Mechano-chemical spinodal decomposition: A phenomenological theory of phase transformations in multi-component, crystalline solids

TL;DR

This paper develops a phenomenological theory for diffusion-driven phase transformations in multi-component crystalline solids, emphasizing the role of mechano-chemical spinodal regions where free energy is non-convex, with applications to battery and ceramic materials.

Contribution

It introduces a new framework for modeling mechano-chemical spinodal decomposition, incorporating nonlinear elasticity and gradient effects, and provides a computational approach for complex microstructure evolution.

Findings

Mechano-chemical spinodal regions identified in phase diagrams.

Numerical simulations demonstrate complex microstructure patterns.

Relevance to electrode materials in Li-ion batteries and ceramics.

Abstract

We present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes diffusional phase transformations that are accompanied by symmetry breaking structural changes of the crystal unit cell and reveals the importance of a mechano-chemical spinodal, defined as the region in strain-composition space where the free energy density function is non-convex. The approach is relevant to phase transformations wherein the structural order parameters can be expressed as linear combinations of strains relative to a high-symmetry reference crystal. The governing equations describing mechano-chemical spinodal decomposition are variationally derived from a free energy density function that accounts for interfacial energy via gradients of the rapidly varying strain and composition fields. A robust computational framework for treating the coupled, higher order diffusion and nonlinear strain gradient elasticity problems is presented. Because the local strains in an inhomogeneous, transforming microstructure can be finite, the elasticity problem must account for geometric nonlinearity. An evaluation of available experimental phase diagrams and first-principles free energies suggests mechano-chemical spinodal decomposition should occur in metal hydrides such as ZrH$_{2-2c}$. The rich physics that ensues is explored in several numerical examples in two and three dimensions and the relevance of the mechanism is discussed in the context of important electrode materials for Li-ion batteries and high temperature ceramics.