Direct measurements of thermal vacancies in BCC4He

X-ray lattice parameters of bcc⁴He crystals in contact with superfluid⁴He were measured with 300 ppm accuracy in the temperature range 1.494–1.711 K, corresponding to solid molar volumes between 20.88 and 21.09 cm³. Thermal vacancy concentrations in the solid at melting were estimated from a comparison of these lattice parameters with bulk solid molar volumes from the literature. Independently, temperature-dependent x-ray lattice parameter measurements on a bcc sample, held at constant macroscopic volume from 1.700 to 1.735 K, were referenced to the same solid sample (at 20.90 cm³) in the hcp phase near 0.8 K, where thermal vacancy content is small. The value of the free energy of formation for vacancies in bcc⁴He obtained from these measurements isf=9±1 K. The relationship between this value and indirect inferences about vacancy formation from ion mobility and NMR experiments is discussed. Comparisons are made between vacancy properties in bcc⁴He and in the more extensively studied bcc phase of³He. There are many parallels between the two systems. But a puzzling apparent difference between the vacancy relaxation energies in the two solids is pointed out.