Direct measurements of thermal vacancies in BCC4He

Abstract

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.