Partial Frequency Distribution Functions and the Problem of the Localization of Atomic Vibrations in Real Layered and Multilayered Crystals
Recently much attention has been directed towards the investigation of the various physical characteristics of polyatomic crystal lattices containing a large number of different atoms in their unit cells. HTS-materials, numerous ferroelectrics, ferroelastics, polymers, biopolymers, intercalated compounds as well as a series of other materials interesting for both their purely scientific and technical aspects are examples of compounds of this type. In many cases these compounds possess multilayer crystal structures. A large lattice parameter along the direction normal to the layers, which is a characteristic of these crystals, greatly weakens the influence of the crystalline regularity of the atoms spatial distribution perpendicular to the layers. Such a large crystal lattice period affects various physical properties of these structures so dramatically that they acquire features more typical of disordered systems. In particular this is the origin of the special features of the phonon spectra and related physical properties. The special character of these features is manifested first of all by the fact that the atomic vibrations in each layer, along different crystallographic directions, contribute differently to the phonon spectrum of a multilayered crystal. Such contributions to the total density of crystal vibrations are characterized by partial distribution functions.
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