Anionic radius

Fluorination of anions of lithium salts offers a possibility for a study of the influence of ion association on the maxima of conductivity, because fluorination of large molecular anions only slightly affects the anionic radius and all other conductivity determining effects (1-3, 5, 6) are elimi-... 

The experimental values for the lithium halides are high. This is due to two different phenomena. In the case of the chloride, bromide and iodide the anions are in mutual contact, that is, the repulsive forces operative are those between the anions, and the anion radius alone determines the inter-atomic distances. The geometry of the sodium chloride structure requires that, for less than 0.414, the anions come into contact... 

In lithium chloride, bromide and iodide, magnesium sulfide and selenide and strontium chloride the inter-atomic distances depend on the anion radius alone, for the anions are in mutual contact the observed anion-anion distances agree satisfactorily with the calculated radii. In lithium fluoride, sodium chloride, bromide and iodide and magnesium oxide the observed anion-cation distances are larger than those calculated because of double repulsion the anions are approaching mutual contact, and the repulsive forces between them as well as those between anion and cation are operative. 

First, the hydrogen bond is a bond by hydrogen between two atoms the coordination number of hydrogen does not exceed two.7 The positive hydrogen ion is a bare proton, with no electron shell about it. This vanishingly small cation would attract one anion (which we idealize here as a rigid sphere of finite radius—see Chap. 13) to the equilibrium intemuclear distance equal to the anion radius, and could then similarly attract a second anion, as shown in Figure 12-1, to form... 

According to the first Pauling rule the cation/anion radii ratio, allowed for octahedral coordination (C ,) has to be in the range of 0.41 - 0.73. For tetrahedral co-ordination this ratio (f,a) has to be within the range of 0.22-0.41. To estimate the above ratios for the cations used a value of 1.4 A is taken for the O anion radius value [14]. Results are presented in the Tab 3... 

The stability of a certain structure type depends essentially on the relative sizes of cations and anions. Even with a larger Madelung constant a structure type can be less stable than another structure type in which cations and anions can approach each other more closely this is so because the lattice energy also depends on the interionic distances [cf. equation (5.4), p. 44], The relative size of the ions is quantified by the radius ratio rm/rx rM being the cation radius and rx the anion radius. In the following the ions are taken to be hard spheres having specific radii. 

Figure 2. Calculated variation of AG° (Na Cs) (kJ mol ) with the equivalent anionic radius (A) at different interlayer molalities (35). Data of Maes and Cremers (17) are also shown. (Figure supplied by D.D. Eberl). Reproduced with permission from Ref. 35. Copyright 1980, The Clay Minerals Society.

The so-called radius ratio principle establishes that, for a cation/anion radius ratio lower than 0.414, the coordination of the complex is 4. The coordination numbers rise to 6 for ratios between 0.414 and 0.732 and to 8 for ratios higher than 0.732. Actually the various compounds conform to this principle only qualitatively. Tossell (1980) has shown that, if Ahrens s ionic radii are adopted, only 60% of compounds conform to the radius ratio principle. ... 

These same arguments are now applied to the alkali-metal hydrides. The following Table shows the nearest-neighbour distances 24) and the anion-radius calculated on the assumption of anion-cation and anion-anion contact if one consistently assumes anion-anion contact in the... 

It was inferred from simple geometrical considerations (condition for contact between neighbouring X anions) that this structure could only be formed if the ratio of the cation radius to the anion radius is between 0.41 and 0.73. It is not easy to check this condition for the AnX compounds because there is some difficulty to define the radius to be used for this comparison. If the tabulated ionic radii are used, many of the AnX compounds are in the range mentioned, but some of them me outside, e.g. the monocarbides. 

This is consistent with the values of Ahyd// becoming less negative as the anion radius increases, for any of the Group 1 halides. Note that for any particular Group 1 cation the sum of the enthalpies of hydration of the cation/fluoride combination is considerably more negative than the other three values. The cation and anion radii are separate as indicated by equations (3.32) and (3.33), and the relatively small fluoride ion has a more dominant influence than it does on lattice enthalpies, which are dependent on the sum of the cation and anion radii. 

Fig. 8.15 The Madelung energy in ionic compounds as a function of the radius ratio for CsCl, NaCl and cubic ZnS lattices (assuming the anion radius, / , is held constant).

Predicted Dependence of Structure Type on Cation/Anion Radius Ratio for Binary Ionic Compounds... 

According to Table 1, the free energy of hydration of anions decreases with increasing anionic radius. Despite this, the smallest, most highly solvated anions are bound most strongly by most host species. Explain this observation. 

Although the ionic radius criterion of Goldschmidt continues to serve as a useful principle of crystal chemistry, attention has been drawn to limitations of it (Bums and Fyfe, 1967b Bums, 1973). As noted earlier, the magnitude of the ionic radius and the concept of radius ratio (i.e. cation radius/anion radius) has proven to be a valuable guide for determining whether an ion may occupy a specific coordination site in a crystal structure. However, subtle differences between ionic radii are often appealed to in interpretations of trace element distributions during mineral formation. 

The fast, ion conduction properties of a-Agl is a result of the large anionic radius of I- and the low cationic radius of Ag+, immersed in a cubic structure containing 42 vacant sites between octahedral and tetrahedral sites. Because of this fact, Ag+ has a high mobility in this cubic structure [22],... 

Generally, anion interstitials are rare, because the anionic radius is greater than the cationic radius. The rule of electrical neutrality in a material containing both Schottky and Frenkel defects requires that the positive and negative point defects must be balanced, that is... 

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