Studies of vibrational surface modes in ionic crystals: III. Vibrational contributions to the surface thermodynamic functions for the (001) face of LiF,MgO, NaF,NaCl, Nal,RbF, and RbCl

The temperature dependence of the vibrational contributions to surface specific heat, surface entropy, surface energy, and surface Helmholtz free energy have been calculated for the (001) face of seven crystals having the rocksalt structure. The calculations assume a perfect, unrelaxed surface and make use of shell models fitted to bulk phonon spectra determined from inelastic neutron scattering. In terms of the bulk zero-temperature Debye temperature θ₀, the surface specific heat C_v^s exhibits an effective power law behavior, T^α, from at least T = 0.02 θ₀ up to 0.05 θ₀ in most cases (and up to 0.07 θ₀ for NaF), with α ≈ 2.5 in most cases — in contrast with the result of α = 2 in a Debye-like model. (Below 0.02 θ₀, results derived for our 15-layer films depart significantly from intrinsic surface effects because of the finite thickness.) C_v^s attains a maximum at a temperature T(C_max^s) ranging from 0.14 θ₀ to 0.20 θ₀, in contrast with the result T(C_max^s) = 0.21 θ₀ for the Debye-like model. The peak value C_max^s ranges from 0.34 k_BA_SUC to 0.41 k_BA_SUC, where A_SUC is the area of the surface unit cell. The shap the peak in C_v^s differs characteristically between that class of crystals in which there is some overlap of the acoustical and optical bulk bands and that class in which there is an appreciable absolute gap between the acoustical and optical bulk bands; in the latter class the peak is flattened on the low side of the maximum, with the maximum pushed to somewhat higher temperature. On those points of comparison with the rather sparse existing data for surface-excess heat capacity in which the value of specific surface area is not required (e.g., the value of T(C^s_max)), the agreement ranges from encouraging to equivocal. On those comparisons which require the surface area of the experimental samples (e.g., the magnitude of C^s_max) the agreement ranges from only fair to bad. Further experimental work is needed, and great care in surface area determinations is necessary.