X-ray studies of high-temperature defects in concentrated isotopic helium solid solutions

Vacancy concentrations in bcc crystals of helium isotope mixtures of nominal composition 12%, 28%, and 51% ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ have been inferred from measurements of temperature dependence of x-ray lattice parameter, a, in samples confined at several different constant macroscopic volumes. The data have been parametrized by an activated form, and in each case some possible separation of the free energy into energy and entropy contributions is discussed. The results for each composition are different, yet certain patterns can be discerned, such as the likelihood of significant vacancy-solute binding. Estimates of the vacancy free volume of formation are obtained for the 28% and 51% ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ mixtures. In low-density 51% crystals the changes in 3 Δa/a are extraordinarily large, up to 5% near melting. The situation is reminiscent of CsCl-structure alloys, except that those alloys show ordering at all temperatures, whereas helium mixtures show isotopic phase separation at low temperatures.