Refinement of scattering factors of atoms and equipoints in crystal structures by least-squares techniques

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Abstract
Least-squares refinement of atomic-scattering factors can be applied not only to physical problems (e.g. electron content or electron-density distribution of atoms) but also to the “analysis” of equipoints in crystal structures. By simple extension of the system of normal equations, “population densities” and “mixing coefficients” of equipoints statistically occupied by one or two kinds of atoms can be investigated. Thus, a number of mineralogical and crystal-chemical problems can be solved. Improved techniques allow the evaluation of (essentially ordered) Si–Al-distributions in framework silicates.