Phase field crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures

TL;DR

This paper derives a phase field crystal model for binary systems from density functional theory, develops an amplitude equation formalism including noise and mobility effects, and applies it to alloy heterostructures revealing composition overshooting phenomena.

Contribution

It introduces a comprehensive derivation of binary PFC dynamics from DDFT and develops an amplitude formalism that incorporates noise and mobility effects for alloy systems.

Findings

Surface segregation and interface intermixing in alloys studied.

Composition overshooting at interfaces observed.

Effects of atomic size and mobility differences analyzed.

Abstract

The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation functions in DDFT, and the lowest order approximation using scale analysis. The complete amplitude equation formalism for binary PFC is developed to describe the coupled dynamics of slowly varying complex amplitudes of structural profile, zeroth-mode average atomic density, and system concentration field. Effects of noise (corresponding to stochastic amplitude equations) and species-dependent atomic mobilities are also incorporated in this formalism. Results of a sample application to the study of surface segregation and interface intermixing in alloy heterostructures and strained layer growth are presented, showing the effects of different atomic sizes and mobilities of alloy components. A phenomenon of composition overshooting at the interface is found, which can be connected to the surface segregation and enrichment of one of the atomic components observed in recent experiments of alloying heterostructures.