Molar volume of solid isotopic helium mixtures

Solid isotopic helium mixtures have been studied by path-integral Monte Carlo simulations in the isothermal-isobaric ensemble. This method allowed us to study the molar volume as a function of temperature, pressure, and isotopic composition. At 25 K and 0.2 GPa, the relative difference between molar volumes of isotopically-pure crystals of 3He and 4He is found to be about 3%. This difference decreases under pressure, and for 12 GPa it is smaller than 1%. For isotopically-mixed crystals, a linear relation between lattice parameters and concentrations of helium isotopes is found, in agreement with Vegard's law. The virtual crystal approximation, valid for isotopic mixtures of heavier atoms, does not give reliable results for solid solutions of helium isotopes.