Statistical Mechanics of Low Angle Grain Boundaries in Two Dimensions

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.

arXiv comment6+5 pages, 3+1 figures

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Cited by in corpus (3)

• Phonon eigenfunctions of inhomogeneous lattices: Can you hear the shape of a cone?
• Hear $\pi$ from Quantum Galperin Billiards
• Statistical Mechanics of Dislocation Pileups in Two Dimensions