A modification of the de Wolff figure of merit for reliability of powder pattern indexing

An accurate expression of the de Wolff figure of merit has been derived from statistical analysis as M′_n = Σ^N_{k = 1}[(Q_(k) − Q_(k−1))²/4]/Q_(N)n, where Q_(k), is the Q value of the kth distinct calculated line and _n, is the average of the actual discrepancies expressed in Q values between the observed lines and the calculated lines up to the last Nth line which is nearest the last nth observed line. This expression more appropriately reflects the reliability of indexing a given powder pattern, and thus the correctness of the original expression of the figure is estimated by this expression. To simplify the calculation, an alternative approximate expression for the figure of merit, M*_n = S/V^2/3_n, is derived from a suggested relationship between the volume of the unit cell, V, and the d values, where S is a symmetry factor. This expression is recommended as an intermediate testing criterion to limit the size of the solution field in the semi-exhaustive trial-and-error computer indexing. A number of examples of indexing are discussed to support the above comments.