The electronic properties of a one-dimensional diatomic crystal have been analyzed by using the MO-LCAO method in the tight binding approximation, with mathematical techniques involved in setting up and solving difference equations. The approach gives the exact sets of analytic solutions for both localized and nonlocalized states. The theory of surface states is developed as a characteristic value problem. To illustrate the method the surface states for a semiinfinite crystal which contains a local imperfection at the surface were examined. It appears that this method has advantages over previous methods developed to solve surface problems in crystalline lattices.
The lattice dynamics of a one-dimensional diatomic lattice with nearest-neighbour interactions is examined with mathematical techniques involving setting up and solving difference equations. The method gives the exact sets of analytical solutions for the normal modes of vibration. The theory of localised vibrational modes due to local imperfection is developed as a characteristic value problem. The approach seems to have advantages over previous methods used to solve local defect problems in lattices.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.