Q.A cubic solid is made of two elements P and Q. Atoms of Q are at the corners of the cube and P at the body-centre. What is the formula of the compound? What are the coordination numbers of P and Q?

The chemical formula of an ionic solid can be deduced from which voids the ions occupy in a close-packed arrangement.

Counting rule — if there are $N$ close-packed particles:

• Octahedral voids $= N$
• Tetrahedral voids $= 2N$

So the formula depends on the fraction of voids filled. Worked examples:

• Anions form ccp and cations fill all octahedral voids ⇒ ratio $1:1$ ⇒ AB (e.g. NaCl).
• Cations fill all tetrahedral voids ⇒ ratio $1:2$... but if they fill half the tetrahedral voids ⇒ $1:1$ (ZnS). …