The scattering of phonons by infinitely long quantum dislocations segments and the generation of thermal transport anisotropy in a solid threaded by many parallel dislocations

TL;DR

This paper develops a quantum theory of phonon interactions with infinitely long dislocations, revealing how dynamic dislocations influence thermal transport anisotropy and differ from static models, with implications for temperature-dependent material behavior.

Contribution

It introduces a comprehensive quantum model for phonon-dislocation interactions, accounting for dislocation dynamics and their impact on thermal transport anisotropy, extending previous static dislocation theories.

Findings

Relaxation time inversely proportional to frequency.

Thermal transport anisotropy is highly sensitive to phonon frequency and temperature.

Dynamic dislocation effects differ significantly from static models.

Abstract

A canonical quantization procedure is applied to the interaction of elastic waves --phonons-- with infinitely long dislocations that can oscillate about an equilibrium, straight line, configuration. The interaction is implemented through the well-known Peach-Koehler force. For small dislocation excursions away from the equilibrium position, the quantum theory can be solved to all orders in the coupling constant. We study in detail the quantum excitations of the dislocation line, and its interactions with phonons. The consequences for the drag on a dislocation caused by the phonon wind are pointed out. We compute the cross-section for phonons incident on the dislocation lines for an arbitrary angle of incidence. The consequences for thermal transport are explored, and we compare our results, involving a dynamic dislocation, with those of Klemens and Carruthers, involving a static dislocation. In our case, the relaxation time is inversely proportional to frequency, rather than directly proportional to frequency. As a consequence, the thermal transport anisotropy generated on a material by the presence of a highly-oriented array of dislocations is considerably more sensitive to the frequency of each propagating mode, and therefore, to the temperature of the material.