Theory of the anharmonic linewidths of surface phonons in aluminum

A theoretical investigation has been made of the linewidth of the Rayleigh mode on the Al(111) surface due to cubic anharmonic interactions between atoms. The normal-mode frequencies and eigenvectors for the harmonic crystal were calculated by using a model containing central interactions extending up to tenth-nearest neighbors and three-body interactions extending up to second-nearest neighbors. This model reproduces with great accuracy the experimental bulk-phonon frequencies as well as the surface-phonon frequencies. The linewidths were evaluated along the SIGMA-BAR direction as a function of the lateral momentum transfer and at the MBAR point as a function of the temperature. The results compare favorably with recent experimental data.