Phase field modelling of precipitate morphologies in systems with tetragonal interfacial free energy anisotropy

TL;DR

This paper introduces an extended Cahn-Hilliard model to simulate various precipitate morphologies in tetragonally anisotropic systems, aligning with equilibrium shapes predicted by the Wulff construction.

Contribution

The paper develops a family of models incorporating tetragonal anisotropy in interfacial free energy, enabling simulation of diverse precipitate morphologies.

Findings

Model can produce di-pyramids, rods, plates, and variants.

Morphologies are confirmed as equilibrium shapes via Wulff construction.

Model parameters are explicitly listed and constrained.

Abstract

A wide variety of morphologies arise due to the tetragonal anisotropy in interfacial free energy. In this paper, we report on a family of Extended Cahn-Hilliard (ECH) models for incorporating tetragonal anisotropy in interfacial free energy. We list the non-zero and independent parameters that are introduced in our model and list the constraints on them. For appropriate choice of these parameters, our model can produce a many of the morphologies seen in tetragonal systems such as di-pyramids, rods, plates and their truncated variants. We analyse these morphologies and show that they indeed are equilibrium morphologies consistent with the Wulff construction.