Question

What is the significance of the radius ratio in determining the structural arrangement and coordination number of an ionic solid?

Answer 1

1. The radius of tetrahedral voids plays an important role in predicting the structural arrangement and coordination number of ionic solids.
2. In close-packed structures, anions usually form the packing and cations occupy the voids (interstitial spaces). Whether a cation occupies a tetrahedral or octahedral void depends on its size in comparison to the size of the anion.
3. If the radius of the cation (r₊) is equal to or smaller than 0.225 times the radius of the anion (r₋), it can fit into a tetrahedral void without disturbing the structure. This results in a coordination number of 4, meaning the cation is surrounded by four anions in a tetrahedral geometry.
4. On the other hand, if the radius ratio `r_+/r_-` is larger (between 0.414 to 0.732), the cation occupies an octahedral void, leading to a coordination number of 6.
5. Thus, the radius of the tetrahedral void (approximately 0.225 R) helps determine:
   1. Which void (tetrahedral or octahedral) the cation will occupy.
   2. The coordination number of the cation.
   3. The resulting crystal structure (e.g., ZnS has cations in tetrahedral voids, and NaCl has cations in octahedral voids).