Limiting radius ratio

This then is the limiting radius ratio for six nearest neighbours— when the anion is said to have a co-ordination number of 6. Similar calculations give the following limiting values ... 

TABLE 1.10 Limiting radius ratios for different coordination numbers... 

Coordination number Geometry Limiting radius ratio 0.225 Possible structures... 

This example was chosen to show that the radius ratio structure predictions work quite well except near the limiting radius ratio values. Here, r+ /r is borderline for MgS, and we predicted the wrong structure. This is not surprising, since the concept of fixed ionic radii is not well founded. 

Ion Radius Ratio Coordination Predicted from Ratio Observed Coordination Number Theoretical Limiting Radius Ratios... 

Table 2.1. Limiting Radius Ratios for Coordination Numbers Commonly Found in Minerals...

Coordination Number Geometry Limiting Radius Ratio... 

Limiting Radius Ratios fob Various Coordination Polyhedra... 

A comparison of the limiting radius-ratio values given in Table I with the radius ratios of alkali halides in Table II shows that the observed structures are not always as predicted. According to the simple theory, the roeksalt structure should be stable only within the range 0.414 rM/rx 0.732. Thus LiCl (0.33), LiBr (0.31), and Lil (0.28) should have tetra-hedrally coordinated structures, while KF (0.98), RbF (1.09), and CsF (1.24) should have eight or twelve coordinated structures. These disagreements are perhaps not surprising in view of the crudeness of the approximations involved, but more realistic models do not lead immediately to an explanation of the persistence of the roeksalt structure not only in the alkali... 

Table 2 Limiting Radius Ratios, Cation Coordination Numbers, and Ionic Arrangements in Ionic Solids...

FIGURE 5.7 Geometric method for calculating limiting radius ratios. 

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