Description Of Crystal Structure Research Articles

Path integral approach to the theory of crystals

An approach is proposed to the description of crystal structure in the formalism of path integration. The transition in the path integral to a new variable, viz., the electric potential field, permits the formulation of crystallization conditions as the appearance of the mean value of this field, having a periodic structure. In the path integral a transition is made to collective variables describing lattice vibrations and plasma fluctuations.

An attempted exact, systematic, geometrical description of crystal structures

An attempted exact, systematic, geometrical description of crystal structures

An attempted exact, systematic, geometrical description of crystal structures

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An attempted exact, systematic, geometrical description of crystal structures

An attempted exact, systematic, geometrical description of crystal structures

Crystal-chemical formulae for simple inorganic crystal structures

Abstraet Crystal-chemical formulae are presented which allow one to denote in condensed form the most important structural features of simple inorganic crystal structures. These formulae are not only an aid for the teaching of crystal chemistry, but are equally useful for a complementary explanation of structural drawings or a rapid description of simple crystal structures. The proposal discussed here is an extension of the constitution formulae proposed by Machatschki [Monatsh. Chem. (1947). 77, 333-342]. The new formulae have been designed to allow the special structural features of polyanionic or polycationic valence compounds or tetrahedral structure compounds to be written down in a simple self-explanatory manner.

Thestella quadrangulaas a structure building unit

In order to get a simple and accurate description of complex crystal structures, the stella quadrangula is used as a building unit to describe the following structures: SiF4, scheelite, NaZn13, Ru7B3 and Ba3Fe3Se7.

Structure of organic paramagnetic nitroxyl radicals

STRUCTURE OF ORGANIC PARAMAGNETIC NITROXYL RADICALS R. N. Shibaeva UDC 548.~/3~/ Results of the structural investigation of 25 stable nitroxyl radicals are presented in the review. Char- acteristics of geometry of )N--O fragments in radical molecules are given, and their mutual ar- rangement in the crystal, which determines exchange interactions in solid paramagnetic substances, is presented, Virtually all original structural papers published before October 1, 1974 are considered. 1. INTRODUCTION Interest in stable iminoxyl radicals has increased significantly lately in connection with their wide use as spin labels in the study of structures and properties of biologically active molecules. In addition, tminoxyl radicals are also used for inhibition of radical reactions in living organisms (in parricular, some of them are able to inhibit the development of malignant tumors); they also find important practical application in polymer investigations [1-3]. Compounds into the composition of which enters the )N--O group having one unpaired electron are called nitroxyl radicals. Iminoxyls are nitroxyls having aliphatic or other substituents on the N atom not participating in conjugation with the unpaired electron [1]. Together with monoradicals, in the molecule of which there is one N'-'O grouping having an unpaired electron, there also exist polyradicals having several unpaired electrons per mol- ecule: in particular, biradicals, already quite a broad class of compounds [1]. Data on the crystal structure of nitroxyl radicals are of interest from two points of view. First, knowledge of molecular conformation (particularly of the )N "--O) fragment) gives additional infor- marion on the electronic structure of the radical, which determines its properties. In addition, it makes it possible sometimes to compare conformation of the molecule in the solid state with its conformation in the liquid, when it is known on the basis of investigation by other methods. Second, knowledge of molecular packing in the crystal makes it possible to judge the mechanism of exchange interactions in solid paramagnetic substances, since the character of such interactions in the crystal is determined by the mutual arrangement of paramagnetic centers (unpaired electrons). It would be hoped that the structural investi- gations of nitroxyls with the simultaneous consecutive investigation ofmagneticinteractionsinthem [4-8] wouldmake it possible to establish experimentally the dependence of exchange energy on interelectronic distance I (r) (at pre- sent there are no reliable quantum-chemical methods of calculating this function). In addition, the knowledge of crystal structure for polyradicals makes it possible to separate intermolecular and intramolecular contributions to ex- change interactions. Formulas of all nitroxyl radicals, the structures of which will be discussed subsequently, are presented be- low. For each discussed radical structure we give the following: name, general characteristics, parameters of the elementary cell, space group, and number of molecules per cell [only two of the discussed radicals (I) and (II) are not crystalline]. In the description of molecular structure the main attention was given to the geometry of the )N~'O fragment, and in the description of crystal structure it was given to the mutual arrangement of paramag- netic centers. Branch of the Institute of Chemical Physics, Academy of Sciences of the USStL Translated from Zhumal Struktumoi Khimii, Vol. 16, No. 2, pp. 330-348, March-April, 1925. Original article submitted November 1, 1974.

Classification, representation and prediction of crystal structures of ionic compounds

The aim of this paper is to show that with the aid of a qualitative model of ionic bonding, including polarizability, many crystal structures, mainly of halides and chalcogenides, can be explained or even predicted. Polarization of O 2− and F − ions may be neglected unless these ions have very small, or small and highly charged cation neighbours. The polarizability of a few large cations is assumed also to play a rôle. The cation polyhedron may have a shape different from that expected for the ionic model as a result of nonionic bonding types; the theoretical shapes can be used empirically in the structure prediction. Section I deals with the background of this ionic picture. Section II deals with the sharing of corners and/or edges and/or faces of cation polyhedra. Pictures of various types of sharing polyhedra are given, with octahedra as an example. An explanation is offered for Wadsley's rule of maximal edge-sharing in his shear-structures, which seemed to violate Pauling's third rule. In Section III a classification of crystal structures is given in plots of cation coordination versus stoichiometry, expressed as the ratio nr. anions/nr. cations, for simple compounds and complex anions. The average cation coordination is plotted against stoichiometry if one is interested in the changes of structure under high pressure. Section IV deals with the description of crystal structures by space-filling polyhedra, which are an aid towards finding relationships between structures and towards predicting new ones. Simple structures with close-packed anions or cations are explained by the ionic model using these SFP in Section V. In Section VI some structure predictions (e.g., of Sc 2S 3, Li 2CuO 2, SrCuO 2, Sr 2CuO 3, and SrCu 2O 2) are discussed, and some results of recent structure determinations carried out in the author's laboratory (of the above-mentioned SrCuO-compounds, β-BaPdO 2, MgAl 2S 4, FeAl 2S 4 and MgGa 2S 4) are given.

Translation-permutation operator algebra for the description of crystal structures. I. Ideal closest packing

The foundation of an abstract algebra for the description of crystal structures is developed in terms of ideally closest-packed structures. All the spatial information of closest-packed structures can be derived in terms of (a) the geometry of the atoms (A positions) and the plane, triangular interstices (B and C positions) of a closest-packed p6mm monolayer, and (b) the permutations induced among these A, B, and C positions by translations from one monolayer midplane to another. The mathematical device used to correlate this information is a translation-permutation vector operator. Since this operator is closely related to the basic concept of a layer-by=layer crystal growth process, the algebra is readily extensible to crystal structures that are defective owing to many kinds of non-periodic elements of structure. Some examples are presented of the application of the algebra to closest-packed structures that are either ideal or exhibit one of two kinds of defect: classical stacking faults or point defects.

A modular algebra for the description of crystal structures

A modular algebra for the description of crystal structures