Line defects in three-dimensional lattices

In the presented paper localized modes near a line defect in a simple cubic lattice with interaction among the nearest neighbours are studied. For the case of a row of atoms with a changed mass and interaction among them, criteria for the occurrence of localized modes are given. It is shown that the frequency band of acoustic localized modes beginning at the frequency=0, insofar as it deals with the frequency spectrum, is very similar to that of a linear chain. This leads, when studying crystal properties which are any additive functions of eigenfrequencies (thermo-dynamical functions, etc.), to the appearance of the contribution characteristic for the linear chain.