Predicting buckling regimes during first lithiation of a crystalline silicon cylindrical anode particle: Influence of size and charging rate

Abstract

A mathematical model for buckling analysis during the first lithiation of cylindrical crystalline silicon (c-Si) anode particles is presented using the finite deformation framework. A reaction–diffusion model that incorporates a reversible alloying-dealloying reaction (ADR) captures the lithiation in the expanding amorphous zone, while an addition reaction models the dynamics of the crystalline-amorphous silicon interface. A “movable” lithium part and an “immovable” lithium part make up the full lithium. In sharp contrast to the case of amorphous silicon (a-Si), the axial force evolution in c-Si is found to show two different peaks during the initial and final stages of lithiation, respectively. These peaks form the basis of two different buckling criteria, which, in turn, are shown to be sensitively influenced by the influx of lithium and a crucial size-dependent parameter. This framework gives an insight towards investigating the buckling phenomena for lithiation with an evolving amorphous silicon zone due to the interface movement, which is still absent in the present literature Additionally, the present model enables us to obtain a quantitative and mechanistic insight into and capture the previous experimental observation that the mechanical stability of a cylindrical silicon particle may be improved by maintaining a crystalline silicon core inside the amorphous shell through controlled first lithiation. It is shown that such a crystalline-amorphous core–shell structure can be advantageous to more complicated designs involving carbon fibre as the core. It is thus hoped that this model will contribute towards improving the theoretical underpinnings of an improved design of mechanically robust electrodes for next-generation batteries.