Calculations of heat capacities of adsorbates

The phonon contribution to the heat capacity has been calculated for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ on Xe; for Ne on Ar, Kr, and Xe; for Ar on Kr and Xe; and for Kr on Xe. These are, to our knowledge, the first such calculations for real systems. In each case, a model was taken in which the substrate has a perfect (100) surface and the adsorbate goes down as a solid monolayer in registry with the substrate. The quasiharmonic approximation was used, and the results for Ne adsorbates were considerably different from those obtained in the harmonic approximation, because the large zero-point vibrations of the Ne atoms produce a substantial expansion normal to the surface. We find that the quasiharmonic approximation does not even exist for He on Ne, Ar, and Kr, or for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ on Xe, just as it does not for bulk ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ or ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. For several cases, including ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ on Xe, the calculated heat capacity becomes slightly negative at low temperatures.