# A phase-field study of elastic stress effects on phase separation in ternary alloys

## TL;DR

This study uses a phase-field model to investigate how elastic stress influences phase separation and microstructure evolution in ternary alloys, revealing the impact of misfit strains and interfacial energies.

## Contribution

The paper introduces a microelastic phase-field model for ternary alloys that accounts for elastic interactions and systematically analyzes their effects on microstructure development.

## Key findings

- Misfit strains influence strain partitioning and morphology.
- Higher misfit leads to coarser phases with wider size distribution.
- Complete wetting conditions can produce stable core-shell structures.

## Abstract

Most of the commercially important alloys are multicomponent, producing multiphase microstructures as a result of processing. When the coexisting phases are elastically coherent, the elastic interactions between these phases play a major role in the development of microstructures. To elucidate the key effects of elastic stress on microstructural evolution when more than two misfitting phases are present in the microstructure, we have developed a microelastic phase-field model in two dimensions to study phase separation in ternary alloy system. Numerical solutions of a set of coupled Cahn-Hilliard equations for the composition fields govern the spatiotemporal evolution of the three-phase microstructure. The model incorporates coherency strain interactions between the phases using Khachaturyan's microelasticity theory. We systematically vary the misfit strains (magnitude and sign) between the phases along with the bulk alloy composition to study their effects on the morphological development of the phases and the resulting phase separation kinetics. We also vary the ratio of interfacial energies between the phases to understand the interplay between elastic and interfacial energies on morphological evolution. The sign and degree of misfit affect strain partitioning between the phases during spinodal decomposition, thereby affecting their compositional history and morphology. Moreover, strain partitioning affects solute partitioning and alters the kinetics of coarsening of the phases. The phases associated with higher misfit strain appear coarser and exhibit wider size distribution compared to those having lower misfit. When the interfacial energies satisfy complete wetting condition, phase separation leads to development of stable core-shell morphology depending on the misfit between the core (wetted) and the shell (wetting) phases.