 Solution

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 factorChanging the phase convention complex-conjugates the structure factor and leaves the diffraction wave intensity unchanged. Since the Miller indices are integers,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. ConsequentlyThe corresponding structure factors are $f_{\mathrm{Au}}+3f_{\mathrm{Cu}}$ and $f_{\mathrm{Au}}-f_{\mathrm{Cu}}$. Reflections with mixed integer parity are superlattice reflections that reveal chemical ordering in alloys.