= Solution
{c}
Use the same <atomic basis> phases as in the ordered <structure factor>, replacing each <atomic scattering factor> by its site average. For the reflection with equal <integer parity>,
$$
S_{111}=\langle f_c\rangle+3\langle f_f\rangle=f_{\rm Au}+3f_{\rm Cu}.
$$
Conservation of the total composition removes the <alloy sublattice order parameter> from this amplitude. For the reflection with mixed <integer parity>,
$$
S_{110}=\langle f_c\rangle-\langle f_f\rangle=\rho(f_{\rm Au}-f_{\rm Cu}).
$$
The coherent <powder diffraction> <wave intensities> consequently satisfy
$$
\boxed{I_{111}(\rho)=I_{111}(1),\qquad I_{110}(\rho)=\rho^2 I_{110}(1).}
$$
Here the <lattice constant>, <atomic scattering factors>, <powder diffraction multiplicities>, and omitted experimental factors are held fixed. The ratio of a <superlattice reflection> to a fundamental reflection can therefore measure the magnitude of the <alloy sublattice order parameter>.
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