Occupational diffuse scattering

Static fluctuations in which chemical element occupies a site produce scattering beyond coherent Bragg diffraction from the mean crystal structure. For independent binary occupations with probabilities $p$ and $1-p$, the variance of the site's atomic scattering factor is $p(1-p)|f_A-f_B{|}^2$. Writing each site amplitude as its mean plus a zero-mean fluctuation shows that the mean squared total amplitude is the coherent contribution plus a term proportional to the number of sites and this variance. Consequently a forbidden reflection of the average crystal structure can still sit on a diffuse background. Correlated occupations add nontrivial scattering vector dependence.