Electrostatic valency principle

The Number of Polyhedra with a Common Corner. The Electrostatic Valence Principle.—The number of polyhedra with a common corner can be determined by the use of an extended conception of electrostatic valence. Let ze be the electric charge of a cation and v its coordination number. Then the strength of the electrostatic valence bond going to each comer of the polyhedron of anions about it is defined as... 

Let — fe be the charge of the anion located at a corner shared among several polyhedra. We now postulate the following electrostatic valence principle II. In a stable coordination structure the electric charge of each anion tends to compensate the strength of the electrostatic valence bonds reaching to it from the cations at the centers of the polyhedra of which it forms a corner that is, for each anion... 

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. 

Pauling s Electrostatic Valence Principle, or the Valence Sum Rule, as it is called in the modified form used here (see Section 10.2.3), provides a useful check on the correctness of a structure and can draw attention to problems in its chemical description. Many workers now use the Valence Sum Rule routinely as a check on the correctness of a structure determination. 

The electrostatic valence principle recently was applied to a large number of silicate structures with some success (83, 84). There, the variations M, (Si—O) and A o of the individual Si—O bonds were correlated. However, in the computations it is assumed that all contributions to the charge balance of the oxygen are controlled solely by the quotient... 

This determination of the coordination number of the ion is predicated on the electrical neutrality principle given earlier (see page 19). This principle is also called the electrostatic valence principle and is part of Pauling s second rule In a stable ionic structure the valence of each anion, with changed sign, is exactly or nearly equal to the sum of the strengths of the electrostatic bonds to it from the adjacent cations. (Pauling, 1960)... 

His first principle stated that the lengths of bonds can be determined by adding the ionic radii of the two terminal ions and that the coordination numbers of the cations can be determined fi om the ratio of these radii. More important was the second principle the electrostatic valence principle, which he stated as ... 

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