Module 4 : Solid State Chemistry
Lecture 17 : Closed Packed Structures
  17.3

Critical Radius Ratios:

We have made a passing mention in the earlier section by placing atoms or ions in the voids or holes generated during triangular, tetrahedral, octahedral or cubic as shown in Fig 17.6. We shall now calculate the critical radius ratios (i.e., the ratio of the radius of the largest sphere that can be fitted in the holes to the radius of the spheres that have generated the hole) for the various coordinations that are possible.

The case of triangular coordination is shown in Fig 17.6(a)
             


        
 
 
Figure 17.6 (a) Triangular Coordination , b) Tetrahedral coordination and c) Cubic coordination.