Angular invariants and local order in the structures of substances
A method is suggested for analyzing the model structures of crystals by calculating the spherical coordinates of the normals to the simplex faces of the simplicial Delaunay partitioning of a set of points (atoms). The normals to the simplex faces of the Delaunay partitioning of the crystal structure characterize the structure at the local level. An algorithm for constructing the invariant of the crystal structure (crystal module) was considered. Crystals modules were constructed for hexagonal and cubic ices.
Keywordscrystal module Delaunay partitioning
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- 1.E. S. Fedorov, Symmetry and Structure of Crystals [in Russian], USSR Academy of Sciences, Moscow (1949).Google Scholar
- 2.B. N. Delaunay, N. P. Dolbilin, M. I. Shtogrin, and R. V. Galiulin, Dokl. Akad. Nauk SSSR, 227, 19–21 (1976).Google Scholar
- 3.N. P. Dolbilin, ibid., 230, 516–519.Google Scholar
- 4.N. A. Bulienkov, in: Vestn. Nizhegorodsk. Univ., Ser. Fiz. Tverd. Tela, issue 1, 19–30 (1998).Google Scholar
- 5.N. A. Bulienkov, in: Quasicrystals and Discrete Geometry. The Fields Institute Monographs, Vol. 10, J. Patera (ed.), Am. Mathem. Soc., Providence, RI (1998), pp. 67–134.Google Scholar
- 6.N. V. Belov, Structure of Ionic Crystals and Metallic Phases [in Russian], USSR Academy of Sciences, Moscow (1947).Google Scholar
- 7.Modern Problems in Physical Chemistry [in Russian], Granitsa, Moscow (2005).Google Scholar
- 8.J.-M. Lehn, Supramolecular Chemistry. Concepts and Prospects [Russian translation], Siberian Division, Russian Academy of Sciences, Novosibirsk (1998).Google Scholar
- 10.N. N. Medvedev, Voronoi Delaunay Method in Structural Studies of Noncrystalline Systems [in Russian], Siberian Division, Russian Academy of Sciences, Novosibirsk (2000).Google Scholar