Surface Vibrations in Semi-Infinite Chains with Consideration of Long-Range Interaction. Surface Vibrations in Cubic Crystals

Abstract

Vibrations within infinite and semi-infinite monoatomic and diatomic chains in approximation of nearest and next nearest neighbors have been considered. Phonon dispersion relations in an infinite and a semi-infinite cubic crystal have been studied. Calculations have been carried out using a unitary methodology based on solving the difference equations. The following methodology is of broad generality and can be used for studying of both continuous and discrete spectrum in crystal models close to real systems. For cubic crystals volume vibrations zones and localized states representing surface waves have been calculated.

Keywords

• phonons
• localized state
• surface waves
• force constants matrix
• adsorbed monolayer