MODEL CALCULATIONS OF DISPERSION DEPENDENCIES OF STRUCTURES OF TYPE BaTiO3 WITH PARTIAL POPULATION OF DIFFERENT CRYSTALLOGRAPHIC POSITIONS

Abstract.

Purpose. The results of model studies of the phonon spectrum of the crystalline structure of the BaTiO3 type are presented. (3+3)-dimensional structures for describing the crystal structure of the perovskite in (2a×2a×2a) a metric and (4a×4a×4a) a superlattice are constructed. The equivalence of the calculations of the dispersion dependences of the phonon spectrum in models of different metrics is shown. The possibility of calculating the phonon dispersion curves of these structures with partial population of crystallographic positions is analysed. The main goal of the present work was to develop (within the superspace symmetry concept) the program suitable for theoretical calculation of the phonon spectra for BaTiO3 perovskite and to conduct the relevant calculations. Methods. In the present study, the crystal structure of BaTiO3 perovskite have been analysed and described by using the superspace symmetry concept. Results. The program operating under the Maple environment and suitable for theoretically calculating the phonon spectra of the BaTiO3 perovskite crystals has been developed. The eigenvalues of the generalized dynamic matrix have been found, and the dispersion dependencies have been built for the directions X-Г-M-R-Г of the Brillouin zone. Conclusions. Model calculations in the (4a×4a×4a) metric are related to the inclusion in the consideration of additional model power constants. Interestingly, there is almost no effect on the implementation of the low-frequency region of the spectrum in the (4a×4a×4a) metric and significant restructuring of the high-frequency phonon spectrum. The simulation in the (4a×4a×4a) metric is due to the significantly smaller distance of the ”jump” of oxygen atoms between the considered orbits

Keywords: perovskite, crystal structure, protocrystal, phonon spectrum, Maple, population of crystallographic positions

https://doi.org/10.24144/2415-8038.2020.48.14-22