- Email: [email protected]
Improvements in the absolute standardization of large-area reference sources
ARTICLE IN PRESS Applied Radiation and Isotopes 67 (2009) 1716–1720
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Improvements in the absolute standardization of large-area reference sources D. Stanga a,, P. De Felice b a b
National Institute of R&D for Physics and Nuclear Engineering ‘‘Horia Hulubei’’, IFIN-HH, P.O. Box MG-6, Bucharest-Magurele R-077125, Romania ENEA- Instituto Nationale di Metrologia delle Radiazioni Ionozzanti, INMR ,C.R. Casaccia, P.O. Box 2400, 00100 Rome, A.D., Italy
a r t i c l e in f o
a b s t r a c t
Article history: Received 6 August 2008 Received in revised form 2 March 2009 Accepted 18 March 2009
Using a simple gas-gain model, the efficiency sensitivity of gas-flow proportional counters to changes in the influence quantities (applied anode voltage, gas purity, gas-flow rate, ambient pressure and temperature) was analyzed and applied for the absolute standardization of large-area reference sources. Thus, the uncertainty of measurement was evaluated by taking into account the fluctuations of these quantities in normal conditions of counter operation. It was shown that the uncertainty is small in these conditions but accidental and large changes in the influence quantities may give rise to large errors of measurement. In addition, a cleaning procedure and a simple way of stabilizing the gain of gas-flow proportional counters were used to improve the absolute standardization of large-area reference sources. As a result, measurements were performed with uncertainties smaller than 0.55% and the reproducibility better than 0.42%. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Large-area reference sources Absolute standardization
1. Introduction Large-area beta and alpha reference sources are widely used for the calibration of surface contamination monitors. According to ISO 8769 (1988), these sources must be calibrated by the national standards laboratory in terms of surface emission rate with relative standard uncertainties smaller than 3% using a gasflow proportional counter. The gain of gas-flow proportional counters is affected by the following important influence quantities: applied anode voltage, gas purity, gas-flow rate, ambient pressure and temperature (Denecke et al., 1998). As a result, changes in these quantities affect the counting efficiency of the detector giving rise to errors of measurement. In this paper, the efficiency sensitivity of gas-flow proportional counters to influence quantities is analyzed using a simple gasgain model (Bateman, 2003). The analysis allowed us to evaluate the uncertainty of measurement by taking into consideration the fluctuations of influence quantities. Thus, it was shown that the uncertainty, due to these fluctuations in normal conditions of counter operation, is much smaller than 3%. However, accidental and large changes in the influence quantities (especially flow rate and gas purity) may give rise to large errors of measurement. A cleaning procedure and a simple way of stabilizing the gain of gasflow proportional counters were also used to improve the absolute standardization of large-area reference sources. As a result, reliable and accurate measurements were performed with Corresponding author. Fax: +40 21 4231701.
E-mail addresses: doru@ifin.nipne.ro, [email protected] (D. Stanga). 0969-8043/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2009.03.056
uncertainties smaller than 0.55% and reproducibility better than 0.42%.
2. Method of measurement 2.1. Basis of the method Absolute standardization of large-area reference sources is based on the internal counting of these sources using a gas-flow, multi-wire, proportional counter. According to ISO 8769, the surface emission rates are determined with the discrimination level set at w0 ¼ 590 eV by means of a 55Fe source for beta emitters and above electronic noise for alpha emitters. Under these conditions, the surface emission rate, E, is given by (Lewis et al., 2003) E¼
R f B 1tR
(1)
where R is the source counting rate, t is the dead-time of the counting system, B is the background and f represents a correction factor. The decay correction was ignored in Eq. (1) because it is insignificant for the reference sources recommended by ISO 8769. The correction factor, f, can be expressed by f ¼ f d f v f q f p f f , where fd, fv, fq, fp and ff are correction factors due to fluctuations of discrimination level settings, applied anode voltage, ambient conditions, gas purity and gas-flow rate, respectively. Under normal conditions of counter operation, all these factors are assumed to have small fluctuations with rectangular distributions and expected values equal to unity. These normal conditions are obtained for ambient pressure and
ARTICLE IN PRESS D. Stanga, P. De Felice / Applied Radiation and Isotopes 67 (2009) 1716–1720
temperature usually encountered in a laboratory when the counter is operated under a steady gas-flow and a high purity (499.95%) of the counting gas is ensured. The relative standard uncertainty of the surface emission rate, e(E), can be derived from Eq. (1) using the law of propagation of uncertainty (ISO, 1995) and taking f ¼ 1. Thus, we obtain sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðE þ BÞ2 R2 R2 B2 2 ðEÞ ¼ 2 ðRÞ þ 2 ðf Þ þ t2 R2 2 ðtÞ þ ðBÞ 2 RE ðE þ BÞ ðE þ BÞ4 (2) where
2 ðf Þ ¼ 2 ðf d Þ þ 2 ðf v Þ þ 2 ðf q Þ þ 2 ðf p Þ þ 2 ðf f Þ
(3)
and e(R), e(f), e(t) and e(B) are relative standard uncertainties of R, f, t and B, respectively. Assuming rectangular distributions for fi (id, v, q, p, f), we have
ðf i Þ ¼
uðf i Þ maxðDf i Þ pffiffiffi ¼ fi fi 3
(4)
where u(fi) and max(Dfi)are the standard uncertainty and the maximum fluctuation of fi, respectively. Neglecting beta spectrum distortion due to the source material, Eq. (4) becomes ð0Þ
p maxðDRi Þ p ðiÞ pffiffiffi ffi pbffiffiffi ¼ pbffiffiffi w (5) R 3 3 3 Rw where pb ¼ w0max f ðwÞ dw (f(w)—normalized beta spectrum of ðiÞ ¼ ðwmax w0 Þ=w0 are the maxthe source), max(DRi)/R and w imum relative fluctuations of the source counting rate and discrimination level corresponding to fluctuations of fi. In are given for Table 1, uncorrected and corrected values of pð0Þ b all reference sources of beta emitting nuclides. Uncorrected values were obtained with the nominal beta spectrum and these values were corrected for the effect of spectrum enhancement at low energies (see Berger et al., 1996). For ffi 0 and e(fd)ffie(fv)ffie(fq)ffie alpha emitting sources we have pð0Þ b (fp)ffie(ff)ffi0. pffiffiffi = 3Þ ðdÞ In the case of the factor fd, we have ðf d Þ ¼ ðpð0Þ w where b ðdÞ w ¼ 0:30 can easily be obtained in the discrimination level settings. In the case of fi (iv, q, p, f), we have
ðf i Þ ¼
p
p
ðf i Þ ¼ pb0ffiffiffi wðiÞ ¼ pb0ffiffiffi ðiÞ G 3
(6)
3
ðiÞ ðiÞ ¼ ðGmax G0 Þ=G0 is the maximum relative gain where GðiÞ ¼ w fluctuation corresponding to fi
2.2. Evaluation of uncertainties due to gain fluctuations A simple model for the avalanche process in proportional counters that gives a good description of the gain dependence on the influence quantities has been used (Bateman, 2003). Thus, the natural logarithm of the gas-gain, G, in a proportional detector is
1717
given by ln G ¼
V B exp A V
(7)
where A, B are two parameters and V is the applied anode voltage. Both A and B depend on the counter geometry and physical parameters of the counting gas. The gain dependence on the counting gas variables pressure (p) and temperature (T) is contained in B as a linear function (B ¼ mq+n) of the ratio q ¼ p/T. These variables are almost identical with ambient variables provided that the gas-flow rate is small and the detector is in thermal equilibrium with the environment. One of the most critical parameters of the counting gas is the gas purity because multi-wire counters used in the absolute standardization of large-area sources have a wide drift space region where the electron attachment has a considerable effect. As a result, small changes in the gas purity by contamination with oxygen contained in air diminish significantly the gain thereby leading to the decrease of the detection efficiency (Curzio et al., 2005; Yoshida et al., 1996). Sources of air impurities may be leakages anywhere in the gas-flow system and outgasing of detector components. These can accidentally give rise to large errors of measurement. The gas-flow rate produces a small drop pressure between the counter and environment and ensures the continuous gas clearing of impurities. As a result, both counting gas pressure and gas purity are affected by flow rate fluctuations. Consequently, the gas-flow rate must be kept constant during the source counting and the same value from the discrimination level setting must be adjusted each time before the source measurement. Eq. (7) also shows that the applied anode voltage can be used to perform the stabilization of the gain against the effect of changes in ambient conditions, gas purity and gas-flow rate. Thus, it was found that a linear servo equation using q could be used to stabilize proportional counters against ambient changes by adjusting the anode voltage (Bateman, 1998). Also, increasing the anode voltage value has the effect of compensating the decrease of the gain due to air impurities (Curzio et al., 2005). Based on experimental results obtained for a gas-flow proportional counter with 10 mm anode and 10 mm cathode radius ðqÞ (Bateman, 1998), ðvÞ G and G were calculated for this counter by using Eq. (7) and taking typical values for maximum fluctuations of V and q. Thus, it was taken VmaxV0 ¼ 71 V and qmaxq0 ¼ 70.25 mb/K. For these values, we have obtained ðvÞ G ¼ ¼ 0:36 using V ¼ 1500 V, q ¼ 3.4 mb/K, m ¼ 220 K/ 0:012 and ðqÞ 0 0 G mb, A ¼ 75 and B0 ¼ 1050 V (see Bateman, 1998). Based on experience (Denecke et al., 1998) and the fact that relative gain fluctuations due to the applied anode voltage and ambient conditions depend slightly on the counter geometry, we can take ðqÞ ðvÞ G ¼ 0:02 and G ¼ 0:5 for all detector geometries practically used in the absolute standardization of large-area reference sources. Table 2 Values of e(fd), e(fv), e(fq), e(fp), e(ff), e(f) in normal conditions of counter operation.
Table 1 Uncorrected and corrected values of pb0 for sources of beta emitting nuclides.
Large-area reference source
pb0(%) Uncorrected values
14
Corrected values
C Pm Cl 204 Tl 90 (Sr+Y) 147
14
147
0.60
0.66
C
Pm
36
204
0.10
0.16
Cl
Tl
90
14
147
36
204
0.09
0.90
0.99
0.20
0.32
(Sr+Y)
C
Pm
Cl
Tl
90
(Sr+Y)
0.18
36
Relative standard uncertainty (%)
e(fd)
e(fv)
e(fq)
e(fp)
e(ff)
e(f)
0.16 0.17 0.03 0.06 0.03
0.01 0.01 0.00 0.00 0.00
0.26 0.29 0.06 0.09 0.05
0.26 0.29 0.06 0.09 0.05
0.26 0.29 0.06 0.09 0.05
0.48 0.52 0.11 0.17 0.10
ARTICLE IN PRESS 1718
D. Stanga, P. De Felice / Applied Radiation and Isotopes 67 (2009) 1716–1720
Counts
Relative gain fluctuations arising from gas purity and flow rate are difficult to calculate. Based on experimental results, it is ðf Þ realistic to assume that ðpÞ G ¼ 0:5 and G ¼ 0:5 for normal conditions of counter operation. In Table 2 are shown (for all reference sources of beta emitters) ðiÞ (id, v, q, values of e(fi) calculated with Eq. (6) using values of w p, f) above mentioned. In the same table, values of e(f) calculated with Eq. (3) are also given. As shown in Table 2, e(f) is much higher in the case of low energy beta emitters (14C and 147Pm). Taking into consideration values of e(f) given in Table 2 and experience, it was realistic to assume for our counting system e(f) ¼ 0.5% for 14C and 147Pm, e(f) ¼ 0.2% for high energy beta emitters and e(f) ¼ 0.1% for alpha emitters. In practice, these values are higher because the reproducibility of the source counting rate is not good enough due to large fluctuations of the flow rate and gas purity (see Wuu et al., 2002).
21
41
61
81
Counts
Fig. 1.
101 121 141 161 Channel number
181
201
221
241
55
Fe pulse height spectrum.
C-14 Pulse height spectrum
5000 4000 3000 2000 1000 0 200
1
Counts
In the absolute standardization of large-area reference sources, normal conditions of counter operation must firstly be ensured because the counter is frequently exposed to air and air impurities affect its operation drastically. Consequently, a cleaning procedure is necessary to be used before each measurement to remove air impurities by flushing the detector with counting gas and then maintaining a small gas-flow rate (usually in the range 1y3 l/h). To elaborate the cleaning procedure, we used a 55Fe source for checking the stability of the 55Fe peak as a function of time because the peak stability is the ultimate test of gas purity. To reduce the uncertainty and for the sake of simplicity, the initial setting of the discrimination level was stabilized by means of a 55Fe source. Thus, each time the counting system was put into service for source measurements, the applied anode voltage was
Fe-55 Pulse height spectrum
24000 20000 16000 12000 8000 4000 0 1
399
598
797 996 1195 Channel number
30000 25000 20000 15000 10000 5000 0
1394
1593
1792
1991
1593
1792
1991
Cl-36 Pulse height spectrum
12000 10000 8000 6000 4000 2000 0 1
Counts
2.3. Improvement of the measurement procedure
200
399
598
797 996 1195 Channel number
1394
Am-241 Pulse height spectrum
1
21
41
61
81
101 121 141 161 181 201 221 241 261 281 Channel number
Fig. 2. Pulse height spectra of the measured sources.
ARTICLE IN PRESS D. Stanga, P. De Felice / Applied Radiation and Isotopes 67 (2009) 1716–1720
slightly adjusted to obtain the same channel number for the 55Fe peak position such as it was initially set (electronic settings were not changed). As a result, the counting rate fluctuations due to changes in ambient conditions, flow rate and gas purity were partly cancelled. Changes in the discrimination level can not be controlled during the source measurement. To avoid large errors of measurements, the shape of the pulse height spectrum (see Fig. 2) was used as a rough estimation of the discrimination level stability during source counting for beta emitters. In practice, it is more convenient to have a small X-ray window on the counter for monitoring the discrimination level stability by means of a point 55 Fe source. In the case of large-area alpha emitting sources, the discrimination level stability is not critical and the peak position in the spectrum of the measured source itself can be used for monitoring large gain deviations. Experience shows that normal conditions of counter operation are difficult to be obtained even if the cleaning procedure was carefully applied. A number of quality assurance (QA) tests performed systematically are necessary because this is the safest way to reach the normal conditions of counter operation and obtain reliable measurements. A checklist for QA should include: (i) the stability of the 55Fe peak; (ii) the tightness of the gas-flow system including the counter; (iii) the length and slope of the detector plateau; and (iv) the measurement of certified reference sources.
1719
dead-time losses. A multi-channel analyzer is used to record pulse height spectra of the 55Fe and reference sources. In Fig. 1, the 55Fe spectrum obtained in the initial setting of the discrimination level is shown. Three large-area reference sources in anodized aluminum foils (14C, 36Cl and 241Am) were measured according to the improved procedure described above. In Fig. 2, their pulse height spectra are shown. Measurement results and uncertainty budget are shown in Table 3. We can see in this table that the uncertainties of measurement are much smaller than the value 3% required by ISO 8769. In order to determine the reproducibility of measurement results, the same sources were ten times measured over four weeks. In Table 4, reproducibility results (expressed as relative standard deviations) are shown. In addition, certified values of the surface emission rate are compared with measurement results and the reproducibility with the relative standard uncertainty. As shown in Table 4, certified values of the surface emission rate agree very well with measured results. Also, reproducibility results are in accordance with the relative standard uncertainties and this shows that measurements were performed under normal conditions of counter operation. Consequently, reliable and accurate measurement results were obtained.
4. Conclusions 3. Measurement results The counting system used for the absolute standardization of large-area reference sources is composed of a gas-flow proportional detector, an integral counting channel and a multi-channel analyzer. The proportional detector was flowed with a mixture of argon (90%) and methane (10%). The gas-flow of about 1 l/h was controlled by a two-stage pressure regulator and needle valves. The counter was operated at +1950 V in the beta plateau and at +1200 V in the alpha plateau. A charge-sensitive pre-amplifier and a spectroscopy amplifier, which feeds a discriminator, amplify the signals of the detector. The pulses from the discriminator are counted by conventional counting logic. A dead-time unit (8.5 ms) was inserted in the counting channel for the precise correction of Table 3 Measurement results and uncertainty budget. Measurement results (s)1
Large-area source 14
36
4407724
5304719
C
E7u(E)
241
Cl
Am
700.671.6
Uncertainty (%)
e(R) e(f) e(t) e(B) e(E)
0.10 0.50 5.00 5.00 0.55
0.10 0.20 5.00 5.00 0.35
0.20 0.10 5.00 10.0 0.23
Using a simple gas-gain model, the efficiency sensitivity of gasflow, multi-wire, proportional counters to changes in the influence quantities was analyzed. Thus, e(f) was calculated on the basis of the gain model and experience. Results showed that the uncertainties due to fluctuations of influence quantities are very small in normal conditions of counter operation. Consequently, large-area reference sources can easily be measured with relative standard uncertainties smaller than the value 3% required by ISO 8769 without stabilizing the ambient conditions. However, these errors are significant especially for low energy beta emitters (0.5%) and they must be taken into consideration for accurate measurements. The analysis also showed that the gas purity and flow rate are the most critical parameters of the counting gas because their accidental changes may give rise to large errors of measurement. For this reason, it is important to obtain normal conditions of counter operation in the absolute standardization of large-area reference sources. To reach these conditions, a cleaning procedure to remove air impurities from the detector must be applied, flow rate reproducibility must be ensured and QA tests must be performed systematically. The analysis also showed that the applied anode voltage can be used to obtain the stabilization of the discrimination level against the effect of changes in influence quantities. Based on this result, the absolute standardization of large-area sources was improved in a very simple way by means of a 55Fe source. As a result, reproducible and accurate measurement results were obtained. Thus, three large-area reference sources were measured with
Table 4 Reproducibility results together with E(measured)/E(certified) and e(E)/reproducibility. Source
E (certified)a(s1)
E(measured)/E(certified)
Reproducibility (%)
e(E)/reproducibility
14
4397 5320 699
1.002 0.997 1.002
0.42 0.25 0.20
1.30 1.40 1.15
C Cl 241 Am 36
a
Values of E(certified) are up-to-dated to the actual date of measurements.
ARTICLE IN PRESS 1720
D. Stanga, P. De Felice / Applied Radiation and Isotopes 67 (2009) 1716–1720
uncertainties smaller than 0.55% and the reproducibility better than 0.42%. References Bateman, J.E., 2003. A general parametric model for the gain of gas avalanche counters with particular attention to non-cylindrical geometries. Phys. Rep. 375, 411–443. Bateman, J.E., 1998. Gas stabilization in proportional counters. Report RAL-TR-98044, Rutherford Appleton Laboratory, UK. Berger, M.J., Unterweger, M.P., Hutchinson, J.M.R., 1996. The influence of backing and covering materials on the 2p-counting efficiency of beta-particle sources. Nucl. Instrum. Methods Phys. Res. A 369, 684–688. Curzio, G., Mazed, D., Ciolini, R., Del Grata, A., Gentili, A., 2005. Effect of air on gas amplification characteristics in argone–propane (1%)-based proportional
counters for airbone radon monitoring. Nucl. Instrum. Methods Phys. Res. A 537, 672–682. Denecke, B., Grosse, G., Szabo, T., 1998. Gain stabilization of gas-flow proportional counters. Appl. Radiat. Isot. 49 (9–11), 1117–1121. ISO 8769, 1988. Sources for the Calibration of Surface Contamination Monitors– Beta-Emitters (maximum beta energy greater than 0.15 MeV) and alphaemitters. International Organization for Standardization, Geneva, Switzerland. ISO/TAG4/WG3, 1995. Guide to the Expression of Uncertainty in Measurement, International Organization for Standardization, Geneva, Switzerland. Lewis, V., Woods, M., Burgess, P., Green, S., Simpson, J., Wardle, J., 2003. The assesment of uncertainty in radiological calibration and testing. Measurement Good Practice Guide no. 49. National Physical Laboratory-IRMF, UK. Wuu, Y.-L., Yuang, M.-C., Hwang, W.-S., 2002. The alpha and beta emitter measurement system in INER. Appl. Radiat. Isot. 5, 261–264. Yoshida, M., Oishi, T., Honda, T., Torii, T., 1996. A calibration technique for gas-flow ionization chambers with short-lived rare gases. Nucl. Instrum. Methods Phys. Res. A 383, 441–446.
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Improvements in the absolute standardization of large-area reference sources D. Stanga a,, P. De Felice b a b
National Institute of R&D for Physics and Nuclear Engineering ‘‘Horia Hulubei’’, IFIN-HH, P.O. Box MG-6, Bucharest-Magurele R-077125, Romania ENEA- Instituto Nationale di Metrologia delle Radiazioni Ionozzanti, INMR ,C.R. Casaccia, P.O. Box 2400, 00100 Rome, A.D., Italy
a r t i c l e in f o
a b s t r a c t
Article history: Received 6 August 2008 Received in revised form 2 March 2009 Accepted 18 March 2009
Using a simple gas-gain model, the efficiency sensitivity of gas-flow proportional counters to changes in the influence quantities (applied anode voltage, gas purity, gas-flow rate, ambient pressure and temperature) was analyzed and applied for the absolute standardization of large-area reference sources. Thus, the uncertainty of measurement was evaluated by taking into account the fluctuations of these quantities in normal conditions of counter operation. It was shown that the uncertainty is small in these conditions but accidental and large changes in the influence quantities may give rise to large errors of measurement. In addition, a cleaning procedure and a simple way of stabilizing the gain of gas-flow proportional counters were used to improve the absolute standardization of large-area reference sources. As a result, measurements were performed with uncertainties smaller than 0.55% and the reproducibility better than 0.42%. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Large-area reference sources Absolute standardization
1. Introduction Large-area beta and alpha reference sources are widely used for the calibration of surface contamination monitors. According to ISO 8769 (1988), these sources must be calibrated by the national standards laboratory in terms of surface emission rate with relative standard uncertainties smaller than 3% using a gasflow proportional counter. The gain of gas-flow proportional counters is affected by the following important influence quantities: applied anode voltage, gas purity, gas-flow rate, ambient pressure and temperature (Denecke et al., 1998). As a result, changes in these quantities affect the counting efficiency of the detector giving rise to errors of measurement. In this paper, the efficiency sensitivity of gas-flow proportional counters to influence quantities is analyzed using a simple gasgain model (Bateman, 2003). The analysis allowed us to evaluate the uncertainty of measurement by taking into consideration the fluctuations of influence quantities. Thus, it was shown that the uncertainty, due to these fluctuations in normal conditions of counter operation, is much smaller than 3%. However, accidental and large changes in the influence quantities (especially flow rate and gas purity) may give rise to large errors of measurement. A cleaning procedure and a simple way of stabilizing the gain of gasflow proportional counters were also used to improve the absolute standardization of large-area reference sources. As a result, reliable and accurate measurements were performed with Corresponding author. Fax: +40 21 4231701.
E-mail addresses: doru@ifin.nipne.ro, [email protected] (D. Stanga). 0969-8043/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2009.03.056
uncertainties smaller than 0.55% and reproducibility better than 0.42%.
2. Method of measurement 2.1. Basis of the method Absolute standardization of large-area reference sources is based on the internal counting of these sources using a gas-flow, multi-wire, proportional counter. According to ISO 8769, the surface emission rates are determined with the discrimination level set at w0 ¼ 590 eV by means of a 55Fe source for beta emitters and above electronic noise for alpha emitters. Under these conditions, the surface emission rate, E, is given by (Lewis et al., 2003) E¼
R f B 1tR
(1)
where R is the source counting rate, t is the dead-time of the counting system, B is the background and f represents a correction factor. The decay correction was ignored in Eq. (1) because it is insignificant for the reference sources recommended by ISO 8769. The correction factor, f, can be expressed by f ¼ f d f v f q f p f f , where fd, fv, fq, fp and ff are correction factors due to fluctuations of discrimination level settings, applied anode voltage, ambient conditions, gas purity and gas-flow rate, respectively. Under normal conditions of counter operation, all these factors are assumed to have small fluctuations with rectangular distributions and expected values equal to unity. These normal conditions are obtained for ambient pressure and
ARTICLE IN PRESS D. Stanga, P. De Felice / Applied Radiation and Isotopes 67 (2009) 1716–1720
temperature usually encountered in a laboratory when the counter is operated under a steady gas-flow and a high purity (499.95%) of the counting gas is ensured. The relative standard uncertainty of the surface emission rate, e(E), can be derived from Eq. (1) using the law of propagation of uncertainty (ISO, 1995) and taking f ¼ 1. Thus, we obtain sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðE þ BÞ2 R2 R2 B2 2 ðEÞ ¼ 2 ðRÞ þ 2 ðf Þ þ t2 R2 2 ðtÞ þ ðBÞ 2 RE ðE þ BÞ ðE þ BÞ4 (2) where
2 ðf Þ ¼ 2 ðf d Þ þ 2 ðf v Þ þ 2 ðf q Þ þ 2 ðf p Þ þ 2 ðf f Þ
(3)
and e(R), e(f), e(t) and e(B) are relative standard uncertainties of R, f, t and B, respectively. Assuming rectangular distributions for fi (id, v, q, p, f), we have
ðf i Þ ¼
uðf i Þ maxðDf i Þ pffiffiffi ¼ fi fi 3
(4)
where u(fi) and max(Dfi)are the standard uncertainty and the maximum fluctuation of fi, respectively. Neglecting beta spectrum distortion due to the source material, Eq. (4) becomes ð0Þ
p maxðDRi Þ p ðiÞ pffiffiffi ffi pbffiffiffi ¼ pbffiffiffi w (5) R 3 3 3 Rw where pb ¼ w0max f ðwÞ dw (f(w)—normalized beta spectrum of ðiÞ ¼ ðwmax w0 Þ=w0 are the maxthe source), max(DRi)/R and w imum relative fluctuations of the source counting rate and discrimination level corresponding to fluctuations of fi. In are given for Table 1, uncorrected and corrected values of pð0Þ b all reference sources of beta emitting nuclides. Uncorrected values were obtained with the nominal beta spectrum and these values were corrected for the effect of spectrum enhancement at low energies (see Berger et al., 1996). For ffi 0 and e(fd)ffie(fv)ffie(fq)ffie alpha emitting sources we have pð0Þ b (fp)ffie(ff)ffi0. pffiffiffi = 3Þ ðdÞ In the case of the factor fd, we have ðf d Þ ¼ ðpð0Þ w where b ðdÞ w ¼ 0:30 can easily be obtained in the discrimination level settings. In the case of fi (iv, q, p, f), we have
ðf i Þ ¼
p
p
ðf i Þ ¼ pb0ffiffiffi wðiÞ ¼ pb0ffiffiffi ðiÞ G 3
(6)
3
ðiÞ ðiÞ ¼ ðGmax G0 Þ=G0 is the maximum relative gain where GðiÞ ¼ w fluctuation corresponding to fi
2.2. Evaluation of uncertainties due to gain fluctuations A simple model for the avalanche process in proportional counters that gives a good description of the gain dependence on the influence quantities has been used (Bateman, 2003). Thus, the natural logarithm of the gas-gain, G, in a proportional detector is
1717
given by ln G ¼
V B exp A V
(7)
where A, B are two parameters and V is the applied anode voltage. Both A and B depend on the counter geometry and physical parameters of the counting gas. The gain dependence on the counting gas variables pressure (p) and temperature (T) is contained in B as a linear function (B ¼ mq+n) of the ratio q ¼ p/T. These variables are almost identical with ambient variables provided that the gas-flow rate is small and the detector is in thermal equilibrium with the environment. One of the most critical parameters of the counting gas is the gas purity because multi-wire counters used in the absolute standardization of large-area sources have a wide drift space region where the electron attachment has a considerable effect. As a result, small changes in the gas purity by contamination with oxygen contained in air diminish significantly the gain thereby leading to the decrease of the detection efficiency (Curzio et al., 2005; Yoshida et al., 1996). Sources of air impurities may be leakages anywhere in the gas-flow system and outgasing of detector components. These can accidentally give rise to large errors of measurement. The gas-flow rate produces a small drop pressure between the counter and environment and ensures the continuous gas clearing of impurities. As a result, both counting gas pressure and gas purity are affected by flow rate fluctuations. Consequently, the gas-flow rate must be kept constant during the source counting and the same value from the discrimination level setting must be adjusted each time before the source measurement. Eq. (7) also shows that the applied anode voltage can be used to perform the stabilization of the gain against the effect of changes in ambient conditions, gas purity and gas-flow rate. Thus, it was found that a linear servo equation using q could be used to stabilize proportional counters against ambient changes by adjusting the anode voltage (Bateman, 1998). Also, increasing the anode voltage value has the effect of compensating the decrease of the gain due to air impurities (Curzio et al., 2005). Based on experimental results obtained for a gas-flow proportional counter with 10 mm anode and 10 mm cathode radius ðqÞ (Bateman, 1998), ðvÞ G and G were calculated for this counter by using Eq. (7) and taking typical values for maximum fluctuations of V and q. Thus, it was taken VmaxV0 ¼ 71 V and qmaxq0 ¼ 70.25 mb/K. For these values, we have obtained ðvÞ G ¼ ¼ 0:36 using V ¼ 1500 V, q ¼ 3.4 mb/K, m ¼ 220 K/ 0:012 and ðqÞ 0 0 G mb, A ¼ 75 and B0 ¼ 1050 V (see Bateman, 1998). Based on experience (Denecke et al., 1998) and the fact that relative gain fluctuations due to the applied anode voltage and ambient conditions depend slightly on the counter geometry, we can take ðqÞ ðvÞ G ¼ 0:02 and G ¼ 0:5 for all detector geometries practically used in the absolute standardization of large-area reference sources. Table 2 Values of e(fd), e(fv), e(fq), e(fp), e(ff), e(f) in normal conditions of counter operation.
Table 1 Uncorrected and corrected values of pb0 for sources of beta emitting nuclides.
Large-area reference source
pb0(%) Uncorrected values
14
Corrected values
C Pm Cl 204 Tl 90 (Sr+Y) 147
14
147
0.60
0.66
C
Pm
36
204
0.10
0.16
Cl
Tl
90
14
147
36
204
0.09
0.90
0.99
0.20
0.32
(Sr+Y)
C
Pm
Cl
Tl
90
(Sr+Y)
0.18
36
Relative standard uncertainty (%)
e(fd)
e(fv)
e(fq)
e(fp)
e(ff)
e(f)
0.16 0.17 0.03 0.06 0.03
0.01 0.01 0.00 0.00 0.00
0.26 0.29 0.06 0.09 0.05
0.26 0.29 0.06 0.09 0.05
0.26 0.29 0.06 0.09 0.05
0.48 0.52 0.11 0.17 0.10
ARTICLE IN PRESS 1718
D. Stanga, P. De Felice / Applied Radiation and Isotopes 67 (2009) 1716–1720
Counts
Relative gain fluctuations arising from gas purity and flow rate are difficult to calculate. Based on experimental results, it is ðf Þ realistic to assume that ðpÞ G ¼ 0:5 and G ¼ 0:5 for normal conditions of counter operation. In Table 2 are shown (for all reference sources of beta emitters) ðiÞ (id, v, q, values of e(fi) calculated with Eq. (6) using values of w p, f) above mentioned. In the same table, values of e(f) calculated with Eq. (3) are also given. As shown in Table 2, e(f) is much higher in the case of low energy beta emitters (14C and 147Pm). Taking into consideration values of e(f) given in Table 2 and experience, it was realistic to assume for our counting system e(f) ¼ 0.5% for 14C and 147Pm, e(f) ¼ 0.2% for high energy beta emitters and e(f) ¼ 0.1% for alpha emitters. In practice, these values are higher because the reproducibility of the source counting rate is not good enough due to large fluctuations of the flow rate and gas purity (see Wuu et al., 2002).
21
41
61
81
Counts
Fig. 1.
101 121 141 161 Channel number
181
201
221
241
55
Fe pulse height spectrum.
C-14 Pulse height spectrum
5000 4000 3000 2000 1000 0 200
1
Counts
In the absolute standardization of large-area reference sources, normal conditions of counter operation must firstly be ensured because the counter is frequently exposed to air and air impurities affect its operation drastically. Consequently, a cleaning procedure is necessary to be used before each measurement to remove air impurities by flushing the detector with counting gas and then maintaining a small gas-flow rate (usually in the range 1y3 l/h). To elaborate the cleaning procedure, we used a 55Fe source for checking the stability of the 55Fe peak as a function of time because the peak stability is the ultimate test of gas purity. To reduce the uncertainty and for the sake of simplicity, the initial setting of the discrimination level was stabilized by means of a 55Fe source. Thus, each time the counting system was put into service for source measurements, the applied anode voltage was
Fe-55 Pulse height spectrum
24000 20000 16000 12000 8000 4000 0 1
399
598
797 996 1195 Channel number
30000 25000 20000 15000 10000 5000 0
1394
1593
1792
1991
1593
1792
1991
Cl-36 Pulse height spectrum
12000 10000 8000 6000 4000 2000 0 1
Counts
2.3. Improvement of the measurement procedure
200
399
598
797 996 1195 Channel number
1394
Am-241 Pulse height spectrum
1
21
41
61
81
101 121 141 161 181 201 221 241 261 281 Channel number
Fig. 2. Pulse height spectra of the measured sources.
ARTICLE IN PRESS D. Stanga, P. De Felice / Applied Radiation and Isotopes 67 (2009) 1716–1720
slightly adjusted to obtain the same channel number for the 55Fe peak position such as it was initially set (electronic settings were not changed). As a result, the counting rate fluctuations due to changes in ambient conditions, flow rate and gas purity were partly cancelled. Changes in the discrimination level can not be controlled during the source measurement. To avoid large errors of measurements, the shape of the pulse height spectrum (see Fig. 2) was used as a rough estimation of the discrimination level stability during source counting for beta emitters. In practice, it is more convenient to have a small X-ray window on the counter for monitoring the discrimination level stability by means of a point 55 Fe source. In the case of large-area alpha emitting sources, the discrimination level stability is not critical and the peak position in the spectrum of the measured source itself can be used for monitoring large gain deviations. Experience shows that normal conditions of counter operation are difficult to be obtained even if the cleaning procedure was carefully applied. A number of quality assurance (QA) tests performed systematically are necessary because this is the safest way to reach the normal conditions of counter operation and obtain reliable measurements. A checklist for QA should include: (i) the stability of the 55Fe peak; (ii) the tightness of the gas-flow system including the counter; (iii) the length and slope of the detector plateau; and (iv) the measurement of certified reference sources.
1719
dead-time losses. A multi-channel analyzer is used to record pulse height spectra of the 55Fe and reference sources. In Fig. 1, the 55Fe spectrum obtained in the initial setting of the discrimination level is shown. Three large-area reference sources in anodized aluminum foils (14C, 36Cl and 241Am) were measured according to the improved procedure described above. In Fig. 2, their pulse height spectra are shown. Measurement results and uncertainty budget are shown in Table 3. We can see in this table that the uncertainties of measurement are much smaller than the value 3% required by ISO 8769. In order to determine the reproducibility of measurement results, the same sources were ten times measured over four weeks. In Table 4, reproducibility results (expressed as relative standard deviations) are shown. In addition, certified values of the surface emission rate are compared with measurement results and the reproducibility with the relative standard uncertainty. As shown in Table 4, certified values of the surface emission rate agree very well with measured results. Also, reproducibility results are in accordance with the relative standard uncertainties and this shows that measurements were performed under normal conditions of counter operation. Consequently, reliable and accurate measurement results were obtained.
4. Conclusions 3. Measurement results The counting system used for the absolute standardization of large-area reference sources is composed of a gas-flow proportional detector, an integral counting channel and a multi-channel analyzer. The proportional detector was flowed with a mixture of argon (90%) and methane (10%). The gas-flow of about 1 l/h was controlled by a two-stage pressure regulator and needle valves. The counter was operated at +1950 V in the beta plateau and at +1200 V in the alpha plateau. A charge-sensitive pre-amplifier and a spectroscopy amplifier, which feeds a discriminator, amplify the signals of the detector. The pulses from the discriminator are counted by conventional counting logic. A dead-time unit (8.5 ms) was inserted in the counting channel for the precise correction of Table 3 Measurement results and uncertainty budget. Measurement results (s)1
Large-area source 14
36
4407724
5304719
C
E7u(E)
241
Cl
Am
700.671.6
Uncertainty (%)
e(R) e(f) e(t) e(B) e(E)
0.10 0.50 5.00 5.00 0.55
0.10 0.20 5.00 5.00 0.35
0.20 0.10 5.00 10.0 0.23
Using a simple gas-gain model, the efficiency sensitivity of gasflow, multi-wire, proportional counters to changes in the influence quantities was analyzed. Thus, e(f) was calculated on the basis of the gain model and experience. Results showed that the uncertainties due to fluctuations of influence quantities are very small in normal conditions of counter operation. Consequently, large-area reference sources can easily be measured with relative standard uncertainties smaller than the value 3% required by ISO 8769 without stabilizing the ambient conditions. However, these errors are significant especially for low energy beta emitters (0.5%) and they must be taken into consideration for accurate measurements. The analysis also showed that the gas purity and flow rate are the most critical parameters of the counting gas because their accidental changes may give rise to large errors of measurement. For this reason, it is important to obtain normal conditions of counter operation in the absolute standardization of large-area reference sources. To reach these conditions, a cleaning procedure to remove air impurities from the detector must be applied, flow rate reproducibility must be ensured and QA tests must be performed systematically. The analysis also showed that the applied anode voltage can be used to obtain the stabilization of the discrimination level against the effect of changes in influence quantities. Based on this result, the absolute standardization of large-area sources was improved in a very simple way by means of a 55Fe source. As a result, reproducible and accurate measurement results were obtained. Thus, three large-area reference sources were measured with
Table 4 Reproducibility results together with E(measured)/E(certified) and e(E)/reproducibility. Source
E (certified)a(s1)
E(measured)/E(certified)
Reproducibility (%)
e(E)/reproducibility
14
4397 5320 699
1.002 0.997 1.002
0.42 0.25 0.20
1.30 1.40 1.15
C Cl 241 Am 36
a
Values of E(certified) are up-to-dated to the actual date of measurements.
ARTICLE IN PRESS 1720
D. Stanga, P. De Felice / Applied Radiation and Isotopes 67 (2009) 1716–1720
uncertainties smaller than 0.55% and the reproducibility better than 0.42%. References Bateman, J.E., 2003. A general parametric model for the gain of gas avalanche counters with particular attention to non-cylindrical geometries. Phys. Rep. 375, 411–443. Bateman, J.E., 1998. Gas stabilization in proportional counters. Report RAL-TR-98044, Rutherford Appleton Laboratory, UK. Berger, M.J., Unterweger, M.P., Hutchinson, J.M.R., 1996. The influence of backing and covering materials on the 2p-counting efficiency of beta-particle sources. Nucl. Instrum. Methods Phys. Res. A 369, 684–688. Curzio, G., Mazed, D., Ciolini, R., Del Grata, A., Gentili, A., 2005. Effect of air on gas amplification characteristics in argone–propane (1%)-based proportional
counters for airbone radon monitoring. Nucl. Instrum. Methods Phys. Res. A 537, 672–682. Denecke, B., Grosse, G., Szabo, T., 1998. Gain stabilization of gas-flow proportional counters. Appl. Radiat. Isot. 49 (9–11), 1117–1121. ISO 8769, 1988. Sources for the Calibration of Surface Contamination Monitors– Beta-Emitters (maximum beta energy greater than 0.15 MeV) and alphaemitters. International Organization for Standardization, Geneva, Switzerland. ISO/TAG4/WG3, 1995. Guide to the Expression of Uncertainty in Measurement, International Organization for Standardization, Geneva, Switzerland. Lewis, V., Woods, M., Burgess, P., Green, S., Simpson, J., Wardle, J., 2003. The assesment of uncertainty in radiological calibration and testing. Measurement Good Practice Guide no. 49. National Physical Laboratory-IRMF, UK. Wuu, Y.-L., Yuang, M.-C., Hwang, W.-S., 2002. The alpha and beta emitter measurement system in INER. Appl. Radiat. Isot. 5, 261–264. Yoshida, M., Oishi, T., Honda, T., Torii, T., 1996. A calibration technique for gas-flow ionization chambers with short-lived rare gases. Nucl. Instrum. Methods Phys. Res. A 383, 441–446.