Abstract
The structures of the coordination spheres or orbits of hexagonal and cubic crystals and their sizes, coordination numbers, and coordinates of atoms and cavities have been studied. The orbits of atoms of all sublattices of octahedral and tetrahedral cavities have been calculated. The close-packed structures (FCC and HCP) of oxygen ions have been considered as basic structures. In both structures, the metal cations are distributed over octahedral and tetrahedral cavities. The developed method is used for calculating the orbits of clusters with the hexagonal crystal structure of magnetoplumbite, ilmenite, and corundum, as well as with the cubic structure of spinel and perovskite.
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