TY - JOUR
T1 - Interface-reaction controlled diffusion in binary solids with applications to lithiation of silicon in lithium-ion batteries
AU - Cui, Zhiwei
AU - Gao, Feng
AU - Qu, Jianmin
N1 - Publisher Copyright:
© 2012 Elsevier Ltd
PY - 2013/2/1
Y1 - 2013/2/1
N2 - Solid state diffusion in a binary system, such as lithiation into crystalline silicon, often involves two symbiotic processes, namely, interfacial chemical reaction and bulk diffusion. Building upon our earlier work (Cui et al., 2012b, J. Mech. Phys. Solids, 60 (7), 1280–1295), we develop a mathematical framework in this study to investigate the interaction between bulk diffusion and interfacial chemical reaction in binary systems. The new model accounts for finite deformation kinematics and stress-diffusion interaction. It is applicable to arbitrary shape of the phase interface. As an example, the model is used to study the lithiation of a spherical silicon particle. It is found that a dimensionless parameter β=kfeVmBR0/D0 plays a significant role in determining the kinetics of the lithiation process. This parameter, analogous to the Biot number in heat transfer, represents the ratio of the rate of interfacial chemical reaction and the rate of bulk diffusion. Smaller β means slower interfacial reaction, which would result in higher and more uniform concentration of lithium in the lithiated region. Furthermore, for a given β, the lithiation process is always controlled by the interfacial chemical reaction initially, until sufficient silicon has been lithiated so that the diffusion distance for lithium reaches a threshold value, beyond which bulk diffusion becomes the slower process and controls the overall lithiation kinetics.
AB - Solid state diffusion in a binary system, such as lithiation into crystalline silicon, often involves two symbiotic processes, namely, interfacial chemical reaction and bulk diffusion. Building upon our earlier work (Cui et al., 2012b, J. Mech. Phys. Solids, 60 (7), 1280–1295), we develop a mathematical framework in this study to investigate the interaction between bulk diffusion and interfacial chemical reaction in binary systems. The new model accounts for finite deformation kinematics and stress-diffusion interaction. It is applicable to arbitrary shape of the phase interface. As an example, the model is used to study the lithiation of a spherical silicon particle. It is found that a dimensionless parameter β=kfeVmBR0/D0 plays a significant role in determining the kinetics of the lithiation process. This parameter, analogous to the Biot number in heat transfer, represents the ratio of the rate of interfacial chemical reaction and the rate of bulk diffusion. Smaller β means slower interfacial reaction, which would result in higher and more uniform concentration of lithium in the lithiated region. Furthermore, for a given β, the lithiation process is always controlled by the interfacial chemical reaction initially, until sufficient silicon has been lithiated so that the diffusion distance for lithium reaches a threshold value, beyond which bulk diffusion becomes the slower process and controls the overall lithiation kinetics.
KW - Amorphization
KW - Chemical reaction
KW - Diffusion
KW - Interface
KW - Lithium-ion battery
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U2 - 10.1016/j.jmps.2012.11.001
DO - 10.1016/j.jmps.2012.11.001
M3 - Article
AN - SCOPUS:84870325571
SN - 0022-5096
VL - 61
SP - 293
EP - 310
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
IS - 2
ER -