Grain Boundary Roughening Transitions

TL;DR

This paper investigates the roughening transitions of small angle grain boundaries, identifying two distinct transitions related to dislocation fluctuations, with implications for understanding crystal orientation changes in materials like solid helium.

Contribution

It introduces a detailed analysis of two separate roughening transitions in grain boundaries, linking theoretical predictions to experimental observations.

Findings

Two distinct roughening transitions identified

Transition temperatures differ significantly

Results align with recent experimental data in solid helium

Abstract

We consider the roughening of small angle grain boundaries consisting of arrays of dislocations and found two transitions, corresponding to fluctuations of the dislocations along and perpendicular to the boundaries. The latter contributes to a large scale fluctuation of the orientation of the crystal but the former does not. The transition temperatures of these transitions are very different, with the latter occuring at a much higher temperature. Order of magnitude estimates of these temperatures are consistent with recent experimental results from elasticity and X-ray measurements in solid $^4$He.