Abstract
Most lithium ion battery electrodes experience large volume expansion and contraction during lithiation and delithiation, respectively. Electrode failure, in the form of fracture and decrepitation, can occur as a result of repeated volume changes. In this paper, we provide an overview of our recent work on modeling the evolution of concentration, stress, and strain energy within a spherical- or cylindrical-electrode element under various charging-discharging conditions. Based on the analytic results, we propose tensile stress and strain energy based criteria for the initiation and propagation of cracks within the electrodes. We will also discuss “size effects” on stresses and fracture of electrodes. These results may help guide the development of new materials for lithium ion batteries with enhanced durability and performance.
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Doyle, M., Fuller, T.F., Electrochem, J.: Modeling of galvanostatic charge and discharge of the lithium polymer insertion cell. J. Electrochem. Soc. 140(6), 1526–1533 (1993)
Fuller, T.F., Doyle, M., Newman, J.: Simulation and optimization of the dual lithium ion insertion cell. J. Electrochem. Soc. 141(1), 1–10 (1994)
Doyle, M., Newman, J., Gozdz, A.S., Schmutz, C.N., Tarascon, J.M.: Comparison of modeling predictions with experimental data from plastic lithium ion cells. J. Electrochem. Soc. 143(6), 1890–1903 (1996)
Darling, R., Newman, J.: Modeling a porous intercalation electrode with two characteristic particle sizes. J. Electrochem. Soc. 144(12), 4201–4208 (1997)
Verbrugge, M.W., Koch, B.J.: Lithium intercalation of carbon-fiber microelectrodes. J. Electrochem. Soc. 143(1), 24–31 (1996)
Verbrugge, M.W., Koch, B.J.: Modeling lithium intercalation of single-fiber carbon microelectrodes. J. Electrochem. Soc. 143(2), 600–608 (1996)
Verbrugge, M.W., Koch, B.J.: Electrochemistry of intercalation materials – Charge-transfer reaction and intercalate diffusion in porous electrodes. J. Electrochem. Soc. 146(3), 833–839 (1999)
Baker, D.R., Verbrugge, M.W.: Temperature and current distribution in thin-film batteries. J. Electrochem. Soc. 146(7), 2413–2424 (1999)
Verbrugge, M.W., Koch, B.J.: Electrochemical analysis of lithiated graphite anodes. J. Electrochem. Soc. 150(3), A374–A384 (2003)
Zhang, D., Popov, B.N., White, R.E.: Modeling lithium intercalation of a single spinel particle under potentiodynamic control. J. Electrochem. Soc. 147(3), 831–838 (2000)
Srinivasan, V., Newman, J.: Design and optimization of a natural graphite/iron phosphate lithium-ion cell. J. Electrochem. Soc. 151(10), A1530–A1538 (2004)
Devan, S., Subramanian, V.R., White, R.E.: Analytical solution for the impedance of a porous electrode. J. Electrochem. Soc. 151(6), A905–A913 (2004)
Dees, D., Gunen, E., Abraham, D., Jansen, A., Prakash, J.: Electrochemical modeling of lithium-ion positive electrodes during hybrid pulse power characterization tests. J. Electrochem. Soc. 155(8), A603–A613 (2008)
Wolfenstine, J.: Critical grain size for microcracking during lithium insertion. J. Power Sources 79(1), 111–113 (1999)
Huggins, R.A., Nix, W.D.: Decrepitation model for capacity loss during cycling of alloys in rechargeable electrochemical systems. Ionics 6, 57–63 (2000)
García, R.E., Chiang, Y.-M., Carter, W.C., Limthongkul, P., Bishop, C.M.: Microstructural modeling and design of rechargeable lithium-ion batteries. J. Electrochem. Soc. 152, A255 (2005)
Christensen, J., Newman, J.: A mathematical model of stress generation and fracture in lithium manganese oxide. J. Electrochem. Soc. 153(6), A1019–A1030 (2006)
Christensen, J., Srinivasan, V., Newman, J.: Optimization of lithium titanate electrodes for high-power cells. J. Electrochem. Soc. 153(3), A560–A565 (2006)
Zhang, X.C., Shyy, W., Sastry, A.M.: Numerical simulation of intercalation-induced stress in Li-ion battery electrode particles. J. Electrochem. Soc. 154(10), A910–A916 (2007)
Zhang, X.C., Sastry, A.M., Shyy, W.: Intercalation-induced stress and heat generation within single lithium-ion battery cathode particles. J. Electrochem. Soc. 155(7), A542–A552 (2008)
Cheng, Y.-T., Verbrugge, M.W.: The influence of surface mechanics on diffusion induced stresses within spherical nanoparticles. J. Appl. Phys. 104(8), 083521 (2008)
Verbrugge, M.W., Cheng, Y.-T.: Stress distribution within spherical particles undergoing electrochemical insertion and extraction. ECS Trans. 16, 127–139 (2008)
Deshpande, R., Cheng, Y.-T., Verbrugge, M.W.: Modeling diffusion-induced stress in nanowire electrode structures. J. Power Sources 195, 5081 (2010)
Cheng, Y.-T., Verbrugge, M.W.: Evolution of stress within a spherical insertion electrode particle under potentiostatic and galvanostatic operation. J. Power. Sources 190(2), 453–460 (2009)
Verbrugge, M.W., Cheng, Y.-T.: Stress and strain-energy distributions within diffusion- controlled insertion-electrode particles subjected to periodic potential excitations. J. Electrochem. Soc. 156, A927–A937 (2009)
Cheng, Y.-T., Verbrugge, M.W.: Diffusion-induced stress, interfacial charge transfer, and criteria for avoiding crack initiation of electrode particles. J. Electrochem. Soc. 157, A508 (2010)
Cheng, Y.-T., Verbrugge, M.W.: Application of Hasselman’s crack propagation model to insertion electrodes. Electrochem. Solid-State Lett. 13, A128 (2010)
Bard, A.J., Faulkner, L.R.: Electrochemical Methods. Wiley, New York (1980)
Newman, J., Thomas-Alyea, K.E.: Electrochemical Systems, 3rd edn. Wiley, Hoboken (2004)
Carslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids, 2nd edn. Clarendon, Oxford (1959)
Crank, J.: The Mathematics of Diffusion. Clarendon, Oxford (1956)
Prussin, S.: Generation and distribution of dislocations by solute diffusion. J. Appl. Phys. 32, 1876 (1961)
Yang, F.Q.: Interaction between diffusion and chemical stresses. Mater. Sci. Eng. A409, 153 (2005)
Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity, 3rd edn. McGraw-Hill, New York (1970)
Hasselman, D.P.H.: Elastic energy at fracture and surface energy as design criteria for thermal shock. J. Am. Ceramic Soc. 46, 535 (1963)
Stauffer, D., Aharony, A.: Introduction to Percolation Theory, 2nd edn. Taylor & Francis, London (1992)
Graetz, J., Ahn, C.C., Yazami, R., Fultz, B.: Highly reversible lithium storage in nanostructured silicon. Electrochem. Solid State Lett. 6(9), A194–A197 (2003)
Kim, I.S., Blomgren, G.E., Kumta, P.N.: Sn/C composite anodes for Li-ion batteries. Electrochem. Solid State Lett. 7(3), A44–A48 (2004)
Jung, Y.S., Lee, K.T., Ryu, J.H., Im, D., Oh, S.M.: Sn-carbon core-shell powder for anode in lithium secondary batteries. J. Electrochem. Soc. 152(7), A1452–A1457 (2005)
Kang, Y.M., Park, M.S., Lee, J.Y., Liu, H.K.: Si-Cu/carbon composites with a core-shell structure for Li-ion secondary battery. Carbon 45(10), 1928–1933 (2007)
Chan, C.K., Peng, H.L., Liu, G., McIlwrath, K., Zhang, X.F., Huggins, R.A., Cui, Y.: High-performance lithium battery anodes using silicon nanowires. Nat. Nanotechnol. 3(1), 31–35 (2008)
Riley, L.A., Cavanagh, A.S., George, S.M., Jung, Y.S., Yan, Y.F., Lee, S.H., Dillon, A.C.: Conformal surface coatings to enable high volume expansion Li-ion anode materials. Chemphyschem 11(10), 2124–2130 (2010)
Gibbs, J.W.: The Scientific Papers of J. Willard Gibbs, vol. 1, p. 55. Longnans-Green, London (1906)
Fischer, F.D., Waitz, T., Vollath, D., Simha, N.K.: On the role of surface energy and surface stress in phase-transforming nanoparticles. Prog. Mater. Sci. 53(3), 481–527 (2008)
Duan, H.L., Wang, J., Karihaloo, B.L.: Theory of elasticity at the nanoscale. In: Advances in Applied Mechanics, vol. 42. Elsevier Academic Press Inc, San Diego (2008), vol. 42, pp. 1–68
Shuttleworth, R.: The surface tension of solids. Proc. Phys. Soc. A63(365), 444–457 (1950)
Gurtin, M.E., Murdoch, A.: Continuum theory of elastic-material surfaces. Arch. Ration. Mech. Anal. 57(4), 291–323 (1975)
Sharma, P., Ganti, S., Bhate, N.: Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82(4), 535–537 (2003)
Miller, R.E., Shenoy, V.B.: Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11(3), 139–147 (2000)
Deshpande, R., Qi, Y., Cheng, Y.-T.: Effects of concentration-dependent elastic modulus on diffusion-induced stresses for battery applications. J. Electrochem. Soc. 157(8), A967–A971 (2010)
Harris, S.J., Deshpande, R.D., Qi, Y., Dutta, I., Cheng, Y.-T.: Mesopores inside electrode particles can change the Li-ion transport mechanism and diffusion-induced stress. J. Mater. Res. 25(8), 1433–1440 (2010)
Renganathan, S., Sikha, G., Santhanagopalan, S., White, R.E.: Theoretical analysis of stresses in a lithium ion cell. J. Electrochem. Soc. 157(2), A155–A163 (2010)
Bhandakkar, T.K., Gao, H.J.: 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 and Struct. 47(10), 1424–1434 (2010)
Golmon, S., Maute, K., Lee, S.H., Dunn, M.L.: Stress generation in silicon particles during lithium insertion. Appl. Phys. Lett. 97(3), 033111 (2010)
Xiao, X.R., Wu, W., Huang, X.S.: A multi-scale approach for the stress analysis of polymeric separators in a lithium-ion battery. J. Power Sources 195(22), 7649–7660 (2010)
Woodford, W.H., Chiang, Y.M., Carter, W.C.: “Electrochemical shock” of intercalation electrodes: a fracture mechanics analysis. J. Electrochem. Soc. 157(10), A1052–A1059 (2010)
Zhao, K.J., Pharr, M., Vlassak, J.J., Suo, Z.G.: Fracture of electrodes in lithium-ion batteries caused by fast charging. J. Appl. Phys. 108(7), 073517 (2010)
Yang, F.Q.: Insertion-induced breakage of materials. J. Appl. Phys. 108(7), 073536 (2010)
Yang, F.Q.: Effect of local solid reaction on diffusion-induced stress. J. Appl. Phys. 107(10), 103516 (2010)
Yang, F.Q.: Criterion for insertion-induced microcracking and debonding of thin films. J. Power Sources 196(1), 465–469 (2011)
Shenoy, V.B., Johari, P., Qi, Y.: Elastic softening of amorphous and crystalline Li-Si Phases with increasing Li concentration: A first-principles study. J. Power Sources 195(19), 6825–6830 (2010)
Acknowledgments
The authors would like to thank the financial support from NSF (CMMI #1000726) and General Motors Global R&D Center.
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Cheng, YT., Verbrugge, M.W., Deshpande, R. (2013). Understanding Diffusion-Induced-Stresses in Lithium Ion Battery Electrodes. In: Cocks, A., Wang, J. (eds) IUTAM Symposium on Surface Effects in the Mechanics of Nanomaterials and Heterostructures. IUTAM Bookseries (closed), vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4911-5_18
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