The structures of complex ionic crystals

For simplicity we shall discuss complex oxides and complex oxy-salts, but the same principles apply to complex fluorides and ionic oxyfluorides. A complex oxide is an assembly of 0 ions and cations of various kinds which have radii ranging from about one-half to values rather larger than the radius of 0 . It is usual to mention in the present context some generalizations concerning the structures of complex ionic crystals which are often referred to as Pauling s rules . The first relates the c.n. of M to the radius ratio rg. The general increase of c.n. with increasing radius ratio is too well known to call for further discussion 

Calcite structure liNOa, NaN03 MgC03, CaC03, FeC03 InB03, YBO3 

Aragonite structure KNO3 CaC03, SrC03 LaB03 

We shall now show that a consideration of both the size factor and the principle of the local balancing of charges leads to some interesting conclusions about salts containing complex ions. 

In the following series of salts the charge on O increases as shown 

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

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. 

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. 

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

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... 

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. 

This simple rule restricts greatly the acceptable structures for a substance, and it has been found useful in the determination of the structures of complex ionic crystals, including especially the silicate minerals. The rule is satisfied nearly completely by most, of the structures that have been reported for the silicate minerals, deviations by as much as i being rare. Somewhat larger deviations from the rule are occasionally found for substances prepared in the laboratory, for which stability as great as for minerals is not expected. 

Pauling L (1927) The sizes of ions and the structure of ionic crystals. J Am Chem Soc 49 765-790 Pauling L (1929) The principles determining the structure of complex ionic crystals. J Am Chem Soc 51 1010-1026... 

In 1929 Pauling proposed as the second of his Principles Determining the Structures of Complex Ionic Crystals [1], that a cation-anion bond could be characterized by the oxidation state (atomic valence) of its cation divided by its coordination number. He showed that the total amount of this quantity, usually now called the Pauling Bond Strength, received by the anion was approximately equal to the anion oxidation state. He called this the Electrostatic Valence Principle, but it is now commonly referred to as Pauling s Second Rule. 

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