Technically Enhanced Naturally Occurring Radionuclides (TENORM) in Phosphogypsum

Transcription

1 Technically Enhanced Naturally Occurring Radionuclides (TENORM) in Phosphogypsum Comparison CCRI(II)-S5 of the Consultative Committee for Ionizing Radiation A. Shakhashiro a, U. Sansone a, H. Wershofen b, A. Bollhöfer c, C. K. Kim a, C. S. Kim d, M. Korun e, M, Moune f, S. H. Lee g, S. Tarjan h a International Atomic Energy Agency, Agency's Laboratories, Seibersdorf, Austria. b Environmental Radioactivity, PTB, Braunschweig, Germany. c Environmental Radioactivity, Dept. of the Environment and Heritage, Darwin, Australia. d Dept. of Environmental Radioactivity Assessment, Korea Institute of Nuclear Safety Daejeon, Republic of Korea. e Jozef Stefan Institute, Ljubljana, Slovenia. f LNE-LNHB, Laboratoire National Henri Becquerel, Gif-sur-Yvette Cedex, France. g Korea Research Institute of Standards and Science, Daejeon, Republic of Korea. h Central Radiological Laboratory, Hungarian Agricultural Authority, Budapest, Hungary. Abstract Within the frame of mutual cooperation between the IAEA and the BIPM, the Consultative Committee for Ionizing Radiation Section II - Measurement of Radionuclides accepted an IAEA-organized interlaboratory comparison in 2008 on the determination of technically enhanced naturally occurring radionuclides in phosphogypsum. The study was piloted by the Chemistry Unit at the IAEA s Laboratories in Seibersdorf (Austria). This report presents the methodology applied in conducting this comparison and the results. Activity results for Pb-210, Ra-226, Th-230, U-234, U-235 and U-238 were reported by three National Metrology Institutes (NMI) and five other expert laboratories or designated institutes. Four different approaches were used to calculate the nominal value of the reported results and associated uncertainties, and the results from each individual participant were evaluated and compared with this nominal reference value. The reported measurement results evaluation demonstrated agreement amongst the participating laboratories. 1/24

2 CONTENTS 1. INTRODUCTION PARTICIPANTS METHODS AND MATERIALS Homogeneity study EVALUATION OF RESULTS Measurands and reporting format Analytical methods Statistical screening of the reported data sets Calculation of the nominal massic activity values and associated uncertainties Degree of equivalence of the reported results CONCLUSIONS REFERENCES LIST OF ABBREVIATIONS AND NOTATIONS /24

3 1. INTRODUCTION The IAEA is a signatory of the Mutual Recognition Arrangement (CIPM, 1999), which was drawn up by the International Committee for Weights and Measures (CIPM), under the authority given to it in the Metre Convention. The objectives of the CIPM MRA are to establish the degrees of equivalence of national measurement standards maintained by national metrology institutes (NMIs), to provide for the mutual recognition of calibration and measurement certificates issued by the NMIs, and to provide governments and other parties with a secure technical foundation for wider agreements related to international trade, commerce and regulatory affairs. Within the frame of mutual cooperation between the IAEA and the BIPM, the IAEA proposed an interlaboratory comparison among NMIs and expert laboratories on the determination of technically enhanced naturally occurring radionuclides in phosphogypsum. The study was piloted by the Chemistry Unit at the IAEA s Laboratories in Seibersdorf (Austria), and is classified by the CCRI as supplementary comparison CCRI(II)-S5. Phosphogypsum is generated as a by-product of the phosphoric acid based fertilizer industry. During the technological process of phosphoric acid production, most of the naturally-occurring radionuclides are concentrated (so-called technically enhanced) in the waste, which is the phosphogypsum. The discharge of phosphogypsum on earth surface deposits is a potential source of enhanced natural radiation and heavy metals, and the resulting environmental impact should be considered carefully to ensure safety and compliance with environmental regulations. In addition, phosphogypsum can be used to make several building materials and it is used in agriculture as a conditioner to maintain soil productivity in areas where soils are poor and erode easily. A reliable determination of technically enhanced naturally occurring radionuclides in phosphogypsum is necessary to comply with the radiation protection and environmental regulations. This comparison was aimed at supporting calibration and measurement capability (CMC) claims of National Metrology and Designated Institutes for technically enhanced naturally occurring radionuclide measurements in phosphogypsum, and to use the produced data to assign the certified values of the IAEA-434 candidate reference material. The certification of the IAEA-434 will assist laboratories in Member States in validating their analytical methods for the determination of naturally occurring radionuclides and to control the quality of the produced analytical results. This report presents the samples preparation methodology, material homogeneity assessment, participants results and the data comparison of the reported results for Pb-210, Ra-226, Th-230, U-234, U-235 and U-238. The deviation of individual results from the mixture model median was calculated and reported. During the planning phase of the comparison, a short analytical protocol and reporting forms were prepared. The participants were asked to report the details of their analytical procedure, traceability of standards and calibration, quality control procedure, uncertainty budget details, test portion mass and dissolution techniques. 3/24

4 2. PARTICIPANTS The material was initially characterized at the Agency s laboratories in Seibersdorf during an earlier feasibility study phase. Final characterization of the material took place within this interlaboratory comparison piloted by the Agency s laboratories in Seibersdorf in cooperation with the Consultative Committee for Ionizing Radiation (CCRI) of the International Bureau des Poids et Mesures (BIPM). The results reported in this comparison were used to derive the values of the measurands of interest. Four laboratories signatory to the CIPM MRA [PTB (Germany), KRISS (Korea), LNE-LNHB (France), and the IAEA Laboratories (Seibersdorf)] and four expert laboratories nominated or designated by their respective NMIs [ERISS (Australia), HAA (Hungary), KINS (Korea), and JSI (Slovenia)], took part in the IAEA-434 interlaboratory comparison. Laboratory Code Regional metrology organization Laboratory Name and address ERISS IAEA LNE-LNHB PTB HAA EXPERT LABORATORY INTERNATIONAL ORGANIZATION EURAMET EURAMET EXPERT LABORATORY 4/24 Andreas Bollhöfer Environmental Radioactivity, Supervising Scientist Division Dept. of the Environment and Heritage Darwin, AUSTRALIA Chang-Kyu Kim Seibersdorf Agency s Laboratories International Atomic Energy Agency, Vienna, AUSTRIA Muriel Moune Laboratoire National Henri Becquerel Gif-sur-Yvette Cedex, FRANCE Herbert Wershofen Environmental Radioactivity Physikalisch-Technische Bundesanstalt Bundesallee 100 D Braunschweig GERMANY Sandor Tarjan Hungarian Agricultural

5 Laboratory Code Regional metrology organization Laboratory Name and address Authority Central Radiological Laboratory Budapest, HUNGARY KINS KRISS JSI EXPERT LABORATORY APMP EURAMET (designated laboratory) Cheol-Su Kim Department of Environmental Radioactivity Assessment Korea Institute of Nuclear Safety 19 Gusong-Dong, Yusong-Ku Yuseong, Taejon, REPUBLIC OF KOREA Sang-Han Lee, Korea Research Institute of Standards and Science 1 Doryong-Dong, Yuseoung-Gu Daejeon REPUBLIC OF KOREA Matjaz Korun JOZEF STEFAN INSTITUTE Ljubljana, SLOVENIA 5/24

6 3. METHODS AND MATERIALS The IAEA-434 RM was collected from a processing plant located in Gdansk (Poland) in The matrix composition is: CaSO 4 *2H 2 O (96 %), P 2 O 5 (1-2 %), F Total (1.2 %), SiO 2 (1 %), Al 2 O 3 (0.2 %). The bulk material of phosphogypsum was received in 60 L drums at a very high level of moisture. First, it was dried at 80 ºC for 36 hours. Three hundred kilograms of bulk material were then processed with a grinder to a mesh size below 250 µm. This material was dried again for 12 hrs at 80 ºC to approx 8 % humidity. The dried phosphogypsum was processed with an air jet-mill. The particle size distribution of the milled material was determined using Mastersizer X, Malvern Instruments 1. Figure 1 shows the particle distribution of the IAEA-434. It can be seen from Figure 1 that the size of the majority of particles is concentrated around 10 µm, which indicates a high level of homogeneity of the material. The milled material was homogenised as one lot in a clean atmosphere at a temperature range of (20 ± 2) C and a relative humidity of 55 %. The homogeniser used was a clone Lödige Ploughshare-Mixer of a 1000 litre capacity. The IAEA-434 material was bottled under normal laboratory conditions; 1000 bottles were filled in one day, with all precautions taken to avoid segregation. The bottles were labeled, arranged into plastic boxes and sterilized using gamma ray irradiation with a total dose of 25 kgy using a Co-60 source. The bottle size was 900 ml with a wide secure-sealed cover to preserve the integrity of the reference material in the bottle. The amount of the material in each bottle was approximately 250 g Homogeneity study For the homogeneity study, 10 bottles covering the whole bottling range were randomly selected. Three independent sample portions of 12.5 g from each bottle were analyzed using gamma-ray spectrometry for Pb-210, Ra-226, Th-230, U-234, U-235 and U-238. The homogeneity of Ra- 226 was also tested by analysing three sample portions of one gram from five bottles using alpha spectrometry. The analysis for the homogeneity study was performed under reproducible conditions to minimise variations. The standard uncertainty associated with the material heterogeneity was calculated using the formulae stated in ISO Guide 35 [2]. Single way ANOVA results were used to apply formulae 1 to 5. 1 Certain commercial equipment, instruments, and materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the IAEA, nor does it necessarily imply that the materials and/or equipment are the best available for the purpose. 6/24

7 2 s wb = MS within (1) s 2 bb MS amon MS g within = (2) n 0 s 2 within = M within (3) s 2 between _ bottles = M between n 0 M within (4) U bb S n 2 n S n 2 = within + bb (5) bot. bot The slope and its uncertainty of the analytical results from 10 bottles were calculated for each measurand. The calculated statistical values were compared to the t-student critical value for a degree of freedom of 9 and probability level of 95 %. From the statistical point of view, there was no significant trend due to the bottling process. Table 1 shows the results of the homogeneity study and trend analysis results. The outcome of the homogeneity study demonstrated that the uncertainties due to between-bottles heterogeneity, u bb, were generally very small, and the material could be considered sufficiently homogeneous for the radionuclides to be analysed at the nominal values anticipated. TABLE 1: HOMOGENEITY STUDY AND TREND ANALYSIS RESULTS Element Pb-210 Ra-226 Th-230 U-234 U-235 U-238 u bb /[Bq kg 1 ] u bb / [%] b u(b 1 ) b 1 / u(b 1) Critical value t 0.95, n The abbreviations in Table 1 and the formulae are explained in the list of abbreviations. 7/24

8 Fig. 1. Particle size distribution of the IAEA-434 reference material Although there are indications that the homogeneity of the material is generally suitable for even smaller test portions, due to the small particle size of this material, it was recommended to the participants that the minimum test portion used for analysis should be 1 g. If a smaller test portion is taken, the uncertainty of the property value should be expanded taking into account the 8/24

9 relationship of mass and heterogeneity explained in the concept of Ingamels sampling constant or other related concepts [3,4,5]. The calculated parameters originating from the homogeneity study are listed in Table 2. It is evident that the uncertainty associated with the between-bottles heterogeneity is reasonably small. The variances in Table 2 [within-bottle (S 2 wb) and between-bottle (S 2 bb)] are obtained from single way ANOVA calculations. TABLE 2: VARIANCES AND BETWEEN-BOTTLES UNCERTAINTIES ASSOCIATED WITH THE MATERIAL S HETEROGENEITY OF THE IAEA-434 Nuclide S 2 wb S 2 bb s bb [%] u bb [%] Pb Ra Th U U The determination of S 2 wb, S 2 bb, s bb and u bb were calculated according to formulae 1-5, which can be also found in ANNEX A of the ISO Guide [2]. The abbreviations in Table 2 are explained in the list of abbreviations on at the end of this paper 9/24

10 4.1. Measurands and reporting format 4. EVALUATION OF RESULTS Each participant had received one bottle of the phosphogypsum material (randomly selected covering the whole bottling sequence) and was asked to analyse total U, Pb-210, Ra-226, Th- 228, Th-230, U-234, U-235 and U-238 using a validated method of their choice. The participating laboratories were asked to report the measurement result along with the associated standard uncertainty, and to report details of the uncertainty budget estimation in addition to the details of the applied quality control procedure. To harmonize the method, participants were requested to dry a separate sample portion of at least 1 gram for 12 hours at 80 C before the dry mass determination. The test portion mass for the analysis was proposed to be at least 1 gram for radiochemical analyses and 50 grams for gamma spectroscopy analyses. To assess the digestion difficulty of the phosphogypsum, and to assist participants and future users of the IAEA-434 reference material in selecting the optimal dissolution technique, the IAEA laboratories in Seibersdorf performed several dissolution experiments; the most effective was based on using HNO 3 and HF acids. The reported results were screened and compared with the calculated Mixture-model median, (described below) of the reported results. The laboratories whose reported result was considered an outlier by this test were contacted to review their result to either confirm or withdraw it. Different laboratories reported results of different sets of radionuclides; only those radionuclides with four or more reported results were evaluated Analytical methods The participating laboratories were asked to use the most stable and reliable analytical method used in their laboratories. Table 3 lists the methods used in each laboratory. 4.3.Statistical screening of the reported data sets The collected set of data of each radionuclide shown in Table 4 was subjected to several statistical tests using the HISTO program. The HISTO is a software package developed by the Chemistry Unit of the Agency s laboratories in Seibersdorf for the statistical evaluation of data. In addition to providing general descriptive statistics, the following tests are included in the software: Outlier tests (Dixon, Grubbs, Skewness, Kurtosis) Directional tests (Skewness, Kurtosis) Normality tests (Kolmogorov-Smirnov, Kolmogorov-Smirnov-Lilliefors) The relative standard deviation of the mean value of all measurements for Pb-210, Ra-226, Th- 230, U-234 and U-238 was below 10 %; for U-235, it was around 20 % due to the low massic activity concentration. No statistically detected outlying data were observed within the set of results finally reported. The directional tests passed the acceptance criteria, the Kolmogorov- 10/24

11 Smirnov and Kolmogorov-Smirnov-Lilliefors normality tests showed normal distributions of the data sets Calculation of the nominal massic activity values and associated uncertainties In order to evaluate the commutability of the results using relative bias, a nominal value of the massic activity was calculated for each radionuclide as a consensus value from the reported results using four different statistical quantifiers namely: arithmetic mean after Dixon and Grubs tests, median, mean value according to algorithm A [6] and mixture model-median (MMmedian) [7]. The last three approaches are based on robust statistics. TABLE 3: ANALYTICAL METHODS USED IN THE STUDY Laboratory ERISS JSI LNE-LNHB PTB HAA IAEA KINS KRISS Analytical method Gamma spectrometry calibrated using a mixture of BL-5 uranium standard with Analytical Grade Gypsum. Gamma spectrometry calibrated using point sources and mathematical algorithm. Gamma spectrometry calibrated using Pb-210 solution and mixture of radionuclides linked to the primary standards of LNE-LNHB. U and Th isotopes: radiochemical separation using ion-exchange resin Dowex 1x8, electro-deposition and alpha spectrometry (PIPS detectors), Th-229 and U-232 were used as tracers. Ra-226: Gamma spectrometry calibrated using PTB activity standard solutions. Pb-210: Gamma spectrometry, calibration made using RZBZ24 (Amersham International) Pb-210 solution. Uranium isotopes: chemical separation using anion-exchange (AG 1x8) column with electro-deposition, and alpha spectrometry with PIPS detector. U-232 tracer SRM 4324B produced by NIST was used. Po-210, Pb-210, U and Th isotopes: sequential radiochemical procedure, using extraction chromatography, determination by isotope dilution alpha-spectrometry, Pb-210 by Liquid Scintillation Spectrometry. Ra-226: LSC Quantulus 1220, EG&G Wallac was used, the efficiency calibration was done using standard solution of Ra-226. U and Th isotopes: electro-deposition and alpha spectrometry, U-232 was used as tracer. U and Th isotopes: electro-deposition and alpha spectrometry. Th-229 and U-232 were used as tracers. 11/24

12 TABLE 4: COMPILATION OF THE REPORTED ANALYTICAL RESULTS WITH THE ASSOCIATED MEASUREMENT RESULT STANDARD UNCERTAINTY EXPRESSED AFTER THE SYMBOL ± Measurand ERISS JSI LNE- LNHB PTB HAA IAEA KINS KRISS K-40-5 ± ± Tl ± Pb ± ± ± ± ± ± Pb ± ± 0.65 Pb ± ± ± 34 Bi ± ± Ra ± ± ± ± ± ± 24 - Ra ± Ac ± Th ± ± ± ± ± 5 Pa ± ± Th ± ± U ± ± ± ± ± ± ± 2 U ± ± ± ± ± ± 0.2 U ± ± ± ± ± ± ± ± 2 Figures 2-7 show the graphical presentation of the reported results and expanded uncertainties (k = 2) versus the value of the MM-median, in the graphs the blue line represents the MMmedian value and the red dotted lines represent the MM-median ± 2 S(MM-median). 12/24

13 1000 Pb-210 Massic activity [Bq/kg] ERISS JSI LNHB PTB HAA IAEA Participants Fig. 2. Reported results and expanded uncertainties of Pb-210 versus the MM-Median Ra-226 Massic activity [Bq/kg] ERISS JSI LNHB PTB IAEA KINS Participants Fig. 3. Reported results and expanded uncertainties of Ra-226 versus the MM-Median. 13/24

14 Th-230 Massic activity [Bq/kg] LNHB PTB IAEA KINS KRISS Participants Fig. 4. Reported results and expanded uncertainties of Th-230 versus the MM-Median. 160 U-234 Massic activity [Bq/kg] ERISS JSI PTB HAA IAEA KINS KRISS Participants Fig. 5. Reported results and expanded uncertainties of U-234 versus the MM-Median. 14/24

15 10 U-235 Massic activity [Bq/kg] JSI LNHB PTB HAA KINS KRISS Participants Fig. 6. Reported results and expanded uncertainties of U-235 versus the MM-Median U-238 Massic activity [Bq/kg] ERISS JSI LNHB PTB HAA IAEA KINS KRISS Participants Fig. 7. Reported results and expanded uncertainties of U-238 versus the MM-Median. 15/24

16 To estimate the standard uncertainty associated with the normative massic activity value, four statistical estimators were used: standard deviation, MAD, algorithm A standard deviation [6] and the mixture model-median based standard deviation S (MM-median) [7]. The results of each calculation are shown in Table 5. TABLE 5: RESULTS OF THE CALCULATED CONSENSUS VALUES WITH THE STANDARD UNCERTAINTIES EXPRESSED AFTER THE SYMBOL ± USING FOUR STATISTICAL APPROACHES Measurand Arithmetic Mean ± S Median ± MAD Alg. A mean ± S(Alg. A) MM-median ± S(MMmedian) *Pb ± ± ± ± 29 Ra ± ± ± ±31 Th ± ± ± ± 5 U ± ± ± ± 5 U ± ± ± ± 1.1 U ± ± ± ± 5 *Reference date: 2008-January-01 It is proposed to adopt the value calculated using the mixture model median based on the probability density function [7] as a normative massic activity value for the evaluation of the results commutability and the calculation of the degree of equivalence; hence the reference value. From the calculated results in Table 5, it can be seen that although there is a slight difference among the values calculated using the four different approaches, they still overlap within the stated range of uncertainty. Figures 8-13 show the graphical presentation of the calculated values and expanded uncertainties according to the approaches listed above in Table 5 versus the value of the MM-median. In the graphs the red line represents the MM-median value and the red dotted lines represent the MMmedian ± 2 S(MM-median). It is clear from the Figures 8-13 that the calculated MM-median is in good agreement with the mean value calculated using robust and classical mathematical approaches. This could indicate that the calculation of the degree of equivalence in 4.5 is not affected by the way in which the reference value was derived. Also, the derived standard uncertainty using the standard deviation of the MM-median was, in most cases, comparable to the uncertainty estimated using other approaches. Therefore, the appropriateness of the use of the standard deviation of the MM-median in the calculation of the degree of equivalence is demonstrated. 16/24

17 To compare the relationship between the reported results and their uncertainties, the following approach was used. An estimator, ε, was calculated by rating the difference between the reported value and the reference value (MM-median) to the total propagated uncertainty of this difference with a coverage factor of two (95 % confidence level). ε= Valueno min al Valuereported / unc no min al + uncreported (6) It is obvious that the smaller ε indicates a better relationship. The calculated values of ε for the studied measurands are listed in Table 6. TABLE 6: THE CALCULATED VALUES OF ε FOR THE STUDIED MEASURANDS ACCORDING TO EQUATION 6. ERISS JSI LNHB PTB HAA IAEA KINS KRISS Pb Ra Th U U U From Table 6 it can be concluded that 90 % of the reported results have an ε value less than 1, which indicates a high level of equivalence of the reported analytical results for such a difficult matrix and analytes. 4.5.Degree of equivalence of the reported results The degrees of equivalence with the reference values for each radionuclide are calculated in terms of the differences (D i ) of each value from the reference value and the expanded uncertainties (k = 2) of this difference, U i. The matrix of these values is presented in Table 7 while the graphs in Figures 2 to 7 compare the absolute values for each radionuclide. 17/24

18 TABLE 7: DEGREES OF EQUIVALENCE FOR EACH PARTICIPANT EXPRESSED AS THE DIFFERENCES (D i ) OF EACH VALUE FROM THE NOMINAL VALUE AND THE EXPANDED UNCERTAINTIES (k = 2) OF THESE DIFFERENCES U i. Lab i ERISS JSI LNHB PTB HAA IAEA KINS KRISS D i U i D i U i D i U i D i U i D i U i D i U i D i U i D i U i Pb Ra Th U U U D i / [Bq kg 1 ]: The differences of each value from the nominal value (MM-median). U i / [Bq kg 1 ]: The expanded uncertainties (k = 2) of the difference D i.. 18/24

19 1000 Massic activity of Pb-210 [Bq/kg] Arithm. Mean / S Median / MAD Alg A / S(Alg A) MM-median/S(MMmedian) Calculation algorithm Fig. 8. Comparison of calculated means and expanded uncertainties of Pb-210 using different calculation algorithms Massic activity of Ra-226 [Bq/kg] Arithm. Mean / S Median / MAD Alg A / S(Alg A) MM-median/S(MMmedian) Calculation algorithm Fig. 9. Comparison of calculated means and expanded uncertainties of Ra-226 using different calculation algorithms. 19/24

20 Massic activity of Th-230 [Bq/kg] Arithm. Mean / S Median / MAD Alg A / S(Alg A) MM-median/S(MMmedian) Calculation algorithm Fig. 10. Comparison of calculated means and expanded uncertainties of Th-230 using different calculation algorithms. 160 Massic activity U-234 [Bq/kg] Arithm. Mean / S Median / MAD Alg A / S(Alg A) MM-median/S(MMmedian) Calculation algorithm Fig. 11. Comparison of calculated means and expanded uncertainties of U-234 using different calculation algorithms. 20/24

21 10 Massic activity of U-235 [Bq/kg] Arithm. Mean / S Median / MAD Alg A / S(Alg A) MM-median/S(MMmedian) Calculation algorithm Fig. 12. Comparison of calculated means and expanded uncertainties of U-235 using different calculation algorithms. 170 Massic activity of U-238 [Bq/kg] Arithm. Mean / S Median / MAD Alg A / S(Alg A) MM-median/S(MMmedian) Calculation algorithm Fig. 13. Comparison of calculated means and expanded uncertainties of U-238 using different calculation algorithms. 21/24

22 5. CONCLUSIONS The CCRI(II)-S5 comparison on technically enhanced naturally occurring radionuclides (TENORM) in phosphogypsum was completed successfully. To verify the effect of the statistical approach used in deriving the comparison reference value and its uncertainty on the calculated degree of equivalence, four approaches were used to calculate the nominal (mean) value of the reported results and associated uncertainty. The mean values obtained using the four different mathematical approaches were comparable and overlapped within the stated expanded uncertainty at a confidence level of 95 %. The comparison of the reported results revealed satisfactory agreement amongst the participating laboratories, where 90 % of the reported results agreed within the expanded uncertainties in spite of the degree of the difficulty for the determination of the studied analytes and the complex nature of the matrix. It was noted during this study that many laboratories did not report all the results requested within the comparison time-frame although the deadline for reporting was extended. The reasons for this are worth investigating. Acknowledgements: The input, support and fruitful discussions with all the participants: D. Arnold, A. Bollhöfer, C. S. Kim, Y. J. Kim, C. K. Kim, G. Kis-Benedik, M. Korun, J. M. Lee, K. B. Lee, S. H. Lee, M. Makarewicz, M. Moune, T. S. Park, S. Tarjan, H. Wershofen, and C. Yonezawa are highly appreciated. Last, but not least, we would like to thank all members of the laboratory staff inside the participating institutes having performed the demanding radiochemical work for the preparation of this difficult material as well as for the determination of the reference values of the future IAEA-434 phosphogypsum reference material. Special thanks to P. Allisy-Roberts, as Executive Secretary of the Consultative Committee for Ionizing Radiation (CCRI), Bureau International des Poids et Mesures (BIPM) for support and assistance. 22/24

23 6. REFERENCES 1. INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, ISO Guide 34: General requirements for the competence of reference material producers, Second edition (2000). 2. INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, ISO Guide 35: Reference materials - General and statistical principles for certification (2005). 3. INGAMELLS C. O., SWITZER P., A proposed sampling constant for use in geochemical analysis, Talanta 20 (1973) PAUWELS J., VANDECASTEELE C., Determination of the minimum sample mass of a solid CRM to be used in chemical analysis, Fresenius J. Anal. Chem., 345 (1993) STOEPPLER M., KURFUERST U., GROBECKER K. H, Der Homogenitaetsfaktor als Kenngroesse fuer pulverisierte Feststoffproben, Fresenius J. Anal Chem., 322 (1985), INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, ISO 13528:2005, Annex C. 7. DUEWER D.L., A Robust Approach for the Determination of CCQM Key Comparison Values and Uncertainties, Paper presented at the 10th meeting of the CIPM Consultative Committee for Amount of Substance - Metrology in Chemistry, Sevres, France, (2004) VAJDA N., LAROSA J., ZEISLER R., DANESI P., KIS-BENEDEK G., (1997). A Novel Technique for the Simultaneous Determination of Pb-210 and Po-210 using a Crown Ether. J. Environ. Radioactivity 37, American National Standard, Traceability of Radioactive Sources to the National Institute of Standards and Technology (NIST) and Associated Instrument Quality Control, ANSI N /24

24 7. LIST OF ABBREVIATIONS AND NOTATIONS List of abbreviations and notations in the equations and tables (number of equation and tables in brackets) if not explained in the text b 1 Slope (Table 1) u(b 1 ) Uncertainty of the slope (Table 1) MS Mean square (ANOVA) between bottles (2) among MS within Mean square (ANOVA) within bottles (1, 2, 3) n Number of observations (5) n bot Number of bottles (5) n 0 (Effective) number of (sub) group members, for complete data sets n = n 0 (2, 3). 2 s bb Variance between bottles (Table 2) S Classical standard deviation S(MM-median) Standard deviation of Mixture Model Median s Variance within bottles (Table 2) 2 wb u bb Uncertainty related to between bottle variations (Table 2) U Expanded uncertainty (coverage factor 2 for 95% probability) MM-median Mixture models median [7] MAD Median of Absolute Deviations Alg. A Mean value calculated according to the robust approach Algorithm A of ISO-13528:2005, Annex C. (Table 5, Figures 2-7) S(Alg. A) Standard deviation calculated according to Algorithm A of ISO :2005, Annex C. D i The differences D of each reported value i from the nominal value (MM-median), Table 7. U i The expanded uncertainty (k = 2) of the difference D i, Table 7. 24/24