X-ray diffraction study of vacancies in bcc helium-3 and bcc helium-4

Direct x-ray diffraction measurements of vacancies in large molar volume samples of bcc 3He and in bcc 4He are reported. With the x-ray diffractometer-position sensitive detector system used, absolute lattice parameters could be measured with an accuracy of 300 ppm. Absolute lattice parameters in bcc 4He crystals in contact with superfluid 4He were measured in the temperature range 1.494 to 1.711 K, corresponding to molar volumes between 20.88 and 21.09 cm3/mole. Vacancy concentrations at melting were estimated from a comparison of these lattice parameters with bulk volumes from the literature. The value of the free energy of formation for vacancies in bcc 4He obtained from these measurements is f/sub v/ = 9 +/- 1K. The relationship between this value and indirect inferences about vacancy formation from ion mobility and NMR experiments is discussed. Comparisons are made between the formation free energy in bcc 4He and the same quantity at the same molar volume in the extensively-studied bcc phase of 3He. A systematic study of the temperature dependence of the lattice parameter in crystals of bcc 3He with molar volumes between 23.35 and 24.80 cm3/mole was made. Present measurements with an improved x-ray technique by-and-large confirm previous x-ray measurements when simple exponentials are fitted to the data. Possible deviations from exponential activation of vacancies and their relationship to effects of a vacancy band are discussed. The difficulties encountered in this careful study using an improved x-ray system reemphasize the nontriviality of performing accurate diffractometry on crystals of bcc 3He with large molar volumes