Research Papers

Analytical Model on Lithiation-Induced Interfacial Debonding of an Active Layer From a Rigid Substrate

[+] Author and Article Information
Bo Lu

Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: riverbug@t.shu.edu.cn

Yanfei Zhao

Materials Genome Institute,
Shanghai University,
Shanghai 200444, China;
Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: yfzhao50@sina.com

Yicheng Song

Department of Mechanics,Shanghai Key Laboratory of
Mechanics in Energy Engineering,
Shanghai University,
Shanghai 200444, China
e-mail: ycsong@shu.edu.cn

Junqian Zhang

Department of Mechanics,Materials Genome Institute,Shanghai Key Laboratory of
Mechanics in Energy Engineering,
Shanghai University,
Shanghai 200444, China
e-mail: jqzhang2@shu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 28, 2016; final manuscript received September 15, 2016; published online October 5, 2016. Assoc. Editor: Kyung-Suk Kim.

J. Appl. Mech 83(12), 121009 (Oct 05, 2016) (8 pages) Paper No: JAM-16-1329; doi: 10.1115/1.4034783 History: Received June 28, 2016; Revised September 15, 2016

By directly solving the prescribed differential equations, an analytical method based on the cohesive model has been developed to investigate the interfacial debonding process induced by lithiation in an axisymmetric thin film electrode where an elastic active layer is bonded on a rigid substrate. The assumption of rigid substrate has been proved acceptable for high-modulus substrates such as copper and aluminum which are common materials for current collectors in lithium-ion batteries. For the case where the weak interface is assumed and the radial concentration gradient is neglected, an extremely simplified solution has been obtained. The simplified solution which has acceptable accuracy provides a good guidance for understanding and predicting the interfacial debonding.

Copyright © 2016 by ASME
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Green, M. , Fielder, E. , Scrosati, B. , Wachtler, M. , and Moreno, J. S. , 2003, “ Structured Silicon Anodes for Lithium Battery Applications,” Electrochem. Solid-State Lett., 6(5), pp. A75–A79. [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]
Boukamp, B. A. , Lesh, G. C. , and Huggins, R. A. , 1981, “ All Solid Lithium Electrodes With Mixed Conductor Matrix,” J. Electrochem. Soc., 128(4), pp. 725–729. [CrossRef]
Winter, M. , and Besenhard, J. O. , 1999, “ Electrochemical Lithiation of Tin and Tin-Based Intermetallics and Composites,” Electrochim. Acta, 45(1–2), pp. 31–50. [CrossRef]
Lee, S.-J. , Lee, J.-K. , Chung, S.-H. , Lee, H.-Y. , Lee, S.-M. , and Baik, H.-K. , 2001, “ Stress Effect on Cycle Properties of the Silicon Thin-Film Anode,” J. Power Sources, 97–98, pp. 191–193. [CrossRef]
Beaulieu, L. , Hatchard, T. , Bonakdarpour, A. , Fleischauer, M. , and Dahn, J. , 2003, “ Reaction of Li With Alloy Thin Films Studied by In Situ AFM,” J. Electrochem. Soc., 150(11), pp. A1457–A1464. [CrossRef]
Ryu, J. H. , Kim, J. W. , Sung, Y.-E. , and Oh, S. M. , 2004, “ Failure Modes of Silicon Powder Negative Electrode in Lithium Secondary Batteries,” Electrochem. Solid-State Lett., 7(10), pp. A306–A309. [CrossRef]
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]
Li, J. , Dozier, A. K. , Li, Y. , Yang, F. , and Cheng, Y.-T. , 2011, “ Crack Pattern Formation in Thin Film Lithium-Ion Battery Electrodes,” J. Electrochem. Soc., 158(6), pp. A689–A694. [CrossRef]
Xiao, X. , Liu, P. , Verbrugge, M. W. , Haftbaradaran, H. , and Gao, H. , 2011, “ Improved Cycling Stability of Silicon Thin Film Electrodes Through Patterning for High Energy Density Lithium Batteries,” J. Power Sources, 196(3), pp. 1409–1416. [CrossRef]
He, Y. , Wang, Y. , Yu, X. , Li, H. , and Huang, X. , 2012, “ Si-Cu Thin Film Electrode With Kirkendall Voids Structure for Lithium-Ion Batteries,” J. Electrochem. Soc., 159(12), pp. A2076–A2081. [CrossRef]
He, Y. , Yu, X. , Li, G. , Wang, R. , Li, H. , Wang, Y. , Gao, H. , and Huang, X. , 2012, “ Shape Evolution of Patterned Amorphous and Polycrystalline Silicon Microarray Thin Film Electrodes Caused by Lithium Insertion and Extraction,” J. Power Sources, 216, pp. 131–138. [CrossRef]
Wang, Y. H. , He, Y. , Xiao, R. J. , Li, H. , Aifantis, K. E. , and Huang, X. J. , 2012, “ Investigation of Crack Patterns and Cyclic Performance of Ti–Si Nanocomposite Thin Film Anodes for Lithium Ion Batteries,” J. Power Sources, 202, pp. 236–245. [CrossRef]
Taheri, P. , Hsieh, S. , and Bahrami, M. , 2011, “ Investigating Electrical Contact Resistance Losses in Lithium-Ion Battery Assemblies for Hybrid and Electric Vehicles,” J. Power Sources, 196(15), pp. 6525–6533. [CrossRef]
Yang, F. , 2011, “ Criterion for Insertion-Induced Microcracking and Debonding of Thin Films,” J. Power Sources, 196(1), pp. 465–469. [CrossRef]
Haftbaradaran, H. , Xiao, X. , Verbrugge, M. W. , and Gao, H. , 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]
Pal, S. , Damle, S. S. , Patel, S. H. , Datta, M. K. , Kumta, P. N. , and Maiti, S. , 2014, “ Modeling the Delamination of Amorphous-Silicon Thin Film Anode for Lithium-Ion Battery,” J. Power Sources, 246, pp. 149–159. [CrossRef]
Liu, M. , 2015, “ Finite Element Analysis of Lithiation-Induced Decohesion of A Silicon Thin Film Adhesively Bonded to A Rigid Substrate Under Potentiostatic Operation,” Int. J. Solids Struct., 67–68, pp. 263–271.
Lu, B. , Song, Y. , Guo, Z. , and Zhang, J. , 2013, “ Modeling of Progressive Delamination in A Thin Film Driven by Diffusion-Induced Stresses,” Int. J. Solids Struct., 50(14–15), pp. 2495–2507. [CrossRef]
Lu, B. , Song, Y.-C. , Guo, Z.-S. , and Zhang, J.-Q. , 2013, “ Analysis of Delamination in Thin Film Electrodes Under Galvanostatic and Potentiostatic Operations With Li-Ion Diffusion From Edge,” Acta Mech. Sin., 29(3), pp. 348–356. [CrossRef]
Lu, B. , Song, Y. , and Zhang, J. , 2015, “ Time to Delamination Onset and Critical Size of Patterned Thin Film Electrodes of Lithium Ion Batteries,” J. Power Sources, 289, pp. 168–183. [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]
Qi, Y. , Hector, L. G., Jr. , 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]
Baggetto, L. , Niessen, R. A. H. , Roozeboom, F. , and Notten, P. H. L. , 2008, “ High Energy Density All-Solid-State Batteries: A Challenging Concept Towards 3D Integration,” Adv. Funct. Mater., 18(7), pp. 1057–1066. [CrossRef]
Liu, X. H. , Wang, J. W. , Huang, S. , Fan, F. , Huang, X. , Liu, Y. , Krylyuk, S. , Yoo, J. , Dayeh, S. A. , Davydov, A. V. , Mao, S. X. , Picraux, S. T. , Zhang, S. , Li, J. , Zhu, T. , and Huang, J. Y. , 2012, “ In Situ Atomic-Scale Imaging of Electrochemical Lithiation in Silicon,” Nat. Nanotechnol., 7(11), pp. 749–756. [CrossRef] [PubMed]
Wang, J. W. , He, Y. , Fan, F. , Liu, X. H. , Xia, S. , Liu, Y. , Harris, C. T. , Li, H. , Huang, J. Y. , Mao, S. X. , and Zhu, T. , 2013, “ Two-Phase Electrochemical Lithiation in Amorphous Silicon,” Nano Lett., 13(2), pp. 709–715. [CrossRef] [PubMed]
Obrovac, M. N. , and Christensen, L. , 2004, “ Structural Changes in Silicon Anodes During Lithium Insertion/Extraction,” Electrochem. Solid-State Lett., 7(5), pp. A93–A96. [CrossRef]
McDowell, M. T. , Lee, S. W. , Harris, J. T. , Korgel, B. A. , Wang, C. , Nix, W. D. , and Cui, Y. , 2013, “ In Situ TEM of Two-Phase Lithiation of Amorphous Silicon Nanospheres,” Nano Lett., 13(2), pp. 758–764. [CrossRef] [PubMed]
Camacho, G. T. , and Ortiz, M. , 1996, “ Computational Modelling of Impact Damage in Brittle Materials,” Int. J. Solids Struct., 33(20–22), pp. 2899–2938. [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]
Zhang, J. , Lu, B. , Song, Y. , and Ji, X. , 2012, “ Diffusion Induced Stress in Layered Li-Ion Battery Electrode Plates,” J. Power Sources, 209, pp. 220–227. [CrossRef]
Lu, B. , Song, Y. , and Zhang, J. , 2016, “ Selection of Charge Methods for Lithium Ion Batteries by Considering Diffusion Induced Stress and Charge Time,” J. Power Sources, 320, pp. 104–110. [CrossRef]
Bhandakkar, T. K. , and Gao, H. , 2010, “ Cohesive Modeling of Crack Nucleation Under Diffusion Induced Stresses in a Thin Strip: Implications on The Critical Size for Flaw Tolerant Battery Electrodes,” Int. J. Solids Struct., 47(10), pp. 1424–1434. [CrossRef]
Yan, Y. , Sumigawa, T. , Shang, F. , and Kitamura, T. , 2011, “ Cohesive Zone Criterion for Cracking along the Cu/Si Interface in Nanoscale Components,” Eng. Fract. Mech., 78(17), pp. 2935–2946. [CrossRef]
Soni, S. K. , Sheldon, B. W. , Xiao, X. , Verbrugge, M. W. , Ahn, D. , Haftbaradaran, H. , and Gao, H. , 2012, “ Stress Mitigation During the Lithiation of Patterned Amorphous Si Islands,” J. Electrochem. Soc., 159(1), pp. A38–A43. [CrossRef]
Song, Y. , Shao, X. , Guo, Z. , and Zhang, J. , 2013, “ Role of Material Properties and Mechanical Constraint on Stress-Assisted Diffusion in Plate Electrodes of Lithium Ion Batteries,” J. Phys. D, 46(10), p. 105307. [CrossRef]
Yang, X.-G. , Bauer, C. , and Wang, C.-Y. , 2016, “ Sinusoidal Current and Stress Evolutions in Lithium-Ion Batteries,” J. Power Sources, 327, pp. 414–422. [CrossRef]


Grahic Jump Location
Fig. 1

A circular active thin film bonded to a rigid substrate: (a) axisymmetric model shown by side view and (b) debonding model shown by top view

Grahic Jump Location
Fig. 3

Size of the debonding zone changing with dimensionless lithiation time t¯ for different α

Grahic Jump Location
Fig. 5

Variation of the debonding onset with respect to α : (a) loading factor I¯=0.002 and (b) loading factor I¯=0.01. The dashed line represents the simplified solution for weak interface with no concentration gradient along the radius.

Grahic Jump Location
Fig. 2

Size of the debonding zone changing with dimensionless lithiation time t¯ for different loading factor I¯

Grahic Jump Location
Fig. 4

Illustration of applicability of the rigid substrate assumption: (a) loading factor I¯=0.002 and (b) loading factor I¯=0.01



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