Heat Capacity of SolidHe3

Abstract

Exploratory specific-heat measurements have been made on solid ${\mathrm{He}}^{3}$ for the temperature range from 0.3 to 2\ifmmode^\circ\else\textdegree\fi{}K and to 1800 bars pressure. The data for the relatively high-pressure hcp $\ensuremath{\beta}{\mathrm{He}}^{3}$ phase could not be represented by a Debye function, since anomalous behavior was found at low temperatures for the smaller molar volumes. Similar effects were found for the same phase in solid ${\mathrm{He}}^{4}$. The data for the low-pressure bcc $\ensuremath{\alpha}{\mathrm{He}}^{3}$ phase could be described within experimental accuracy by the sum of a Debye function and an Einstein function representing two degrees of freedom. The characteristic temperatures which are associated with the Debye function and the Einstein function, respectively, were found to be functions of the molar volume, and to be linearly related. These data, together with earlier values of the thermodynamic parameters along the melting line given by other workers, were used to calculate the equation of state for $\ensuremath{\alpha}{\mathrm{He}}^{3}$, and, hence, the thermal expansion and compressibility as a function of temperature and pressure. Several unusual features were found as a result of this analysis; these include the Einstein anomaly in the specific heat of $\ensuremath{\alpha}{\mathrm{He}}^{3}$, the fact that the compressibility of $\ensuremath{\alpha}{\mathrm{He}}^{3}$ is appreciably greater than that of the fluid or $\ensuremath{\beta}{\mathrm{He}}^{3}$ at the same molar volume, and the relatively large difference between the Debye $\ensuremath{\theta}'\mathrm{s}$ for the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases (about 20%) which differ in molar volume by only 0.5%. These effects do not appear to be due to nuclear ordering. No evidence for a previously predicted negative thermal expansion in $\ensuremath{\alpha}{\mathrm{He}}^{3}$ was found.