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Object. The object of the study was the intercrystalline boundaries with a periodic atomic structure in two-component cubic crystals. Special boundaries are characterized by increased thermodynamic stability due to the relatively low energy of formation and specifi c electrical characteristics, such as Schottky barriers. Therefore, they are of great interest to researchers and developers of materials and devices. This study was carried out in the grain boundary engineering direction based on ion crystals. Aim of the study. The goal of the study was the atomic structure of these boundaries, classifi cation of intercrystalline boundaries based on their elemental composition, and the evaluation of intercrystalline boundaries as sources of electric fi elds in the crystal volume. Methods and methodology. As a method of research, the ideas of crystallographic symmetry of lattices having a simple, face-centred, and bulk-centred geometric structure were used. Results. A new method was developed for the appliance of lattice sites to certain elements of chemical composition using a specially constructed crystallographic group called the group of displacements. Specifi c groups of displacements for crystals of BCC, FCC, and simple cubic structure with two-component chemical composition were constructed. Based on this, the conditions determining the families of planes with the same elemental compositions and the relative arrangement of elements in the intercrystalline contact were formulated. Families of neutral atomic planes and families containing excess positive and negative charges were specifi ed. Conclusion. The technique of determining the sequence of alternation of these planes in the intercrystalline boundary region was described. NaCl, CsCl, and other crystals are considered as examples. For each crystal family, the orientations of the charged and neutral planes were indicated.

The object of this study is polycrystalline materials containing intercrystalline boundaries in face centered cubic and body centered cubic crystals. A wide variety of geometric characteristics that determine the atomic structure and physical properties of intercrystalline boundaries, gives rise to the expediency of systematization of the entire set of possible boundaries. The intercrystalline boundaries obtained on the basis of the coincidence of nodes are an important family of defects in polycrystals, so these defects are given a lot of research, but currently there is no complete systematization. The construction of such systematization was the purpose of this paper. The basis of classifi cation is the coordination polyhedron of the face centered cubic and body centered cubic lattice. As parameters defi ning the geometry of the lattice matching of the nodes of the selected pair of vectors and the lattice vector that defi nes the axis of rotation was used. Using algebraic methods used in studies of solid rotation, formulas are obtained for the crystallographic plane in which all possible axes of turns and vectors of the lattice cell of matching nodes should lie. As a result, it was shown that the coincidence lattices of general form belong to monoclinic crystal structure. In particular cases they may belong to cubic crystal structure. It is shown that such lattices of coinciding nodes are possible, which are obtained at different parameters of rotation, so polycrystals on the basis of the common lattice of coincidences are possible. The tables for face centered cubic and body centered cubic crystals is constructed in which the data are systematized for the vectors of the cell of the lattice of coincidences, rotation angles, the number of atoms in the cell at different initial characteristics of rotation.

Abstract. The object of this study is polycrystalline materials containing intercrystalline boundaries as one of the accompanying components of the defective structure. A wide variety of geometric characteristics that determine the atomic structure and physical properties of intergranular boundaries, gives rise to the expediency of systematization of the entire set of possible intergranular boundaries. The intercrystalline boundaries obtained on the basis of the coincidence of nodes are an important family of defects in polycrystals, so these defects are given a lot of research, but currently there is no complete systematization. The construction of such systematization was the purpose of this paper. The basis of classifi cation is the coordination polyhedron of the simple cubic lattice. Seven different polytopes with different topological characteristics are given. As parameters defi ning the geometry of the lattice matching of the nodes of the selected pair of vectors the vertices of these polyhedra and the lattice vector that defi nes the axis of rotation was used. Using algebraic methods used in studies of solid rotation, formulas are obtained for the crystallographic plane in which all possible axes of turns and vectors of the lattice cell of matching nodes should lie. As a result, it was shown that the coincidence lattices of General form belong to monoclinic crystal structure. In particular cases they may belong to orthorhombic and tetragonal crystal structure. It is shown that such lattices of coinciding nodes are possible, which are obtained at different parameters of rotation, so polycrystals on the basis of the common lattice of coincidences are possible. A table is constructed in which the data are systematized for the vectors of the cell of the lattice of coincidences, rotation angles, the number of atoms in the cell at different initial characteristics of rotation.