Heat Capacity of hcp and bcc Solid Helium 3

Experimental data are presented for the heat capacity of hcp ${\mathrm{He}}^{3}$ at five molar volumes (19.05 to 11.42 ${\mathrm{cm}}^{3}$) and for bcc ${\mathrm{He}}^{3}$ at four molar volumes (20.18 to 23.80 ${\mathrm{cm}}^{3}$). These data extend from the true ${T}^{3}$ region ($\frac{T}{{\ensuremath{\Theta}}_{0}}<0.03$) to the melting line in all cases with sufficient precision (at least 1% in ${\ensuremath{\Theta}}_{D}$) so that the volume dependence of both ${\ensuremath{\Theta}}_{0}$ and the reduced ${\ensuremath{\Theta}}_{\ensuremath{-}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{u}\mathrm{s}\ensuremath{-}}T (\frac{\frac{\ensuremath{\Theta}}{{\ensuremath{\Theta}}_{0\ensuremath{-}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{u}\mathrm{s}\ensuremath{-}}T}}{{\ensuremath{\Theta}}_{0}})$ relationship can be determined. In general, when a comparison is made with other ${\mathrm{He}}^{4}$ data, $\frac{{\ensuremath{\theta}}_{03}}{{\ensuremath{\theta}}_{04}}=1.18$. The quantity ${\ensuremath{\gamma}}_{0}=\frac{\ensuremath{-}d\mathrm{ln}{\ensuremath{\Theta}}_{0}}{d\mathrm{ln}V}$ varies from 2.6 to 2.0 for the hcp data with decreasing molar volume, while ${\ensuremath{\gamma}}_{0}=2.2$ for the bcc phase. The changes in the shapes of the reduced ${\ensuremath{\Theta}}_{\ensuremath{-}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{u}\mathrm{s}\ensuremath{-}}T$ curves for the hcp phase can be understood in terms of a slightly temperature-dependent Gr\"ueneisen constant $\ensuremath{\gamma}$, the ratio $\frac{\ensuremath{\gamma}}{{\ensuremath{\gamma}}_{0}}$ being independent of volume to a first approximation and increasing to approximately 1.07 at $\frac{T}{{\ensuremath{\Theta}}_{0}}=0.12$. The shapes of these reduced ${\ensuremath{\Theta}}_{\ensuremath{-}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{u}\mathrm{s}\ensuremath{-}}T$ curves at the smallest molar volumes are almost identical for hcp ${\mathrm{He}}^{3}$ and for our one hcp ${\mathrm{He}}^{4}$ run, and agree with comparable previous data at relatively high temperature. These shapes resemble closely the zero-pressure data for argon and krypton and the theoretical calculations of Horton and Leech. The bcc ${\mathrm{He}}^{3}$ data can be represented quite precisely as the sum of a Debye-like term [involving ${\ensuremath{\Theta}}_{0}(V)$] and an exponential Schottky-like term [involving a characteristic temperature $\ensuremath{\varphi}(V)$]. When compared with the hcp data, the bcc data cannot be explained solely in terms of conventional lattice dynamics.

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