Amplitude expansion of the binary phase field crystal model

TL;DR

This paper develops amplitude representations for a binary phase field crystal model across various crystal structures, linking it explicitly to standard phase field models and demonstrating its application in simulating microstructural phenomena.

Contribution

It introduces amplitude equations for binary PFC models in multiple crystal structures and connects these to classical phase field models, with practical simulation examples.

Findings

Explicit amplitude equations for binary PFC in 2D and 3D structures

Established relationship between PFC and phase field models

Simulated solute migration, eutectic solidification, and quantum dot formation

Abstract

Amplitude representations of a binary phase field crystal model are developed for a two dimensional triangular lattice and three dimensional BCC and FCC crystal structures. The relationship between these amplitude equations and the standard phase field models for binary alloy solidification with elasticity are derived, providing an explicit connection between phase field crystal and phase field models. Sample simulations of solute migration at grain boundaries, eutectic solidification and quantum dot formation on nano-membranes are also presented.