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PRECISION AND ACCURACY
IN XRF, TXRF AND SRXRF
P.S. Hoffmann
Darmstadt Technical University, Materials and Earth
Sciences, Chemical Analytics,
Petersenstr. 23, D-64287 Darmstadt, Germany dg7j hrzpub.tu-darmstadt.de
Each analytical result has to be
characterized by an uncertainty. This uncertainty (or error of the
result) has to be distinguished into “random errors“ and into
“systematic errors“ (1). To determine a random error usually the
arithmetic or geometrical mean of the results of repeated measurements
is used for calculation of the “relative standard deviation (RSD)“.
This RSD (or the multiple) is a measure for the width of the scatter of
all data produced at identical conditions and therefore for the
precision (repeatability) of the result. The determination of the
systematic error and of the accuracy (difference to the true value) will
be performed by very different methods:
Use of two, or better more different, independant
analytical methods,
Use of Certified Reference Materials as test
samples,
Spiking of samples with analytes,
Participation in round robins,
Use of control charts and duplicate plots, use of
Identity Line plots.
For the X-ray methods in
discussion all these methods can be used. But in practice not all can be
recommended. The reason for the selection of the method of quality
assurance (QA) is in this case mainly dominated by the advantage of
X-ray fluorescence analysis (XRF) of non-destructive characterization of
solid material. For comparison of results for different samples
absorption and scattering effects (matrix effects) and enhancement
effects (secondary excitation) have to be considered. The method of
quantification and of QA to be used in XRF is in practice a function
only of the sample thickness: infinitely thick specimen,
intermediate-thick samples, and practically infinitely thin samples (2).
In XRF-methods the laboratory
standards, the certified standards and the samples for examination need
not only a similar chemical composition but additionally similar
physical properties (e.g., particle size distribution). For infinitely
thick samples the total matrix effect can be compensated by application
of the Compton scatter intensity, by internal standardization, standard
addition, dilution methods, and can be calculated by mathematical
methods (fundamental parameter, influence coefficient algorithms,
algorithms with constant coefficients, algorithms with variable
coefficients, specimen with more than two compounds, algorithms with
empirical coefficients). For intermediate-thick samples the Compton and
the Rayleigh scattering intensities ratio is a measure for the total
mass absorption coefficient. Additionally, the particle effect has to be
considered in intermediate-thick and thin specimen. Infinitely thin
samples can be analysed quantitatively by internal standardization, as
matrix effects and secondary excitation do not play any role.
References:
(1) Wenclawiak B.W., Koch M., Hadjicostas E. (Eds.)
Quality Assurance in Analytical Chemistry, Springer-Verlag, Berlin, 2004
(2) Van Grieken R.E., Markowicz A.A. (Eds.) Handbook
of X-Ray Spectrometry, Marcel Dekker, New York – Basel, 2002
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