= Solution
In the conventional cubic <unit cell>, the four <face-centered cubic lattice> positions contribute
$$
S_{\rm FCC}=1+e^{i\pi(k+l)}+e^{i\pi(h+l)}+e^{i\pi(h+k)}.
$$
The two-atom <atomic basis of a crystal> gives the <zinc blende structure factor>
$$
\boxed{F_{hkl}=S_{\rm FCC}\left[f_{\rm Ga}+f_{\rm As}e^{i\pi(h+k+l)/2}\right].}
$$
Mixed-parity <Miller indices> have $S_{\rm FCC}=0$. With all indices even or all odd, $S_{\rm FCC}=4$. For real <atomic scattering factors>,
$$
|F_{hkl}|^2=16\begin{cases}
f_{\rm Ga}^2+f_{\rm As}^2,&h,k,l\text{ all odd},\\
(f_{\rm Ga}+f_{\rm As})^2,&h,k,l\text{ all even},\ h+k+l=0\pmod4,\\
(f_{\rm Ga}-f_{\rm As})^2,&h,k,l\text{ all even},\ h+k+l=2\pmod4.
\end{cases}
$$
Hence \b[all same-parity reflections are generally permitted in GaAs], although the last class is weak when the two <atomic scattering factors> nearly coincide. These are the structural selection rules; a particular experiment must also satisfy the <elastic Bragg scattering condition>.
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