Quantitative Phase Analysis Using the Whole-Powder-Pattern Decomposition Method: II. Solution Using External Standard Materials

Abstract A new procedure for the quantitative phase analysis using the whole–powder–pattern decomposition method has been proposed (Toraya and Tsusaka, 1995). The procedure is based on the determination of the scale factor for the profile intensity of each phase in a mixture, which is identical to the ratio of integrated intensity in a mixture to that of the corresponding reflection in a single component sample. Weight fractious were obtained by solving the simultaneous equations, of which coefficients include the scale factors and the mass absorption coefficients. In a previous study, the mass absorption coefficients were calculated from chemical compositions and u,/p data of respective phases. In the present study, an alternative way of deriving the weight fraction without using the knowledge of chemical composition is proposed.

Download Full-text

Estimation of statistical uncertainties in quantitative phase analysis using the Rietveld method and the whole-powder-pattern decomposition method

Journal of Applied Crystallography ◽

10.1107/s0021889800010402 ◽

2000 ◽

Vol 33 (6) ◽

pp. 1324-1328 ◽

Cited By ~ 33

Author(s):

H. Toraya

Keyword(s):

Phase Analysis ◽

Decomposition Method ◽

Goodness Of Fit ◽

Rietveld Method ◽

Weight Fraction ◽

Relative Magnitude ◽

Powder Pattern ◽

Quantitative Phase Analysis ◽

Quantitative Phase ◽

Pattern Decomposition

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.

Download Full-text

Quantitative phase analysis of natural products using whole-powder-pattern decomposition

Powder Diffraction ◽

10.1017/s0885715600010885 ◽

2000 ◽

Vol 15 (2) ◽

pp. 86-90 ◽

Cited By ~ 1

Author(s):

Shigeo Hayashi ◽

Hideo Toraya

Keyword(s):

Natural Products ◽

Phase Analysis ◽

Raw Materials ◽

Fluorescence Analysis ◽

Weight Percent ◽

Powder Pattern ◽

Quantitative Phase Analysis ◽

X Ray ◽

Quantitative Phase ◽

Pattern Decomposition

The capability of whole-powder-pattern decomposition in the quantitative phase analysis (QPA) of natural products was investigated using three- to six-component mixtures and pottery bodies. Here, the term pottery body means plastic clay suitable for making pottery and it is compounded of ceramic raw materials. Average errors of the weight fractions for each phase were within 1 weight percent in each mixture of natural products. The amounts of reduced oxides in pottery bodies derived from the X-ray diffraction technique were in good agreement with results obtained by X-ray fluorescence analysis. The present procedure does not require knowledge of crystal structures; it appears adequate for the QPA of natural products.

Download Full-text

Three approaches to total quantitative phase analysis of organic mixtures using an external standard

Journal of Applied Crystallography ◽

10.1107/s0021889810053082 ◽

2011 ◽

Vol 44 (1) ◽

pp. 17-24 ◽

Cited By ~ 9

Author(s):

Martin Schreyer ◽

Liangfeng Guo ◽

Martin Tjahjono ◽

Marc Garland

Keyword(s):

Phase Analysis ◽

Rietveld Analysis ◽

Pure Component ◽

Quantitative Phase Analysis ◽

Average Error ◽

Powder Mixtures ◽

Organic Mixture ◽

Organic Mixtures ◽

Quantitative Phase ◽

External Standard

Three different approaches for a total quantitative phase analysis of organic mixture data were presented and subsequently tested on a set of ten ternary powder mixtures consisting of α-glycine, α-lactose monohydrate and paracetamol form I. In each of these methods, an external standard was used (in the present study, diamond) to determine the diffractometer constant, which was employed to place the crystalline intensities of all other samples on an absolute scale. In Method A, pure component diffractograms were also measured. In Methods B and C, no pure component diffractograms were used. Using Methods A–C, both the absolute crystalline compositions and all the amorphous compositions of the samples were determined. These methods outperform the quantitative phase analysis provided by conventional Rietveld analysis. An average error of less than 0.5 wt% was achieved with the present approaches, whereas the average error from conventional Rietveld analysis wasca1.3 wt%.

Download Full-text

Quantitative phase analysis by combining the Rietveld and the whole-pattern decomposition methods

Journal of Applied Crystallography ◽

10.1107/s0021889802008737 ◽

2002 ◽

Vol 35 (4) ◽

pp. 481-490 ◽

Cited By ~ 8

Author(s):

Cinzia Giannini ◽

Antonietta Guagliardi ◽

Roberto Millini

Keyword(s):

Phase Analysis ◽

Structural Model ◽

Structural Information ◽

Complex Structure ◽

Quantitative Phase Analysis ◽

Quantitative Phase ◽

Absolute Scale ◽

Pattern Decomposition ◽

The Absolute ◽

Rietveld Quantitative Phase Analysis

The Rietveld quantitative phase analysis of polycrystalline mixtures is a model-dependent method. The absence of any structural information about even one phase in the mixture prevents the application of the method; on the other hand, the availability of a structural model that is not sufficiently representative of real data can actually reduce the accuracy of the weight-fraction estimates. In these cases, when the experimental pattern of one (or more) pure phase(s) with unknown or imperfectly known crystal structure is available, the whole-pattern decomposition techniques can be applied to extract a list of `observed' amplitudes to be used instead of those calculated from the model. Observed and calculated amplitudes can be successfully combined to carry out the Rietveld quantitative phase analysis of even complex structure mixtures, provided that the initial amplitudes are correctly placed on the absolute scale. In the absence of any structural model, the absolute scale supplied by the Wilson plot technique can be applied. A general scheme of the method is proposed here; it has been implemented into the programQUANTOand tested on real zeolites mixtures. The method is basically independent of the program used for the extraction of the integrated intensities.

Download Full-text