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A chemo-mechanical model for fully-coupled lithiation reaction and stress generation in viscoplastic lithiated silicon

  • YiMing Burebi
  • Zheng JiaEmail author
  • ShaoXing Qu
Article Special Topic: Chemomechanics

Abstract

Development of stresses in silicon (Si) anodes of lithium-ion batteries is strongly affected by its mechanical properties. Recent experiments reveal that the mechanical behavior of lithiated silicon is viscoplastic, thereby indicating that lithiation-induced mechanical stresses are dependent on the lithiation reaction rate. Experimental evidence also accumulates that the rate of lithiation reaction is conversely affected by the magnitude of mechanical stresses. These experimental observations demonstrate that lithiation reaction and stress generation in silicon anodes are fully coupled. In this work, we formulate a chemo-mechanical model considering the two-way coupling between lithiation reaction and viscoplastic deformation in silicon nanoparticle anodes. Based on the model, the position of the lithiation interface, the interface velocity, and the lithiation-induced stresses can be solved simultaneously via numerical methods. The predicted interface velocity is in line with experimental measurements reported in the literature. We demonstrate that the lithiation-induced stress field depends on the lithiation reaction through two parameters: the migration velocity and the position of the lithiation interface. We identify a stress-mitigation mechanism in viscoplastic silicon anodes: the stress-regulated lithiation reaction at the interface serves as a “brake” to reduce the interface velocity and mitigate the lithiation-induced stresses, protecting the Si nanoparticle anode from being subjected to excessive mechanical stresses.

Keywords

lithium-ion battery lithiation-induced stress stress-regulated lithiation viscoplasticity 

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References

  1. 1.
    Armand M, Tarascon J M. Building better batteries. Nature, 2008, 451: 652–657CrossRefGoogle Scholar
  2. 2.
    Chan C K, Peng H, Liu G, et al. High-performance lithium battery anodes using silicon nanowires. Nat Nanotech, 2008, 3: 31–35CrossRefGoogle Scholar
  3. 3.
    Kasavajjula U, Wang C, Appleby A J. Nano- and bulk-silicon-based insertion anodes for lithium-ion secondary cells. J Power Sources, 2007, 163: 1003–1039CrossRefGoogle Scholar
  4. 4.
    Liu X H, Zhong L, Huang S, et al. Size-dependent fracture of silicon nanoparticles during lithiation. ACS Nano, 2012, 6: 1522–1531CrossRefGoogle Scholar
  5. 5.
    Li D, Wang Y, Hu J, et al. In situ measurement of mechanical property and stress evolution in a composite silicon electrode. J Power Sources, 2017, 366: 80–85CrossRefGoogle Scholar
  6. 6.
    Zhang X, Song W L, Liu Z, et al. Geometric design of micron-sized crystalline silicon anodes through in situ observation of deformation and fracture behaviors. J Mater Chem A, 2017, 5: 12793–12802CrossRefGoogle Scholar
  7. 7.
    Yang L, Chen H S, Jiang H, et al. Failure mechanisms of 2D silicon film anodes: In situ observations and simulations on crack evolution. Chem Commun, 2018, 54: 3997–4000CrossRefGoogle Scholar
  8. 8.
    Zhao K, Cui Y. Understanding the role of mechanics in energy materials: A perspective. Extreme Mech Lett, 2016, 9: 347–352CrossRefGoogle Scholar
  9. 9.
    McDowell M T, Xia S, Zhu T. The mechanics of large-volume-change transformations in high-capacity battery materials. Extreme Mech Lett, 2016, 9: 480–494CrossRefGoogle Scholar
  10. 10.
    Liu X H, Wang J W, Huang S, et al. In situ atomic-scale imaging of electrochemical lithiation in silicon. Nat Nanotech, 2012, 7: 749–756CrossRefGoogle Scholar
  11. 11.
    Liu X H, Zheng H, Zhong L, et al. Anisotropic swelling and fracture of silicon nanowires during lithiation. Nano Lett, 2011, 11: 3312–3318CrossRefGoogle Scholar
  12. 12.
    McDowell M T, Ryu I, Lee S W, et al. Studying the kinetics of crystalline silicon nanoparticle lithiation with in situ transmission electron microscopy. Adv Mater, 2012, 24: 6034–6041CrossRefGoogle Scholar
  13. 13.
    Liu X H, Fan F, Yang H, et al. Self-limiting lithiation in silicon nanowires. ACS Nano, 2013, 7: 1495–1503CrossRefGoogle Scholar
  14. 14.
    Zhao K, Pharr M, Wan Q, et al. Concurrent reaction and plasticity during initial lithiation of crystalline silicon in lithium-ion batteries. J Electrochem Soc, 2012, 159: A238–A243CrossRefGoogle Scholar
  15. 15.
    Yang H, Liang W, Guo X, et al. Strong kinetics-stress coupling in lithiation of Si and Ge anodes. Extreme Mech Lett, 2015, 2: 1–6CrossRefGoogle Scholar
  16. 16.
    Jia Z, Li T. Stress-modulated driving force for lithiation reaction in hollow nano-anodes. J Power Sources, 2015, 275: 866–876CrossRefGoogle Scholar
  17. 17.
    Lang J, Ding B, Zhu T, et al. Cycling of a lithium-ion battery with a silicon anode drives large mechanical actuation. Adv Mater, 2016, 28: 10236–10243CrossRefGoogle Scholar
  18. 18.
    Zhang S, Zhao K, Zhu T, et al. Electrochemomechanical degradation of high-capacity battery electrode materials. Prog Mater Sci, 2017, 89: 479–521CrossRefGoogle Scholar
  19. 19.
    Bucci G, Swamy T, Bishop S, et al. The effect of stress on battery-electrode capacity. J Electrochem Soc, 2017, 164: A645–A654CrossRefGoogle Scholar
  20. 20.
    Ding B, Wu H, Xu Z, et al. Stress effects on lithiation in silicon. Nano Energy, 2017, 38: 486–493CrossRefGoogle Scholar
  21. 21.
    Sethuraman V A, Chon M J, Shimshak M, et al. In situ measurements of stress evolution in silicon thin films during electrochemical lithiation and delithiation. J Power Sources, 2010, 195: 5062–5066CrossRefGoogle Scholar
  22. 22.
    Chon M J, Sethuraman V A, McCormick A, et al. Real-time measurement of stress and damage evolution during initial lithiation of crystalline silicon. Phys Rev Lett, 2011, 107: 045503CrossRefGoogle Scholar
  23. 23.
    Fan F, Huang S, Yang H, et al. Mechanical properties of amorphous Li x Si alloys: A reactive force field study. Model Simul Mater Sci Eng, 2013, 21: 074002CrossRefGoogle Scholar
  24. 24.
    Boles S T, Thompson C V, Kraft O, et al. In situ tensile and creep testing of lithiated silicon nanowires. Appl Phys Lett, 2013, 103: 263906CrossRefGoogle Scholar
  25. 25.
    Berla L A, Lee S W, Cui Y, et al. Mechanical behavior of electrochemically lithiated silicon. J Power Sources, 2015, 273: 41–51CrossRefGoogle Scholar
  26. 26.
    Pharr M, Suo Z, Vlassak J J. Variation of stress with charging rate due to strain-rate sensitivity of silicon electrodes of Li-ion batteries. J Power Sources, 2014, 270: 569–575CrossRefGoogle Scholar
  27. 27.
    Huang S, Zhu T. Atomistic mechanisms of lithium insertion in amorphous silicon. J Power Sources, 2011, 196: 3664–3668CrossRefGoogle Scholar
  28. 28.
    Wen J, Wei Y, Cheng Y T. Stress evolution in elastic-plastic electrodes during electrochemical processes: A numerical method and its applications. J Mech Phys Solids, 2018, 116: 403–415MathSciNetCrossRefGoogle Scholar
  29. 29.
    Jia Z, Li T. Intrinsic stress mitigation via elastic softening during two-step electrochemical lithiation of amorphous silicon. J Mech Phys Solids, 2016, 91: 278–290CrossRefGoogle Scholar
  30. 30.
    Zhang X, Krischok A, Linder C. A variational framework to model diffusion induced large plastic deformation and phase field fracture during initial two-phase lithiation of silicon electrodes. Comput Methods Appl Mech Eng, 2016, 312: 51–77MathSciNetCrossRefGoogle Scholar
  31. 31.
    Zuo P, Zhao Y P. Phase field modeling of lithium diffusion, finite deformation, stress evolution and crack propagation in lithium ion battery. Extreme Mech Lett, 2016, 9: 467–479CrossRefGoogle Scholar
  32. 32.
    Cui Z, Gao F, Qu J. A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries. J Mech Phys Solids, 2012, 60: 1280–1295MathSciNetCrossRefGoogle Scholar
  33. 33.
    Lu B, Song Y, Zhang Q, et al. Voltage hysteresis of lithium ion batteries caused by mechanical stress. Phys Chem Chem Phys, 2016, 18: 4721–4727CrossRefGoogle Scholar
  34. 34.
    Yin J, Shao X, Lu B, et al. Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries. Appl Math Mech-Engl Ed, 2018, 39: 1567–1586MathSciNetCrossRefGoogle Scholar
  35. 35.
    Yang H, Fan F, Liang W, et al. A chemo-mechanical model of lithiation in silicon. J Mech Phys Solids, 2014, 70: 349–361CrossRefGoogle Scholar
  36. 36.
    Zhang X, Lee S W, Lee H W, et al. A reaction-controlled diffusion model for the lithiation of silicon in lithium-ion batteries. Extreme Mech Lett, 2015, 4: 61–75CrossRefGoogle Scholar
  37. 37.
    Jia Z, Liu W K. Rate-dependent stress evolution in nanostructured Si anodes upon lithiation. Appl Phys Lett, 2016, 109: 163903CrossRefGoogle Scholar
  38. 38.
    Pharr M, Zhao K, Wang X, et al. Kinetics of initial lithiation of crystalline silicon electrodes of lithium-ion batteries. Nano Lett, 2012, 12: 5039–5047CrossRefGoogle Scholar
  39. 39.
    McDowell M T, Lee S W, Harris J T, et al. In situ TEM of two-phase lithiation of amorphous silicon nanospheres. Nano Lett, 2013, 13: 758–764CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Center for X-Mechanics, Department of Engineering MechanicsZhejiang UniversityHangzhouChina

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