Phonon dispersion on Ag(100) surface:A modified analytic embedded atom method study

Within the harmonic approximation, the analytic expression of the dynamical matrix is derived based on the modified analytic embedded atom method (MAEAM) and the dynamics theory of surface lattice. The surface phonon dispersions along three major symmetry directions Γ X, Γ M, and XM are calculated for the clean Ag (100) surface by using our derived formulas. We then discuss the polarization and localization of surface modes at points X and M by plotting the squared polarization vectors as a function of the layer index. The phonon frequencies of the surface modes calculated by MAEAM are compared with the available experimental and other theoretical data. It is found that the present results are generally in agreement with the referenced experimental or theoretical results, with a maximum deviation of 10.4%. The agreement shows that the modified analytic embedded atom method is a reasonable many-body potential model to quickly describe the surface lattice vibration. It also lays a significant foundation for studying the surface lattice vibration in other metals.