Phase Diagram and Commensurate-Incommensurate Transitions in the Phase Field Crystal Model with an External Pinning Potential

TL;DR

This paper investigates the phase diagram and transition mechanisms between commensurate and incommensurate states in a two-dimensional crystal model with external pinning, combining analytical and numerical methods.

Contribution

It introduces a continuum phase field model capable of describing elastic and plastic deformations, analyzing transitions with mode expansion and numerical minimization.

Findings

First-order transition for small mismatch

Good agreement between analytical and numerical results

Consistent with atomistic simulation data

Abstract

We study the phase diagram and the commensurate-incommensurate transitions in a phase field model of a two-dimensional crystal lattice in the presence of an external pinning potential. The model allows for both elastic and plastic deformations and provides a continuum description of lattice systems, such as for adsorbed atomic layers or two-dimensional vortex lattices. Analytically, a mode expansion analysis is used to determine the ground states and the commensurate-incommensurate transitions in the model as a function of the strength of the pinning potential and the lattice mismatch parameter. Numerical minimization of the corresponding free energy shows good agreement with the analytical predictions and provides details on the topological defects in the transition region. We find that for small mismatch the transition is of first-order, and it remains so for the largest values of mismatch studied here. Our results are consistent with results of simulations for atomistic models of adsorbed overlayers.