ARTICLE IN PRESS Applied Radiation and Isotopes 68 (2010) 1196–1199
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Traceability in gamma-ray spectrometry D. Glavicˇ-Cindro, M. Korun Jozˇef Stefan Institute, Jamova cesta 39, Ljubljana, Slovenia
a r t i c l e in f o
Keywords: Metrological traceability Calibration Software-measurement standard Measurement model Gamma-ray spectrometry
a b s t r a c t The new edition of the International vocabulary of metrology—basic and general concepts and associated terms (VIM) defines metrological traceability in a different way than was defined in the previous edition. The reference to an ‘‘unbroken chain of comparisons’’ is replaced by a ‘‘chain of calibrations.’’ Calibrations, unlike comparisons, render possible an interpolation of the quantity values between indicated parameters where the calibration was performed. Calibrations of software may be performed using software-measurement standards as well. Furthermore, the traceability of quantities having a minor influence on the measurement result is not mandatory. As a consequence of these modifications, the traceability of gamma-ray spectrometric results can also be attained when gammaray spectrometry is implemented other than as a relative method. & 2009 Elsevier Ltd. All rights reserved.
1. Introduction
form
In most laboratories, gamma-ray spectrometry is used as a relative method. The measurements on unknown samples are performed relative to a sample of a reference source which agrees in terms of density, chemical composition and gamma-ray emission characteristics with the unknown sample as closely as possible. In the relative method, the traceability chain is achieved by the use of certified reference materials (CRMs). However, because of the relatively limited availability of CRMs, the applicability of this method has severe restrictions. Therefore, other methods need to be introduced to achieve traceability under more general conditions. Ways on how to implement metrological traceability for measurement results depend on the definition of metrological traceability itself. The ISO/IEC Guide 99 (2007), International vocabulary of metrology—basic and general concepts and associated terms (VIM), which supersedes the International vocabulary of basic and general terms in metrology [VIM (ISO/IEC Guide, 1993)], defines the term ‘‘metrological traceability’’ in a way different from ‘‘traceability’’ as defined in the previous vocabulary. With respect to the previous definition, the traceability of results obtained with gamma-ray spectroscopic measurements cannot be claimed for radionuclides that were not used during the calibration procedure. According to the old definition, measurement results are traceable only if gamma-ray spectrometry is used as a relative method. The unknown activity, A(E), which is calculated from the count rate, n(E), in a peak at the energy, E, can be expressed in the
AðEÞ ¼
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nðEÞ ACRM ; nCRM ðEÞ
ð1Þ
where nCRM(E) denotes the count rate in the peak at energy E during the calibration with the spectrometer using a CRM with an activity, ACRM. It is important that the calibration sample, which is made from the certified reference material, resembles the unknown sample as closely as possible; the traceability chain is established by the CRM. The influences on the activity determination resulting from possible differences between the calibration and the unknown sample in terms of the sample dimensions, density, chemical composition and sample-detector arrangement must be covered by the uncertainties. It is relatively easy to ensure the agreement of sample dimensions between the calibration source and the unknown sample. However, it is more difficult to ensure the agreement of densities and chemical compositions because of the relatively small choice of certified reference materials when compared to the variety of frequently measured sample matrices. It should also be mentioned that the peak area at energy E, used for the comparison of count rates, must be free of the influence of other gamma-ray emitters present in either the sample or the reference material. These requirements significantly restrict the use of gamma-ray spectrometry as a relative method and, consequently, the possibility to produce traceable results. To overcome these limitations, gamma-ray spectrometry measurements are performed in two steps. In the first step, the counting efficiency, Z(ECi), is measured at the energies, ECi, of gamma-rays emitted by the CRM
ZðECi Þ ¼
nðECi Þ ; bðECi ÞACRM
ð2Þ
ARTICLE IN PRESS D. Glavicˇ-Cindro, M. Korun / Applied Radiation and Isotopes 68 (2010) 1196–1199
nðESi Þ : AðESi Þ ¼ ZðESi ÞbðESi Þ
ð3Þ
The traceability of the efficiency is ensured by the traceability of the CRM at the energies ECi, where the CRM radiates gamma rays free of interferences and the influence of summing effects. The interpolation to energies ESi that are different from the energies used for the efficiency measurement are not traceable since, in this case, the chain of comparison to a stated reference cannot be established. However, within the new VIM, the situation is different.
2. The new VIM Within the new VIM, metrological traceability is achieved by an unbroken chain of calibrations rather than comparisons. Calibrations are operations which establish the relationship between quantity values provided by measurement standards and quantity values provided by measurement systems. The results of a calibration may be expressed by diagrams or curves, implying a relationship between the indicated parameter and the measurement result, where the range of measurement results is represented by a continuous interval along its axis. It follows that, in such a case, a calibration is valid for all the values of the indicated parameter within the interval, although the calibration was performed on only a finite system of values of the parameter. The result of a calibration with a sample of a certified reference material, with its uncertainty as a function of a value of a parameter describing the conditions under which the measurement was performed, is presented in Fig. 1. In gamma-ray spectrometry, the parameter indication is count rate and the parameter itself may be a property of the sample, sample to detector arrangement, or the gamma-ray energy. According to the old VIM, by comparing the count rate in the sample measurement and the count rate in the calibration, as expressed by Eq. (1), only measurement results obtained under experimental conditions where the calibration was performed are traceable. By considering the parameter value as an indication, and the count rate with its uncertainty as a measurement result, the new VIM allows that the calibration diagram can be constructed by interpolation. In this case, the traceability of the measurement
Indication (count rate)
25 20 15 10 5 0 0
1
2
3 Parameter value
4
5
Fig. 1. According to the old VIM, the traceability of a calibration is established for only isolated measurement results obtained under the experimental conditions where the calibration was performed.
25 Measurement result (count rate)
where b(ECi) denotes the probability of the emission of gammarays with the energies ECi. In the second step, the measurement of the unknown sample is performed. The radionuclides in this sample emit photons at different energies, ESi, and their activities can be expressed as
1197
20 15 10 5 0
0
1
2 3 4 Indication (parameter value)
5
Fig. 2. According to the new VIM, measurement traceability can be established by a calibration diagram which establishes a relation between the indication (parameter value) and the measurement result provided by a measurement standard. In this case, the measurement traceability is established within the interpolated range between dashed lines.
results is attained for all values of the parameter within the range where the calibrations were performed (Fig. 2). To maintain traceability, the Laboratory for Radiological Measurement Systems and Radioactivity Measurements at the Jozˇef Stefan Institute calibrates its gamma-ray spectrometers as a function of energy, sample radius and sample thickness. The traceability is maintained using the calibrated solution 9MLELMH05, produced by CERCA, France, to prepare water samples of different radii and thicknesses. By measuring these samples, efficiency calibration curves for different sample geometries are measured, and the traceability for water samples is achieved. In gamma-ray spectrometry, many input quantities may be necessary to define the output quantity in terms of a measurement function. For gamma rays from complex cascade schemes, the activity [A(E)], obtained from the number of counts [N(E)] in a peak at an energy E over time T, is expressed as AðEÞ ¼
NðEÞ ; MEðEÞT
ð4Þ
where ME(E) denotes the matrix element (Semkow et al., 1990). This matrix element expresses the probability that, during a nuclear decay, a gamma ray with an energy E is emitted and registered in the spectrum in the peak at the corresponding energy. The main contribution to the number of counts originates in the registration of gamma rays with the energy E. Other gamma rays emitted in the cascade influence the number of counts predominantly via the summing-out effect, the magnitude of which is proportional to the total efficiency. Therefore, in the first order of approximation, the matrix element is given as the product of the emission probability, b(E), and the counting efficiency, Z(E). For complex decay schemes, the matrix element may be a complicated function of the peak and the total efficiencies at all the gamma-ray energies appearing in the cascade. The total efficiency, including its contribution from scattering outside the detector, can be measured only with samples containing a single gamma-ray emitter. Namely, a spectrum with overlapping components cannot be deconvoluted into individual components without assuming their shape as a function of energy. The choice of single gamma-ray emitters for which measurements are possible is very restricted. It is, therefore, difficult to establish the traceability of the total efficiencies. Although, for measurement functions with more input quantities, each quantity should be metrologically traceable, the effort involved in establishing that traceability should be commensurate with the relative contribution of the quantity to the measurement
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result. Since the activity does not depend on the total efficiencies in the first order of the approximation, and since the calibration of spectrometers for the total efficiency is extremely difficult (Korun and Martincˇicˇ, 1997; Korun, 2001), we infer that metrological traceability of the total efficiency is not a prerequisite for the traceability of the activity A(E). Regarding the other input quantities, the metrological traceability of time-measurement results can be achieved by using the pulser method for measuring the effective duration of the acquisition time. The number of counts is obtained by model calculations. Here, the term model calculation designates a calculation of a simplified physical or statistical process which is used to calculate input quantities for efficiency calculations. Pure mathematical procedures such as interpolations or iterations are not considered as model calculations. For calculation of the net peak area of an isolated peak, it is necessary to define where the peak starts, where the peak ends, and the height of the continuous background under the peak. In the peak-area calculations, these definitions constitute a model, which is then applied to specific spectral regions. Similarly, model calculations are also applied when analyzing overlapping peaks. Here, the spectral region is fitted with functions resembling the supposed peak shape and the continuous background. Since the results of model calculations are not measurement results, they are not metrologically traceable. Nevertheless, they can be calibrated, since a calibration is not necessarily a measurement, with a software-measurement standard, which is a set of reference data or reference software intended to reproduce the value of a measurand with a known uncertainty in order to verify the software used in a measuring instrument (ISO 5436-2). It should be mentioned that, in the optimization of the data set (peak widths, sensitivities, convergence criteria, etc.) steering the execution of the peak-analysis programs, test spectra are often used. However, the use of test spectra, produced in the framework of IAEA research projects (IAEA, 1977; Blaauw et al., 1997; Los Arcos et al., 2005), cannot alone substitute for the softwaremeasurement standard, which may be used for comparing only the results obtained by the peak-analysis program with certified results given by its certificate. In the next step, the calibration of the already-optimized peak-analysis software with a softwaremeasurement standard is necessary; this would ensure the traceability of the peak-analysis results. In this step, another standard spectrum with certified values of the peak areas could be used as the software-measurement standard. When measuring efficiencies of a CRM sample having different values of thickness, radius and density, the counting efficiency at a given energy can be interpolated between values corresponding to samples having different values of these physical properties. According to the new VIM, the traceability of the interpolated efficiencies is ensured since the counting efficiency is calibrated as a function of these sample properties. The interpolation can be performed because the counting efficiency may be considered a monotonous function of these sample properties and does not exhibit any discontinuities. To overcome the problems encountered with efficiency measurements for a large variety of sample densities and compositions, the counting efficiency is often calculated. If it is calculated using a detector model, a situation analogous to that with the peak area arises. The actions of the ICRM Gamma-ray Spectrometry Working Group on the comparisons of different codes used in counting efficiency calculations can be regarded as a first step towards the comparability of these results (Vidmar et al., 2008). However, we are still far away from a standard detector model that is realistic enough to represent a true detector and which could be used as a software-measurement standard for efficiency calculations.
In efficiency calculations, a detector model which comprises the properties of the detector crystal and its housing must be established. The details of the dimensions of the core, rounding of edges and thickness of the inactive layers are usually not available. Therefore, it is difficult to assure the accuracy of the calculated efficiency in the whole energy range where the detector is sensitive. It has been shown by Le´py et al. (2001) that counting efficiencies obtained by direct calculations are less reliable than the efficiencies obtained by the efficiency transfer method. In this method, the counting efficiency is measured in a standard geometry and the result of the direct calculation is corrected by the ratio of the measured efficiency and the calculated efficiency for the reference geometry. The influence of the detector properties cancels out in the first approximation and, therefore, the result is less sensitive to systematic influences arising from the imperfections of the detector model. To reduce the influence of imperfections of the detector model as much as possible, more standard sample geometries may be used. For a specific sample type, the most similar standard geometry is selected. It should be noted that, in this approach, the assumption on the continuity of the calculated counting efficiency on the sample properties may not be justified. It follows that calibration of the efficiency calculation results by a software measurement standard is also hampered by poor reliability of the data on detector properties. To improve these data, iterative procedures are used in order to achieve agreement between the measured and calculated efficiencies for the standard geometry; the detector data are adjusted in order to improve the agreement. As several parameters must be adjusted, these procedures may not lead to unique sets of parameter values.
3. Discussion and conclusion The new VIM relaxes the conditions under which metrological traceability of measurement results can be achieved in several ways:
the chain of comparisons is substituted by a chain of calibrations;
for quantity values where the traceability is difficult to achieve
and which have a small influence on the measurement result, traceability is not mandatory; calibrations can be performed by software-measurement standards.
The results of a calibration can be a calibration diagram, enabling an interpolation between the values of the parameter indication where the calibration was performed. In this way, by calibrating the counting efficiency as a function of the energy, the sample thickness and the density, the traceability of the counting efficiency can be achieved. The presence of coincidence summing effects, the total efficiency entering into the measurement function does not need to be metrologically traceable, as it has only a minor influence on the measurement result. For samples placed on top of the detector, the influence of the summing-out effect on the count rates in the peaks is typically 10% for two-step cascades. Here, an error of 10% in the total efficiency is reflected in the activity with a systematic influence of 1%. The new VIM permits calibration using software-measurement standards for the results of model calculations, the number of counts in a peak, and the counting efficiency. Since the execution of peak-analyzing software is often optimized by analyzing standard spectra having certified peak areas, this requirement represents only an additional step. The execution of the optimized
ARTICLE IN PRESS D. Glavicˇ-Cindro, M. Korun / Applied Radiation and Isotopes 68 (2010) 1196–1199
software must be calibrated by analyzing another spectrum with certified peak areas. For model calculations of the peak efficiencies, at present, the calibration cannot be performed since neither realistic detector models that provide certified counting efficiencies, nor certified codes for efficiency calculations exist yet. In addition, the data set describing the detector properties usually needs to be adjusted in order to improve the agreement between the measured and counting efficiencies. By optimizing the data set, the traceability of its values is lost. Therefore, activities obtained with efficiencies calculated using methods with detector models cannot be regarded as traceable.
Appendix: Discussion Q (Pierino de Felice): Regarding the last slide don’t you think that traceability is not so important if you use the same software both in calibration and in analysis phase so that the possible systematic error that is shown before is cancelled? A (Matjaz Korun): Yes this refers to the relative measurement of the sample and of the unknown substance. Here in the ratio of the two count rates, this will cancel out. But in real situations it is much more complicated; mainly the problem is in gamma ray characteristics. If I have a reference sample then the situation is much clearer. Here we have singlet peaks and in a non-standard sample we may have an overlapping peak so the program which performs the peak evaluation will, at the same energy in one sample, encounter a singlet peak and in the other sample part of the multiplet. Therefore, the subroutines which perform the evaluation imposed in both cases would be quite different. Therefore, we cannot suppose that the influences cancel out in every case. Q (Ryan Fitzgerald): Just in general if you want to have the activity be traceable, how do you have the gamma ray emission probability traceable, when often times those tabulations are not based on certified materials? A (Matjaz Korun): Well these are nuclear decay data and they are not traceable in the metrological sense because they are traceable to the reference from where you have got the data. Q (Ryan Fitzgerald): But it seems like the calibration sources you are using are traceable back to a standard, certified by some laboratory, whereas these gamma ray emission probabilities may
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be from a paper but they are not usually based on any certified value by a metrology institute or something. A (Matjaz Korun): Well the emission probabilities should be evaluated and the evaluation of gamma ray emission probability is very thorough and tedious work and just the evaluators know exactly how to do it. Q (Guy Ratel): What do you think the uncertainty would be if you can apply all these computations for the calibration of your gamma-ray spectrometer? A (Matjaz Korun): You mean if you have a good reference material that forms the basis for the efficiency and then what are your uncertainty of the results? Q (Guy Ratel): Yes the expected uncertainties. Would it be a progress in comparison with your older procedure? A (Matjaz Korun): Well I don’t think so but the uncertainty, the additional items included in the uncertainty budget because of the extended range of traceability is the interpolation error so this may be quite small. So, I think that usually the certified reference materials are calibrated with an accuracy of 2 or 2.5 % so if the end result is 3 to 3.5 % this is a very good result. References Blaauw, M., Fernandez, V.O., Westmeier, W., 1997. IAEA gamma-ray spectra for testing of spectrum analysis software. Nuc. Instr. Meth. A 387, 410–415. IAEA, 1977. IAEA Information Sheet G-1. ISO/IEC, Guide 99, 2007. International vocabulary of metrology—basic and general concepts and associated terms. ISO/IEC, Switzerland. ISO Guide 99, 1993. International vocabulary of basic and general terms in metrology. ISO/IEC, Switzerland. ISO 5436-2, 2001. Geometrical product specifications (GPS)—surface texture: profile method; measurement standards, part 2: software measurement standards. ISO, Switzerland. Korun, M., Martincˇicˇ, R., 1997. Measurements of the total-to-peak ratio of a semiconductor gamma-ray detector. Nucl. Instr. Meth. A 385, 511–518. Korun, M., 2001. Measurement of the total-to-peak ratio of a low-energy germanium gamma-ray detector. Nucl. Instr. Meth. A 475, 245–252. Los Arcos, J.M., Blaauw, M., Fazinic´, S., Kolotov, V.P., 2005. The 2002 IAEA test spectra for low-level gamma-ray spectra software. Nucl. Instr. Meth. A 536, 196–210. Le´py, M.C., Altzitzouglou, T., Arnold, D., Bronson, F., Noy, R.C., De´combaz, M., De Corte, F., Edelmaier, R., Peraza, E.H., Klemola, S., Korun, M., Kralik, M., Neder, H., Plagnard, J., Pomme´, S., De Sanoit, J., Sima, O., Ugletveit, F., Van Veltzen, L., Vidmar, T., 2001. Intercomparison of efficiency transfer software for gammaray spectrometry. Appl. Radiat. Isot. 55 (4), 493–503. Semkow, T.M., Mehmood, G., Parekh, P.P., Virgil, M., 1990. Coincidence summing in gamma-ray spectrometry. Nucl. Instr. Meth. A 290, 437–444. Vidmar, T., et al., 2008. An intercomparison of Monte Carlo codes used in gammaray spectrometry. Appl. Radiat. Isot. 66, 764–768.
