= Solution
{c}
For the <reciprocal lattice vector> $\mathbf G_{hkl}=(2\pi/a)(h,k,l)$, sum the <atomic scattering factors> with the <atomic basis> phase factors. Taking the positive phase convention gives the <structure factor>
$$
S_{hkl}=f_{\rm Au}(G_{hkl})+f_{\rm Cu}(G_{hkl})
\left[e^{i\pi(k+l)}+e^{i\pi(h+l)}+e^{i\pi(h+k)}\right].
$$
Changing the phase convention complex-conjugates the <structure factor> and leaves the <diffraction> <wave intensity> unchanged. Since the <Miller indices> are integers,
$$
\alpha_{hkl}=(-1)^{k+l}+(-1)^{h+l}+(-1)^{h+k}.
$$
If all three <Miller indices> have the same <integer parity>, all pairwise sums are even. Otherwise exactly one pairwise sum is even and two are odd. Consequently
$$
\boxed{\alpha_{hkl}=\begin{cases}3,&h,k,l\text{ all even or all odd},\\-1,&\text{mixed parity}.\end{cases}}
$$
The corresponding <structure factors> are $f_{\rm Au}+3f_{\rm Cu}$ and $f_{\rm Au}-f_{\rm Cu}$. Reflections with mixed <integer parity> are <superlattice reflections> that reveal <chemical ordering in alloys>.
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