Scale coupling and interface pinning effects in the phase-field-crystal model

TL;DR

This paper investigates how scale coupling and lattice pinning influence the phase-field-crystal model, deriving effective interface equations and analyzing growth dynamics, including pinning effects and universal scaling behaviors.

Contribution

It introduces nonadiabatic corrections to PFC amplitude equations and derives a generalized interface equation incorporating lattice pinning effects.

Findings

Identification of a generalized Gibbs-Thomson relation with pinning effects

Derivation of a driven sine-Gordon equation with KPZ nonlinearity

Universal scaling laws for pinning strength and interface properties

Abstract

Effects of scale coupling between mesoscopic slowly-varying envelopes of liquid-solid profile and the underlying microscopic crystalline structure are studied in the phase-field-crystal (PFC) model. Such scale coupling leads to nonadiabatic corrections to the PFC amplitude equations, the effect of which increases strongly with decreasing system temperature below the melting point. This nonadiabatic amplitude representation is further coarse-grained for the derivation of effective sharp-interface equations of motion in the limit of small but finite interface thickness. We identify a generalized form of the Gibbs-Thomson relation with the incorporation of coupling and pinning effects of the crystalline lattice structure. This generalized interface equation can be reduced to the form of a driven sine-Gordon equation with KPZ nonlinearity, and be combined with other two dynamic equations in the sharp interface limit obeying the conservation condition of atomic number density in a liquid-solid system. A sample application to the study of crystal layer growth is given, and the corresponding analytic solutions showing lattice pinning and depinning effects and two distinct modes of continuous vs. nucleated growth are presented. We also identify the universal scaling behaviors governing the properties of pinning strength, surface tension, interface kinetic coefficient, and activation energy of atomic layer growth, which accommodate all range of liquid-solid interface thickness and different material elastic modulus.