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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,Conservation of the total composition removes the alloy sublattice order parameter from this amplitude. For the reflection with mixed integer parity,The coherent powder diffraction wave intensities consequently satisfyHere 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.

Specify the normalization of the alloy sublattice order parameter rather than assuming that its endpoint values uniquely define it. Let $p_c$ be the probability of gold occupation at a corner site and defineThe complementary copper probability is $3(1-\rho )/4$, so the corner-site atomic scattering factor isThe stoichiometry provides one gold chemical atom per four-site unit cell. If all three face sublattices are equivalent, their gold occupation probability $p_f$ obeys $p_c+3p_f=1$. ThereforeAt $\rho =1$ the corner and face sites carry pure gold and pure copper; at $\rho =0$ they have identical statistical compositions. These formulas describe the branch with $0\le \rho \le 1$ and equivalent face-site averages.