Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Evaluation of Crack Propagation in Silicon Anode using Cohesive Zone Model during Two-phase Lithiation

접착영역 모델을 사용한 2상 리튬 이온 충전 시 실리콘 음극 전극의 균열진전 해석

  • Kim, Yong-Woo (Department of Civil and Environmental Engineering, Yonsei University) ;
  • Han, Tong-Seok (Department of Civil and Environmental Engineering, Yonsei University)
  • 김용우 (연세대학교 건설환경공학과) ;
  • 한동석 (연세대학교 건설환경공학과)
  • Accepted : 2019.07.06
  • Published : 2019.10.31
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Abstract

In this research, crack propagation in a silicon anode during two-phase lithiation was evaluated using a cohesive zone model. The phase transition from crystalline silicon to lithiated silicon causes compressive yielding due to the high volume expansion rate. Li-ion diffuses from the surface of the silicon to its core, and the complex deformation mechanisms during lithiation cause tensile hoop stress along the surface. The Park-Paulino-Roesler (PPR) potential-based cohesive zone model that guarantees consistent energy dissipation in mixed-mode fracture was adopted to simulate edge crack propagation. It was confirmed that the edge crack propagation characteristics during lithiation from the FEM simulation results coincided with the real experimental results. Crack turning observed from real experiments could also be predicted by evaluating the angles of maximum tensile stress directions.

본 논문에서는 접착영역 모델을 이용하여 2상 리튬이온 충전 시 실리콘 음극 전극의 균열진전 해석을 수행하였다. 리튬화 실리콘은 결정질 실리콘에 비해 부피가 약 3배 이상 크므로 리튬이온 충전 시 외각의 리튬화 실리콘에 매우 큰 압축력이 작용하여 압축항복이 발생한다. 리튬이온 충전 시 외각의 리튬화 실리콘은 압축항복 후에 내부의 결정질 실리콘이 리튬화 실리콘으로 상 변이하면서 발생하는 부피 팽창으로 인해 인장력이 작용한다. 이러한 인장력으로 인해 발생하는 균열진전을 접착영역 모델을 이용하여 모사하였다. 사용한 접착영역 모델은 PPR 포텐셜 기반 접착영역 모델로 하나의 포텐셜을 사용하여 복합모드에 대해서도 에너지 소산에 일관성을 지니고 있다. 유한요소 수치해석 모델로 2상 리튬이온 충전 시 모서리 균열진전을 모사한 결과가 실제 실험결과와 일치함을 확인하였고, 균열 팁에서의 최대 인장응력의 각도를 분석하여 실제 실험처럼 균열진전 방향이 회전할 것을 예측할 수 있었다.

Keywords

References

  1. Chan, C.K., Peng, H., Liu, G., McIlwrath, K., Zhang, X.F., Huggins, R.A., Cui, Y. (2008) High-Performance lithium Battery Anodes using Silicon Nanowires, Nat. Nanotechnol., 3(1), pp.31-35. https://doi.org/10.1038/nnano.2007.411
  2. Choi, J.W., Cui, Y., Nix, W.D. (2011) Size-Dependent Fracture of Si Nanowire Battery Anodes, J. Mech. & Phys. Solids, 59(9), pp.1717-1730. https://doi.org/10.1016/j.jmps.2011.06.003
  3. Ebrahimi, F., Kalwani, L. (1999) Fracture Anisotropy in Silicon Single Crystal, Materials Sci. & Eng.: A, 268(1), pp.116-126. https://doi.org/10.1016/S0921-5093(99)00077-5
  4. Hall, J.J. (1967) Electronic Effects in the Elastic Constants of N-Type Silicon, Phys. Rev., 161(3), p.756. https://doi.org/10.1103/PhysRev.161.756
  5. Hauch, J.A., Holland, D., Marder, M., Swinney, H.L. (1999) Dynamic Fracture in Single Cystal Silicon, Phys. Rev. Lett., 82(19), p.3823. https://doi.org/10.1103/PhysRevLett.82.3823
  6. Hertzberg, B., Benson, J., Yushin, G. (2011) Ex-situ Depth-sensing Indentation Measurements of Electrochemically Produced Sili Alloy Films, Electrochem. Commun., 13(8), pp.818-821. https://doi.org/10.1016/j.elecom.2011.05.011
  7. Kluge, M.D., Ray, J.R.,Rahman, A. (1986) Molecular Dynamic Calculation of Elastic Constants of Silicon, J. Chem. Phys., 85(7), pp.4028-4031. https://doi.org/10.1063/1.450871
  8. Lee, S.W., Gao, H., Cui, Y., Nix, W.D. (2014) Microscopic Model for Fracture of Crystalline Si Nanopillars during Lithiation, J. Power Sources, 255, pp.274-282. https://doi.org/10.1016/j.jpowsour.2013.12.137
  9. Lee, S.W., McDowell, M.T., Berla, L.A., Nix, W.D., Cui, Y. (2012) Fracture of Crystalline Silicon Nanopillars during Electrochemical Lithium Insertion, Proc. Nat. Academ. Sci., 109(11), pp.4080-4085. https://doi.org/10.1073/pnas.1201088109
  10. Liu, X.H., Zhong, L., Huang, S., Mao, S.X., Zhu, T., Huang, J.Y. (2012) Size-Dependent Fracture of Silicon Nanoparticles during Lithiation, Acs Nano, 6(2), pp.1522-1531. https://doi.org/10.1021/nn204476h
  11. McDowell, M.T., Lee, S.W., Harris, J.T., Korgel, B.A., Wang, C., Nix, W.D., Cui, Y. (2013) In Situ Tem of Two-Phase Lithiation of Aorphous Silicon Nanospheres, Nano Lett., 13(2), pp.758-764. https://doi.org/10.1021/nl3044508
  12. Park, K., Paulino, G.H., Roesler, J.R. (2009) A Unified Potential-based Cohesive Model of Mixed-Mode Fracture, J. Mech. & Phys. Solids, 57(6), pp.891-908. https://doi.org/10.1016/j.jmps.2008.10.003
  13. Pharr, M., Suo, Z., Vlassak, J.J. (2013) Measurements of the Fracture Energy of Lithiated Silicon Electrodes of Li-ion Batteries, Nano Lett., 13(11), pp.5570-5577. https://doi.org/10.1021/nl403197m
  14. Sethuraman, V.A., Chon, M.J., Shimshak, M., Srinivasan, V., 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. https://doi.org/10.1016/j.jpowsour.2010.02.013
  15. Swadener, J., Baskes, M., Nastasi, M. (2002) Molecular Dynamics Simulation of Brittle Fracture in Silicon, Phys. Rev. Lett., 89(8), p.085503. https://doi.org/10.1103/PhysRevLett.89.085503
  16. Wortman, J.J., Evans, R.A. (1965) Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon and Germanium, J. Appl. Phys., 36(1), pp.153-156. https://doi.org/10.1063/1.1713863
  17. Zhao, K., Pharr, M., Wan, Q., Wang, W.L., Kaxiras, E., Vlassak, J.J., 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. https://doi.org/10.1149/2.020203jes