Question

A compound formed by elements $A$ and $B$ crystallizes in the cubic structure where $A$ atoms are at the corners of a cube and $B$ atoms are at the face-center. What is the formula of the compound?

Answer 1

An atom at the corner of the cube contributes $\frac{1}{8}$ to the unit cell. Hence, number of atoms of $A$ in the unit cell $=8\times \frac{1}{8}=1$.
An atom at the face of the cube contributes $\frac{1}{2}$ to the unit cell.
Hence, number of atoms of $B$ in the unit cell $=6\times \frac{1}{2}=3$.
Thus, the formula is $A{B}_3$.