= Solution
{c}
The ordered <crystal structure> consists of a <primitive cubic lattice> with the four-site <atomic basis>
$$
\mathrm{Au}:(0,0,0),\qquad
\mathrm{Cu}:\left(0,\frac12,\frac12\right),\left(\frac12,0,\frac12\right),\left(\frac12,\frac12,0\right),
$$
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
$$
\boxed{N_{\rm Au}=8\times\frac18=1,\qquad N_{\rm Cu}=6\times\frac12=3,}
$$
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>.
\Image[/past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2022-ordered-alloy-unit-cell.png]
{title=Ordered copper–gold unit cell with corner and face-site counting}
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