Shkyrta I. Studies of dispersion dependences of complex cubic crystals phonon spectrum in the concept of superspace symmetry

The method of determining the complex crystal structure as (3+d)-dimensional structure in the form of motive convolution with repetition mechanism was used. The gradual complication of crystals with (2a2a2a)- and (2а2а4с)-superlattices has been considered, proceeding from the simple cubic protocrystal lattice, the Fourier components of mass defect operator matrix have been given. The principles of the dynamics theory of a crystalline lattice, also taking into account the consequences of superspace symmetry for crystals of NaCl, AuCu3 and BaTiO3 structural typeshave been considered. The general symmetry relations imposed by generalized symmetry on the description of the modulated crystals lattice dynamics have been formulated. The structures of generalized dynamic matrices of complex crystals in the traditional and superspace approaches with the consideration of amplitudes of modulation functions of mass and force disturbance have been analyzed. The lattice dynamics of BaTiO3 crystals type in the concept of superspace symmetry has been considered. On the basis of the constructed generalized dynamic matrices, the general scheme for calculating the phonon spectra of complex crystals in equidistant and non-equidistant approximations has been analyzed. The symmetry analysis of the branches of the phonon spectrum has been performed for high-symmetry points and directions of the Brillouin zone. Superspace approach has been used to study the dynamics of lattices of perovskite natural (2а2а4с)-superlattices. On the basis of the constructed generalized dynamic matrices of the BaSrTi2O6 type complex crystals of the tetragonal syngony the calculations of the natural (2а2а4с)-superlattices model phonon spectra in equidistant and non- equidistant approximations for the chain of structural complications genesis have been made: package D (Ba2Ti2O4) - package B (C) (Ba2Ti2O5) - package A (Ba2Ti2O6) - BaSrTi2O6. Superspace approach has been applied to study the lattice dynamics of perovskite solid solutions systems for different substitution models in cation superlattices (A|0.5A||0.5)(B|0.5B||0.5)O3, (A|0.5A||0.5)BO3 and A(B|0.5B||0.5)O3 (x,y=0.5) types, the general scheme of transformation of solid solutions complex systems phonon branches as (4a4a4a)-superlattices, proceeding from the face-centered cubic lattice of the protocrystal has been analysed. By fitting the calculated values of the phonon modes frequencies at the point Г(0,0,0) with the experimental values and calculations of other authors, the power constant of the inter-atomic interaction has been determined, in this connection, the question of reconciliation of the calculation with the experiment is provided a priori.