Improving predictions of amorphous-crystalline silicon interface velocity through alloying-dealloying reactions in lithium-ion battery anode particles

Abstract

An improved mathematical model for the first lithiation of crystalline silicon is presented in the finite deformation framework. The crystalline-amorphous silicon interface kinetics is modelled through an addition reaction while the lithiation in the growing amorphous zone is captured through a reaction–diffusion model, incorporating a reversible alloying-dealloying reaction (ADR). The entire lithium is divided into two parts: a “movable” lithium part and an “immovable” lithium part. Through a parametric analysis for the different possible combinations of alloying and dealloying reaction constants, appropriate values are obtained that reproduce experimentally observed interface velocity. Thus, a key result of our study is the improvement of previous theoretical predictions through the incorporation of ADR. Comparative results are shown with and without ADR. Importantly, with ADR, a higher state of charge is obtained while the interface moves slower compared to the case without ADR. The non-uniformity in the lithium concentration distribution, which is a major criterion of generating diffusion-induced stress, is represented through the variance of concentraton. With ADR, this variance is initially higher but this trend reverses as the interface moves forward. Corresponding effects are observed for the stresses as well. It is expected that the improved predictions from this model will contribute towards better structural design of next-generation lithium-ion battery electrodes.