Thermal Excitations in SolidHe4

Abstract

The present paper is devoted to an extension of recent work on solid ${\mathrm{He}}^4$ using a heuristic approach. The anomalous or negative isobaric expansion coefficients of the solid, in equilibrium with the anomalous liquid ${\mathrm{He}}^4$II, will be re-evaluated in terms of the here derived approximate compressibilities of the solid based on sound velocity data. The entropy of solid ${\mathrm{He}}^4$ will then be obtained in terms of the recent Los Alamos determinations of entropy changes on solidification and of two different sets of entropy values of the liquid along the melting line. The latter yield two distinct sets of solid entropy values. While numerically these are different, they appear to be much too large to be accommodated by simple phonon excitations of the solid at temperatures below $T_0\left(p_m\right)$, the temperature of the heat capacity anomaly of the liquid at the melting pressure line $p_m$. Below $T_0\left(p_m\right)$, both of these numerically different solid entropies exhibit temperature variations of such strength as to rule out their description in terms of simple phonon entropies. In addition, the two sets of solid entropies give rise to molar heat capacities of the order of the gas constant $R$, at the approaches of $T_0\left(p_m\right)$. The preceding thermal anomalies will be discussed from the viewpoint of the equilibrium between the fundamentally anomalous liquid and the solid. Analysis of the liquid entropy yields a new set of onset temperatures of the ordering process responsible for its peculiar transition phenomenon. The thermal anomalies, at or in the vicinity of the melting line, suggest peculiar dispersion and distribution properties of the frequency spectrum of solid ${\mathrm{He}}^4$. Direct experimental investigations of the above apparent anomalies of the static thermal properties as well as of transport properties of this solid near the phase separation line seem to be of interest.