X-ray measurements of thermal vacancies in hcpHe4

Changes in the x-ray lattice parameter have been used to measure directly the thermal generation of vacant substitutional atomic sites in hcp ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ crystals held at constant macroscopic volume, for samples with molar volumes in the range 20.2 to 20.9 ${\mathrm{cm}}^3$. A progressive decrease of the apparent formation energy, from 12.6 to 8.6 K, with increase of molar volume, is seen. This variation is consistent with variations observed in the NMR diffusion activation energy for small concentrations of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The magnitudes are also similar, with some exceptions, which suggests that, unlike hcp ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, the vacancy in low-density hcp ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ moves by tunneling. By various means, values for the monovacancy free volume are deduced. Comparisons with other studies of defects in hcp ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, such as ion transport, recovery of ultrasonic attenuation, and calorimetry, are less direct and less unambiguous.