Thermodynamic phase-field model for microstructure with multiple components and phases: the possibility of metastable phases

TL;DR

This paper introduces a thermodynamic phase-field model for multi-component, multi-phase microstructures that incorporates interface width effects and metastability, enabling detailed simulations of phenomena like nucleation and premelting.

Contribution

It develops a variational diffuse-interface model based on thermodynamic principles, including composition gradient energy and phase constraints, to study complex microstructure evolution.

Findings

Metastable free energy surfaces influence microstructure evolution.

The model captures phenomena like nucleation, premelting, and particle instability.

Interface width effects are significant in phase transformations.

Abstract

A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition gradient energy to capture solute trapping, and is therefore suited for studying phenomena where the width of the interface plays an important role. Derivation of the inhomogeneous free energy functional from a Taylor expansion of homogeneous free energy reveals how the interfacial properties of each component and phase may be specified under a mass constraint. A diffusion potential for components was defined away from the dilute solution limit, and a multi-obstacle barrier function was used to constrain phase fractions. The model was used to simulate solidification via nucleation, premelting at phase boundaries and triple junctions, the intrinsic instability of small particles, and solutal melting resulting from differing diffusivities in solid and liquid. The shape of metastable free energy surfaces is found to play an important role in microstructure evolution and may explain why some systems premelt at phase boundaries and phase triple junctions while others do not.