Ionic radii Pauling

Mass magnetic susceptibility (as a solid) Ionic radius (Pauling)... 

Ahrens (1952) proposed the first extended tabulation of ionic radii, partially modifying the univalent radii in the Vl-fold coordination of Pauling (1927a) on the basis of the observed correlation between ionic radius (r) and ionization potential (/), which can be expressed in the forms... 

The Pauling electronegativities of carbon and tellurium are, respectively, 2.5 and 2.1. This, in addition to the large volume of the tellurium atom (atomic radius 1.37, ionic radius 2.21), promotes easy polarization of Te-C bonds. The ionic character of the bonds increases in the order C(sp ) Te>C(sp ) Te>C(sp)-Te, in accordance with the electronegativity of carbon accompanying the s character (Table 1.1). 

Element Atomic number Atomic mass Electronic configuration Pauling electronegativity Ionization potential Ionic radius Atomic radius... 

As early as 1920 s Goldschmidt, Pauling and Zachariasen (5—7) observed the additivity of atomic and ionic radii to reproduce the interatomic distances very closely. However, the early lists of ionic radii were based on a cation coordination number of six and a fixed value for the ionic radius of either O - or F. Goldschmidt was first to notice that the radii varied with CN. 

However, since only values of rexpti are obtained, it is necessary to assume a value for the ionic radius of either r+ or r- in order to derive the ionic radius of the other. It is usual to assume a value of 1.40 A for the radius of the and 1.94 A for the radius of CP (Pauling, 1948) because these are half the minimum anion-anion distances found in crystal structures. Values for ionic radii (Shannon and Prewitt, 1969 Shannon, 1976 Brown, 1988) are listed in Table V for a coordination number of 6 around the metal atoms. Thus, values of radii are hypothetical, based on the idea of an additivity rule and a few initial assumptions on anion size. 

With an ionic radius of 0.81 A (Pauling), the ion Sc3+ lies on the borderline between six-coordination and higher coordination numbers. In those crystal structures which are known, Sc3+ is predominantly six-coordinated, but examples of seven-, eight- and nine-coordination do occur, together with a limited number of examples of lower coordination numbers than six where ligands are very bulky. 

The compression energies so calculated are higher than the experimental values unless r is relatively large. It is scarcely possible to consider values of the ionic radius of Li+ less than 0.9 A. This is in agreement with the experimentally determined plot of electronic densities but is very much above the values normally accepted (Goldschmidt, 0.78 A, and Pauling, 0.60 A). 

Pauling subsequently introduced three mles governing ionic sfructures (Pauling, 1928, 1929). The first is known as the radius ratio rule. The idea is that the relative sizes of the ions determine the sfructure adopted by an ionic compound. Pauling proposed specific values for the ratios of the cation radius to the anion radius as lower limits for different coordination types. These values are given in Table 3.5. 

In addition to the reinterpretation of Pauling s rules developed by Burdett and McLarnan (1984), there have been a number of other studies related to various aspects of these standard rules. Due to the substantial number of errors in classifying AB compounds in terms of ionic radius ratio (e.g., Phillips, 1970 Tossell, 1980b), there have been numerous attempts to create structure maps that have two atomic quantities as coordinates and that can provide a unique separation of the different structure types. Such atom quantities may be related primarily to size or energy or to some combination of the two. Some of the most important such approaches are those of Mooser and Pearson (1959), Phillips (1970), and Simons and Bloch (1973). 

Fig. 2. Relation between hydration number of alkali and alkaline earth ions and Pauling s ionic radius with an assumed isotopic shift...

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