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Silicon, as the next-generation cathode material in lithium-ion batteries, exhibits excellent electrochemical performances compared with traditional cathode material, such as high capacity and cheap price. However, its cycling performances are greatly affected by the volume change of silicon due to the insertion of Li atoms. Lots of work focuses on the analysis of diffusion-induced stresses in electrode, but the convection term is seldom considered in analyzing the diffusion-induced stress in an electrode. In this paper, a mathematical model is established, where the convection term is taken into consideration in the diffusion process. The mechanics equations and diffusion equation are derived based on continuum mechanics and the diffusion theory. Diffusion-induced stress, axial reaction force and the critical buckling time in a hollow cylindrical electrode under galvanostatic charging are calculated. The effects of local velocity, ratio of the outer radius to inner radius, charging rate, material parameters and lithiation induced softening factors on stress field and the critical buckling time are studied. According to the results, it is found that the influence of local velocity on stress distribution increases with the increasing of Li concentration, and the contribution of local velocity to axial reaction force is insignificant. Compared with the results without local velocity, the tensile hoop stress of inner surface is large, and compressive stress at the outer surface is small. The axial reaction force and the critical buckling time are calculated with different ratios of outer radius to inner radius. As the radius ratio increases, the axial reaction force and critical buckling time decrease. The effects of three main material parameters (elastic modulus, diffusion coefficient, partial molar volume) on axial reaction force are discussed. The dimensionless force is independent of elastic modulus due to stress varying linearly with Young's modulus. The critical time is inversely proportional to diffusion coefficient. As the partial molar volume increases, which indicates larger volume change induced by the intercalation of the same quantity of Li-ions, the critical buckling time drops and the effect of local velocity on stress field increases. It takes less time for axial reaction force to reach the critical buckling force at a higher charging rate. The elastic properties of silicon in the lithiation process should be a function of Li concentration due to the formation of Li-Si alloy. The elastic modulus is assumed to be a linear function of Li concentration. The hollow cylindrical electrodes with increasing absolute value of lithiation induced softening factor have lower maximum axial reaction force. However, the lithiation induced softening factor has a limited effect on the critical buckling time due to the fact that the Li concentration at critical buckling time is relatively small.
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[9] Sun Y, Liu N, Cui Y 2016 Nat. Energy 1 1
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[15] Feng H, Fang D 2013 J. Appl. Phys. 113 013507
[16] Peng Y Z, Zhang K, Zheng B L, Li Y 2016 Acta Phys. Sin. 65 100201 (in Chinese) [彭颖吒, 张锴, 郑百林, 李泳 2016 物理学报 65 100201]
[17] Zhang K, Li Y, Zheng B L 2015 J. Appl. Phys. 118 105102
[18] Li Y, Zhang K, Zheng B L, Yang F 2016 J. Phys. D: Appl. Phys. 49 285602
[19] Li Y, Zhang K, Zheng B L, Yang F 2016 J. Power Sources 319 168
[20] Gere J, Goodno B 2012 Mechanics of Materials (Toronto: Nelson Education) p902
[21] Pal S, Damle S S, Patel S H, Datta M K, Kumta P N, Maiti S 2014 J. Power Sources 246 149
[22] Zhao K J, Pharr M, Cai S Q, Vlassak J J, Suo Z G 2011 J. Am. Ceram. Soc. 94 S226
[23] Deshpande R, Qi Y, Cheng Y T 2010 J. Electron. Mater. 157 A967
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[1] Lockwood D J 1999 Nanostructure Science and Technology (New York: Springer) pp1-20
[2] Guo B K, Li X H, Yang S Q 2009 Chemical Power Source-Principle and Manufacturing Technology of Battery (Hunan: Central South University Press) p315 (in Chinese) [郭炳焜, 李新海, 杨松青 2009 化学电源电池原理及制造技术 (湖南: 中南大学出版社) 第315页]
[3] Aifantis K E, Hackney S A, Kumar R V 2010 High Energy Density Lithium Batteries: Material, Engineering, Application (Hoboken: Wiley-VCH) p129
[4] Besenhard J O, Yang J, Winter M 1997 J. Power Sources 68 87
[5] Liu R, Duay J, Lee S B 2011 Chem. Commun. 47 1384
[6] McDowell M T, Lee S W, Nix W D, Cui Y 2013 Adv. Mater. 25 4966
[7] Shenoy V B, Johari P, Qi Y 2010 J. Power Sources 195 6825
[8] Yang F Q 2010 J. Appl. Phys. 108 073536
[9] Sun Y, Liu N, Cui Y 2016 Nat. Energy 1 1
[10] Park M H, Kim M G, Joo J, Kim K, Kim J, Ahn S, Cui Y, Cho J 2009 Nano Lett. 9 3844
[11] Wu H, Chan G, Choi J W, Ryu I, Yao Y, McDowell1 T T, Lee S W, Jackson A, Yang Y, Hu L B, Cui Y 2012 Nature Nanotech. 7 310
[12] Prussin S 1961 J. Appl. Phys. 32 1876
[13] Li J C, Dozier A K, Li Y, Yang F, Cheng Y T 2011 J. Electrochem. Soc. 158 A689
[14] Christensen J, Newman J 2005 J. Solid State Electrochem. 10 293
[15] Feng H, Fang D 2013 J. Appl. Phys. 113 013507
[16] Peng Y Z, Zhang K, Zheng B L, Li Y 2016 Acta Phys. Sin. 65 100201 (in Chinese) [彭颖吒, 张锴, 郑百林, 李泳 2016 物理学报 65 100201]
[17] Zhang K, Li Y, Zheng B L 2015 J. Appl. Phys. 118 105102
[18] Li Y, Zhang K, Zheng B L, Yang F 2016 J. Phys. D: Appl. Phys. 49 285602
[19] Li Y, Zhang K, Zheng B L, Yang F 2016 J. Power Sources 319 168
[20] Gere J, Goodno B 2012 Mechanics of Materials (Toronto: Nelson Education) p902
[21] Pal S, Damle S S, Patel S H, Datta M K, Kumta P N, Maiti S 2014 J. Power Sources 246 149
[22] Zhao K J, Pharr M, Cai S Q, Vlassak J J, Suo Z G 2011 J. Am. Ceram. Soc. 94 S226
[23] Deshpande R, Qi Y, Cheng Y T 2010 J. Electron. Mater. 157 A967
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