Studies of vibrational surface modes in ionic crystals. I. Detailed shell-model studies for the unrelaxed (001) face of seven crystals having the rocksalt structure

Abstract

We present a comprehensive, unified account of the lattice dynamics of unrelaxed (001) faces of seven crystals having the rocksalt structure, three of which have an absolute gap between the acoustical and optical bulk bands (RbF, RbCl, and NaI) and four of which have overlap between these bulk bands (NaF, NaCl, LiF, and MgO). The results are obtained from calculations of the normal modes of a thin crystal film in which the ionic interactions are described by the rigid-shell model. An outline of the formulation of the shell model for the film is given, and the rapid convergence of surface-phonon frequencies with increasing film thickness is demonstrated. Surface- and pseudosurface-phonon dispersion curves and bulk bands are displayed in the form of the dispersion curves of a 15-layer film over the two-dimensional surface Brillouin zone. The surface-excess phonon density of states ${f}^{s}(\ensuremath{\omega})$ is given, and its peaks and valleys are correlated with features in the film dispersion curves. The domains of existence and the vibrational character of the more prominent surface-phonon bands are discussed. We establish the relation between the surface modes of the lattice models and the macroscopic surface waves of the dielectric and elastic continuum theories (Fuchs-Kliewer and Rayleigh waves, respectively). Comparison with experiments is made; the agreement with low-energy atom scattering from single-crystal surfaces of LiF and with inelastic neutron scattering from microcrystallite samples of MgO is particularly notable, although the latter comparison also displays some significant discrepancies.