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Assessment of quality of trace element measurements by EDXRF technique: a statistical approach
ARTICLE IN PRESS
Radiation Physics and Chemistry 71 (2004) 791–792
Assessment of quality of trace element measurements by EDXRF technique: a statistical approach N.O. Hashima,*, I.V.S. Rathorea, A.M. Kinyuab, R.L. Stangla, A.O. Mustaphac a Department of Physics, Kenyatta University, P.O. Box 43844 Nairobi, Kenya Institute of Nuclear Science, University of Nairobi, P.O. Box 30197, Nairobi, Kenya c Department of Physics, University of Nairobi, Kenya, P.O. Box 30197, Nairobi, Kenya b
1. Introduction Sample preparation and matrix effects are some of the factors which contribute to variations in analytical data. In this work quality of trace element measurements was investigated using mean and median elemental concentration values, coefficients of skewness, kurtosis and analysis of variance (ANOVA) for the sources of uncertainty in the measurements.
analyte element i (Criss and Birks, 1968); 1 eðardÞ Ii ¼ G0 ki ri d ; ðardÞ
ð1Þ
where the term in parenthesis is the absorption correction factor, G0 is a geometrical factor, ki is elemental constant and a is the absorption coefficient. The X-ray spectral data fitting and analyses were performed using the IAEA-QXAS (Quantitative X-ray System) software (IAEA, 1995).
2. Methodology 2.1. The EDXRF spectrometer The EDXRF analysis system consists of a radioisotope excitation source, 109Cd (10 mCi), a Si(Li) detector (EG&G Ortec, 30 mm2 10 mm sensitive volume, 25 mm Be window) and the associated electronics (Kinyua, 1982). The energy resolution of the detector is 180 eV at 5.9 keV Mn Ka line. The spectral data for analysis were collected using PC-based multi-channel analyser (Canberra S100 MCA). The acquisition time for spectral data was 1000 s. The detection limits and analysis of IAEA—Soil 7 standard are described elsewhere (Hashim, 2001). 2.2. Trace element measurements
2.3. Statistical design of the measurements Ten sub-samples of sediment and plant samples from the coast of Kenya (Hashim, 2001) were prepared for analysis. Each of the sub-samples was analysed 10 times in a randomised complete block design (Hines and Montgomery, 1980). The asymmetry of the distribution is measured from the coefficient of skewness s defined as: n X n xi x% 3 s¼ ð2Þ ðn 1Þðn 2Þ i¼1 s while the relative peakedness is evaluated by the coefficient of kurtosis, k, defined as: ( ) n X nðn 1Þ xix% 4 k¼ ðn 1Þðn 2Þðn 3Þ i¼1 s
The elemental concentrations were evaluated using the equation for the fluorescence intensity Ii of the *Corresponding author. Fachbereich 7 - Physik, Universita¨t Siegen, Emmy-Noether-Campus, Walter-Flex-Str. 3, D-57068, Siegen, Germany. E-mail address: [email protected] (N.O. Hashim).
3ðn 1Þ2 ; ðn 2Þðn 3Þ
ð3Þ
where the terms have their usual meanings. The sources of variation are evaluated by the ANOVA based on a linear statistical model (Hines and Montgomery, 1980): xi;j ¼ x% þ Zi þ dj þ ei;j ;
0969-806X/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2004.04.094
ð4Þ
ARTICLE IN PRESS N.O. Hashim et al. / Radiation Physics and Chemistry 71 (2004) 791–792
792 12
Sources of variation Sediments Plant
8
(a) Sediments Spectrometer Sample
100
6
F-Statistic
(Mean - Median) / Median %
10
4 2 0 -2
Control value (Fc)
(b) Plants
Fc = 1.99
Spectrometer Sample
10
2
-4
1
-6 Cl
-8
K
Ca
Ti
Mn
Fe
Cu
Zn
Pb
Br
Sr
Zr
Element
-10 Cl
K Ca Ti Mn Fe Cu Zn Pb Br Sr
Zr
Fig. 2. Summarised ANOVA results.
Element analysed Fig. 1. Dispersion of mean from median values of elemental concentrations.
where x is an overall mean, Zi is the uncertainty contribution from the ith measurement (the effect of repeat measurements), dj is the uncertainty contribution from the jth sample (the effect of the sample preparation), and ei;j is the random error term.
3. Results, discussion and conclusion The range of elemental concentration levels measured in the samples is described elsewhere (Hashim, 2001). The percentage difference between the mean and the median values was within 10% of the median elemental concentration values for most elements analysed as shown in Fig. 1. At the 5% confidence level, for normal distribution of the elements analysed, the coefficients of skewness and kurtosis were within the limits of 0.389 to +0.389 and 0.49 to +0.59, respectively (Taylor, 1990), with the exception of Ca, Fe, Zn, Pb and Br. This could be due to specimen inhomogeneity during preparation, X-ray line interference between the K-Kb and the Ca-Ka lines for the case of Ca, or due to inefficient charge collection and spectral data deconvolution during the analyses. Sample preparation is shown to be a statistically significant source of variation, particularly for the measurements of plant samples (Fig. 2). This is an indicator of inadequate homogeneity of the plant samples. Inhomogeneity of the plant samples is mainly due to their complex organic structure. Improvement of the homogeneity of the plant material can be achieved
by adding liquid nitrogen to the pestle and mortar so as to make the material brittle and easier to grind.
Acknowledgements The authors thank Kenyatta University and University of Nairobi for the research grant and laboratory facilities, Kenya Belgian Project in Marine Science, Kenya Marine and Fisheries Research Institute and Moi University School of Environmental Science for facilitating sample collection.
References Criss, J.W., Birks, L.S., 1968. Calculation methods fluorescent X-ray spectrometry. Anal. Chem. 40, 1080–1086. Hashim, N.O., 2001. The levels of radionuclides and trace elements in selected Kenyan coastal ecosystems. M.Sc.(Physics) Thesis, Kenyatta University, Nairobi, Kenya. Hines, W.W., Montgomery, D.C., 1980. Probability and Statistics in Engineering and Management Science, 2nd Edition. Wiley, New York, USA, 634pp. IAEA, 1995. Quantitative X-ray analysis system (QXAS). Distributed by the International Atomic Energy Agency, IAEA, Vienna, Austria. Kinyua, A.M., 1982. Multi-element analysis of solid and liquid samples by X-ray Fluorescence Analysis (XRFA). M.Sc.(Physics) Thesis, University of Nairobi, Nairobi, Kenya. Taylor, J.K., 1990. Statistical Techniques for Data Analysis. Lewis Publications, FL, USA, 200pp.
Radiation Physics and Chemistry 71 (2004) 791–792
Assessment of quality of trace element measurements by EDXRF technique: a statistical approach N.O. Hashima,*, I.V.S. Rathorea, A.M. Kinyuab, R.L. Stangla, A.O. Mustaphac a Department of Physics, Kenyatta University, P.O. Box 43844 Nairobi, Kenya Institute of Nuclear Science, University of Nairobi, P.O. Box 30197, Nairobi, Kenya c Department of Physics, University of Nairobi, Kenya, P.O. Box 30197, Nairobi, Kenya b
1. Introduction Sample preparation and matrix effects are some of the factors which contribute to variations in analytical data. In this work quality of trace element measurements was investigated using mean and median elemental concentration values, coefficients of skewness, kurtosis and analysis of variance (ANOVA) for the sources of uncertainty in the measurements.
analyte element i (Criss and Birks, 1968); 1 eðardÞ Ii ¼ G0 ki ri d ; ðardÞ
ð1Þ
where the term in parenthesis is the absorption correction factor, G0 is a geometrical factor, ki is elemental constant and a is the absorption coefficient. The X-ray spectral data fitting and analyses were performed using the IAEA-QXAS (Quantitative X-ray System) software (IAEA, 1995).
2. Methodology 2.1. The EDXRF spectrometer The EDXRF analysis system consists of a radioisotope excitation source, 109Cd (10 mCi), a Si(Li) detector (EG&G Ortec, 30 mm2 10 mm sensitive volume, 25 mm Be window) and the associated electronics (Kinyua, 1982). The energy resolution of the detector is 180 eV at 5.9 keV Mn Ka line. The spectral data for analysis were collected using PC-based multi-channel analyser (Canberra S100 MCA). The acquisition time for spectral data was 1000 s. The detection limits and analysis of IAEA—Soil 7 standard are described elsewhere (Hashim, 2001). 2.2. Trace element measurements
2.3. Statistical design of the measurements Ten sub-samples of sediment and plant samples from the coast of Kenya (Hashim, 2001) were prepared for analysis. Each of the sub-samples was analysed 10 times in a randomised complete block design (Hines and Montgomery, 1980). The asymmetry of the distribution is measured from the coefficient of skewness s defined as: n X n xi x% 3 s¼ ð2Þ ðn 1Þðn 2Þ i¼1 s while the relative peakedness is evaluated by the coefficient of kurtosis, k, defined as: ( ) n X nðn 1Þ xix% 4 k¼ ðn 1Þðn 2Þðn 3Þ i¼1 s
The elemental concentrations were evaluated using the equation for the fluorescence intensity Ii of the *Corresponding author. Fachbereich 7 - Physik, Universita¨t Siegen, Emmy-Noether-Campus, Walter-Flex-Str. 3, D-57068, Siegen, Germany. E-mail address: [email protected] (N.O. Hashim).
3ðn 1Þ2 ; ðn 2Þðn 3Þ
ð3Þ
where the terms have their usual meanings. The sources of variation are evaluated by the ANOVA based on a linear statistical model (Hines and Montgomery, 1980): xi;j ¼ x% þ Zi þ dj þ ei;j ;
0969-806X/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2004.04.094
ð4Þ
ARTICLE IN PRESS N.O. Hashim et al. / Radiation Physics and Chemistry 71 (2004) 791–792
792 12
Sources of variation Sediments Plant
8
(a) Sediments Spectrometer Sample
100
6
F-Statistic
(Mean - Median) / Median %
10
4 2 0 -2
Control value (Fc)
(b) Plants
Fc = 1.99
Spectrometer Sample
10
2
-4
1
-6 Cl
-8
K
Ca
Ti
Mn
Fe
Cu
Zn
Pb
Br
Sr
Zr
Element
-10 Cl
K Ca Ti Mn Fe Cu Zn Pb Br Sr
Zr
Fig. 2. Summarised ANOVA results.
Element analysed Fig. 1. Dispersion of mean from median values of elemental concentrations.
where x is an overall mean, Zi is the uncertainty contribution from the ith measurement (the effect of repeat measurements), dj is the uncertainty contribution from the jth sample (the effect of the sample preparation), and ei;j is the random error term.
3. Results, discussion and conclusion The range of elemental concentration levels measured in the samples is described elsewhere (Hashim, 2001). The percentage difference between the mean and the median values was within 10% of the median elemental concentration values for most elements analysed as shown in Fig. 1. At the 5% confidence level, for normal distribution of the elements analysed, the coefficients of skewness and kurtosis were within the limits of 0.389 to +0.389 and 0.49 to +0.59, respectively (Taylor, 1990), with the exception of Ca, Fe, Zn, Pb and Br. This could be due to specimen inhomogeneity during preparation, X-ray line interference between the K-Kb and the Ca-Ka lines for the case of Ca, or due to inefficient charge collection and spectral data deconvolution during the analyses. Sample preparation is shown to be a statistically significant source of variation, particularly for the measurements of plant samples (Fig. 2). This is an indicator of inadequate homogeneity of the plant samples. Inhomogeneity of the plant samples is mainly due to their complex organic structure. Improvement of the homogeneity of the plant material can be achieved
by adding liquid nitrogen to the pestle and mortar so as to make the material brittle and easier to grind.
Acknowledgements The authors thank Kenyatta University and University of Nairobi for the research grant and laboratory facilities, Kenya Belgian Project in Marine Science, Kenya Marine and Fisheries Research Institute and Moi University School of Environmental Science for facilitating sample collection.
References Criss, J.W., Birks, L.S., 1968. Calculation methods fluorescent X-ray spectrometry. Anal. Chem. 40, 1080–1086. Hashim, N.O., 2001. The levels of radionuclides and trace elements in selected Kenyan coastal ecosystems. M.Sc.(Physics) Thesis, Kenyatta University, Nairobi, Kenya. Hines, W.W., Montgomery, D.C., 1980. Probability and Statistics in Engineering and Management Science, 2nd Edition. Wiley, New York, USA, 634pp. IAEA, 1995. Quantitative X-ray analysis system (QXAS). Distributed by the International Atomic Energy Agency, IAEA, Vienna, Austria. Kinyua, A.M., 1982. Multi-element analysis of solid and liquid samples by X-ray Fluorescence Analysis (XRFA). M.Sc.(Physics) Thesis, University of Nairobi, Nairobi, Kenya. Taylor, J.K., 1990. Statistical Techniques for Data Analysis. Lewis Publications, FL, USA, 200pp.