Phase field modelling of interfacial anisotropy driven faceting of precipitates

TL;DR

This paper employs extended Cahn-Hilliard equations to model and predict faceted precipitate shapes driven by interfacial anisotropy, capturing complex morphologies in systems with cubic and hexagonal symmetries.

Contribution

It provides a comprehensive formulation of ECH equations including sixth rank tensor terms and details parameter extraction for modeling precipitate morphologies.

Findings

Predicted four-sided and dodecahedral precipitates in 2D and 3D with cubic anisotropy.

Modeled six-sided, hexagonal dipyramids, and hexagonal prisms with hexagonal anisotropy.

Established methods to determine model parameters from interfacial energy data.

Abstract

We use extended Cahn-Hilliard (ECH) equations to study faceted precipitate morphologies; specifically, we obtain four sided precipitates (in 2-D) and dodecahedron (in 3-D) in a system with cubic anisotropy, and, six-sided precipitates (in 2-D, in the basal plane), hexagonal dipyramids and hexagonal prisms (in 3-D) in systems with hexagonal anisotropy. Our listing of these ECH equations is fairly comprehensive and complete (upto sixth rank tensor terms of the Taylor expansion of the free energy). We also show how the parameters that enter the model are to be obtained if either the interfacial energy anisotropy or the equilibrium morphology of the precipitate is known.