Some dynamical properties of the alloy disordered chain on a semi-infinite solid square lattice

The dynamics of an alloy disordered first surface layer of a simple cubic semi-infinite crystal is considered, where defect and host atoms are of equal masses. The host-defect and defect-defect interactions are unequal in general, and taken different from host-host interactions. The calculations are exemplified by the results for the surface phonon and resonance modes localized on a linear alloy disordered chain terminating a simple square solid lattice with nearest neighbour central force interactions. One phonon mode polarized parallel to the chain is decoupled from the bulk continuum. The mode polarized perpendicular to the chain is a resonance with signature characteristics depending on the model domains of the concentration of defect atoms in the chain, and on the host-defect interactions. This mode is also investigated outside the bulk continuum, where it is a surface mode whose frequency is dependent on the strength of host-defect interactions, and on the defect concentration. In mean field the mode disappears for sufficiently low concentrations.