Heat Capacity of hcp and bcc Solid Helium 3

Experimental data are presented for the heat capacity of hcp He³ at five molar volumes (19.05 to 11.42 cm³) and for bcc He³ at four molar volumes (20.18 to 23.80 cm³). These data extend from the true T³ region (TΘ₀<0.03) to the melting line in all cases with sufficient precision (at least 1% in ΘD) so that the volume dependence of both Θ₀ and the reduced ${{Θ}}_{{-}versus{-}}T ({{{Θ}}{{{Θ}}_{0{-}versus{-}}T}}{{{Θ}}₀})$ relationship can be determined. In general, when a comparison is made with other ${He}⁴$ data, ${{{θ}}₀₃}{{{θ}}₀₄}=1.18$. The quantity ${{γ}}₀={{-}dln{{Θ}}₀}{dlnV}$ varies from 2.6 to 2.0 for the hcp data with decreasing molar volume, while ${{γ}}₀=2.2$ for the bcc phase. The changes in the shapes of the reduced ${{Θ}}_{{-}versus{-}}T$ curves for the hcp phase can be understood in terms of a slightly temperature-dependent Gr\"ueneisen constant ${γ}$, the ratio ${{γ}}{{{γ}}₀}$ being independent of volume to a first approximation and increasing to approximately 1.07 at ${T}{{{Θ}}₀}=0.12$. The shapes of these reduced ${{Θ}}_{{-}versus{-}}T$ curves at the smallest molar volumes are almost identical for hcp ${He}³$ and for our one hcp ${He}⁴$ 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 He³ data can be represented quite precisely as the sum of a Debye-like term [involving Θ₀(V)] and an exponential Schottky-like term [involving a characteristic temperature φ(V)]. When compared with the hcp data, the bcc data cannot be explained solely in terms of conventional lattice dynamics.