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A novel cylindrical composition-gradient electrode is considered to be one of most potential structures in lithium-ion battery. To investigate the mechanism of a cylindrical composition-gradient electrode under potentiostatic operation, we take Li1.2(Mn0.62Ni0.38)0.8O2 for example. The effects of the three main factors, i.e., diffusion coefficient, Youngs modulus, partial molar volume of solute, on the stress field in the cylindrical electrode are discussed. Each of the three material parameters is assumed to be a linear function of the distance from the center to surface. The small deformation theory and thermodynamic theory are employed to establish the mathematical model of composition-gradient cylindrical electrode. The mechanics equations and diffusion equation of cylindrical electrode are derived for an inhomogeneous material in plane strain condition. By comparing with single-phase electrode, it is found that Youngs modulus increasing from the center to the surface greatly reduces the max tensile radial stress and tensile hoop stress and changes the location of max radial stress since the radial displacement of the center is restricted. The time for the lithium-ions to reach the center is longer and the tensile stress near the center decreases at dimensionless time =0.0574 when diffusion coefficient decreases along the radial direction. Owing to the smaller diffusion coefficient at the surface, there is a reduction in the number of lithium-ions through the unit area in unit time when their corresponding concentration gradients are the same. The variation of partial molar volume means that the volume expansion caused by the intercalation of lithium-ions decreases along the radial direction. Therefore the partial molar volume decreasing along the radial direction considerably reduces the radial stress and the distribution of tangential stress becomes flat. The center point is picked, showing the development of hoop stress. The results show that the hoop stress increases and reaches a maximal value close to the dimensionless time =0.0574. Maximal tensile hoop stress at the center is reduced in an inhomogeneous material. The tensile hoop stress turns into compressive stress over time when elastic modulus and partial molar volume are denoted with E(r) and (r) respectively. The results indicate that the cylindrical composition-gradient electrode with core enriched Ni and edge enriched Mn reduces the max tensile radial stress and tensile hoop stress. It is an efficient way to avoid mechanical fracture in electrode since evidence has accumulated that tensile stress is the lead cause of crack in electrode. The result also provides useful guidance for mitigating the stresses in a cylindrical electrode.
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Keywords:
- diffusion-induced stresses /
- composition-gradient materials /
- generalized plane strain /
- lithium-ion battery
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[2] Pesaran A, Market T, Tataria H, Howell D 2007 Battery Requirements for Plug-in Hybrid Electricvehicles: Analysis and Rationale California,USA, December 2-5, 2007 p42467
[3] Cheng Y, Li J, Jia M, Tang Y W, Du S L, Ai L H, Yin B H, Ai L 2015 Acta Phys. Sin. 56 210202 (in Chinese) [程昀, 李劼, 贾明, 汤依伟, 杜双龙, 艾立华, 殷宝华,艾亮 2015 56 210202]
[4] Wu M S, Xu B, Ouyang C Y 2016 Chin. Phys. B 25 018206
[5] Woo K C, Kamitakahara W A, DiVincenzo D P, Robinson D S, Mertwoy H, Milliken J W, Fischer J E 1893 Phys. Rev. Lett. 50 182
[6] Besenhard J O, Yang J, Winter M 1997 J. Power Sources 68 87
[7] Fuqian Y 2010 J. Appl. Phys. 108 073536
[8] Zhu T 2016 Chin. Phys. B 25 014601
[9] Hao F, Fang D N 2013 J. Electro. Soc. 160 A595
[10] Gary M K, Belharouak Jr I, Deng H, Sun Y K, Amine K 2011 Chemical of Materials 23 1954
[11] Hu G J, Ouyang C Y 2010 Acta Phys. Sin. 59 5863 (in Chinese) [胡国进, 欧阳楚英 2010 59 5863]
[12] Liu R, Duay J, Lee S 2011 Chem. Commun. 47 1384
[13] Prussin S 1961 J. Appl. Phys. 32 1876
[14] Li J C, Dozier A K, Li Yang F Q, Cheng Y T 2011 J. Electrochem. Soc. 158 A689
[15] Lee S, Wang W L, Chen J R 2000 Mater. Chem. Phys. 64 123
[16] Song Y C, Lu B, Ji X, Zhang J Q 2012 J. Electrochem. Soc. 159 A2060
[17] Zhang T, Guo Z S, Wang Y H 2014 J. Appl. Phys. 115 083504
[18] Guo Z S, Zhang T, Hu H J, Song Y C, Zhang J Q 2013 J. Appl. Mech. 81 031013
[19] Li Y, Zhang K, Zheng B 2015 J. Appl. Phys. 117 245103
[20] Wei Q, Wang X, Yang X, Ju B, Hu B, Shu H, Wen W, Zhou M, Song Y, Wu H, Hu H 2013 J. Mater. Chem. A 1 4010
[21] Crank J 1979 The Mathematics of Diffusion (Oxford: Oxford University Press) pp69-89
[22] Cheng Y T, Verbrugge M W 2008 J. Appl. Phys. 104 083521
[23] Hu Y H, Zhao X H, Suo Z G 2010 J. Mater. Res. 25 1007
[24] Huggins R A, Nix W D 2000 Ionics 6 57
[25] Bhandakkar T K, Gao H J 2010 Int. J. Solids Struc. 47 1424
[26] Woodford W H, Chiang Y M, Carter W C 2010 J. Electrochem. Soc. 157 A1052
[27] Zhao K J, Pharr M, Vlassak J J, Suo Z G 2010 J. Appl. Phys. 108 073517
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[1] Lockwood D J 1999 Nanostructure Science and Technology (New York: Springer) pp1-20
[2] Pesaran A, Market T, Tataria H, Howell D 2007 Battery Requirements for Plug-in Hybrid Electricvehicles: Analysis and Rationale California,USA, December 2-5, 2007 p42467
[3] Cheng Y, Li J, Jia M, Tang Y W, Du S L, Ai L H, Yin B H, Ai L 2015 Acta Phys. Sin. 56 210202 (in Chinese) [程昀, 李劼, 贾明, 汤依伟, 杜双龙, 艾立华, 殷宝华,艾亮 2015 56 210202]
[4] Wu M S, Xu B, Ouyang C Y 2016 Chin. Phys. B 25 018206
[5] Woo K C, Kamitakahara W A, DiVincenzo D P, Robinson D S, Mertwoy H, Milliken J W, Fischer J E 1893 Phys. Rev. Lett. 50 182
[6] Besenhard J O, Yang J, Winter M 1997 J. Power Sources 68 87
[7] Fuqian Y 2010 J. Appl. Phys. 108 073536
[8] Zhu T 2016 Chin. Phys. B 25 014601
[9] Hao F, Fang D N 2013 J. Electro. Soc. 160 A595
[10] Gary M K, Belharouak Jr I, Deng H, Sun Y K, Amine K 2011 Chemical of Materials 23 1954
[11] Hu G J, Ouyang C Y 2010 Acta Phys. Sin. 59 5863 (in Chinese) [胡国进, 欧阳楚英 2010 59 5863]
[12] Liu R, Duay J, Lee S 2011 Chem. Commun. 47 1384
[13] Prussin S 1961 J. Appl. Phys. 32 1876
[14] Li J C, Dozier A K, Li Yang F Q, Cheng Y T 2011 J. Electrochem. Soc. 158 A689
[15] Lee S, Wang W L, Chen J R 2000 Mater. Chem. Phys. 64 123
[16] Song Y C, Lu B, Ji X, Zhang J Q 2012 J. Electrochem. Soc. 159 A2060
[17] Zhang T, Guo Z S, Wang Y H 2014 J. Appl. Phys. 115 083504
[18] Guo Z S, Zhang T, Hu H J, Song Y C, Zhang J Q 2013 J. Appl. Mech. 81 031013
[19] Li Y, Zhang K, Zheng B 2015 J. Appl. Phys. 117 245103
[20] Wei Q, Wang X, Yang X, Ju B, Hu B, Shu H, Wen W, Zhou M, Song Y, Wu H, Hu H 2013 J. Mater. Chem. A 1 4010
[21] Crank J 1979 The Mathematics of Diffusion (Oxford: Oxford University Press) pp69-89
[22] Cheng Y T, Verbrugge M W 2008 J. Appl. Phys. 104 083521
[23] Hu Y H, Zhao X H, Suo Z G 2010 J. Mater. Res. 25 1007
[24] Huggins R A, Nix W D 2000 Ionics 6 57
[25] Bhandakkar T K, Gao H J 2010 Int. J. Solids Struc. 47 1424
[26] Woodford W H, Chiang Y M, Carter W C 2010 J. Electrochem. Soc. 157 A1052
[27] Zhao K J, Pharr M, Vlassak J J, Suo Z G 2010 J. Appl. Phys. 108 073517
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