Multiquantum vibrational energy transfer into surface Rayleigh, bulk shear, and pressure waves by atom-solid-surface collisions: A discrete-continuum hybrid treatment with applications to He-Pt(111)

A discrete-continuum hybrid treatment is developed for energy transfer into solid-surface vibrations by atomic collisions. Surface vibrations are described in terms of the displacement field of a three-dimensional elastic continuum with a stress-free boundary. The displacement field is evaluated discretely at the surface lattice sites and it is quantized by the standard methods for harmonic vibrations. This hybrid approach can extend classical Debye models to incorporate surface corrugation, lattice structure, and the Bose-Einstein statistics of phonons. The treatment is illustrated on He scattering from Pt(111) at superthermal collision energies, e.g., E=0.5 eV, to probe the repulsive cores of the gas-surface potential. Accordingly, the projectile motion is approximated by classical trajectories, whereas all vibrational modes are treated quantum mechanically. The differential (in final angles and transferred energy) scattered intensity is obtained from time-correlation functions of the semiclassical transition operator, which incorporate numerous vibrational states as well as surface temperature. A computational procedure is described for efficiently calculating multiquantum transitions of very high order using fast Fourier transforms. Scattered intensities are calculated for the He-Pt(111) system over a wide range of angles (0°-75°) and surface temperatures (0-600 K). The distributions of transferred energies are analyzed in terms of the continuum vibrational modes, which include surface Rayleigh, shear-horizontal (SH), and coupled pressure/shear-vertical (PSV) waves. The mode-specific distributions are found to vary in distinct ways as one changes collisional angles. On average, surface Rayleigh waves absorb approximately one-half of the transferred energy and the remainder is shared in comparable amounts by bulk SH and PSV waves.