F_N: A criterion for rating powder diffraction patterns and evaluating the reliability of powder-pattern indexing

At present, over 30 000 powder diffraction patterns are available as references. It is proposed that the patterns on file as well as new patterns submitted for publication be assigned quantitative quality factors. A simple-to-use figure of merit, F_N, covering both accuracy in the measurement of the positions of the diffraction lines and completeness of the pattern, has been derived: F_N = (1/||) (N/N_poss), where N_poss is the number of independent diffraction lines possible up to the Nth observed line and || is the average absolute discrepancy between observed and calculated 2θ values. This figure of merit provides a rapid evaluation of powder patterns, in much the same way as the R factor provides a rating for single-crystal structure determinations. This figure of merit also provides a means to assess the reliability of a unit derived solely from powder data. At present F_N ranking scheme is shown to be superior to de Wolff's M₂₀ for ranking patterns. It is recommended that use of the latter be discontinued for that purpose. Guidelines are given on the use and implementation of the F_N rating of powder diffraction patterns.