PHYSICAL REVIE% 8 VOLUME 27, NUMBER 6 15 MARCH 1983 High-resolution helium time-of-flight studies of Rayleigh surface-phonon dispersion curves of LiF, NaF, and KC1 G. Brusdeylins, R. Bruce Doak, ' and J. Peter Toennies Max Plan-ck Insti-tut fiir Stromungsforschung, Bottingerstrasse 4-8, D 3400 -Gottingen, Federal Republic of Germany (Received 22 October 1982) A molecular-beam apparatus is described in which a cold He beam (=20 meV) of very high velocity resolution (b U/v=0. 8%) is scattered from alkali halide single-crystal surfaces. The velocity distribution of the scattered beam is analyzed using time-of-flight (TOF) tech- niques. 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 pho- nons. 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% lo~er at the zone boundary. For KC1 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 mea- surements 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 poten- tial 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 indi- cate that a similar kinematic focusing effect may be expected in azimuthal angular distribu- tions. I. INTRODUCTION Very little experimental data are available on the dispersion relations of surface phonons despite their importance for understanding the physics of solid surfaces. ' Surface phonons also play an important role in gas-surface interactions. The energy transfer from atoms and molecules to phonons is fundamental to an understanding of accommodation coefficients and adsorption and desorption kinetics, as well as sticking coefficients. These are all impor- tant elementary steps in catalysis. Broadly speaking, two types of modes are present at the surface: bulk modes and true surface modes. The latter are characterized by their spatial localiza- tion at the surface; they have wave vectors Q paral- lel to the surface and their frequencies u appear in a two-dimensional dispersion relation co(Q) as discrete curves. The bulk phonons are not localized at the surface and have three-dimensional wave vectors q which project out as bands in the two-dimensional plot to(Q). The true surface modes may further be classified as microscopic or macroscopic depending upon whether the depth of penetration is indepen- dent of or proportional to the phonon wavelength, respectively. Rayleigh waves are the best known ex- ample of the macroscopic phonons. At large wave- lengths they are nondispersive and their properties are well described by continuum theory. Long- wavelength Rayleigh waves find extensive applica- tions in electroacoustical microelectronic devices be- cause of their small damping, constant velocity, and the accessibility provided by their surface localiza- tion. At wavelengths comparable with lattice dimen- sions, atomic theories predict a multitude of acousti- cal and optical surface modes with significant dispersion. The theory of small-wavelength (disper- sive) surface phonons has developed along two lines. de bette and his co-workers ' have solved the Oc1983 The American Physical Society