Effective coordination number ECoN

ECoN is a useful generalization of the classical definition of coordination number (number of anions in contact with a cation) it considers the lengths of the bonds (Hoppe 

For a cation X establishing R(X)i bonds with equal anions, ECoN is defined as [Nespolo et al. (1999a) on the basis of Hoppe et al. (1989)]  

R X)av represents a weighted average bond distance for the coordination polyhedron around the cation Xand is defined as 

R X)min being the shortest R X)i distance (the exponent 6 is valid when the anion is O ). The sum over i is in principle extended to all the oxygen atoms practically, however, note that the contribution falls to zero as R X)i exceeds R(X)av [Eqn. (1)] or R(X)min [Eqn. 

A correlation between ECoN calculated for the interlayer cation / and the ditrigonal rotation a can intuitively be expected from the discussion of this section. Such correlation has been investigated by Weiss et al. (1992) and found to be quite regular (Fig. 16). In fact, ECoN for / smoothly decreases from about 12 (null ditrigonal rotation) to 6 (for a ditrigonal rotation higher than about 16° ). 

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Higashi S (1982) Tobelite, a new ammonium dioctahedral mica. Mineral J 11 138-146 Hirschmaim M, Evans BV, Yang H (1994) Composition and temperature dependence of Fe-Mg ordering in cummingtonite-granerite as determined by X-ray diffraction. Am Mineral 79 862-877 Hoppe R (1979) Effective coordination numbers (ECON) and mean fictive ionic radii (MEFIR). Z Kristallogr 150 23-52... 

Quantitative phase analysis, agreement factors and refinement details, unit cell parameters, mean metal-oxygen bond distances and interatomic angles, and the effective coordination number (ECoN) at cubic site of orthogallate perovskites are listed in Tables 12.2 and 12.3. 

Figure 16. Correlation between ECoN (effective coordination number) of the interlayer cation I and the di-trigonal rotation a in micas. [Modified after Weiss et al. (1992)].

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