Non-uniform Stress-free Strains in a Spherically Symmetrical Nano-sized Particle and Its Applications to Lithium-ion Batteries

Meng, Qingping; Wu, Lijun; Welch, David O.; Tang, Ming; Zhu, Yimei

doi:10.1038/s41598-018-23320-7

Title: Non-uniform Stress-free Strains in a Spherically Symmetrical Nano-sized Particle and Its Applications to Lithium-ion Batteries

Journal Article · 20 March 2018 · Scientific Reports

DOI: https://doi.org/10.1038/s41598-018-23320-7 · OSTI ID:1624390

Meng, Qingping ^[1];

^[2]; Welch, David O. ^[2];

^[3]; Zhu, Yimei ^[2]

Brookhaven National Lab. (BNL), Upton, NY (United States); DOE/OSTI
Brookhaven National Lab. (BNL), Upton, NY (United States)
Rice Univ., Houston, TX (United States)

The stress-free strain originated from local chemical composition and phase transformation can significantly alter the microstructures of materials; and then affect their properties. In this paper, we developed an analytical method to calculate stress-strain field due to the non-uniform stress-free strain in a spherically symmetrical particle. Applying the method to a lithium ion (Li-ion) battery electrode, the evolution of Li-ion concentration and strain field during the lithiation process is studied. Our studies reveal that the maximum strain in the electrode generally occurs on surface of sample, and is mainly dependent on the difference of Li-ion concentration of surface and of center in sample. Decreasing the difference of Li-ion concentration can efficiently decrease the maximum strain so that cracks of electrodes can been prevented. Our analytical results provide a useful guidance for practical applications of energy storage materials.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: AC02-98CH10886

OSTI ID:: 1624390

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 8; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (65)

Numerical Simulation of Intercalation-Induced Stress in Li-Ion Battery Electrode Particles Zhang, Xiangchun; Shyy, Wei; Marie Sastry, Ann Journal of The Electrochemical Society, Vol. 154, Issue 10 https://doi.org/10.1149/1.2759840	journal	January 2007
Model for the Particle Size, Overpotential, and Strain Dependence of Phase Transition Pathways in Storage Electrodes: Application to Nanoscale Olivines Tang, M.; Huang, H. -Y.; Meethong, N. Chemistry of Materials, Vol. 21, Issue 8 https://doi.org/10.1021/cm803172s	journal	April 2009
Concurrent Reaction and Plasticity during Initial Lithiation of Crystalline Silicon in Lithium-Ion Batteries Zhao, Kejie; Pharr, Matt; Wan, Qiang Journal of The Electrochemical Society, Vol. 159, Issue 3 https://doi.org/10.1149/2.020203jes	journal	January 2012
Effect of internal stress on autocatalytic nucleation of martensitic transformation Meng, Q. P.; Rong, Y. H.; Hsu (Xu Zuyao), T. Y. Metallurgical and Materials Transactions A, Vol. 37, Issue 5 https://doi.org/10.1007/s11661-006-0085-z	journal	May 2006
The elastic field outside an ellipsoidal inclusion Eshelby, John Douglas Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 252, Issue 1271, p. 561-569 https://doi.org/10.1098/rspa.1959.0173	journal	October 1959
Cracking causing cyclic instability of LiFePO4 cathode material Wang, Deyu; Wu, Xiaodong; Wang, Zhaoxiang Journal of Power Sources, Vol. 140, Issue 1 https://doi.org/10.1016/j.jpowsour.2004.06.059	journal	January 2005
Stress generation and fracture in lithium insertion materials Christensen, John; Newman, John Journal of Solid State Electrochemistry, Vol. 10, Issue 5 https://doi.org/10.1007/s10008-006-0095-1	journal	March 2006
TEM Study of Electrochemical Cycling-Induced Damage and Disorder in LiCoO[sub 2] Cathodes for Rechargeable Lithium Batteries Wang, Haifeng Journal of The Electrochemical Society, Vol. 146, Issue 2 https://doi.org/10.1149/1.1391631	journal	January 1999
Electrochemical stiffness in lithium-ion batteries Tavassol, Hadi; Jones, Elizabeth M. C.; Sottos, Nancy R. Nature Materials, Vol. 15, Issue 11 https://doi.org/10.1038/nmat4708	journal	August 2016
A continuum theory of elastic material surfaces Gurtin, Morton E.; Ian Murdoch, A. Archive for Rational Mechanics and Analysis, Vol. 57, Issue 4 https://doi.org/10.1007/bf00261375	journal	December 1975
Strain Coupling of Conversion-type Fe ₃ O ₄ Thin Films for Lithium Ion Batteries Hwang, Sooyeon; Meng, Qingping; Chen, Ping-Fan Angewandte Chemie International Edition, Vol. 56, Issue 27 https://doi.org/10.1002/anie.201703168	journal	May 2017
Recent findings and prospects in the field of pure metals as negative electrodes for Li-ion batteries Larcher, Dominique; Beattie, Shane; Morcrette, Mathieu Journal of Materials Chemistry, Vol. 17, Issue 36 https://doi.org/10.1039/b705421c	journal	January 2007
Visualization and Quantification of Electrochemical and Mechanical Degradation in Li Ion Batteries Ebner, M.; Marone, F.; Stampanoni, M. Science, Vol. 342, Issue 6159 https://doi.org/10.1126/science.1241882	journal	October 2013
Nanostructured materials: basic concepts and microstructure Gleiter, H. Acta Materialia, Vol. 48, Issue 1 https://doi.org/10.1016/S1359-6454(99)00285-2	journal	January 2000
Size-dependent fracture of Si nanowire battery anodes Ryu, Ill; Choi, Jang Wook; Cui, Yi Journal of the Mechanics and Physics of Solids, Vol. 59, Issue 9 https://doi.org/10.1016/j.jmps.2011.06.003	journal	September 2011
Stress generation during lithiation of high-capacity electrode particles in lithium ion batteries Huang, S.; Fan, F.; Li, J. Acta Materialia, Vol. 61, Issue 12 https://doi.org/10.1016/j.actamat.2013.04.007	journal	July 2013
Surface stress and the chemical equilibrium of small crystals—II. Solid particles embedded in a solid matrix Cahn, J. W.; Lärché, F. Acta Metallurgica, Vol. 30, Issue 1 https://doi.org/10.1016/0001-6160(82)90043-8	journal	January 1982
Surface Energy of Solids Bikerman, J. J. physica status solidi (b), Vol. 12, Issue 2 https://doi.org/10.1002/pssb.19650120249	journal	January 1965
Surface Energy of Solids Cherepanov, G. P. Methods of Fracture Mechanics: Solid Matter Physics https://doi.org/10.1007/978-94-017-2262-9_1	book	January 1997
Effect of heterogeneity on failure of natural rock samples Alzaki, Taqi; Al-Dughaimi, Saud; Muqtadir, Arqam Scientific Reports, Vol. 10, Issue 1 https://doi.org/10.1038/s41598-020-71780-7	journal	September 2020
Nucleation barrier for phase transformations in nanosized crystals Meng, Qingping; Rong, Yonghua; Hsu, T. Y. Physical Review B, Vol. 65, Issue 17 https://doi.org/10.1103/PhysRevB.65.174118	journal	May 2002
Spinodal decomposition in a small radially stressed sphere Johnson, W. C. Acta Materialia, Vol. 49, Issue 17 https://doi.org/10.1016/S1359-6454(01)00255-5	journal	October 2001
Surface energy of solids Linford, R. G. Chemical Society Reviews, Vol. 1, Issue 4 https://doi.org/10.1039/cs9720100445	journal	January 1972
The elastic field outside an ellipsoidal inclusion Eshelby, J. D. Solid Mechanics and its Applications https://doi.org/10.1007/1-4020-4499-2_25	book	January 1959
Electrochemically Driven Phase Transitions in Insertion Electrodes for Lithium-Ion Batteries: Examples in Lithium Metal Phosphate Olivines Tang, Ming; Carter, W. Craig; Chiang, Yet-Ming Annual Review of Materials Research, Vol. 40, Issue 1 https://doi.org/10.1146/annurev-matsci-070909-104435	journal	June 2010
Visualization of lithium-ion transport and phase evolution within and between manganese oxide nanorods Xu, Feng; Wu, Lijun; Meng, Qingping Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15400	journal	May 2017
The elastic field outside an ellipsoidal inclusion Eshelby, John Douglas Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 252, Issue 1271, p. 561-569 https://doi.org/10.1098/rspa.1959.0173	journal	October 1959
A continuum theory of elastic material surfaces Gurtin, Morton E.; Ian Murdoch, A. Archive for Rational Mechanics and Analysis, Vol. 57, Issue 4 https://doi.org/10.1007/BF00261375	journal	December 1975
Stress generation and fracture in lithium insertion materials Christensen, John; Newman, John Journal of Solid State Electrochemistry, Vol. 10, Issue 5 https://doi.org/10.1007/s10008-006-0095-1	journal	March 2006
The nanoscale circuitry of battery electrodes Zhu, Changbao; Usiskin, Robert E.; Yu, Yan Science, Vol. 358, Issue 6369 https://doi.org/10.1126/science.aao2808	journal	December 2017
Kinetics of non-equilibrium lithium incorporation in LiFePO4 Malik, Rahul; Zhou, Fei; Ceder, G. Nature Materials, Vol. 10, Issue 8 https://doi.org/10.1038/nmat3065	journal	July 2011
Recent findings and prospects in the field of pure metals as negative electrodes for Li-ion batteries Larcher, Dominique; Beattie, Shane; Morcrette, Mathieu Journal of Materials Chemistry, Vol. 17, Issue 36 https://doi.org/10.1039/b705421c	journal	January 2007
An attempt to estimate the degree of precipitation hardening, with a simple model Mott, N. F.; Nabarro, F. R. N. Proceedings of the Physical Society, Vol. 52, Issue 1 https://doi.org/10.1088/0959-5309/52/1/312	journal	January 1940
Visualization of lithium-ion transport and phase evolution within and between manganese oxide nanorods Xu, Feng; Wu, Lijun; Meng, Qingping Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15400	journal	May 2017
Size-dependent fracture of Si nanowire battery anodes Ryu, Ill; Choi, Jang Wook; Cui, Yi Journal of the Mechanics and Physics of Solids, Vol. 59, Issue 9 https://doi.org/10.1016/j.jmps.2011.06.003	journal	September 2011
Electron Microscopy Study of the LiFePO[sub 4] to FePO[sub 4] Phase Transition Chen, Guoying; Song, Xiangyun; Richardson, Thomas J. Electrochemical and Solid-State Letters, Vol. 9, Issue 6 https://doi.org/10.1149/1.2192695	journal	January 2006
The determination of the elastic field of an ellipsoidal inclusion, and related problems Eshelby, John Douglas Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 241, Issue 1226, p. 376-396 https://doi.org/10.1098/rspa.1957.0133	journal	August 1957
Surface Energy of Solids Bikerman, J. J. physica status solidi (b), Vol. 12, Issue 2 https://doi.org/10.1002/pssb.19650120249	journal	January 1965
Model for the Particle Size, Overpotential, and Strain Dependence of Phase Transition Pathways in Storage Electrodes: Application to Nanoscale Olivines Tang, M.; Huang, H. -Y.; Meethong, N. Chemistry of Materials, Vol. 21, Issue 8 https://doi.org/10.1021/cm803172s	journal	April 2009
Size-Dependent Fracture of Silicon Nanoparticles During Lithiation Liu, Xiao Hua; Zhong, Li; Huang, Shan ACS Nano, Vol. 6, Issue 2 https://doi.org/10.1021/nn204476h	journal	January 2012
Stress generation during lithiation of high-capacity electrode particles in lithium ion batteries Huang, S.; Fan, F.; Li, J. Acta Materialia, Vol. 61, Issue 12 https://doi.org/10.1016/j.actamat.2013.04.007	journal	July 2013
Nonlinear Volterra Integral Equations Wazwaz, Abdul-Majid A First Course in Integral Equations https://doi.org/10.1142/9789814675161_0008	book	May 2015
Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics Bazant, Martin Z. Accounts of Chemical Research, Vol. 46, Issue 5 https://doi.org/10.1021/ar300145c	journal	June 2012
Visualization and Quantification of Electrochemical and Mechanical Degradation in Li Ion Batteries Ebner, M.; Marone, F.; Stampanoni, M. Science, Vol. 342, Issue 6159 https://doi.org/10.1126/science.1241882	journal	October 2013
Measurement of three-dimensional microstructure in a LiCoO2 positive electrode Wilson, James R.; Cronin, J. Scott; Barnett, Scott A. Journal of Power Sources, Vol. 196, Issue 7 https://doi.org/10.1016/j.jpowsour.2010.04.066	journal	April 2011
Size-Dependent Fracture of Silicon Nanoparticles During Lithiation Liu, Xiao Hua; Zhong, Li; Huang, Shan ACS Nano, Vol. 6, Issue 2 https://doi.org/10.1021/nn204476h	journal	January 2012
The influence of surface mechanics on diffusion induced stresses within spherical nanoparticles Cheng, Yang-Tse; Verbrugge, Mark W. Journal of Applied Physics, Vol. 104, Issue 8 https://doi.org/10.1063/1.3000442	journal	October 2008
Surface Energy of Solids Bikerman, J. J. physica status solidi (b), Vol. 10, Issue 1 https://doi.org/10.1002/pssb.19650100102	journal	January 1965
Kinetics of non-equilibrium lithium incorporation in LiFePO4 Malik, Rahul; Zhou, Fei; Ceder, G. Nature Materials, Vol. 10, Issue 8 https://doi.org/10.1038/nmat3065	journal	July 2011
A Mathematical Model of Stress Generation and Fracture in Lithium Manganese Oxide Christensen, John; Newman, John Journal of The Electrochemical Society, Vol. 153, Issue 6 https://doi.org/10.1149/1.2185287	journal	January 2006
Strain Coupling of Conversion-type Fe ₃ O ₄ Thin Films for Lithium Ion Batteries Hwang, Sooyeon; Meng, Qingping; Chen, Ping-Fan Angewandte Chemie International Edition, Vol. 56, Issue 27 https://doi.org/10.1002/anie.201703168	journal	May 2017
Measurement of three-dimensional microstructure in a LiCoO2 positive electrode Wilson, James R.; Cronin, J. Scott; Barnett, Scott A. Journal of Power Sources, Vol. 196, Issue 7 https://doi.org/10.1016/j.jpowsour.2010.04.066	journal	April 2011
Cracking causing cyclic instability of LiFePO4 cathode material Wang, Deyu; Wu, Xiaodong; Wang, Zhaoxiang Journal of Power Sources, Vol. 140, Issue 1 https://doi.org/10.1016/j.jpowsour.2004.06.059	journal	January 2005
Fracture of electrodes in lithium-ion batteries caused by fast charging Zhao, Kejie; Pharr, Matt; Vlassak, Joost J. Journal of Applied Physics, Vol. 108, Issue 7 https://doi.org/10.1063/1.3492617	journal	October 2010
Evolution of stress within a spherical insertion electrode particle under potentiostatic and galvanostatic operation Cheng, Yang-Tse; Verbrugge, Mark W. Journal of Power Sources, Vol. 190, Issue 2, p. 453-460 https://doi.org/10.1016/j.jpowsour.2009.01.021	journal	May 2009
Effect of internal stress on autocatalytic nucleation of martensitic transformation Meng, Q. P.; Rong, Y. H.; Hsu (Xu Zuyao), T. Y. Metallurgical and Materials Transactions A, Vol. 37, Issue 5 https://doi.org/10.1007/s11661-006-0085-z	journal	May 2006
Surface stress and the chemical equilibrium of small crystals—II. Solid particles embedded in a solid matrix Cahn, J. W.; Lärché, F. Acta Metallurgica, Vol. 30, Issue 1 https://doi.org/10.1016/0001-6160(82)90043-8	journal	January 1982
LiMn2O4-based composites processed by a chemical-route Microstructural, electrical, electrochemical, and mechanical characterization Lazarraga, M. Journal of Power Sources, Vol. 115, Issue 2 https://doi.org/10.1016/S0378-7753(03)00011-9	journal	April 2003
TEM Study of Electrochemical Cycling-Induced Damage and Disorder in LiCoO[sub 2] Cathodes for Rechargeable Lithium Batteries Wang, Haifeng Journal of The Electrochemical Society, Vol. 146, Issue 2 https://doi.org/10.1149/1.1391631	journal	January 1999
Electrochemically Driven Phase Transitions in Insertion Electrodes for Lithium-Ion Batteries: Examples in Lithium Metal Phosphate Olivines Tang, Ming; Carter, W. Craig; Chiang, Yet-Ming Annual Review of Materials Research, Vol. 40, Issue 1 https://doi.org/10.1146/annurev-matsci-070909-104435	journal	June 2010
Evolution of stress within a spherical insertion electrode particle under potentiostatic and galvanostatic operation Cheng, Yang-Tse; Verbrugge, Mark W. Journal of Power Sources, Vol. 190, Issue 2, p. 453-460 https://doi.org/10.1016/j.jpowsour.2009.01.021	journal	May 2009
Electrochemical stiffness in lithium-ion batteries Tavassol, Hadi; Jones, Elizabeth M. C.; Sottos, Nancy R. Nature Materials, Vol. 15, Issue 11 https://doi.org/10.1038/nmat4708	journal	August 2016
Strain Coupling of Conversion‐type Fe ₃ O ₄ Thin Films for Lithium Ion Batteries Hwang, Sooyeon; Meng, Qingping; Chen, Ping‐Fan Angewandte Chemie, Vol. 129, Issue 27 https://doi.org/10.1002/ange.201703168	journal	May 2017
Nonlinear Volterra Integral Equations Wazwaz, Abdul-Majid Linear and Nonlinear Integral Equations https://doi.org/10.1007/978-3-642-21449-3_13	book	January 2011
A Phase-Field Model Coupled with Large Elasto-Plastic Deformation: Application to Lithiated Silicon Electrodes Chen, L.; Fan, F.; Hong, L. Journal of The Electrochemical Society, Vol. 161, Issue 11 https://doi.org/10.1149/2.0171411jes	journal	January 2014