Interface-reaction controlled diffusion in binary solids with applications to lithiation of silicon in lithium-ion batteries

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 b1⁄4 kef V B mR0=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 b means slower interfacial reaction, which would result in higher and more uniform concentration of lithium in the lithiated region. Furthermore, for a given b, 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. & 2012 Elsevier Ltd. All rights reserved.