Calculus of Variations and Geometric Measure Theory

L. Scardia - E. G. Tolotti

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

created by tolotti on 23 Apr 2026
modified on 04 Sep 2026

[BibTeX]

Published Paper

Inserted: 23 apr 2026
Last Updated: 4 sep 2026

Journal: Journal of Elasticity
Volume: 158
Number: 52
Year: 2026
Doi: https://doi.org/10.1007/s10659-026-10227-y

ArXiv: 2604.20287 PDF

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.