Self-consistent modeling of anisotropic interfaces and missing orientations: Derivation from phase-field crystal

TL;DR

This paper develops a phase-field model derived from the phase-field crystal formalism to accurately describe highly anisotropic interfaces and missing orientations in crystal growth, capturing complex surface phenomena.

Contribution

It introduces a self-consistent phase-field limit from the PFC model that describes anisotropic surface energies, missing orientations, and facet formation.

Findings

The model reproduces Wulff shapes with missing orientations.

It captures the transition to missing orientations and facet formation.

The phase-field limit provides a regularized, orientation-dependent surface description.

Abstract

Highly anisotropic interfaces play an important role in the development of material microstructure. Using the diffusive atomistic phase-field crystal (PFC) formalism, we determine the capability of the model to quantitatively describe these interfaces. Specifically, we coarse grain the PFC model to attain both its complex amplitude formulation and its corresponding phase-field limit. Using this latter formulation, in one-dimensional calculations, we determine the surface energy and the properties of the Wulff shape. We find that the model can yield Wulff shapes with missing orientations, the transition to missing orientations, and facet formation. We show that the corresponding phase-field limit of the complex amplitude model yields a self-consistent description of highly anisotropic surface properties that are a function of the surface orientation with respect to the underlying crystal lattice. The phase-field model is also capable of describing missing orientations on equilibrium shapes of crystals and naturally includes a regularizing contribution. We demonstrate, in two dimensions, how the resultant model can be used to study growth of crystals with varying degrees of anisotropy in the phase-field limit.