Coordination number cation

The physical and chemical properties of silicate glasses depend on the composition of the material, ion size, and cation coordination number (9). A melt or glass having a Si02/Na20 ratio of 1, ie, sodium metasiUcate [1344-09-8] is expected to possess a high proportion of (SiO ) chains. At a ratio of 2, sheets might predominate. However, litde direct evidence has been shown for a clear predominance of any of these stmctures. The potential stmctures of sihcate melts of different ratios are discussed in detail elsewhere (10—12). 

In an ionic solid, the coordination number means the number of ions of opposite charge immediately surrounding a specific ion. In the rock-salt structure, the coordination numbers of the cations and the anions are both 6, and the structure overall is described as having (6,6)-coordination. In this notation, the first number is the cation coordination number and the second is that of the anion. The rock-salt structure is found for a number of other minerals having ions of the same charge number, including KBr, Rbl, MgO, CaO, and AgCl. It is common whenever the cations and anions have very different radii, in which case the smaller cations can fit into the octahedral holes in a face-centered cubic array of anions. The radius ratio, p (rho), which is defined as... 

Table 3.1 Range of Radius Ratio Values for Various Cationic Coordination Numbers... 

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. 

Brown, I. D. (1988). What factors determine cation coordination numbers Acta Crystallogr. Sect. B 44, 545-553. 

The cation coordination number is determined by the rjr ratio, which implies that the larger the cation radius, the larger is its coordination number. Many examples can be given to show that this assumption is wrong. In MgAl204 (spinel), it is the larger Mg that has tetrahedral coordination and the smaller AP octahedral coordination. 

C = anion charge, z = cation charge, v = cation coordination number, 5 = (Pauling) bond strength.]... 

Cation coordination numbers using Rule 4.1 as a criterion have been determined for some 14000 cation environments (Brown 1988a). Some cations, such as are known with only one coordination number (4 in this case), but others, such as Cs+, can be found with every coordination number between 3 and 12. Whatever the total range, the frequency distribution of the coordination number for a given cation usually peaks close to the average. It is therefore convenient to take the average observed coordination number as a characteristic chemical property of the cation. 

This result can be used to see whether an assumed cation coordination number leads to an acceptable anion coordination number. For example, if A1... 

Rule 11.3 (Corollary 2). Compounds that have a high anion content will stabilize high cation coordination numbers. 

Fig. 13.1. The lattice parameter of a perovskite layer as a function of its cation coordination number. Cations in the BO2 layers are shown on the left, those in the AO layers are shown on the right.

Crystal Type Cation Coordination Number Anion Coordination Number Examples... 

This rule was regarded by Bragg (1930) as a corollary of Rule 1 (which limits variation in cation coordination number) and Rule 2 (which when combined with Rule 1 limits the number and type of cations around each anion). It is not clear that this rule can be elucidated using any particular... 

Coordination of ionic solid Represented as (cation coordination number, anion... 

Radius Ratio (rcation/fanion) Arrangement of Anions Around Cations Coordination Number of Central Cation... 

The most important effect of the repulsion between anions is to limit cation coordination numbers. Strongly bonding cations tend to surround themselves with as many ligands as they can fit into their coordination sphere, but the closeness with which two ligands can approach will depend on the valences of the bonds to their common cation, the stronger these bonds, the closer the... 

If the ratio r jr+ exceeds 2.44, then the NaCl structure becomes disfavored, and a structure with cation coordination number 4, for which the critical value of r /r+ is 4.44, may become more favorable. To summarize, in this simple approximation, packing considerations lead us to expect the various structures to have the following ranges of stability in terms of the r jr+... 

McCauley and Newman (1971) and Weiss et al. (1992) related a to the coordination of the interlayer cation. In an ideal structure a = 0° and the interlayer cation is in 12-fold coordination. In non-ideal structures, a values of greater than 0° reduce the interlayer-cation coordination number from 12 to 6. Weiss et al. (1992) determined the coordination number of the interlayer cation using the equation of Hoppe (1979) ... 

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