Mathematical Modeling of the Perovskite and Double Perovskite Crystal Structure

Due to the complexity of obtaining micro- and nanoscale objects, data on the structure and properties of such materials are especially important. This makes it relevant to use computer modeling to predict the required characteristics of materials. The electronic, magnetic, mechanical, and other properties of crystalline substances are determined by the specificity of their structure: the periodicity and symmetry of the lattice. This paper considers compounds with the common chemical formulas ABO3 and A2BB'O6, as well as the crystal lattice of the cubic symmetry type: the structural types Perovskite and Double Perovskite. The model of ionatomic radii, widely used in modeling various crystal structures, is applied. The application of the annealing simulation algorithm to calculate the metric parameters of the compounds under consideration is shown. The software implementation of the algorithm used in the study makes it possible to calculate the coordinates of the atoms included in the elementary cell of the crystal lattice, the lattice constant, and the packing density of atoms in the crystal cell according to the given chemical formula and the spatial symmetry group. The listed structural characteristics can be used for the subsequent determination of the electronic, magnetic, and thermal properties of perovskite-like compounds. This article presents a comparison of the values of the lattice constants obtained as a result of numerical modeling with the data published in open sources.