Theory of Isotope Effect in the Thermodynamics of “Classical” Crystals

Abstract

Based on general expressions for quantum contributions to the free energy of a statistical system, an approach is developed making it possible to carry out a complete theoretical analysis of the equilibrium thermodynamic characteristics of argon-type crystals as a function of the isotopic mass. The theory is based on independently calculated (in fact, without fitting parameters) one-particle and two-particle distribution functions of the classical crystal and permits one to quantitatively describe the data on the lattice parameters of isotope crystals obtained from numerical experiments. It is pointed out that real experiments are needed to study the isotope effect in crystals of noble gases, especially in view of the fact that, according to the literature data, xenon undergoes an fcc–hcp phase transition under increased pressure.