Coupling Diffusion and Finite Deformation in Intercalation Materials

We present a multiscale theoretical framework to investigate the interplay between diffusion and finite lattice deformation in intercalation materials. In this framework, we couple the diffusion of a guest species (Cahn-Hilliard type) with the finite deformation of host lattices (nonlinear gradient elasticity). We adapt this theory to LiMn₂O₄to investigate the delicate interplay between Li-diffusion and the cubic-to-tetragonal deformation of lattices. Our computations reveal fundamental insights into the microstructural evolution pathways under dynamic discharge conditions, provide quantitative insights into the nucleation and growth of twinned microstructures during intercalation, and identify regions of stress concentrations (e.g., at phase boundaries, particle surfaces) that arise from lattice misfit. These findings suggest a potential mechanism for structural decay in LiMn₂O₄. More generally, we establish a theoretical framework that can be used to investigate microstructural evolution pathways, across multiple length scales, in first-order phase transformation materials.