Abstract
A method is described to search for the most probable assignment of indices to powder diffractograms starting from approximate unit-cell parameters. The difference ΔQi = ΔQoi−ΔQci between observed and calculated quadratic forms of the ith peak is attributed to three contributions: ΔQi* due to imprecise unit-cell constants, ΔQi′ due to incorrect indexing and ∊i due to experimental error. The points ΔQi plotted as a function of ΔQoi give rise to distributions D′, D* (or under special conditions Dg*) and D∊. The differences between these distributions are evinced by differences in their moments and probability function. At the start the nearly normal distribution Dg* is searched for, by changing the initial reciprocal-cell parameters by small increments δa*, δb*, δc*. Highly probable indices can then be assigned to the Qoi's and the unit-cell constants refined by the least-squares method. At the end the normal distribution D∊ with mean μ = 0 must be obtained. Statistically significant deviations of D∊ from the normal distribution with μ = 0 indicate that some systematic experimental errors affect the data. The method is suitable for applications to electronic computers and is particularly recommended for plotters.
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