Buletsa E. Description and lattice dynamics of spinel-type crystals in superspace symmetry approach.

The thesis is devoted to investigation of structural features of complex crystals, and their influence in lattice dynamics using superspace symmetry approach. In terms of simple lattice the occupying modulation is considered alongside with the modulation of displacement vectors of atoms concerning crystallographic sites of one-atomic lattice in case of spinel type crystals. The mechanism of force constants modulation one can easily extend on a case of arbitrary crystalline solids is clarified. The alternative expression of a dynamical matrix of complex crystal as natural compositional modulated superlattice is suggested. Based on the generalised dynamical matrix the phonon spectra for spinels LiTi2O4, Li4/3Ti5/3O4 and MgCr2O4 are calculated in symmetry directions, using a short-range force constants model. The behaviour of phonon modes has been investigated in systems of solid solutions Cu1-xMgxCr2O4, Li1+xTi2-xO4 and Li1-xMgxTi2O4, using different models of substitution in a cationic sublattice.