Geometrical aspect of solving the problem of real structure growth on the model of alkali metal halides of the NaCl type
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HEORY OF CRYSTAL STRUCTURES
Geometrical Aspect of Solving the Problem of Real Structure Growth on the Model of Alkali Metal Halides of the NaCl Type V. G. Rau, A. A. Pugaev, T. F. Rau, and A. V. Maleev Vladimir State Humanitarian University, Vladimir, 600024 Russia email: [email protected] Received November 24, 2008
Abstract—The formation of a nanoscale packing polyhedron of layerbylayer modelstructure growth using a specified system of bonds between structural units, which determines the space partition in crystalline or quasicrystalline state of matter, was described in [1]. In a continuation of these studies, the application of the mechanism of sectorial layerbylayer growth of the structural unit neighborhood graph to the formation of the spectrum of model coordination packing growth polyhedra of NaCltype alkali metal halides is consid ered. A computer experiment based on the cell content clusterization and application of the radial algorithm of neighborhood graph growth showed that the existence of small (NaCl)2 clusters in the form of planar dimers is preferential for the equilibrium growth shape of sodium chloride crystal as a regular cube in the pre crystallization state of vapor phase. PACS numbers: 61.50.Ah DOI: 10.1134/S1063774509070037
PRELIMINARY INFORMATION Discussion of the NaCl cluster structure is the most significant aspect in determining the growth shape, because “free clusters are the transient objects between isolated atoms, molecules, and solids” [2]. The forma tion of doubly charged [(NaCl)mNa2]2+ clusters (m = 11, 12) composed of two 2D atomic grids was con firmed by experimental massspectrometry data [3]. The structure finder (a term introduced by Kitaigor odsky), which was constructed based on the close packing of molecules of a certain shape and which works according to the “convexity to concavity” rule [4], can, in theory, be a prototype of any cluster assem bly mechanism. However, its construction is a com plex mathematical and technical problem. Finally, the concept of molecule shape is also nonelemen tary; it was most adequately introduced in Bader’s studies [5], where the shape of an atom (or mole cule) is set by the zero gradient surface of the elec tron density of an atom in a molecule or a molecule in an atomic–molecular system (agglomerates, sol vates, clusters, solids, etc.). In any case, regardless of how the structure is described, it leads us to a partition of space into to atoms, molecules, clusters, structural motifs, voids, etc. Therefore, the basis of searching for the mecha nism of structure formation is the representation of the crystal cell content as a partition (or packing) into such fragments that actually existed in the vapor phase
and then passed into the solid. Apparent exceptions are cases where either a molecule or its shape is not retained during crystal growth as a result of chemical reaction; i.e., the molecule lacks transferability with shape conservation (according to Bader [5]). At the same time, studies of the free cluster geom etry by
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