Molar volume of solid isotopic helium mixtures

Abstract

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 3 He and 4 He 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.

Compressibility of solid helium

“…This isotopic effect can be readily obtained from PIMC simulations, since the mass is an input parameter in these calculations. Similar isotopic effects have been studied earlier for the melting curve [20,21] and molar volume [23,24] of solid helium. For a given material, lighter isotopes form more compressible solids, as a consequence of an increase in the molar volume.…”

“…This relative change in bulk modulus associated to the isotopic mass is appreciable, and slightly larger than that found for the isotopic effect on the molar volume of helium crystals. Thus, at a pressure of 1 and 7 GPa and T = 25 K, we find a volume difference of 1.8 and 0.9%, when comparing 3 He and 4 He [24]. In general, given a temperature, the relative changes in volume and compressibility decrease for increasing pressure, since the solid behaves as if it was 'more classical' [30,49], and isotopic effects (of quantum origin) are consequently reduced.…”

“…The path-integral Monte Carlo (PIMC) method has been used to study several properties of solid helium [7,[19][20][21][22][23][24], as well as heavier rare-gas solids [25][26][27][28][29][30]. For helium, in particular, this method has predicted kinetic-energy values [19] and Debye-Waller factors [31] in good agreement with data derived from experiments [32,33].…”