes,” J. Electrochem. Soc., 161(14), pp. A2138–A2152. [CrossRef]
Barai, P. , and Mukherjee, P. P. , 2016, “ Mechano-Electrochemical Stochastics in High-Capacity Electrodes for Energy Storage,” J. Electrochem. Soc., 163(6), pp. A1120–A1137. [CrossRef]
Bower, A. F. , Guduru, P. R. , and Sethuraman, V . A. , 2011, “ A Finite Strain Model of Stress, Diffusion, Plastic Flow, and Electrochemical Reactions in a Lithium-Ion Half-Cell,” J. Mech. Phys. Solids, 59(4), pp. 804–828. [CrossRef]
Di Leo, C. V. , Rejovitzky, E. , and Anand, L. , 2015, “ Diffusion–Deformation Theory for Amorphous Silicon Anodes: The Role of Plastic Deformation on Electrochemical Performance,” Int. J. Solids Struct., 67–68, pp. 283–296. [CrossRef]
Zhao, K. , Pharr, M. , Vlassak, J. J. , and Suo, Z. , 2011, “ Inelastic Hosts as Electrodes for High-Capacity Lithium-Ion Batteries,” J. Appl. Phys., 109(1), p. 016110. [CrossRef]
Brassart, L. , Zhao, K. , and Suo, Z. , 2013, “ Cyclic Plasticity and Shakedown in High-Capacity Electrodes of Lithium-Ion Batteries,” Int. J. Solids Struct., 50(7), pp. 1120–1129. [CrossRef]
Cui, Z. , Gao, F. , and Qu, J. , 2012, “ A Finite Deformation Stress-Dependent Chemical Potential and Its Applications to Lithium Ion Batteries,” J. Mech. Phys. Solids, 60(7), pp. 1280–1295. [CrossRef]
Xu, R. , and Zhao, K. , 2015, “ Mechanical Interactions Regulated Kinetics and Morphology of Composite Electrodes in Li-Ion Batteries,” Extreme Mech. Lett., 8, pp. 13–21. [CrossRef]
Verbrugge, M. W. , and Koch, B. J. , 1996, “ Modeling Li Intercalation of Single-Fiber Carbon Microelectrodes,” J. Electrochem. Soc., 143(2), pp. 600–608. [CrossRef]
Karthikeyan, D. K. , Sikha, G. , and White, R. E. , 2008, “ Thermodynamic Model Development for Li Intercalation Electrodes,” J. Power Sources, 185(2), pp. 1398–1407. [CrossRef]
Sethuraman, V . A. , Srinivasan, V. , Bower, A. F. , and Guduru, P. R. , 2010, “ In Situ Measurements of Stress-Potential Coupling in Lithiated Silicon,” J. Electrochem. Soc., 157(11), pp. A1253–A1261. [CrossRef]
Piper, D. M. , Yersak, T. A. , and Lee, S. H. , 2013, “ Effect of Compressive Stress on Electrochemical Performance of Silicon Anodes,” J. Electrochem. Soc., 160(1), pp. A77–A81. [CrossRef]
Lu, B. , Song, Y. , Zhang, Q. , Pan, J. , Cheng, Y. T. , and Zhang, J. , 2016, “ Voltage Hysteresis of Lithium Ion Batteries Caused by Mechanical Stress,” Phys. Chem. Chem. Phys., 18(6), pp. 4721–4727. [CrossRef] [PubMed]
Kim, S. , Choi, S. J. , Zhao, K. , Yang, H. , Gobbi, G. , Zhang, S. , and Li, J. , 2016, “ Electrochemically Driven Mechanical Energy Harvesting,” Nat. Commun., 7, p. 10146. [CrossRef] [PubMed]
Chon, M. J. , Sethuraman, V. A. , McCormick, A. , Srinivasan, V. , and Guduru, P. R. , 2011, “ Real-Time Measurement of Stress and Damage Evolution During Initial Lithiation of Crystalline Silicon,” Phys. Rev. Lett., 107(4), p. 045503. [CrossRef] [PubMed]
Liu, X. H. , Zheng, H. , Zhong, L. , Huang, S. , Karki, K. , Zhang, L. Q. , Liu, Y. , Kushima, A. , Liang, W. T. , Wang, J. W. , Cho, J.-H. , Epstein, E. , Dayeh, S. A. , Picraux, S. T. , Zhu, T. , Li, J. , Sullivan, J. P. , Cumings, J. , Wang, C. , Mao, S. X. , Ye, Z. Z. , Zhang, S. , and Huang, J. Y. , 2011, “ Anisotropic Swelling and Fracture of Silicon Nanowires During Lithiation,” Nano Lett., 11(8), pp. 3312–3318. [CrossRef] [PubMed]
Yang, H. , Fan, F. , Liang, W. , Guo, X. , Zhu, T. , and Zhang, S. , 2014, “ A Chemo-Mechanical Model of Lithiation in Silicon,” J. Mech. Phys. Solids, 70, pp. 349–361. [CrossRef]
Limthongkul, P. , Jang, Y. I. , Dudney, N. J. , and Chiang, Y. M. , 2003, “ Electrochemically-Driven Solid-State Amorphization in Lithium–Silicon Alloys and Implications for Lithium Storage,” Acta Mater., 51(4), pp. 1103–1113. [CrossRef]
McDowell, M. T. , Lee, S. W. , Wang, C. , Nix, W. D. , and Cui, Y. , 2012, “ Studying the Kinetics of Crystalline Silicon Nanoparticle Lithiation With In Situ Transmission Electron Microscopy,” Adv. Mater., 24(45), pp. 6034–6041. [CrossRef] [PubMed]
Zhang, Y. , Li, Y. , Wang, Z. , and Zhao, K. , 2014, “ Lithiation of SiO2 in Li-Ion Batteries: In Situ Transmission Electron Microscopy Experiments and Theoretical Studies,” Nano Lett., 14(12), pp. 7161–7170. [CrossRef] [PubMed]
Liu, D. J. , Weeks, J. D. , and Kandel, D. , 1998, “ Current-Induced Step Bending Instability on Vicinal Surfaces,” Phys. Rev. Lett., 81(13), p. 2743. [CrossRef]
Nielsen, J. F. , Pelz, J. P. , and Pettersen, M. S. , 2000, “ Observation of Direct-Current-Induced Step Bending Patterns on Si (001),” Surf. Rev. Lett., 7(5–6), pp. 577–582. [CrossRef]
Zhang, Y. , Wang, Z. , Li, Y. , and Zhao, K. , 2015, “ Lithiation of ZnO Nanowires Studied by In Situ Transmission Electron Microscopy and Theoretical Analysis,” Mech. Mater., 91(Pt. 2), pp. 313–322. [CrossRef]
Jia, Z. , and Li, T. , 2016, “ Intrinsic Stress Mitigation Via Elastic Softening During Two-Step Electrochemical Lithiation of Amorphous Silicon,” J. Mech. Phys. Solids, 91, pp. 278–290. [CrossRef]
Hertzberg, B. , Benson, J. , and Yushin, G. , 2011, “ Ex-Situ Depth-Sensing Indentation Measurements of Electrochemically Produced Si-Li Alloy Films,” Electrochem. Commun., 13(8), pp. 818–821. [CrossRef]
Ratchford, J. B. , Crawford, B. A. , Wolfenstine, J. , Allen, J. L. , and Lundgren, C. A. , 2012, “ Young's Modulus of Polycrystalline Li12Si7 Using Nanoindentation Testing,” J. Power Sources, 211, pp. 1–3. [CrossRef]
Levitas, V. I. , and Attariani, H. , 2013, “ Anisotropic Compositional Expansion and Chemical Potential for Amorphous Lithiated Silicon Under Stress Tensor,” Sci. Rep., 3, p. 1615.
Levitas, V. I. , and Attariani, H. , 2014, “ Anisotropic Compositional Expansion in Elastoplastic Materials and Corresponding Chemical Potential: Large-Strain Formulation and Application to Amorphous Lithiated Silicon,” J. Mech. Phys. Solids, 69, pp. 84–111. [CrossRef]
Hong, W. , 2015, “ A Kinetic Model for Anisotropic Reactions in Amorphous Solids,” Extreme Mech. Lett., 2, pp. 46–51. [CrossRef]
Khosrownejad, S. M. , and Curtin, W. A. , 2016, “ Model for Charge/Discharge-Rate-Dependent Plastic Flow in Amorphous Battery Materials,” J. Mech. Phys. Solids, 94, pp. 167–180. [CrossRef]
Choi, J. W. , Cui, Y. , and Nix, W. D. , 2011, “ Size-Dependent Fracture of Si Nanowire Battery Anodes,” J. Mech. Phys. Solids, 59(9), pp. 1717–1730. [CrossRef]
Liu, X. H. , Zhong, L. , Huang, S. , Mao, S. X. , Zhu, T. , and Huang, J. Y. , 2012, “ Size-Dependent Fracture of Silicon Nanoparticles During Lithiation,” ACS Nano, 6(2), pp. 1522–1531. [CrossRef] [PubMed]
Zhao, K. , Pharr, M. , Hartle, L. , Vlassak, J. J. , and Suo, Z. , 2012, “ Fracture and Debonding in Lithium-Ion Batteries With Electrodes of Hollow Core–Shell Nanostructures,” J. Power Sources, 218, pp. 6–14. [CrossRef]
Lee, S. W. , Lee, H. W. , Nix, W. D. , Gao, H. , and Cui, Y. , 2015, “ Kinetics and Fracture Resistance of Lithiated Silicon Nanostructure Pairs Controlled by Their Mechanical Interaction,” Nat. Commun., 6, p. 7533. [CrossRef] [PubMed]
Deshpande, R. , Verbrugge, M. , Cheng, Y. T. , Wang, J. , and Liu, P. , 2012, “ Battery Cycle Life Prediction With Coupled Chemical Degradation and Fatigue Mechanics,” J. Electrochem. Soc., 159(10), pp. A1730–A1738. [CrossRef]
Sethuraman, V. A. , Chon, M. J. , Shimshak, M. , Van Winkle, N. , and Guduru, P. R. , 2010, “ In Situ Measurement of Biaxial Modulus of Si Anode for Li-Ion Batteries,” Electrochem. Commun., 12(11), pp. 1614–1617. [CrossRef]
Vasconcelos, L. S. , Xu, R. , Li, J. , and Zhao, K. , 2016, “ Grid Indentation Analysis of Mechanical Properties of Composite Electrodes in Li-Ion Batteries,” Extreme Mech. Lett., 9(Pt. 3), pp. 495–502. [CrossRef]
Qi, Y. , Hector, L. G. , James, C. , and Kim, K. J. , 2014, “ Lithium Concentration Dependent Elastic Properties of Battery Electrode Materials From First Principles Calculations,” J. Electrochem. Soc., 161(11), pp. F3010–F3018. [CrossRef]
Shenoy, V. B. , Johari, P. , and Qi, Y. , 2010, “ Elastic Softening of Amorphous and Crystalline Li-Si Phases With Increasing Li Concentration: A First-Principles Study,” J. Power Sources, 195(19), pp. 6825–6830. [CrossRef]
Choi, Y. S. , Pharr, M. , Oh, K. H. , and Vlassak, J. J. , 2015, “ A Simple Technique for Measuring the Fracture Energy of Lithiated Thin-Film Silicon Electrodes at Various Lithium Concentrations,” J. Power Sources, 294, pp. 159–166. [CrossRef]
Berla, L. A. , Lee, S. W. , Cui, Y. , and Nix, W. D. , 2014, “ Robustness of Amorphous Silicon During the Initial Lithiation/Delithiation Cycle,” J. Power Sources, 258, pp. 253–259. [CrossRef]
Grantab, R. , and Shenoy, V . B. , 2012, “ Pressure-Gradient Dependent Diffusion and Crack Propagation in Lithiated Silicon Nanowires,” J. Electrochem. Soc., 159(5), pp. A584–A591. [CrossRef]
Yang, H. , Huang, X. , Liang, W. , Van Duin, A. C. , Raju, M. , and Zhang, S. , 2013, “ Self-Weakening in Lithiated Graphene Electrodes,” Chem. Phys. Lett., 563, pp. 58–62. [CrossRef]
Yang, F. , Liu, B. , and Fang, D. N. , 2011, “ Interplay Between Fracture and Diffusion Behaviors: Modeling and Phase Field Computation,” Comput. Mater. Sci., 50(9), pp. 2554–2560. [CrossRef]
Evans, A. G. , Mumm, D. R. , Hutchinson, J. W. , Meier, G. H. , and Pettit, F. S. , 2001, “ Mechanisms Controlling the Durability of Thermal Barrier Coatings,” Prog. Mater. Sci., 46(5), pp. 505–553. [CrossRef]
Xu, R. , Fan, X. L. , Zhang, W. X. , and Wang, T. J. , 2014, “ Interfacial Fracture Mechanism Associated With Mixed Oxides Growth in Thermal Barrier Coating System,” Surf. Coat. Technol., 253, pp. 139–147. [CrossRef]
Klinsmann, M. , Rosato, D. , Kamlah, M. , and McMeeking, R. M. , 2016, “ Modeling Crack Growth During Li Insertion in Storage Particles Using a Fracture Phase Field Approach,” J. Mech. Phys. Solids, 92, pp. 313–344. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) Schematic of diffusion-induced stress in a free-standing spherical particle. Li insertion causes deformation of the host material, and the inhomogeneous distribution of Li induces a field of stress within the particle. The shell region (Li rich) is under compression and the core region (Li poor) is under tension. (b) Sketch of the stress effect on radial distribution of Li in the spherical particle. The stress gradient tends to homogenize the Li distribution. The red line represents the Li profile calculated by considering both effects of stress and Li concentration gradient, while the blue line represents the case that Li diffusion is driven only by the concentration gradient.

Grahic Jump Location
Fig. 2

Free-energy diagram for the surface charge transfer process altered by the applied electrical potential and mechanical stresses. The activation energies of the redox reactions at equilibrium states are identical, ΔG0O = ΔG0R (black-solid lines). The chemical equilibrium will be broken by the electrical overpotential as well as mechanical stress. The electrical overpotential E − E0 promotes electron transfer and decreases the free energy of the oxidized state by F(E − E0) (red-dashed line). The tensile stress in the surface layer causes a change of elastic energy ΔW = σmΩ (blue-dashed line) and promotes the formation of neutral Li atoms. The change in the total free energy of the reduced state relative to the oxidized state is F(E − E0) − σmΩ.

Grahic Jump Location
Fig. 3

(a) Design of mechanical energy harvester based on the stress-driven Li diffusion. Two identical partially lithiated Si films act as electrodes, separated by electrolyte-soaked polymer membranes (the size of the electrodes and electrolyte is not in scale). Bending-induced asymmetric stresses generate chemical potential difference, driving migration of Li ions from the compressed electrode (red) to the tensed side (blue). (b) Schematic of short circuit current density during the release of bending. The peak current is determined by the Butler–Volmer surface charge transfer process, and the subsequent state is controlled by Li diffusion in the electrodes. (Figure 3(a) is reproduced with permission from Kim et al. [87]. Copyright 2015 by the Nature Publishing Group.)

Grahic Jump Location
Fig. 4

(a) Stress-regulated interfacial reaction during lithiation of a crystalline Si spherical particle. Stress modifies the free energy associated with the reaction that converts one Li and 1/x Si atoms into lithiated Si at the reaction front. The figure plots the evolution of the free energy contributed by mechanical stresses as a function of the position of the reaction front. The inset shows the schematic of the stress field within the particle (Reproduced with permission from Zhao et al. [29]. Copyright 2012 by the Electrochemical Society). (b) Experimental evidence of the stagnation of lithiation reaction due to the stress effect. Lithiation in the particles of different sizes significantly slows down at similar a/b ratios suggesting that stress gradually builds up as the a/b ratio decreases and retards the progression of the reaction front (Reproduced with permission from McDowell et al. [92]. Copyright 2012 by John Wiley and Sons).

Grahic Jump Location
Fig. 5

(a) Schematic of inhomogeneous growth of lithiated phase due to the stress-regulated lithiation reaction. The lithiated phase of convex curvature develops a field of tensile stresses, facilitating Li transport through the lithiated material and promoting the interfacial reaction at the phase boundary. On the contrary, the lithiated phase of concave curvature is under a field of compressive stresses, retarding the electrochemical growth of the layer. (b) In situ TEM observation of the inhomogeneous growth of the SiO2 layer during the cycle of lithiation and delithiation. (Reproduced with permission from Zhang et al. [93]. Copyright 2014 by the American Chemical Society).

Grahic Jump Location
Fig. 6

(a) Stress-induced instability of solid-state reaction front (SSRF) during lithiation of the ZnO nanowires. Li ions diffuse quickly on the nanowire surface, forming a thin wetting layer with typical thickness of a few nanometers. The primary SSRF propagates along the longitudinal direction of the nanowire away from the electrolyte. Lithiation induces a field of tensile stress in the lithiated shell, and compressive stress in the unlithiated core. The stress field regulates the lithiation reaction and breaks the planar SSRF into a curved interface. (b)–(e) In situ TEM observation on the evolution of the curved reaction front. The radius of curvature gradually decreases, and the core is eventually lithiated as the reaction front propagates (Reproduced with permission from Zhang et al. [96]. Copyright 2015 by Elsevier).

Grahic Jump Location
Fig. 7

(a) Schematic illustration of concurrent Li insertion and plastic deformation. The host atom bonds are broken by the insertion of Li, and the valence state of matter is under dynamic change. (b) The stress needed to maintain a given shear displacement with ongoing chemical reaction is lower than that needed for pure mechanical load. (c) A yield function Q(s1,s2,s3,ζ) is sketched in the space of (sk,ζ); the condition Q = 0 defines the yield. (δeik, ΩδC) represents the increment of inelastic deformation driven by both the mechanical load sk and the chemomechanical load ζ. Under pure shear loading, plastic flow occurs when the shear stress sk reaches the yield strength τY. Under the condition of insertion without stress, inelastic volume change occurs when the chemomechanical load ζ reaches τY/√q.

Grahic Jump Location
Fig. 8

(a)–(c) Schematic of the wait-and-go fracture behavior induced by the concurrent Li diffusion, Li weakening at the crack tip, and crack propagation. (d) Stress–strain curves of the SWCNTs containing a holelike defect. (e) Three stages of SWCNTs showing the corrosive fracture behavior of SWCNTs studied by molecular dynamics simulations (Reproduced with permission from Huang et al. [35]. Copyright 2013 by AIP Publishing LLC).

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