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

Abstract

)) 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 Larché-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 recent experiments and connects characteristic features of the curve with the structure 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.

Sharp-interface formation during lithium intercalation into silicon

“…For a more realistic model effects of charge and electrical potential will have to be included, but at this stage our aim was first to understand the role of non-homogeneous elasticity in the stress-lithiation curve, see [23]. In addition, the underlying phase-field model is only applicable for regimes that depart little from equilibrium, and we are actually considering non-equilibrium phase transitions between what can be at best characterized as metastable states.…”

“…In Figure 2 are displayed snapshots of such an event (see Section 4 below and Ref. [23] for more information on the numerics). It shows the concentration and σ xx before and after the formation of the sharp interface in the presence of a non-uniform flux.…”

“…The simulations are performed using a non-linear adaptive multigrid algorithm [32]. For details on the simulations, see [23]. Figure 5 summarizes the effect of parameters β and δ on the convergence.…”

“…We see how σ xx is more negative in the transformed phase, indicating a strong compression and this compression is highest near the triple junctions. In this example, we have prescribed a constant flux as in [23], and taken lateral periodic boundary conditions for simplicity.…”

“…Lithium insertion causes a stress-free strain. For a discussion of the effect of this phase transformation on stress in this process, we have formulated a mathematical model in [23] and we will briefly introduce the complete phase-field model here.…”