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S.V. Rudnev, “Application of Elliptic Riemannian Geometry to Problems Crystallography,” Computers and Mathematics with Applications, Vol. 16, No. 5-8, 1988, pp. 597-616.

has been cited by the following article:

• TITLE: Geometrical Modeling of Crystal Structures with Use of Space of Elliptic Riemannian Geometry

  AUTHORS: Stanislav Rudnev, Boris Semukhin, Andrey Klishin

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

  JOURNAL NAME: Materials Sciences and Applications, Vol.2 No.6, June 24, 2011

  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.