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

Abstract

The investigation addresses the problem to what extent 1-demensional defect structures in a crystalline surrounding are able to affect the low-frequency vibrational mode density. This problem is of importance for the thermodynamics and the energy transport properties of disordered materials like glasses. Employing an extended Lifshitz procedure, a Green function technique is used to calculate the mode density of several prototypical linear defect structures within a 3-dimensional reference lattice of Montroll-Potts type. Generally, soft defect structures produce a low-frequency increase of the mode density. In particular for a soft disturbance of the transversal springs around a lattice line a transition of the additional mode density to 1-dimensional behaviour (Δϱ ∝ ω 0) takes place already at low frequencies. This would provide an additional mechanism for a linear T-behaviour of the specific heat as measured in glassy materials at low temperatures.