Question

A compound alloy of gold and copper crystallizes in a cubic lattice in which gold occupy the lattice points at corners of the cube and copper atom occupy the centres of each of the cube faces. What is the total number of atoms in a unit cell?

Answer 1

From the given description of the lattice, we can figure that this is $FCC$ (face-centred cubic lattice).
Now as gold occupies the corners, total gold atoms = $\frac{1}{8}\times 8$ corners = $1$ atom.
Secondly, copper occupies the centre of faces and there are $6$ faces.
So, total copper atoms =$\frac{1}{2}\times 6=3$ atoms.
Adding both the number of gold and copper atoms, we get the total number of atoms is $4$.