Shear Modulus of an Elastic Solid under External Pressure as a function of Temperature: The case of Helium

TL;DR

This paper investigates how the shear modulus of solid helium varies with temperature and external pressure, highlighting the role of dislocation loops and pinned dislocations in its mechanical response.

Contribution

It introduces a classical mechanics model of dislocation loop energy under pressure, explaining shear modulus variations without requiring unpinning of dislocations.

Findings

Dislocation loops can be thermally activated by pressure within experimental ranges.

Pinned dislocations significantly influence shear response without unpinning.

The model aligns with current experimental measurements.

Abstract

The energy of a dislocation loop in a continuum elastic solid under pressure is considered within the framework of classical mechanics. For a circular loop, this is a function with a maximum at pressures that are well within reach of experimental conditions for solid helium suggesting, in this case, that dislocation loops can be generated by a pressure-assisted thermally activated process. It is also pointed out that pinned dislocations segments can alter the shear response of solid helium, by an amount consistent with current measurements, without any unpinning.