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

Molar volume of solid isotopic helium mixtures