High-resolution helium time-of-flight studies of Rayleigh surface-phonon dispersion curves of LiF, NaF, and KCl

Abstract

A molecular-beam apparatus is described in which a cold He beam ($\ensuremath{\simeq}20$ meV) of very high velocity resolution ($\frac{\ensuremath{\Delta}v}{v}\ensuremath{\simeq}0.8%$) is scattered from alkali halide single-crystal surfaces. The velocity distribution of the scattered beam is analyzed using time-of-flight (TOF) techniques. The variation of the TOF spectra with target temperature reveals the influence of multiphonon processes, allowing the regime of single-phonon scattering to be experimentally delineated. The inelastic scattering TOF spectra reveal as many as six sharp maxima, most of which can be attributed to creation or annihilation of single Rayleigh-mode surface phonons. Some evidence is also found for interactions with bulk modes at the surface. Phonon frequencies and wave vectors determined from the TOF spectra allow Rayleigh-mode dispersion curves to be measured out to the Brillouin-zone boundary for the (001) face of LiF, NaF, and KCl along the $〈100〉$ azimuth. The measured dispersion curves agree well with theoretical predictions except for LiF, for which the experimental frequencies are about 10% lower at the zone boundary. For KCl possible evidence is found for a "crossing mode" embedded in the bulk continuum bands. Measurements were also made in the $〈110〉$ azimuth for LiF; however, the scattering intensities were observed to be so weak that measurements to the zone boundary were not possible. The inelastic scattering is found to be significantly affected by resonant processes involving bound states of the gas-surface potential well. However, Benedek's mechanism of kinematic focusing is shown to have usually only a minor effect upon the distribution of scattered intensity with polar incident angle under the present experimental conditions. TOF spectra for different azimuthal angles indicate that a similar kinematic focusing effect may be expected in azimuthal angular distributions.