Abstract
We study through extensive finite element analysis the lithium diffusion in small elements of Si anodes under the forms of spheres, rods, and circular disks for Li-ion batteries. Elastoplastic properties of the amorphous silicon are assumed to be lithium concentration-dependent. Effects of the normalized flux of Li-ions on the lithium concentrations, stresses, and total equivalent plastic strains are considered. Effects of the disk's thickness are also included. At a given normalized flux, the heterogeneity of the lithiation, stresses, and plastic deformation increases in the order: disk, sphere, and rod. The thinner disk the better performance is. Below a critical value of the normalized flux of Li-ions, silicon spheres and disks exhibit linear elasticity and homogeneous distribution of Li-ions, whereas silicon rods undergo always plastic deformation after lithiation. When the radii of these three structures are smaller than several micrometers and the normalized flux is taken as 95% of their critical value, the charge time falls in the range from minutes to several hours. Our findings will help to optimize the charge and geometrical parameters for silicon anodes.
Issue Section:
Research Papers
Topics:
Anodes,
Deformation,
Diffusion (Physics),
Disks,
Lithium,
Rods,
Silicon,
Stress,
Ions,
Finite element analysis
References
1.
Obrovac
, M.
, Christensen
, L.
, Le
, D. B.
, and Dahn
, J.
, 2007
, “Alloy Design for Lithium-Ion Battery Anodes
,” J. Electrochem. Soc.
, 154
(9
), pp. A849
–A855
. 10.1149/1.27529852.
Obrovac
, M.
, and Christensen
, L.
, 2004
, “Structural Changes in Silicon Anodes During Lithium Insertion/Extraction
,” Electrochem. Solid-State Lett.
, 7
(5
), pp. A93
–A96
. 10.1149/1.16524213.
Noel
, M.
, and Suryanarayanan
, V.
, 2002
, “Role of Carbon Host Lattices in Li-Ion Intercalation/De-Intercalation Processes
,” J. Power Sources
, 111
(2
), pp. 193
–209
. 10.1016/S0378-7753(02)00308-74.
Dahn
, J. R.
, Zheng
, T.
, Liu
, Y.
, and Xue
, J.
, 1995
, “Mechanisms for Lithium Insertion in Carbonaceous Materials
,” Science
, 270
(5236
), p. 590
. 10.1126/science.270.5236.5905.
Mahmood
, N.
, Tang
, T.
, and Hou
, Y.
, 2016
, “Nanostructured Anode Materials for Lithium Ion Batteries: Progress, Challenge and Perspective
,” Adv. Energy Mater.
, 6
(17
), pp. 1
–22
. 10.1002/aenm.2016003746.
Li
, X.
, Chen
, Y.
, Huang
, H.
, Mai
, Y.-W.
, and Zhou
, L.
, 2016
, “Electrospun Carbon-Based Nanostructured Electrodes for Advanced Energy Storage—A Review
,” Energy Storage Mater.
, 5
, pp. 58
–92
. 10.1016/j.ensm.2016.06.0027.
Balogun
, M.-S.
, Qiu
, W.
, Luo
, Y.
, Meng
, H.
, Mai
, W.
, Onasanya
, A.
, Olaniyi
, T. K.
, and Tong
, Y.
, 2016
, “A Review of the Development of Full Cell Lithium-Ion Batteries: The Impact of Nanostructured Anode Materials
,” Nano Res.
, 9
(10
), pp. 2823
–2851
. 10.1007/s12274-016-1171-18.
Reddy
, M.
, Subba Rao
, G.
, and Chowdari
, B.
, 2013
, “Metal Oxides and Oxysalts as Anode Materials for Li Ion Batteries
,” Chem. Rev.
, 113
(7
), pp. 5364
–5457
. 10.1021/cr30018849.
Park
, C.-M.
, Kim
, J.-H.
, Kim
, H.
, and Sohn
, H.-J.
, 2010
, “Li-Alloy Based Anode Materials for Li Secondary Batteries
,” Chem. Soc. Rev.
, 39
(8
), pp. 3115
–3141
. 10.1039/b919877f10.
Liu
, X. H.
, Zhong
, L.
, Huang
, S.
, Mao
, S. X.
, Zhu
, T.
, and Huang
, J. Y.
, 2012
, “Size-Dependent Fracture of Silicon Nanoparticles During Lithiation
,” ACS Nano
, 6
(2
), pp. 1522
–1531
. 10.1021/nn204476h11.
Beattie
, S. D.
, Larcher
, D.
, Morcrette
, M.
, Simon
, B.
, and Tarascon
, J.-M.
, 2008
, “Si Electrodes for Li-Ion Batteries—A New Way to Look at an Old Problem
,” J. Electrochem. Soc.
, 155
(2
), pp. A158
–A163
. 10.1149/1.281782812.
Chen
, Z.
, Christensen
, L.
, and Dahn
, J.
, 2003
, “Large-Volume-Change Electrodes for Li-Ion Batteries of Amorphous Alloy Particles Held by Elastomeric Tethers
,” Electrochem. Commun.
, 5
(11
), pp. 919
–923
. 10.1016/j.elecom.2003.08.01713.
McDowell
, M. T.
, Xia
, S.
, and Zhu
, T.
, 2016
, “The Mechanics of Large-Volume-Change Transformations in High-Capacity Battery Materials
,” Extreme Mech. Lett.
, 9
(Part 3
), pp. 480
–494
. 10.1016/j.eml.2016.03.00414.
Liu
, X. H.
, Zheng
, H.
, Zhong
, L.
, Huang
, S.
, Karki
, K.
, Zhang
, L. Q.
, Liu
, Y.
, Kushima
, A.
, Liang
, W. T.
, and Wang
, J. W.
, 2011
, “Anisotropic Swelling and Fracture of Silicon Nanowires During Lithiation
,” Nano Lett.
, 11
(8
), pp. 3312
–3318
. 10.1021/nl201684d15.
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
. 10.1021/nl304450816.
Berla
, L. A.
, Lee
, S. W.
, Ryu
, I.
, Cui
, Y.
, and Nix
, W. D.
, 2014
, “Robustness of Amorphous Silicon During the Initial Lithiation/Delithiation Cycle
,” J. Power Sources
, 258
, pp. 253
–259
. 10.1016/j.jpowsour.2014.02.03217.
Bucci
, G.
, Nadimpalli
, S. P.
, Sethuraman
, V. A.
, Bower
, A. F.
, and Guduru
, P. R.
, 2014
, “Measurement and Modeling of the Mechanical and Electrochemical Response of Amorphous Si Thin Film Electrodes During Cyclic Lithiation
,” J. Mech. Phys. Solids
, 62
(1
), pp. 276
–294
. 10.1016/j.jmps.2013.10.00518.
Sethuraman
, V. A.
, Chon
, M. J.
, Shimshak
, M.
, Srinivasan
, V.
, and Guduru
, P. R.
, 2010
, “In Situ Measurements of Stress Evolution in Silicon Thin Films During Electrochemical Lithiation and Delithiation
,” J. Power Sources
, 195
(15
), pp. 5062
–5066
. 10.1016/j.jpowsour.2010.02.01319.
Ding
, N.
, Xu
, J.
, Yao
, Y.
, Wegner
, G.
, Fang
, X.
, Chen
, C.
, and Lieberwirth
, I.
, 2009
, “Determination of the Diffusion Coefficient of Lithium Ions in Nano-Si
,” Solid State Ionics
, 180
(2
), pp. 222
–225
. 10.1016/j.ssi.2008.12.01520.
Xia
, H.
, Tang
, S.
, and Lu
, L.
, 2007
, “Properties of Amorphous Si Thin Film Anodes Prepared by Pulsed Laser Deposition
,” Mater. Res. Bull.
, 42
(7
), pp. 1301
–1309
. 10.1016/j.materresbull.2006.10.00721.
Xie
, J.
, Imanishi
, N.
, Zhang
, T.
, Hirano
, A.
, Takeda
, Y.
, and Yamamoto
, O.
, 2010
, “Li-Ion Diffusion in Amorphous Si Films Prepared by RF Magnetron Sputtering: A Comparison of Using Liquid and Polymer Electrolytes
,” Mater. Chem. Phys.
, 120
(2–3
), pp. 421
–425
. 10.1016/j.matchemphys.2009.11.03122.
Li
, J.
, Xiao
, X.
, Yang
, F.
, Verbrugge
, M. W.
, and Cheng
, Y.-T.
, 2011
, “Potentiostatic Intermittent Titration Technique for Electrodes Governed by Diffusion and Interfacial Reaction
,” J. Phys. Chem. C
, 116
(1
), pp. 1472
–1478
. 10.1021/jp207919q23.
Zhao
, K.
, Pharr
, M.
, Cai
, S.
, Vlassak
, J. J.
, and Suo
, Z.
, 2011
, “Large Plastic Deformation in High-Capacity Lithium-Ion Batteries Caused by Charge and Discharge
,” J. Am. Ceram. Soc.
, 94
(s1
), pp. s226
–s235
. 10.1111/j.1551-2916.2011.04432.x24.
Bower
, A. F.
, Guduru
, P. R.
, and Sethuraman
, V. A.
, 2011
, “A Finite Strain Model of Stress, Diffusion, Plastic Flow, and Electrochemical Reactions in a Lithium-Ion Half-Cell
,” J. Mech. Phys. Solids
, 59
(4
), pp. 804
–828
. 10.1016/j.jmps.2011.01.00325.
Chew
, H. B.
, Hou
, B.
, Wang
, X.
, and Xia
, S.
, 2014
, “Cracking Mechanisms in Lithiated Silicon Thin Film Electrodes
,” Int. J. Solids Struct.
, 51
(23
), pp. 4176
–4187
. 10.1016/j.ijsolstr.2014.08.00826.
Pal
, S.
, Damle
, S. S.
, Kumta
, P. N.
, and Maiti
, S.
, 2013
, “Modeling of Lithium Segregation Induced Delamination of a-Si Thin Film Anode in Li-Ion Batteries
,” Comput. Mater. Sci.
, 79
, pp. 877
–887
. 10.1016/j.commatsci.2013.06.05127.
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
, pp. 263
–271
. 10.1016/j.ijsolstr.2015.04.02628.
Wang
, M.
, and Xiao
, X.
, 2016
, “Investigation of the Chemo-Mechanical Coupling in Lithiation/Delithiation of Amorphous Si Through Simulations of Si Thin Films and Si Nanospheres
,” J. Power Sources
, 326
, pp. 365
–376
. 10.1016/j.jpowsour.2016.07.01129.
Wang
, H.
, Nadimpalli
, S. P.
, and Shenoy
, V. B.
, 2016
, “Inelastic Shape Changes of Silicon Particles and Stress Evolution at Binder/Particle Interface in a Composite Electrode During Lithiation/Delithiation Cycling
,” Extreme Mech. Lett.
, 9
(3
), pp. 430
–438
. 10.1016/j.eml.2016.03.02030.
Xu
, R.
, and Zhao
, K.
, 2016
, “Mechanical Interactions Regulated Kinetics and Morphology of Composite Electrodes in Li-Ion Batteries
,” Extreme Mech. Lett.
, 8
, pp. 13
–21
. 10.1016/j.eml.2015.10.00431.
Wang
, M.
, Xiao
, X.
, and Huang
, X.
, 2016
, “Study of Lithium Diffusivity in Amorphous Silicon Via Finite Element Analysis
,” J. Power Sources
, 307
, pp. 77
–85
. 10.1016/j.jpowsour.2015.12.08232.
Di Leo
, C. V.
, Rejovitzky
, E.
, and Anand
, L.
, 2015
, “Diffusion–Deformation Theory for Amorphous Silicon Anodes: The Role of Plastic Deformation on Electrochemical Performance
,” Int. J. Solids Struct.
, 67
, pp. 283
–296
. 10.1016/j.ijsolstr.2015.04.02833.
Cui
, Z.
, Gao
, F.
, and Qu
, J.
, 2012
, “A Finite Deformation Stress-Dependent Chemical Potential and Its Applications to Lithium Ion Batteries
,” J. Mech. Phys. Solids
, 60
(7
), pp. 1280
–1295
. 10.1016/j.jmps.2012.03.00834.
An
, Y.
, and Jiang
, H.
, 2013
, “A Finite Element Simulation on Transient Large Deformation and Mass Diffusion in Electrodes for Lithium Ion Batteries
,” Model. Simul. Mater. Sci. Eng.
, 21
(7
), p. 074007
. 10.1088/0965-0393/21/7/07400735.
Brassart
, L.
, Zhao
, K.
, and Suo
, Z.
, 2013
, “Cyclic Plasticity and Shakedown in High-Capacity Electrodes of Lithium-Ion Batteries
,” Int. J. Solids Struct.
, 50
(7–8
), pp. 1120
–1129
. 10.1016/j.ijsolstr.2012.12.01936.
Zhao
, K.
, Pharr
, M.
, Vlassak
, J. J.
, and Suo
, Z.
, 2011
, “Inelastic Hosts as Electrodes for High-Capacity Lithium-Ion Batteries
,” J. Appl. Phys.
, 109
(1
), p. 016110
. 10.1063/1.352599037.
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
. 10.1016/j.jpowsour.2010.04.04438.
Zhao
, K.
, Wang
, W. L.
, Gregoire
, J.
, Pharr
, M.
, Suo
, Z.
, Vlassak
, J. J.
, and Kaxiras
, E.
, 2011
, “Lithium-Assisted Plastic Deformation of Silicon Electrodes in Lithium-Ion Batteries: A First-Principles Theoretical Study
,” Nano Lett.
, 11
(7
), pp. 2962
–2967
. 10.1021/nl201501s39.
Chou
, C.-Y.
, Kim
, H.
, and Hwang
, G. S.
, 2011
, “A Comparative First-Principles Study of the Structure, Energetics, and Properties of Li–M (M = Si, Ge, Sn) Alloys
,” J. Phys. Chem. C
, 115
(40
), pp. 20018
–20026
. 10.1021/jp205484v40.
Johari
, P.
, Qi
, Y.
, and Shenoy
, V. B.
, 2011
, “The Mixing Mechanism During Lithiation of Si Negative Electrode in Li-Ion Batteries: An Ab Initio Molecular Dynamics Study
,” Nano Lett.
, 11
(12
), pp. 5494
–5500
. 10.1021/nl203302d41.
Xie
, Z.
, Ma
, Z.
, Wang
, Y.
, Zhou
, Y.
, and Lu
, C.
, 2016
, “A Kinetic Model for Diffusion and Chemical Reaction of Silicon Anode Lithiation in Lithium Ion Batteries
,” RSC Adv.
, 6
(27
), pp. 22383
–22388
. 10.1039/C5RA27817A42.
Liu
, P.
, Sridhar
, N.
, and Zhang
, Y.-W.
, 2012
, “Lithiation-Induced Tensile Stress and Surface Cracking in Silicon Thin Film Anode for Rechargeable Lithium Battery
,” J. Appl. Phys.
, 112
(9
), p. 093507
. 10.1063/1.476432943.
Jia
, Z.
, and Li
, T.
, 2016
, “Failure Mechanics of a Wrinkling Thin Film Anode on a Substrate Under Cyclic Charging and Discharging
,” Extreme Mech. Lett.
, 8
, pp. 273
–282
. 10.1016/j.eml.2016.03.00644.
Damle
, S. S.
, Pal
, S.
, Kumta
, P. N.
, and Maiti
, S.
, 2016
, “Effect of Silicon Configurations on the Mechanical Integrity of Silicon–Carbon Nanotube Heterostructured Anode for Lithium Ion Battery: A Computational Study
,” J. Power Sources
, 304
, pp. 373
–383
. 10.1016/j.jpowsour.2015.11.02745.
Custer
, J.
, Thompson
, M. O.
, Jacobson
, D.
, Poate
, J.
, Roorda
, S.
, Sinke
, W.
, and Spaepen
, F.
, 1994
, “Density of Amorphous Si
,” Appl. Phys. Lett.
, 64
(4
), pp. 437
–439
. 10.1063/1.11112146.
Searle
, T.
, 1998
, Properties of Amorphous Silicon and Its Alloys
, The Institution of Electrical Engineers
, London, UK
.47.
Zhang
, X.
, Shyy
, W.
, and Sastry
, A. M.
, 2007
, “Numerical Simulation of Intercalation-Induced Stress in Li-Ion Battery Electrode Particles
,” J. Electrochem. Soc.
, 154
(10
), pp. A910
–A916
. 10.1149/1.275984048.
Crank
, J.
, 1975
, The Mathematics of Diffusion
, 2nd ed., Oxford University Press
, UK
.49.
Ryu
, I.
, Choi
, J. W.
, Cui
, Y.
, and Nix
, W. D.
, 2011
, “Size-Dependent Fracture of Si Nanowire Battery Anodes
,” J. Mech. Phys. Solids
, 59
(9
), pp. 1717
–1730
. 10.1016/j.jmps.2011.06.00350.
Chan
, M. K.
, Wolverton
, C.
, and Greeley
, J. P.
, 2012
, “First Principles Simulations of the Electrochemical Lithiation and Delithiation of Faceted Crystalline Silicon
,” J. Am. Chem. Soc.
, 134
(35
), pp. 14362
–14374
. 10.1021/ja301766z51.
Cui
, Z.
, Gao
, F.
, Cui
, Z.
, and Qu
, J.
, 2012
, “A Second Nearest-Neighbor Embedded Atom Method Interatomic Potential for Li–Si Alloys
,” J. Power Sources
, 207
, pp. 150
–159
. 10.1016/j.jpowsour.2012.01.14552.
Freund
, L. B.
, and Suresh
, S.
, 2004
, Thin Film Materials: Stress, Defect Formation and Surface Evolution
, Cambridge University Press
, UK
.53.
Hull
, R.
, 1988
, Properties of Silicon
, INSPEC, The Institution of Electrical Engineers
, New York
.54.
Follstaedt
, D. M.
, Knapp
, J.
, and Myers
, S.
, 2004
, “Mechanical Properties of Ion-Implanted Amorphous Silicon
,” J. Mater. Res.
, 19
(1
), pp. 338
–346
. 10.1557/jmr.2004.19.1.33855.
Hopcroft
, M. A.
, Nix
, W. D.
, and Kenny
, T. W.
, 2010
, “What is the Young's Modulus of Silicon?
” J. Microelectromech. Syst.
, 19
(2
), pp. 229
–238
. 10.1109/JMEMS.2009.203969756.
Yang
, F.
, 2005
, “Interaction Between Diffusion and Chemical Stresses
,” Mater. Sci. Eng. A
, 409
(1–2
), pp. 153
–159
. 10.1016/j.msea.2005.05.11757.
Vanimisetti
, S. K.
, and Ramakrishnan
, N.
, 2012
, “Effect of the Electrode Particle Shape in Li-Ion Battery on the Mechanical Degradation During Charge–Discharge Cycling
,” Proc. Inst. Mech. Eng. C
, 226
(9
), pp. 2192
–2213
. 10.1177/095440621143266858.
Cheng
, Y.-T.
, and Verbrugge
, M. W.
, 2008
, “The Influence of Surface Mechanics on Diffusion Induced Stresses Within Spherical Nanoparticles
,” J. Appl. Phys.
, 104
(8
), p. 083521
. 10.1063/1.300044259.
Yoshimura
, K.
, Suzuki
, J.
, Sekine
, K.
, and Takamura
, T.
, 2007
, “Measurement of the Diffusion Rate of Li in Silicon by the Use of Bipolar Cells
,” J. Power Sources
, 174
(2
), pp. 653
–657
. 10.1016/j.jpowsour.2007.06.115Copyright © 2020 by ASME
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