Read--Shockley formula for a general Bravais lattice in two dimensions

TL;DR

This paper extends the Read-Shockley dislocation energy model to general two-dimensional Bravais lattices, providing a simple construction that aligns with the predicted logarithmic scaling.

Contribution

It introduces a new physically motivated construction for grain boundaries in 2D crystals with general Bravais lattices, matching theoretical energy predictions.

Findings

Energy of the construction matches logarithmic scaling predicted by Read and Shockley.

Provides a simple, physically motivated model for grain boundary energy in 2D crystals.

Applicable to general Bravais lattices, broadening the model's scope.

Abstract

In this note we consider a two-dimensional semi-discrete dislocation energy and propose a simple and physically motivated construction for the grain boundary between two crystal grains with a small orientation difference. In the case of a general Bravais lattice, the energy of this construction matches the logarithmic scaling predicted by Read and Shockley.