SYSTEMATICS OF COINCIDENCE SITE LATTICES FOR BCC AND FCC CRYSTALS
Abstract
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 classification is the coordination polyhedron of the face centered cubic and body centered cubic lattice. As parameters defining the geometry of the lattice matching of the nodes of the selected pair of vectors and the lattice vector that defines 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.
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References
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