Ionic crystals principles

Linus Pauling, The Principles Determining the Structure of Complex Ionic Crystals,... 

This by no means exhaustive discussion may serve to indicate the value of the information provided by magnetic data relative to the nature of the chemical bond. The quantum-mechanical rules for electron-pair bonds are essential to the treatment. Much further information is provided when these methods of attack are combined with crystal structure data, a topic which has been almost completely neglected in this paper. It has been found that the rules for electron-pair bonds permit the formulation of a set of structural principles for non-ionic inorganic crystals similar to that for complex ionic crystals the statement of these principles and applications illustrating their use will be the subject of an article to be published in the Zeitschrift fur Kristallographie. 

THE PRINCIPLES DETERMINING THE STRUCTURE OF COMPLEX IONIC CRYSTALS... 

The Principles Determining the Structure of Complex Ionic Crystals.—The success of the coordination method in predicting structures for brookite and topaz has led to the proposal of a set of principles governing the structure of a rather extensive class of complex ionic crystals. 

The coordination theory and the principles governing coordinated structures provide the foundation for an interpretation of the structure of the complex silicates and other complex ionic crystals which may ultimately lead to the understanding of the nature and the explanation of the properties of these interesting substances. This will be achieved completely only after the investigation of the structures of many crystals with x-rays. To illustrate the clarification introduced by the new conception the following by no means exhaustive examples are discussed. 

A set of principles governing the structure of complex ionic crystals, based upon the assumption of a coordinated arrangement of anions about each cation at the comers of an approximately regular polyhedron, is formulated with the aid of considerations based upon the crystal energy. Included in the set is a new electrostatic principle which is of wide application and considerable power. 

Important structural principles for ionic crystals, which had already been recognized in part by V. Goldschmidt, were summarized by L. Pauling in the following rules. First rule Coordination polyhedra... 

Pauling L. (1929). The principles determining the structure of complex ionic crystals. Jour. 

The object of this paper is to discuss some of these problems. We start with the evidence for the new system of ionic radii. X-rays are diffracted by electrons in principle therefore X-ray diffraction should always locate the few outer electrons involved in bonding, but in fact this requires sophisticated treatment of meticulous measurements on crystals of high symmetry [6—9). But it has long been clear that some ionic crystals show round each ion an electron density which is approximately spherical but falls away to a very low background the following Table shows a typical example. 

Acta Cryst. B39 165-170 Pauling, L. Hendricks, S.B. (1925) The crystal structures of hematite and corundum. J. Am. Chem. Soc. 47 781-790 Pauling, L. (1929) The principles of determining the structure of complex ionic crystals. J. Amer. Chem. Soc. 51 289-296 Payne, J.E. Davis, J.A. Waite,T.D. (1996) Uranium adsorption on ferrihydrite — effect of phosphate und humic add. Radiochemica Acta 74 239-243... 

Analyses of metal coordination and the bond strengths started with the publication by Pauling (1929) of an article entitled The Principles Determining the Structure of Complex Ionic Crystals. In this article Pauling defined the bond strength as listed above. Later, it became clear from measurements of bond lengths by X-ray crystallographic analyses that... 

This opening chapter has introduced many of the principles and ideas that lie behind a discussion of the crystalline solid state. We have discussed in detail the structure of a number of important ionic crystal structures and shown how they can be linked to a simple view of ions as hard spheres that pack together as closely as possible, but can also be viewed as the linking of octahedra or tetrahedra in various ways. Taking these ideas further, we have investigated the size of these ions in terms of their radii, and... 

The concept of bond valence, which, as will be shown below, is the same as the bond flux derived in Chapter 2, grew out of attempts to refine Pauling s principles determining the structures of complex ionic crystals (Section 1.7). In this empirical evolution of Pauling s model, both the electrostatic and short-range components were developed simultaneously. Only later did it become apparent that it was also possible to derive the properties of the electrostatic component independently using the ionic theory. 

If the coupling of the electrons to certain centers is strong, their spectra may be distinguished from that of the crystal as a whole (point defect color centers in ionic crystals, polarons in semiconductors). The spectra of defects can therefore be used for analytical or even kinetic investigations. In principle, it should be possible to construct devices which have, under favorable conditions, a sufficient spatial resolution to experimentally determine the basic kinetic quantity c,( , t). 

The theoretical prediction of the optical absorption profile of a solid using first-principles methods has produced results in reasonable agreement with experiment for a variety of systems [2-4], For example, several ionic crystals were studied extensively, generally using the Hartree-Fock one-electron approximation [5], through the extreme-ultraviolet. Lithium fluoride was the focus of a particularly detailed comparison [6-8], providing excellent confirmation of the applicability of the band theory of solids for optical absorption. 

In the case of an ionic crystal the interacting units are readily identified as cations and anions, which exchange virtual photons. The ions are formed by the transfer of valence electrons to the more electronegative partners. Only a small fraction of the valence density remains in interstitial space. The resulting closed-shell ionic spheres are prevented from interpenetrating by the exclusion principle. 

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