Thermodynamics of an incommensurate quantum crystal

TL;DR

This paper develops a simple thermodynamic theory for incommensurate quantum crystals, explaining vacancy behavior and specific heat variations at low temperatures, consistent with experimental observations in solid helium-4.

Contribution

It introduces a theoretical model for the thermodynamics of incommensurate quantum solids with zero-point vacancies, connecting theory with experimental data.

Findings

Net vacancy concentration varies as T^4 at low temperatures.

Specific heat correction due to vacancies varies as T^7.

Experimental data on solid helium-4 aligns with the model's predictions.

Abstract

We present a simple theory of the thermodynamics of an incommensurate quantum solid. The ground state of the solid is assumed to be an incommensurate crystal, with quantum zero-point vacancies and interstitials and thus a non-integer number of atoms per unit cell. We show that the low temperature variation of the net vacancy concentration should be as $T^4$, and that the first correction to the specific heat due to this varies as $T^7$; these are quite consistent with experiments on solid $^4$He. We also make some observations about the recent experimental reports of ``supersolidity'' in solid $^4$He that motivate a renewed interest in quantum crystals.