Atomic scale lattice distortions and domain wall profiles

TL;DR

This paper develops an atomic scale theory linking lattice distortions to continuum elasticity, analyzing domain wall profiles and atomic relaxations in a 2D lattice, clarifying the microscopic origin of gradient terms.

Contribution

It introduces a novel atomic scale approach connecting atomic distortions with continuum elasticity, applied to domain walls in a 2D lattice, revealing anisotropic gradient effects.

Findings

Atomic scale lattice distortions are connected to continuum elasticity.

Hierarchical atomic relaxations near domain walls are characterized.

Gradient terms are shown to be anisotropic, clarifying their microscopic origin.

Abstract

We present an atomic scale theory of lattice distortions using strain related variables and their constraint equations. Our approach connects constrained {\it atomic length} scale variations to {\it continuum} elasticity and describes elasticity at several length scales. We apply the approach to a two-dimensional square lattice with a monatomic basis, and find the elastic deformations and hierarchical atomic relaxations in the vicinity of a domain wall between two different homogeneous strain states. We clarify the microscopic origin of gradient terms, some of which are included phenomenologically in Ginzburg-Landau theory, by showing that they are anisotropic.