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.

在有限变形框架中提出了一种改进的数学模型，用于结晶硅的第一次锂化。结晶-非晶硅界面动力学通过加成反应进行建模，而生长中的非晶区中的锂化则通过反应扩散模型（结合了可逆的合金化-脱合金反应（ADR））进行捕获。整个锂分为两部分：“可移动”锂部分和“不可移动”锂部分。通过对合金化和脱合金反应常数的不同可能组合进行参数分析，可以获得适当的值，该值可再现实验观察到的界面速度。因此，我们研究的关键结果是通过合并ADR改进了先前的理论预测。显示了有和没有ADR的对比结果。重要的是，与不使用ADR的情况相比，使用ADR可以获得更高的电荷状态，而接口的移动速度更慢。锂浓度分布的不均匀性是产生扩散诱导应力的主要标准，它通过浓度变化来表示。使用ADR，这种差异最初会更高，但是随着界面向前移动，这种趋势会逆转。对于应力也观察到相应的效果。预计该模型的改进预测将有助于下一代锂离子电池电极的更好结构设计。锂浓度分布的不均匀性是产生扩散诱导应力的主要标准，它通过浓度变化来表示。使用ADR，这种差异最初会更高，但是随着界面向前移动，这种趋势会逆转。对于应力也观察到相应的效果。预计该模型的改进预测将有助于下一代锂离子电池电极的更好结构设计。锂浓度分布的不均匀性是产生扩散诱导应力的主要标准，它通过浓度变化来表示。使用ADR，这种差异最初会更高，但是随着界面向前移动，这种趋势会逆转。对于应力也观察到相应的效果。预计该模型的改进预测将有助于下一代锂离子电池电极的更好结构设计。