Solution

ID: past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2022/1/a/i/solution

The ordered crystal structure consists of a primitive cubic lattice with the four-site atomic basis
in fractional crystal coordinates. The drawing shows all boundary representatives of these sites. Eight corner gold chemical atoms, shared among eight unit cells each, contribute one gold chemical atom. Six face-centred copper chemical atoms, shared between two unit cells each, contribute three copper chemical atoms. Thus
which gives the required stoichiometry. Although the unlabelled positions form a face-centered cubic lattice, a face-centering lattice translation exchanges gold and copper and therefore fails to preserve the ordered crystal structure. Its Bravais lattice is primitive cubic lattice.
Figure 1.
Ordered copper–gold unit cell with corner and face-site counting
. Details.

New to topics? Read the docs here!