MODE DENSITIES OF DEFECT LINES IN 2-DIMENSIONAL MONTROLL-POTTS LATTICES

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. 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 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 is similar to omega) to a form which is characteristic of one-dimensional oscillatory dynamics (rho is similar to constant).