Bond graphs and coordination number

Even if the connectivity is not known, one can predict many properties if one can make a reasonable estimate of the coordination number. Chapter 6 describes the different factors that determine the coordination number, but at this point in the discussion it is sufficient, and simpler, to work with coordination numbers that are determined experimentally. 

The coordination number of a cation is defined as the number of bonds that it forms. Although it was shown in Section 2.6 that the number of bonds is uniquely defined by the partitioning of the Madelung field, extensive calculation is needed to extract this information. It is, therefore, convenient to use a simpler, if more arbitrary, definition. 

There have been many attempts to define coordination number using a simple criterion to decide when two atoms are bonded (Brunner and Laves 1970). Rules have been proposed based on bond lengths, ionic radii, and topological properties such as the Voronoi partitioning of space, but none has proved entirely satisfactory. In this book the coordination number is determined by setting an arbitrary, though reasonable, lower threshold for the experimental bond valence (Altermatt and Brown 1985). 

Rule 4.1 (An operational definition of a bond). A bond exists between a cation and an anion if its experimental bond valence is larger than 0.04 x the cation valence. 

While this definition is arbitrary it is appropriate because it is based on chemical as well as geometric considerations and, like other definitions, it agrees with the conventional assignment in cases where there is no dispute. The definition can be justified for use with the bond valence model since any true bond that is excluded by this definition contributes at most only 4 per cent to the cation bond valence sum, and generally much less given that eqn (3.1) tends to overestimate the valence of weak bonds. 

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