Andreev-Lifshitz hydrodynamics applied to an ordinary solid under pressure

Abstract

We have applied the Andreev-Lifshitz hydrodynamic theory of supersolids to an ordinary solid. This theory includes an internal pressure P, distinct from the applied pressure Pa and the stress tensor λik. Under uniform static Pa, we have λik=(P−Pa)δik. For Pa≠0, Maxwell relations imply that P∼Pa2. The theory also permits vacancy diffusion but treats vacancies as conserved. It gives three sets of propagating elastic modes; it also gives two diffusive modes, one largely of entropy density and one largely of vacancy density (or, more generally, defect density). For the vacancy diffusion mode (or, equivalently, the lattice diffusion mode) the vacancies behave like a fluid within the solid with the deviations of internal pressure associated with density changes nearly canceling the deviations of stress associated with strain. We briefly consider pressurization experiments in solid H4e at low temperatures in light of this lattice diffusion mode, which for small Pa has diffusion constant DL∼Pa2. The general principles of the theory—that both volume and strain should be included as thermodynamic variables, with the result that both P and λik appear—should apply to all solids under pressure, especially near the solid-liquid transition. The lattice diffusion mode provides an additional degree of freedom that may permit surfaces with different surface treatments to generate different responses in the bulk.

Similar papers