Combining phase field crystal methods with a Cahn-Hilliard model for binary alloys

TL;DR

This paper introduces a coupled 2D theoretical framework combining the Cahn-Hilliard and phase field crystal models to analyze microstructure evolution and lattice symmetry distortions during phase transitions in binary alloys.

Contribution

The novel integration of coordinate transformation coefficients as functions of composition fields to couple CH and PFC models for binary alloys.

Findings

Successfully models lattice symmetry interpolation across phase boundaries.

Demonstrates lattice distortions during phase transitions.

Provides a versatile framework for microstructure analysis.

Abstract

During phase transitions certain properties of a material change, such as composition field and lattice-symmetry distortions. These changes are typically coupled, and affect the microstructures that form in materials. Here, we propose a 2D theoretical framework that couples a Cahn-Hilliard (CH) model describing the composition field of a material system, with a phase field crystal (PFC) model describing its underlying microscopic configurations. We couple the two continuum models via coordinate transformation coefficients. We introduce the transformation coefficients in the PFC method, to describe affine lattice deformations. These transformation coefficients are modeled as functions of the composition field. Using this coupled approach, we explore the effects of coarse-grained lattice symmetry and distortions on a phase transition process. In this paper, we demonstrate the working of the CH-PFC model through three representative examples: First, we describe base cases with hexagonal and square lattice symmetries for two composition fields. Next, we illustrate how the CH-PFC method interpolates lattice symmetry across a diffuse composition phase boundary. Finally, we compute a Cahn-Hilliard type of diffusion and model the accompanying changes to lattice symmetry during a phase transition process.