Feodosyev S. Lattice dynamics of crystals with complicated defects, layered and disordered structures

In the thesis, the results of microscale theoretical investigation of phonon spectra and vibration properties of the inhomogeneous and disordered crystalline systems are presented. Object of research the crystalline systems with complex defects, disordered solid solutions and alloys, quasi-low-dimensional and multilayer crystals, as well as nanoclusters are considered. Aim of research is a novel data acquisition for the phonon spectra and vibration-mediated properties of the crystalline systems with rather weak influence of crystal regularity on their vibration behavior. Methods of research include a local Green's function technique, method of regular degenerate perturbation and the Jacobi matrices technique. Main results: it was established that the boson peaks in disordered systems and van Hove singularities in regular crystals have the same origin, which is the excess phonon dispersion, rendered by the scattering of rapidly propagating phonons on slow quasiparticles. The boson-peak effects on heat capacity variation at low temperatures were discovered. The character of a discrete local level evolution towards the impurity band with doping was determined. The phonon spectra of the layered and multi-layer crystals such as graphite, transition-metal dichalcogenides and high-temperature superconductors of the 1-2-3 type, were calculated and scrutinized. The atomic dynamics in nanoclusters, either free or absorbed on a substrate with atomically smooth surface, is described.