Long wavelength properties of phase field crystal models with second order dynamics

TL;DR

This paper compares different phase field crystal models with second order dynamics to determine which best captures elastic relaxation, concluding that full hydrodynamical modeling is necessary for accurate elastic stress relaxation.

Contribution

It introduces a comparison between hydrodynamic and simplified PFC amplitude models, highlighting the importance of full hydrodynamics for elastic relaxation.

Findings

Full hydrodynamical PFC models accurately relax elastic excitations.

Simpler models fail to capture elastic stress relaxation properly.

Analytical and numerical comparisons support the necessity of hydrodynamics.

Abstract

The phase field crystal (PFC) approach extends the notion of phase field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance creates an elastic excitation. The dynamics of these excitations poses a challenge: pure diffusive dynamics cannot describe relaxation of elastic stresses that happen through phonon emission. To this end, several different models with fast dynamics have been proposed. In this article we use the amplitude expansion of the PFC model to compare the recently proposed hydrodynamic PFC amplitude model with two simpler models with fast dynamics. We compare these different models analytically and numerically. The results suggest that in order to have proper relaxation of elastic excitations, the full hydrodynamical description of the PFC amplitudes is required.