Surface phonons on the (001) surface of a fcc crystal covered with aC(2×2)monolayer

Abstract

We present here a calculation of the energies and the polarizations of the surface phonons in a realistic case: a (001) surface of a fcc crystal covered with a $C(2\mathrm{}\times 2)$ monolayer [experimental case of $\mathrm{Ni}\mathrm{}\left(100\right)+\mathrm{S}C(2\mathrm{}\times 2)$ for instance]. The method, derived from a former calculation by Gazis and Wallis on the clean (001) surface of a bcc crystal, is applied to any type of $C(2\mathrm{}\times 2)$ monolayer: reconstructed, nonreconstructed, and $P(1\mathrm{}\times 1)$ structure. The results are given for the waves propagating in the [100] direction. A correspondence between the spectra of the $P(1\mathrm{}\times 1)$ and reconstructed $C(2\mathrm{}\times 2)$ structures is demonstrated. For $C(2\mathrm{}\times 2)$ structures, the low-wave-vector phonons depend mainly on the bonds between adsorbate and substrate atoms. The high-wave-vector phonons depend, in addition, on the bonds between the adsorbate atoms. In particular, a clear-cut test is provided for deciding between the reconstructed and nonreconstructed $C(2\mathrm{}\times 2)$ structures.