166 Acta Chim. Slov. 2008, 55, 166–171 Scientific paper Quality Assessment of k0-NAA by Statistical Evaluation of CRM Results Tinkara Bu~ar, Borut Smodi{*, Radojko Ja}imovi} and Zvonka Jeran Odsek za znanosti o okolju, Institut Jo`ef Stefan, Jamova 39, SI-1000 Ljubljana * Corresponding author: E-mail: borut.smodis@ijs.si Received: 06-07-2007 Abstract The k0-based neutron activation analysis (k0-NAA) is an analytical method based on nuclear properties of atoms. Since it is a multi-element technique, correlations among repeated measurement results for different elements can in principle be observed in case of certain systematic errors. For a deeper insight into potential sources of uncertainty and potential systematical errors of the analytical method, a set of measurement results for the Standard Reference Material (SRM) 2782 obtained from the National Institute for Standards and Technology (NIST) was analyzed using standard statistical approach. The measurements results were examined over an extended period of time to obtain reproducibility of the method. Correlations of repeated measurements among several elements, although dispersions are small, were indeed observed, and the origin of the correlations as the potential source of uncertainty is discussed. A comparison of the measurements with the NIST SRM 2782 reference values was made to benchmark the k0–NAA setup at the TRIGA Mark II reactor of the Jo`ef Stefan Institute and proved the overall accuracy of the method. The article is focused on the possible sources of the correlations of the measurement results and not on the uncertainty of the method itself. Keywords: NAA, QA, uncertainty, correlation, reproducibility, reference material. 1. Introduction The k0-NAA is an analytical method primarily intended for simultaneous determination of many elements in a sample. Consequently, it offers comprehensive insight into the sample composition. It is most frequently applied in “instrumental” mode, i.e. by analyzing the sample as it is, without any chemical treatment. In this case, the sample is just irradiated in a neutron flux and measured on a gamma spectrometer; under the given experimental conditions. In this case, the response signal cannot be intensified and the limit of detection cannot be altered. In the simplified model based on the original approach developed by its founders1, the mass fraction of an analy-te (wa) in a sample irradiated by whole spectrum reactor neutrons using the k0 –NAA is calculated by2: (1) where Asp is specific count rate of the analyte (a) and co-irradiated gold monitor (Au), respectively, k0,Au (a) is the K0 factor of the analyte (a) relative to gold, f is thermal-to-epithermal neutron flux ratio, ep is full-en- ergy peak detection efficiency and (2) where Er is the effective resonance energy, Q0 is ratio of the resonance integral and thermal cross-section (Q0 = I0/(70), and a is the epithermal neutron spectrum shape factor. As evident from Eq.1, there are three main sources of uncertainty: (1) specific count rates, depending mostly on amount of the analyte present in the sample, connected with counting statistics of the signal obtained as response to the activation following neutron irradiation, (2) irradiation conditions involving parameters f, a (both experimentally determined) and Q0 (nuclear constant) and (3) detection efficiency including measurement geometry, represented primarily by e . The prevailing uncertainty component in analyses of environmental samples is usually the counting statistics.2 This uncertainty can partly be influenced by carefully selecting irradiation/counting conditions, but generally the sample should be treated as a whole and consequently compromises should be taken if panoramic analysis is in focus in order to extract as much as possible information from the analysis. Bu~ar et al.: Quality Assessment of k0-NAA by Statistical Evaluation of CRM Results Acta Chim. Slov. 2008, 55, 166–171 167 The purpose of this work was an attempt to reveal the latent information about the uncertainty sources other than the unavoidable and already well known ones by statistical analysis of the existing measurements results. The measurements can contain information other than just measurement result and the statistical analysis tools might be effective enough to disclose/reveal it. The statistical analysis was done posteriori, on already existing repetitive measurements of a certified reference material (CRM). For this purpose, the standard reference material of the National Institute of Science and Technology NIST SRM 2782 Industrial Sludge was used, measured within a framework of an international project SOILSAMP (Assessment of uncertainty associated with soil sampling in agricultural, semi-natural, urban and contaminated environment, during the years 2000–2006). The project was coordinated by APAT (Agencia per la protezione dell’ambiente e per servizi tecnici, Italy), involving national and international experts in the field of soil sampling and the analysis, uncertainty quantification and quality assurance3. 2. Experimental About 0.1 g NIST SRM 2782 sample was sealed in a polyethylene ampoule (SPRONK system, Lexmond, The Netherlands). The sample and comparator (Al-0.1% Au IRMM-530 disc of 6 mm diameter and 0.2 mm high) were fixed together in the polyethylene ampoule and irradiated for about 20 hours in the carousel facility of the TRI-GA Mark II reactor at the Jo`ef Stefan Institute (neutron thermal flux about 1.1 × 1012 n cm2 s–1). The flux parameters fand a were determined according to the multi monitor “Cd-ratio” method.4,5 Each irradiated sample was counted two times, after 6 and 14 days cooling time, on one of four calibrated high purity Ge detectors (OR2 and OR4 from ORTEC and CA1 and CA5 from CANBERRA, USA) connected to a multichannel analyzer (CANBERRA Genie 2000 for CA1 detector, ORTEC DSPECPLUS™ for CA5 detector, G&G ORTEC Spectrum Master high-rate MCA for OR2 detector and CANBERRA S100 MCA for OR4 detector). The software HYPERLAB6,7 was used for the peak deconvolution. KAYZERO/SOLCOI®8 was used for the calculation of the effective solid angle and elemental mass fractions. A total of 25 NIST SRM 2782 samples were irradiated and analyzed in the period from February 2004 to April 2005. The element content of the NIST SRM 2782 material is summarized in Table 1, along with our measurements results. A NIST certified value is the value for which NIST has the highest confidence in its accuracy in that all known or suspected sources of bias have been investigated or accounted for by NIST. Reference values are non-certified values that are the best estimate of the true value; however, the values do not meet NIST criteria for certification and are provided with associated uncertainties that may Table 1: Certificate of the NIST SRM 2782 and the values measured in our laboratory. All values are reported as mass fractions on a dry mass basis in [mg kg-1]. Certified value element xref Uref(k = 2) xlab Ulab(k = 2) Ç-score As 166 20 173 12 0.57 Cr 109 6.0 99 9.1 -1.76 Hg 1.10 0.19 1.23 0.20 0.94 Mo 10.07 0.20 10.05 2.29 -0.02 Se 0.44 0.11 0.45 0.17 0.11 Zn 1254 196 1284 90 0.28 Reference value element xref Uref(k = 2) xlab Ulab(k = 2) Ç-score Ag 30.6 4.7 36.9 2.6 2.35 Ba 254 24 248 24 -0.35 Ca 6,700 600 6.753 2344 0.04 Ce 1240 110 1234 88 -0.08 Co 66.3 4.8 65.5 4.6 -0.24 Fe 269.000 7.000 262.466 18414 -0.66 In 238 70 283 20 1.22 K 3.200 100 3.249 1314 0.07 La 58.1 2.4 56.8 4.1 -0.54 Na 13.000 500 13.120 934 0.23 Information value element xref x lab Ulab (k = 2) Au 2.2 2.5 0.2 Eu 0.34 0.33 0.09 Hf 0.77 0.76 0.08 Rb 23 18 4 Sb 2.0 2.0 0.2 Sc 3.4 2.7 0.2 Sm 1.3 1.2 0.1 Ta 0.73 0.68 0.06 Tb 0.48 0.48 0.04 Th 2.4 2.3 0.2 U 8.3 8.1 0.7 Yb 0.74 0.66 0.10 reflect only measurement precision and may not include all sources of uncertainty. For the information values insufficient information is available to adequately assess the uncertainty associated with these values.9 In the Table 1 our results are compared with the NIST assigned values by means of Ç-scores. The definition for C-score is £= !,, \ ,, where u(x) is standard uncer- tainty and results are assumed to be satisfactory if | Ç | < 2 and questionable if 2 < | Ç | < 3. As evident from the Table 1, all our results are satisfactory according to this criterion, except for Ag with a questionable result. The relatively large set of collected data (25 measurements) allowed for the relevant statistical analysis. The set was tested for normal distribution and the dispersion of measurements was examined over time and among diffe- Bu~ar et al.: Quality Assessment of k0-NAA by Statistical Evaluation of CRM Results 168 Acta Chim. Slov. 2008, 55, 166–171 rent detectors. Since measurements were performed over a long period of time, the closeness of the agreement between the results of measurements of the same measurand is represented as reproducibility7. Other conditions besides time of irradiation and measurement were unchanged. For the quantitative expression of the reproducibility in terms of the dispersion characteristics of the results the standard deviation of all measurements over the observed period of time is used. Since mass fractions of many elements in each sample were determined, correlations between different elements were evaluated. 4. Results and Discussion 4. 1. Reproducibility The reproducibility for the determination of each element on each detector was determined and examined in terms of the nominal mass fraction of the element. The changed condition for the reproducibility is a relatively long period of time for the successive measurements. Fig.1 shows no considerable reproducibility dependence on the mass fraction. For most of the measurement results the reproducibility standard deviation is less than 10%, for some of them up to 15% and only four of them more than 20% (Se up to 45%, K up to 40%, Hg up to 25%, Rb around 20%, and Ca up to 22%). The higher measurement reproducibility standard deviations are due to measurements of the mass fractions close to the detection limit for that elements under given irradiation and measurement conditions. Consequently, the specific count rates for that elements were low and the related counting statistics, contributing the most to overall measurement uncertainty, relatively poor. 4. 2. Accuracy Measured mass fractions of the elements in the sample are compared with reference values from the certificate (Table 1) in Fig.2. Dashed error bars of reference values in Fig.2 represent 95% confidence intervals for uncertainty stated in the certificate. Solid error bars for measurement values represent the combined uncertainty of the weighted averages of the measurements with coverage factor 2. For most of the elements having stated certified and reference mass fractions, the measured values agree with the mass fractions reported in the certificate and accuracy of the method used is satisfactory. The comparison confirmed the reliability of the k0–NAA measurement results obtained during the SOILSAMP project and of the method itself. The results are questionable only for Ag (Table 1), whose mass fraction determined is about 20% higher than the reference value. The reason for the deviation is for the time being unknown. However, it should be noted that the Ag value is not a certified value and does therefore not meet NIST criteria for certification. The relatively high ?-score (1.76) is also for Cr (Table 1), where the determined mass fraction is about 10% lower than the reference value, although the value for ?-score is satisfactory. The reason for the lower chromium value can be attributed to two sources; (1) erroneous blank correction and (2) erroneous correction for an interfering nuclear reaction. The samples were measured in the irradiated polyethylene vials. It was found that the vials contain some chromium. Although this blank value was corrected for, it might have happened that the correction was not appropriate, since it was based on another experiment. It is estimated that an erroneous correction might have contributed up to 3% of the total Cr content. Furtheremo-re, chromium was determined via the 50Cr (n, ?) 51Cr reac- Figure 1: Reproducibility of measured mass fractions for different elements in dependence of mass fraction. The relative standard deviation of all measurements of mass fraction for certain element on one detector is plotted as a single point. Four vertical points correspond to four relative standard deviations for the same element, measured on four different detectors. Bu~ar et al.: Quality Assessment of k0-NAA by Statistical Evaluation of CRM Results Acta Chim. Slov. 2008, 55, 166–171 169 Figure 2: Measured mass fractions normalized on certified, reference or information values for different elements, compared with the certified, reference or information value of mass fraction as stated in certificate. Uncertainties of certificate values (k = 2) are presented with dashed error bars and uncertainties of measurement averages (k = 2) with solid error bars. tion that might be interfered by the 54Fe (n, a) 51Cr reaction. Due to the very high Fe content in this particular sample (Table 1), this interference took place in relatively high amount and it might have happened that the correction made to compensate for this contribution was overestimated, resulting in lower Cr value determined. For particular irradiation channel the experimental estimated interference correction is about 2% based on experiment with 99.9% Fe wire irradiated under the Cd cover. The uncertainties of some elements (Se, K, Ca) are extremely high due to the measurements close to the detection limit, which is confirmed by the high value of relative standard deviation data for those elements (Fig. 1), that indicate high dispersion of the measured data. There are several other elements that appear not to be in accordance with the information value. However, it should be considered that there are no uncertainties stated in the certificate for the information values of mass fractions. Therefore, only error bars for the measured uncertainty are given in Fig. 2. The measurement results are an additional characterisation of the NIST SRM 2782, especially for gold, which is accurately determined by k0-NAA. 4. 3. Correlations Correlation is the relationship between two or several random variables within a distribution of two or more random variables. The degree of correlation between xj in xj is characterized by the estimated correlation coefficient: «d, )m(i, ) . The correlation coefficient is a measure of the relative mutual dependence of two variables, equal to the ratio of their covariances to the positive square root of the product of their variances. The correlation coefficient is a pure number such that -1 < r < 110. For each pair of elements correlations among measurement results obtained at different times were calculated. Since amount of the elements present in the sample is constant, the successive measurement results should vary randomly for approximately up to two standard deviations. For most of the elements determined indeed no correlations were found indicating absence of systematic errors in the measurements. The results for those elements do not follow each other through the repeated measurements. However, for some elements correlations were established and the elements with the highest (> 0.7) mutual correlation factors are shown in Table 2. All significant correlation factors are positive; when the value for the mass fraction of one element increases, the value for the mass fraction of correlated element increases as well. The origin of such correlations is usually in a common mechanism/influence that forces both measurement results into the same direction. There are several elements that are by pairs correlated among each other, but a group of elements is observable. Those are the elements, where measurement results are consistently correlated among each other with an absolute value of correlation factor between 0.9 and 1. The strongly correlated group of elements consists of Ce, Co, Fe, Sc and Zn. The correlations are observed among the measurements on all Bu~ar et al.: Quality Assessment of k0-NAA by Statistical Evaluation of CRM Results 170 Acta Chim. Slov. 2008, 55, 166–171 Table 2: Elements having absolute correlation factors higher than or ted on the top left side and marked with a rectangle. Fe Zn Co Sc Ce Na La Th Au Fe 1 0.99 0.99 0.98 0.97 0.82 0.71 0.68 Zn 0.99 1 0.98 0.98 0.97 0.79 0.67 0.67 Co 0.99 0.98 1 0.97 0.95 0.79 0.68 0.74 Sc 0.98 0.98 0.97 1 0.93 0.79 0.68 0.68 Ce 0.97 0.97 0.95 0.93 1 0.80 1 0.73 0.95 0.55 Na 0.82 0.79 0.79 0.79 0.80 0.54 La 0.71 0.67 0.68 0.68 0.73 0.95 1 0.40 Th 0.68 0.67 0.74 0.68 0.55 0.54 0.40 1 Au 0.60 0.63 0.66 0.59 0.53 0.51 0.39 0.79 Cr 0.57 0.58 0.60 0.59 0.43 0.47 0.34 0.70 Br 0.05 0.08 0.09 0.07 -0.01 0.32 0.33 0.44 As 0.07 0.08 0.10 0.08 0.03 0.30 0.36 0.39 In 0.23 0.29 0.30 0.22 0.20 0.01 -0.08 0.62 Ag 0.59 0.59 0.62 0.59 0.52 0.33 0.31 0.70 Se -0.11 -0.06 -0.08 -0.12 -0.08 -0.21 -0.28 0.25 U 0.01 0.05 0.05 0.01 -0.02 0.05 -0.07 0.35 detectors and among isolated measurements on a single detector as well. All correlation factors are close to 1, which indicate extremely strong correlations. Given the fact that the correlations were observed for the measurements carried out on all detectors, systematic error due to detection efficiency including measurement geometry (e ) could be eliminated. Each of the four detectors was calibrated independently and particular nuclides emit gamma rays at different energy having different efficiency, so any systematic uncertainty would be detectable. It was observed that all the correlated measured radionuclides had relatively high specific count rates and consequently relatively low statistical uncertainty in their peak areas. Therefore, it can be assumed that in these cases other sources of uncertainty might be revealed. The correlated elements all have low Q0 factors and consequently also low Q0(a), since a has low impact on Q0(a) in this case. As presented in Eq.1, the Q0 factor en- ters the equation in form of expression . Since the numerator is a constant for the given irradiation channel (Q 0,Au(a) is constant for the gold monitor irrespective of the analyte element), the only variable factor for a different radionuclide is the denominator. The factor fand its fluctuations around the constant value used in the calculations are properties common to all correlated and non-correlated elements. It can be assumed that f varies among different irradiations for the amount comparable to its uncertainty (f~ 28 ± 1)11. For the nuclides with larger values of Q0, the variation of fdoes not have observable influence on the denominator sum. For the nuclides with low Q0 factor (Q0 around 1), on the contrary, Q0 is negligible compared with fand fremains the only term in the denominator that defines the behavior of the whole expression. When f is a major to 0.7. The elements having extremely high correlation factors are loca- Cr Br As In Ag Se U 0.60 0.57 0.05 0.07 0.23 0.08 -0.11 0.01 0.63 0.58 0.08 0.08 0.29 0.09 -0.06 0.05 0.66 0.60 0.09 0.10 0.30 0.08 -0.08 0.05 0.59 0.59 0.07 0.08 0.22 0.09 -0.12 0.01 0.53 0.43 -0.01 0.03 0.20 0.02 -0.08 -0.02 0.51 0.47 0.32 0.30 0.01 0.01 -0.21 0.05 0.39 0.34 0.33 0.36 -0.08 -0.01 -0.28 -0.07 0.79 0.70 0.44 0.39 0.62 0.29 0.25 0.35 1 0.75 0.63 0.63 0.78 0.09 0.10 0.39 0.75 1 0.53 0.48 0.58 0.08 0.18 0.36 0.63 0.53 1 0.86 0.52 -0.06 0.13 0.38 0.63 0.48 0.86 1 0.57 0.10 0.16 0.41 0.78 0.58 0.52 0.57 1 0.12 0.55 0.57 0.59 0.45 0.22 0.33 0.54 1 0.19 0.26 0.10 0.18 0.13 0.16 1 0.06 1 0.70 0.39 0.36 0.38 0.41 0.57 0 0.70 1 part of the sum, the sum fluctuates simultaneously with fand the fluctuations of fare seen in the result as correlation. Uncertainty of a certain factor in the Eq.1 propagates to the final result with the uncertainty propagation factors, dependent on other quantities10. Uncertainty propagation factor for A of the analyte is 1, but the uncertainty propa- gation factor of fis z(/> = f !r "'*, „,, '"——-. Using the numerical values for our measurements and for elements with low Q0 factors, the uncertainty propagation factor of A is found to be three times higher than the uncertainty sp propagation factor for f. In case that the uncertainty of fis three times higher than those of A , both would contribute about equally to the final uncertainty and the correlations would not be observable. However, in case of the correlated elements, the uncertainties of A are in the ran- sp ge of 0.5% or lower due to high specific count rates, whilst the uncertainty in experimental determination of f is estimated to be approximately 3%11. In that case the uncertainty contribution of f prevails over the contribution of A more than six times and the correlations could be revealed. In the calculations fis usually treated as a constant and the corresponding fluctuations are not accounted for. It is assumed that the observed correlations might arose from this unaccounted fluctuations. The small systematic uncertainty belonging to the fluctuations of f, detected in the above correlation analysis, is obviously a part of every k0-NAA measurement uncertainty, but is usually not observable. There are several other elements that are correlated, but the correlation factors are lower, correlations differ from detector to detector and there is no evident pattern that would lead to straightforward conclusions on origin of those almost negligible variations. Bu~ar et al.: Quality Assessment of k0-NAA by Statistical Evaluation of CRM Results Acta Chim. Slov. 2008, 55, 166–171 171 5. Conclusions The set of 25 NIST SRM 2782 measurement results was posteriori analyzed using standard statistical approach. Reproducibility of the measurements using the k0-NAA was calculated and the long term stability of the results was proved. The quality performance of the k0-NAA measurements was reconfirmed and accuracy of the results evidenced by comparing measurement results with the reference values. Particular deviations existed but can reasonably be explained by the expertise and knowledge of the method. The correlations between measurement results of mass fraction of different elements found in successive measurements were calculated. The systematic uncertainties could be identified for the elements with the highest correlation factors, Fe, Zn, Co, Sc, Ce. It was shown that the small counting statistic uncertainty is the primary condition for the other uncertainties to become visible. In case of a nuclide having the Q0 value negligible in comparison to f, the influence of fluctuations in fon the measurement result could be observed. The effect was observed for the above-mentioned elements in case of NIST SRM 2782 analysis. The counting uncertainty was small enough and the Q0 factors for the nuclides measured low, so that the measurement results were dependent on the fluctuations of factor f , which in equation is a constant. The observations indicated that calculated mass fractions varied proportionally with variations in f , which was demonstrated as correlations, since f was held constant in calculations. For further uncertainty reduction of k0-NAA measurement results, i.e. below the generally proposed level of 3.5%2, research into more accurate determination of the thermal-to-epithermal neutron flux ratio fis needed. If assumed that the observed correlations are based mostly on f , it should be possible to determine the deviation of parameter f from its mean value by observing deviation of measurement results of mass fraction and knowing the sensitivity coefficient !v-. This approach would reveal uncertainty of f from the observed correlated variations of experimental result. By knowing its deviation, f can be corrected for each individual irradiation session and the result could be re-calculated using the corrected value. Such approach that would yield lower variations of the measurement results and hence lower uncertainty, will be further investigated. 6. Acknowledgment The Slovenian Research Agency (Contracts No. P2-0075 and P1-0143) are greatly acknowledged for its financial support. We kindly acknowledge Dr. Paolo de Zorzi, the coordinator of the international SOILSAMP project, funded by the Italian Environmental Protection Agency (APAT, Italy). The authors would also like to thank Dr. Andrej Trkov for helpful discussions. 7. References 1. A. Simonits et al., J. Radioanal. Chem., 1975, 24, 31–46. 2. F. De Corte, Habilitation Thesis, University of Gent, 1987. 3. S. Barbizzi et al., Environmental pollution, 2004, 127, 131– 135. 4. R. Ja}imovi} et al., Vestn. Slov. Kem. Drus.,1989, 36, 35–43. 5. R. Ja}imovi} et al., J. Radioanal. Chem., 2003, 257, 659– 663. 6. HyperLab 2002 System, Installation and Quick Start Guide, HyperLabs Software, Budapest, Hungary, 2002. 7. A. Simonits et al., J. Radioanal. Chem., 2003, 257, 589–595. 8. KAYZERO/SOLCOI® for reactor-neutron activation analysis (NAA) using the k0-NAA standardization method, DSM Research, Geleen, Netherlands, 1996. 9. www.nist.gov 10. Guide to the Expression of Uncertainty in Measurement, International Organization for Standardization (ISO), Geneva, 1995. 11. R. Ja}imovi}, PhD Thesis, University of Ljubljana, 2003. Povzetek S pomo~jo standardnih statisti~nih orodij smo ovrednotili merilne rezultate, ugotovljene s k0-metodo nevtronske aktiva-cijske analize (k0-NAA), za standardni referen~ni material NIST 2782 Industrijsko blato. Pri tem so nas zanimali predvsem potencialni viri negotovosti in potencialne sistematske napake uporabljene analizne metode. Pregledali smo merilne rezultate, dobljene v dalj{em ~asovnem obdobju in ugotovili korelacije med vsebnostmi nekaterih elementov (Fe, Zn, Co, Sc in Ce). Ugotovljene korelacije smo lahko pripisali fluktuaciji razmerja med hitrostma fluenc termi~nih in epitermi~nih nevtronov (parameter f) od obi~ajno uporabljene povpre~ne vrednosti. Z opazovanjem odmika merilnih rezultatov za masno frakcijo izbranega elementa in poznavanjem faktorja {irjenja negotovosti parametra f lahko zanesljiveje izra~unamo njegovo pravilno vrednost za posamezno obsevanje z nevtroni in s tem zmanj{amo skupno negotovost merilnega rezultata. Bu~ar et al.: Quality Assessment of k0-NAA by Statistical Evaluation of CRM Results