Unified derivation of phase-field models for alloy solidification from a grand-potential functional

TL;DR

This paper unifies different alloy solidification phase-field models by deriving them from a grand-potential functional, enabling a consistent approach using chemical potential as the dynamical variable and facilitating quantitative simulations.

Contribution

It introduces a unified variational framework based on grand-potential functionals that derives existing models and extends to alloys with arbitrary phase diagrams.

Findings

Both types of phase-field models can be derived from a grand-potential functional.

The framework establishes an analogy with pure substance solidification models.

Numerical simulations demonstrate the method's accuracy with varying interface thickness.

Abstract

In the literature, two quite different phase-field formulations for the problem of alloy solidification can be found. In the first, the material in the diffuse interfaces is assumed to be in an intermediate state between solid and liquid, with a unique local composition. In the second, the interface is seen as a mixture of two phases that each retain their macroscopic properties, and a separate concentration field for each phase is introduced. It is shown here that both types of models can be obtained by the standard variational procedure if a grand-potential functional is used as a starting point instead of a free-energy functional. The dynamical variable is then the chemical potential instead of the composition. In this framework, a complete analogy with phase-field models for the solidification of a pure substance can be established. This analogy is then exploited to formulate quantitative phase-field models for alloys with arbitrary phase diagrams. The precision of the method is illustrated by numerical simulations with varying interface thickness.