An analytical model for the study of anharmonic dynamics in surfaces

An exact analytic formulation is presented for the dynamics of anharmonic low index surfaces of fcc crystals, based on an anharmonic pair potential coupling the first and second surface layers. This yields a general analytic expression for helium specular scattering at thermal energies in low index surfaces. The theoretical results are in agreement, in particular, with experimental data for Cu(1 0 0). The mean square displacements for surface layer sites are calculated as a function of temperature in this approach, and found to be in agreement with the results of the molecular dynamics simulation for Cu(1 0 0). The anharmonic pair potential strength is evaluated. The analytic formulation for the thermal attenuation of helium specular scattering in anharmonic surfaces, should make possible the selective access to the scattered intensities from other quasi-elastic surface processes notably at high temperature.