Mode densities of defect lines in two-dimensional Montroll-Potts lattices

Abstract

The investigation addresses the problem, to what extent one-dimensional defect structures in a crystalline surrounding are able to affect the low-frequency vibrational-mode density. Employing an extended Lifshitz procedure, a Green function technique is used to calculate the mode density of several prototypical linear defect structures within a two-dimensional reference lattice of Montroll-Potts type. It is shown that, depending on the softness of the chosen defect lines, even at very low frequencies the power law of the mode density may switch from the two-dimensional behaviour of the bulk ( rho approximately omega ) to a form which is characteristic of one-dimensional oscillatory dynamics ( rho approximately constant).