Thin-film electrodes for high-capacity lithium-ion batteries: Influence of phase transformations on stress

In this study we revisit experiments by Sethuraman et al. [J. Power Sources, 195, 5062 (2010)] on the stress evolution during the lithiation/delithiation cycle of a thin film of amorphous silicon. Based on recent work that show a two-phase process of lithiation of amorphous silicon, we formulate a phase-field model coupled to elasticity in the framework of Larch'e-Cahn. Using an adaptive nonlinear multigrid algorithm for the finite-volume discretization of this model, our two-dimensional numerical simulations show the formation of a sharp phase boundary between the lithiated and the amorphous silicon that continues to move as a front through the thin layer. We show that our model captures the non-monotone stress loading curve and rate dependence, as observed in experiments and connects characteristic features of the curve with the stucture formation within the layer. We take advantage of the thin film geometry and study the corresponding one-dimensional model to establish the dependence on the material parameters and obtain a comprehensive picture of the behaviour of the system