Tóm tắt
Formulae for estimating statistical uncertainties in quantitative phase analysis using the Rietveld method and the whole-powder-pattern decomposition method have been derived. The relative magnitude of statistical uncertainty for a derived weight fraction of a component in a mixture is given by σ(Wm)/Wm= (1/Wm− 1)1/2F(D\textstyle\sum_{i = 1}^NYoi)−1/2, whereWmis the weight fraction of themth component,Fis the goodness-of-fit index,D(≤1) is a factor depending on the degree of peak overlap, and ∑Yoiis the total sum of profile intensities in the 2θ range used for whole-powder-pattern fitting. If the step width Δ2θ in step scanning is halved, ∑Yoiis almost doubled; on the other hand, ∑Yoiis proportional to the fixed counting timeT. Therefore, σ(Wm)/Wm∝ (Δ2θ/T)1/2. Extension of the 2θ range for whole-powder-pattern fitting towards the high-angle region is not effective for improving the precision of the derived weight fractions if the profile intensities in that region are weak. The formulae provide guidelines for optimizing experimental parameters in order to obtain a required precision.
