 Alloy sublattice order parameter

For a stoichiometric $A_{3}B$ alloy with one corner sublattice and three equivalent face sublattices, let $p_c$ and $p_f$ be the respective occupation probabilities of species $B$. Define $\rho =(4p_c-1)/3$. Conservation of composition, $p_c+3p_f=1$, gives $p_c=(1+3\rho )/4$ and $p_f=(1-\rho )/4$. Thus the random alloy has $\rho =0$ and the fully ordered corner-$B$ pattern has $\rho =1$. The coherent superlattice reflection amplitude is $\rho (f_B-f_A)$, so its wave intensity scales as ${\rho }^2$, while the equal-parity fundamental amplitude $f_B+3f_A$ is composition-fixed. The definition assumes equivalent face sublattices; endpoint normalization alone does not uniquely specify an arbitrary order coordinate.