Isotopic effect in the lattice parameter of rare-gas solids

The dependence of the lattice parameter of rare-gas (Lennard-Jones) solids on isotopic mass has been studied by the path-integral Monte Carlo method. Simulations were carried out in the isothermal–isobaric ensemble, which allows us to study this isotopic effect as a function of temperature and pressure. In the limit T → 0 and at ambient pressure, the difference Δa between lattice parameters of isotopically pure crystals with lightest and heaviest isotopic mass is found to range from 8.7 × 10−3 A for Ne to 1.2 × 10−3 A for Xe. This isotopic effect decreases appreciably upon increasing temperature. At 80 K, Δa for Ar, Kr and Xe is found to be less than one-third of the corresponding low-temperature value. An applied hydrostatic pressure also causes an important decrease in Δa. For Ne and Xe, a pressure of 30 kbar reduces this difference by a factor of 6.5 and 3.1, respectively. These differences in lattice parameter are larger than the sensitivity limit presently achieved in experimental studies, even for solid xenon at its Debye temperature.