Anharmonic Forces and the Vapor-Pressure Ratio of Monatomic Isotopic Solids

An expression for the vapor pressure ratio of two monatomic anharmonic isotopic solids is derived for T≳θ. At constant volume the contribution of the anharmonicity can be represented by an effective shift in the normal mode frequencies; this shift differs from that appropriate to neutron scattering and the entropy in that at high temperatures φ3 (the third-order term in the expansion of the lattice potential energy) makes no contribution. The effect of thermal expansion can be represented by an additional frequency shift. Lattice vacancies may also contribute to the vapor-pressure ratio but this effect should be small. In the harmonic approximation the vapor pressure ratio can be related to the isotope separation factor; this relationship is discussed in some detail. The isotope separation factor is evaluated approximately for a fcc lattice with various interaction potentials, and compared with the experimental results for solid argon; it appears that the anharmonic contribution due to φ4 is important. A systematic method is proposed for the analysis of experimental data.