Statistical Mechanics of Low Angle Grain Boundaries in Two Dimensions

TL;DR

This paper investigates the thermal behavior and phase transitions of low angle grain boundaries in two-dimensional crystals, revealing depinning and melting phenomena with universal critical exponents.

Contribution

It introduces a theoretical framework for understanding thermal depinning and melting transitions in 2D LAGBs, connecting them to random matrix theory.

Findings

Depinning transition occurs at a critical temperature.

Transverse fluctuations grow logarithmically with dislocation distance.

Sequential melting transitions characterized by algebraic Bragg peak disappearance.

Abstract

We explore order in low angle grain boundaries (LAGBs) embedded in a two-dimensional crystal at thermal equilibrium. Symmetric LAGBs subject to a periodic Peierls potential undergo, with increasing temperatures, a thermal depinning transition, above which the potential is irrelevant at long wavelengths and the LAGB exhibits transverse fluctuations that grow logarithmically with inter-dislocation distance. Longitudinal fluctuations lead to a series of melting transitions marked by the sequential disappearance of diverging algebraic Bragg peaks with universal critical exponents. Aspects of our theory are checked by a mapping onto random matrix theory.