Radius Ratio, Ligancy, and the Properties of Substances

Some of the properties of substances can be discussed in a useful way in terms of the sizes of ions or atoms. Many of the substances mentioned in the later sections of this chapter and in the following chapter are compounds of metals, with small electronegativity, and nonmetals, with large electronegativity. The bonds between these atoms may have a sufficiently large amount of ionic character to justify the discussion of the substance as composed of cations and anions. Such a discussion may be helpful even for substances in which the bonds have a large amount of covalent character. 

For example, let us consider the fluorides of the elements of the second short period of the periodic table. Their formulas, melting points, boiling points, heats of fusion, and heats of vaporization (or sublimation) are the following  

Linear, triangular, tetrahedral, octahedral, and cubic arrangements of anions around a central cation of increasing radius. 

Thus for the planar triangular structure MX , the distances /m + r and 2 have the relative values 1 V3, from which we calculate = 2/V3 — 1 = 0.155. In a similar way the values 0.225 for ligancy 4 (a tetrahedron of anions about the cation), 0.414 for ligancy 6 (octahedron), and 0.732 for ligancy 8 (cube) are obtained. 

The increase in stability (decrease in energy) with increase in ligancy is easy to understand. Let us consider two ionic molecules, M X, with  

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