Luzzati Plot

Luzzati (1952) derived a formula, which determines the R-factor as a function of (Ar), the average radial error of the atomic position. His analysis shows that the R-factor is a linear function of S = 2 sin 8/X and (Ar) for a substantial range of S(Ar), with

The theoretical Luzzati plots of the R-factor are nearly linear for small-to-medium S. If one plots the R-factor as a function of S, it is possible to determine the actual average radial error (Ar) by comparing the curve with the theoretical curves given in Eq. (7.45). The determination of (Ar) by a Luzzati plot has been common in the past. However, as Luzzati plots are very different from other statistical estimates of error, they have been criticized (see Cruickshank, 2001), and the use of other estimates derived by a more suitable statistical analysis has been recommended.

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