The validity of approximations made in differential anomalous X-ray scattering

Approximations of weighting-factor functions are used when determining coordination numbers from differential anomalous scattering (DAS) experiments. The accuracy of two single-value approximations for the weighting functions are tested using non-interacting hard-sphere models of systems that have been studied previously with DAS. The first approximation is an average of the weighting-factor function over the experimental wave-vector range. The second is the weighting-function value at the wave vector that is related to a peak position in the corresponding differential radial distribution function (dRDF). It was found that the first approximation introduced up to 10% error into calculated coordination numbers. The second weighting-factor approximation introduced minimal error into the coordination-number calculations and is simple to use. K(n, m) are tabulated for all colour lattice groups n ≤ 20 and all corresponding values of m. The method may be extended to a larger number of subunit types by a simple change to the figure-generating function. (orig.)