Coupling Diffusion and Finite Deformation in Phase Transformation Materials

TL;DR

This paper develops a multiscale theoretical framework coupling diffusion and finite lattice deformation to better understand phase transformations in materials like Li$_{1-2}$Mn$_2$O$_4$, revealing insights into microstructural evolution and potential degradation mechanisms.

Contribution

It introduces a thermodynamically consistent multiscale theory combining diffusion and nonlinear elasticity, specifically applied to intercalation materials, advancing understanding of phase transformation microstructures.

Findings

Identifies stress concentration regions at phase boundaries and surfaces.

Provides quantitative analysis of twinned microstructure growth.

Suggests mechanisms for structural decay in battery materials.

Abstract

We present a multiscale theoretical framework to investigate the interplay between diffusion and finite lattice deformation in phase transformation materials. In this framework, we use the Cauchy-Born Rule and the Principle of Virtual Power to derive a thermodynamically consistent theory coupling the diffusion of a guest species (Cahn-Hilliard type) with the finite deformation of host lattices (nonlinear gradient elasticity). We adapt this theory to intercalation materials--specifically Li$_{1-2}$Mn$_2$O$_4$--to 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, and provide quantitative insights into the nucleation and growth of twinned microstructures during intercalation. Additionally, our results identify regions of stress concentrations (e.g., at phase boundaries, particle surfaces) that arise from lattice misfit and accumulate in the electrode with repeated cycling. These findings suggest a potential mechanism for structural decay in Li$_2$Mn$_2$O$_4$. 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.