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.