Steyfan A. Description of stability of the crystal structures of the complex crystals and model calculations of the dispersions of their phonon spectra

The thesis is devoted to the investigation of the stability parameters of the crystal structures within the framework of the bond valence model (BVM), and also to the model calculations of the dispersions of the phonons for the superionic materials Cu6PS5Br, sapphire α-Al2O3, quasi-fullerites С30 and С42, pyrochlores of the А2В2Х6Y stoichiometry, and boric anhydrides В2О3. For the first time, the two BVM-based calculation schemes have been developed for predicting the structures of the ideal A2B2X6Y oxide pyrochlores. The structures examined for stability were then used as a basis for the models in calculations of their single-particle spectra. The calculations of the dispersion dependences of phonons of these structures were carried out within the framework of the superspace symmetry concept which has been used for building of their (3+d)-dimension models, based on the protocrystal metrics complicated by perturbations of different types. As a first step, the mass perturbation has been determined, providing the adequate distribution of the mass parameters; the obtained force field of interatomic interaction was taken to be dependent solely on the distance r0. The description of the models of all the structures was reduced to the construction of the proper sets of modulation vectors, the definition of the mass modulation function, the construction of the generalized dynamic matrix taken as the superposition of the dynamic matrixes of single-atom structures; the eigenvalues of the dispersion dependences of the single-particle perturbations were obtained for the high-symmetry directions of the Brillouin zone. The developed software allowed one to calculate the phonon spectra for the considered crystals. For all the investigated structures, the vibrational representations have been decomposed into the irreducible representations at the  point of the Brillouin zone. For the superionic Cu6PS5Br crystals, ab initio calculations of electronic spectra of different model structures have been performed.