Geometrical Modeling of Crystal Structures with Use of Space of Elliptic Riemannian Geometry

Stanislav Rudnev, Boris Semukhin, Andrey Klishin

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DOI: 10.4236/msa.2011.26071                

Abstract

The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fedorov groups of transformations. For visualizing computations, the interpretation of geometrical objects on a Clifford surface (SK) in Riemannian geometry with the help of a 2D torus in a Euclidean space is used. The F-algorithm ensures a computation of 2D sections of models of point systems arranged perpendicularly to the symmetry axes l3, l4, and l6. The results of modeling can be used for calculations of geometrical sizes of crystal structures, nanostructures, parameters of the cluster organization of oxides, as well as for the development of practical applications connected with improving the structural characteristics of crystalline materials.

Keywords

F-Algorithm, Crystal Lattice Systems, Microstructure, Riemannian Geometry, Space of Interpretation

Conflicts of Interest

The authors declare no conflicts of interest.

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