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The lack of fast convergence sometimes encountered during a least-squares refinement can be attributed to two factors that may be present in addition to the interaction of two or more parameters. One may be caused by the linear approximation of the structure-amplitude function, which actually may have appreciable curvature. This can be eliminated by a damping factor computable from the experimental data. Another possible cause contributing to retarded convergence is related to an“image” atom symmetrical to the real atom with respect to the extreme of the structure-amplitude function. This effect can be eliminated by the selection of data according to a criterion developed in this paper. These approaches should lead to a maximum rate of convergence within a range of 2 πhΔx i   that is nearly as large as the maximum possible range inherent in the basic premises of the technique.

On damping factors and convergence in the least-squares refinement of atomic-position parameters