Anal Bioanal Chem (2004) 379 : 210–217 DOI 10.1007/s00216-004-2557-6

S P E C I A L I S S U E PA P E R

X. Lin · R. Henkelmann

The internal comparator method

Received: 17 September 2003 / Revised: 1 February 2004 / Accepted: 10 February 2004 / Published online: 19 March 2004 © Springer-Verlag 2004

Abstract An internal comparator method is proposed which offers reliable instrumental neutron activation analysis (INAA) results for samples with an irregular geometry and/or measured at the closest position to the Ge detector. Because the selected internal comparator in the sample analyzed will receive exactly the same thermal neutron flux as the other components, this method can be applied to the INAA of materials suffering from thermal neutron self-shielding. To apply the internal comparator method, the k0-method must be installed and the analytes, including the internal comparator, should be homogeneously distributed in the test portion. Keywords Internal comparator · Internal comparator method · k0-method · k0-instrumental neutron activation analysis

Introduction The highest sensitivity or the lowest detection limit in instrumental neutron activation analysis (INAA) will be achieved when irradiated samples are counted at the closest position to the Ge detector, if all of the other experimental conditions remain the same. Indeed, in the energy range of 60–2,000 keV, the peak efficiency for a small sample at the entrance window of a 30% high-purity germanium (HPGe) detector is 33–42 times higher than that of the same sample at the 15 cm position. To measure samples at the closest position would offer many advantages: lower detection limits or more detectable elements, shorter counting times or better counting statistics, and shorter turn-out time or higher throughput. However, the INAA results from the counting positions closer to the detector are often accompanied by reduced accuracy. This

X. Lin (✉) · R. Henkelmann Institut für Radiochemie der Technischen Universität München, 85748 Garching, Germany e-mail: [email protected]

Fig. 1 Irregular sample geometry of the botanical materials after irradiation

problem is particularly pronounced for samples with an irregular geometry, such as those shown in Fig. 1. The reasons are simple: a closer counting position is much more sensitive to counting geometry and, on the other hand, an ideal standard having exactly the same counting geometry as the sample is difficult to make. For instance, peak efficiency calculations based on the semi-empirical method [1] showed that, when measuring a disk source at the endcap of a 30% HPGe detector, a very small variation of 0.5 mm in the counting geometry in the axial direction of the detector will cause about a 3% change in peak efficiency, and thus in the INAA results. The influence of the same variation decreases to 0.5% at the 15 cm distance and becomes negligible when the 25 cm position is used. Consequently, whenever possible, large counting distances should be applied in INAA, particularly for experiments requiring high accuracy [2]. The price paid is high: all the advantages of using the lower counting positions are lost. The k0-INAA using an internal comparator (the internal comparator method, ICM in short) is a solution. The

211

analyzed sample but the content of the comparator should be known before performing NAA calculations for all the other elements. There are different ways to determine the component selected as the internal comparator. The easiest way is to use the conventional k0-method and gamma-ray spectra collected at a far counting distance (15 cm or further). This procedure will be demonstrated in this work. The coirradiated flux monitor Au-Al wire can be applied to calculate the internal comparator mass content. A drawback of this practice is greater uncertainty. For better accuracy, the relative method should be used to determine the selected internal comparator. The internal comparator can also be determined by an independent technique. Then the ICM may be used to analyze materials suffering from thermal neutron self-shielding, because the internal comparator in the analyzed portion will receive exactly the same thermal neutron flux as the other components.

equations used to calculate the k0-INAA results [3] show that, when all the other experimental parameters are fixed, a calculated NAA result (ρ) is proportional to the peak efficiency ratio of comparator to sample, namely ρ∝εp*/εp, where εp* is the peak efficiency of the comparator (198Au 411.8 keV line of a flux monitor Au-Al wire, for instance) and εp is the efficiency of the concerned nuclide in sample (65Zn 1115.5 keV line, for instance). Conventional k0-INAA [4] employs external comparators (often the co-irradiated flux monitors, 198Au/411.8 keV line), then the two efficiencies εp* and εp should be accurately evaluated to get a reliable value of the ratio εp*/εp. This is a difficult task for samples of irregular shape and/or measured at the closer positions to the detector. In an intercomparison [5], 15 different efficiency transfer programs for gamma-ray spectrometry, including Monte Carlo simulation and semi-empirical computation, were examined. This project showed that the deviations between the computed results and the measured efficiencies are mostly 5–10% for the simplest case, i.e., point sources at 2 cm and 5 cm from detector entrance window, and cylindrical sources with well-defined dimensions and matrices. Obviously, much larger uncertainties on calculated efficiencies can be expected for samples with irregular geometry and/or measured at the closest position to the detector. This problem will be practically eliminated when an internal comparator is used instead of the external one, because in this case the ratio εp*/εp is calculated from one counting geometry (the sample’s geometry). The ICM takes advantage of the peak efficiency curves having similar shapes so that the ratio εp*/εp calculated from one source is not as sensitive as the εp to counting geometry (source shape, dimension, and/or counting position). The selection of the internal comparator depends on the material actually analyzed. To add a comparator to a sample is straightforward, but it carries a risk of contamination and a homogeneity problem. To use a component in a sample as the internal comparator will not disturb the

Two radioactive standard sources were made by pipetting suitable quantities of radioactive standard solutions (QCY48 from Amersham and home-made 65Zn) on filter papers of disk and strip shapes respectively. After drying, each paper source was closed in a PE bag and fixed at a 0.15 cm-thick Plexiglas plate. The disk source had a round shape with 1.66 cm of diameter and the strip source was a rectangle of 4.3 ×0.4 cm. The radioactivity of the 65Zn solution was established by counting the 65Zn disk sources at the 15 cm positions of three calibrated detectors. These sources were measured at six positions (0 cm, 1 cm, 2 cm, 5 cm, 10 cm, and 15 cm) from the entrance window of a p-type HPGe detector, which has a 30% relative efficiency and 1.8 keV of FWHM. The distance from its Ge crystal entrance surface to the 0 cm position is 0.93 cm, covering the vacuum layer in cap, Al-entrance window and sample-holder’s foot. Peak efficiencies for the sources

Table 1 Peak efficiencies for the disk source at 0 cm and 2 cm counting positions. The last column gives the difference of the two ratios, εp*/εp at 0 cm position and εp*/εp at 2 cm position. εp (0 cm),

εp (2 cm)-peak efficiencies at 0 cm and 2 cm positions respectively; εp*-peak efficiencies for a comparator energy 1,076.6 keV, which is arbitrarily selected

Materials and methods Peak efficiency and peak efficiency ratio εp*/εp for different counting geometries

Energy (keV)

εp (0 cm)

Ratio εp*/εp at 0 cm position

εp (2 cm)

Ratio εp*/εp at 2 cm position

Relative difference between εp (0 cm) and εp (2 cm) (%)

Relative difference between εp*/εp at 0 cm and εp*/εp at 2 cm (%)

60 80 100 150 200 250 300 400 500 1000 1076.6* 1500 2000

0.0369 0.0820 0.1117 0.1206 0.1001 0.0825 0.0704 0.0549 0.0453 0.0250 0.0235 0.0177 0.0139

0.636 0.287 0.210 0.195 0.235 0.285 0.334 0.428 0.518 0.939 1.000 1.326 1.692

0.016 0.033 0.044 0.046 0.039 0.032 0.027 0.021 0.018 0.010 0.009 0.007 0.005

0.563 0.275 0.210 0.197 0.237 0.287 0.335 0.429 0.519 0.939 1.000 1.330 1.703

127 146 155 160 159 158 157 156 156 156 156 157 158

12.9 4.17 0.27 –1.40 –1.17 –0.77 –0.51 –0.18 –0.01 0.04 0 –0.27 –0.63

212 Table 2 Peak efficiencies for the disk and strip sources at 0 cm counting position. The last column gives the difference of the two ratios εp*/εp for disk source and for strip source. εp (disk), εp (strip)-

peak efficiencies at 0 cm position for the disk and strip sources, respectively; εp*-peak efficiencies for a comparator energy 1,076.6 keV, which is arbitrarily selected

Energy (keV)

εp for disk source

Ratio εp*/εp for disk source

εp for strip source

Ratio εp*/εp for strip source

Relative difference between εp (disk) and εp (strip) (%)

Relative difference between εp*/εp for disk source and εp*/εp for strip source (%)

60 80 100 150 200 250 300 400 500 1000 1076.6* 1500 2000

0.0369 0.0820 0.1117 0.1206 0.1001 0.0825 0.0704 0.0549 0.0453 0.0250 0.0235 0.0177 0.0139

0.636 0.287 0.210 0.195 0.235 0.285 0.334 0.428 0.518 0.939 1.000 1.326 1.692

0.031 0.070 0.096 0.106 0.088 0.073 0.062 0.049 0.040 0.022 0.021 0.016 0.012

0.673 0.299 0.218 0.196 0.237 0.287 0.336 0.430 0.520 0.939 1.000 1.325 1.691

19.2 17.5 16.6 13.3 13.6 13.4 13.3 13.0 12.9 12.6 12.5 12.5 12.4

–5.6 –4.3 –3.5 –0.67 –0.97 –0.78 –0.63 –0.43 –0.30 –0.02 0 0.06 0.08

Table 3 Peak efficiencies for the large and small quartz sources at 0 cm counting position. The last column gives the difference of the two ratios εp*/εp for large source and for small source. εp (L),

εp (S)-peak efficiencies at 0 cm position for the large and small quartz sources, respectively; εp*-peak efficiencies for a comparator energy 1,076.6 keV, which is arbitrarily selected

Energy (keV)

εp (L) for large source

Ratio εp*/εp for large source

εp (S), for small source

Ratio εp*/εp for small source

Relative difference between εp (L) and εp (S) (%)

Relative difference between εp*/εp for large source and εp*/εp for small source (%)

60 80 100 150 200 250 300 400 500 1000 1076.6* 1500 2000

0.0824 0.1344 0.1544 0.1490 0.1261 0.1044 0.0877 0.0677 0.0555 0.0304 0.0285 0.0216 0.0170

0.346 0.212 0.185 0.192 0.226 0.273 0.325 0.422 0.514 0.939 1.000 1.322 1.678

0.089 0.145 0.167 0.161 0.136 0.112 0.094 0.073 0.060 0.032 0.030 0.023 0.018

0.341 0.210 0.182 0.189 0.224 0.271 0.323 0.419 0.512 0.939 1.000 1.325 1.684

–7.60 –7.48 –7.49 –7.44 –7.32 –7.18 –7.06 –6.85 –6.70 –6.27 –6.23 –6.05 –5.90

1.48 1.35 1.36 1.31 1.17 1.02 –0.63 –0.43 –0.30 –0.02 0 0.06 0.08

at all the counting positions were calculated for the following gamma-lines: 241Am 59.6 keV, 109Cd 88.03 keV, 57Co 122.1 keV, 139Ce 165.9 keV, 203Hg 279.2 keV, 113Tn 391.7 keV, 85Sr 514.0 keV, 137Cs 661.6 keV, 88Y 898.0 and 1,836 keV, 65Zn 1115.5 keV, and 60Co 1,173 and 1,333 keV. Polynomial fittings were followed for the low energy range from 59.6 keV to 391.7 keV and linear fittings for the higher energy range, with the aid of a fitting program in the gamma-ray spectrometry software employed [6]. Due to the cascade coincidence effect, the determined efficiencies from the nuclides 88Y and 60Co were used only in fittings for the 15 cm position. Then the peak efficiency εp and efficiency ratio εp*/εp were calculated for 12 energies covering the energy range from 60 keV to 2,000 keV. Although any energy could be used to calculate the εp*, 86Rb 1,076.6 keV was actually selected for this purpose, because it was used as the internal comparator in the ICM of pine needles as discussed later. The εp and εp*/εp results for the disk and strip sources are given in Table 1 and Table 2 respectively for the closer counting positions, where the efficiency problem is most pronounced.

To check the responses of the εp and εp*/εp to variations in sample size, the semi-empirical method [1] was applied to calculate the εp and εp*/εp for two quartz cylinders at the closest position. The large quartz cylinder was Φ2 cm with 0.5 cm of thickness. The small one had the same diameter but a smaller thickness of 0.3 cm. The experimentally determined peak efficiencies at 15 cm were used as the reference efficiencies in the semi-empirical computation. The results are given in Table 3. INAA of standard reference material SRM1575a (pine needles) using the ICM Samples and irradiation The ICM was applied to analyze a new reference material in an interlaboratory comparison sponsored by NIST [7]. A bottle of standard reference material SRM1575a (pine needles, bottle no.1280–2) was received, which was accompanied by a small bottle of

213 SRM1547 (peach leaves) as a control material. Aliquots (200 mg) were sealed in quartz ampoules (Φ8 mm with 0.5 mm of wall thickness) and coirradiated with Au-Al monitors (IRMM-530R, 0.1003% Au) for 3 days inside the beryllium reflector of BER-II reactor in Berlin. Five blank quartz ampoules and three Au-Al monitors were irradiated separately. The neutron flux parameters at this irradiation position were determined and found to be as follow: epithermal flux shape factor α=0.296±0.026, thermal to epithermal flux ratio f=149±24, thermal to fast neutron flux ratio fFast=506±15, Westcott flux index U (α ) 7Q  7 =0.00604±0.00090, thermal neutron temperature tn= 40.6±2.0 °C, and conventional thermal neutron fluxΦth=5.20× 1016 n/m2s. It is notable that the interferences from fast neutron induced reactions are negligible due to the high thermal to fast neutron flux ratio of 506. For the same reason, it is impossible to determine Ni contents in the plant leaves via the 58Ni (n, p) 58Co reaction. The burn-up factor of 198Au was calculated from the Au-Al monitors using nuclides 198Au and 199Au [8] and found to be 0.983, which was consistent with the result calculated from the neutron flux parameters. The water contents and relative standard deviations (1 s) from three determinations were found to be 3.787% (2.2%) and 2.92% (7.2%), respectively, for SRM1575a (pine needles) and SRM1547 (peach leaves) by desiccator-drying in glass vials over magnesium perchlorate from Merck. Constant weights were observed only after 24 days, which was much longer than expected.

Gamma-ray spectrometry and elemental mass content calculation Three days after irradiation, all of the activated samples were measured at positions of 15 cm from the Ge detectors. Later, all of the samples were measured at the 0 cm position for 3–5 days. All of the Au-Al monitors were measured only once at the 15 cm positions. The semi-empirical method [1] was used in the efficiency calculation. For the irradiated samples with irregular geometries as shown in Fig. 1, a simple model of cylindrical source was used, which took the measured length of the sample in the ampoule as the diameter and the ampoule’s inner-diameter (0.7 cm) as the thickness. Nuclide 86Rb was selected as the internal comparator. Its mass contents in the irradiated samples were calculated from the gammaray counting at the 15 cm position. The program MULTINAA [3] was applied for Rb content calculation, using the Au-Al wires as the external comparators. When the Rb contents in irradiated samples had been established, the mass contents of all of the other elements in the analyzed samples were calculated. The same program, MULTINAA, was applied, but using the 86Rb 1076.6 keV line as the internal comparator. INAA results and uncertainties of three individual determinations were then submitted to the organizer of the interlaboratory comparison in NIST. The uncertainties attached to the submitted NAA results were evaluated in accordance with the ISO-GUM [9], including all the influence parameters. Later, the mean values and uncertainties (1 s) evaluated by the organizer from our submitted threefold determinations were received [7]. The results are given in Table 1 together with NIST values which were announced at the end of the comparison. For the control material SRM1547 (peach leaves), the INAA results were found to be as good as the results for SRM1575a (pine needles). Therefore, they are not presented here.

0 cm position is about 1.2–1.5 times higher than that at 2 cm position, but the differences of the two εp*/εp from the two positions are less than 1% for energies higher than 100 keV. The larger differences of 4–13% are found only in the low energy range of less than 100 keV. Or in other words, the ICM results would be practically the same for a disk sample measured at the 0 cm position but using the efficiencies for the 2 cm position – a very wrong one – in the NAA calculation, provided that no low energy gammalines are used. This is not a serious limitation because only a few radioactive nuclides employed in NAA emit photons only with energy less than 100 keV. On the other hand, in INAA practice, an uncertainty of a few centimeters in counting positioning is unimaginable. A peak efficiency calculated with a smaller uncertainty in counting geometry also improves the εp*/εp in the low energy range. The results in Table 1, as well as in Table 2 and Table 3, may be accepted as an up-limit of the εp*/εp variation. A similar conclusion can be reached for sources with different shapes. Table 2 shows the εp and εp*/εp for a disk and a strip source, which were very different in shape: the disk source had Φ1.66 cm, but the strip source was rectangle of 4.3×0.4 cm. The absolute peak efficiencies at 0 cm for the disk source are more than 10% higher than that for the strip source, but the differences of the efficiency ratios εp*/εp for the two sources are less than 1% for energies higher than 150 keV. The larger differences up to 6% are found in the low energy range where the differences of εp for the two sources are more than 16%. Table 3 shows εp and εp*/εp for two cylindrical quartz sources with the same diameter. The large quartz source was 2 mm thicker than the small one, resulting in about 6–8% lower peak efficiencies. The difference between the two εp*/εp, however, are less than 1.5% over the whole energy range of 60–2,000 keV. The improvement at the low energy range comes from the fact that, due to serious self-attenuation of the low energy photons in the quartz (density=2 g/cm3), the radioactivity in the part closer to the detector plays a more important role in gamma-ray counting than the further part. As a summary, the results given above suggest that the ICM should have high tolerance on uncertainties in the sample’s counting geometry (counting position, source shape, and/or source dimension). Consequently, closer counting positions can be used in the ICM. This also allows simplification of irregular geometries to a regular module (cylinder, for example) for peak efficiency evaluation, and meanwhile provides reliable NAA results. The ICM results of a new reference material as given below verified these statements.

Results and discussion

INAA results of SRM1575a (pine needles) from the ICM

Peak efficiency and peak efficiency ratio εp*/εp

A photo of the irradiated samples and a piece of Au-Al wire is shown in Fig. 1. After irradiation, the powder of the leaves contracted, resulting in irregular shapes. Their dimensions in the ampoules could not be identified accurately. For SRM1575a (pine needles) samples, most of the powder contracted, part fell to pieces and adhered to the

Table 1 clearly shows a big influence of the counting position on the absolute peak efficiency εp but only a little influence on the peak efficiency ratio εp*/εp. As can be seen in the last two columns, for the disk source, the εp at

214 Table 4 INAA results of SRM1575a (pine needles) from the ICM

aBold

type type cItalic type bNormal

Element

As Au Ba Br Ca Ce Co Cr Cs Eu Fe Hf Hg K La Lu Na Rb Sb Sc Se Sm Sr Ta Tb Th Yb Zn

Mass content (mg kg-1, or indicated otherwise) This work

NIST certificatea, Employed counting position referenceb, or (aproximately the distance to informationc values detector’s entrance window)

0.040±0.003 0.000225, 0.000251, 0.003065 4.96±0.30 2.72±0.14 0.247±0.012% 0.0981±0.0057 0.0645±0.0037 0.365±0.020 0.266±0.014 0.00144±0.00012 46.4±2.7 0.0128±0.0016 0.0391±0.0028 0.422±0.019% 0.0479±0.0028 0.00055±0.00006 64.7±3.1 16.73±0.76 0.00856±0.00046 0.0104±0.0006 0.0985±0.0063 0.00695±0.00044 6.76±0.41 0.00135±0.00012 0.00053±0.00010 0.0142±0.0007 0.00215±0.00026 37.6±2.0

0.039±0.002 – 6.0±0.2 – 0.251%±0.010% 0.110 0.061±0.002 0.3–0.5 0.283±0.009 – 46±2 – 0.0399±0.0007 0.417%±0.007% – – 63±1 16.5±0.9 – 0.0101±0.0003 0.099±0.004 – – – – – – 38±2

ampoule wall but it also tumbled about and changed position. It was found to be impossible to make standards with the same geometry or to evaluate accurate peak efficiencies for these samples, particularly when they were measured at the 0 cm position. Instead, the sample’s efficiency was calculated from a simple model of cylindrical source as described in the experimental section and the ICM was applied to calculate the INAA results. For the plant leaves analyzed in this work, the 86Rb 1,076.6 keV line was selected as the internal comparator. The 86Rb 1,076.6 keV line is practically free of gammaray spectrum interference and can be measured with good accuracy at far and near counting positions over a long period of time. The nuclide 65Zn was not used in this work as an internal comparator due to overlapping, mainly with the 46Sc 1120.5 keV peak. However, in INAA of hair, 65Zn was used as the internal comparator [10] because this interference was negligible due to the relatively high content of Zn in hair. When turn-out time is the main concern, a dominant nuclide/gamma-line, like the 46Sc 889.3 keV, 60Co 1,173.2 keV or 59Fe 1099.2 keV line, may be used in many cases as the internal comparator. However, these gamma-lines suffer from cascade coincidence. Table 4 shows INAA results for 28 elements. The large number of determined elements from a single irradiation

15 cm Three individual results from 15 cm 0 cm 15 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm 0 cm Mainly from 0 cm 15 cm 15 cm 0 cm 15 cm 15 cm 0 cm Mainly from 0 cm 0 cm 15 cm 0 cm 0 cm 0 cm 0 cm Mainly from 0 cm Mainly from 0 cm

came mainly from a high counting efficiency at the 0 cm position. High quality, of course, is more important, which can be judged easily by comparison with the NIST values given. The quality of the ICM results is also demonstrated by Fig. 2, where the INAA results (as ratios to the certificate values) of all of the participants using INAA are presented for six elements Ca, Fe, K, Rb, Zn, and Ba. The actual values and uncertainties of the quoted INAA results can be found in the interlabaratory report [7]. It can be seen that reliable ICM results given by the Institut für Radiochemie der Technischen Universität München (RCM), #20, were reported for all of the elements, except for Ba. The Ba result was 17% too low as shown in Fig. 2f. Investigation revealed that the recommended k0-values for the 130Ba (n, γ) 131Ba reaction [11, 12] were incorrect. Redetermination of the k0-values was carried out [13]. The Ba mass content in SRM1575a (pine needles) was re-calculated and is also given in Fig. 2 (f). The reliability of the ICM is more notable in the determination of Hg and Se. These two elements are of much interest in studies of biological materials but are not easy to determine reliably. The nuclide 203Hg has only one gamma-line of 279.2 keV which is interfered with mainly by the 75Se-279.5 keV line. Obviously, the Se contents in

215 Fig. 2 Instrumental neutron activation analysis (INAA) results compared to NIST certificate values of all of the participants using INAA for the elements Ca, Fe, K, Rb, Zn and Ba (the range of the certificate value is indicated by two lines. Up- and down-pointing triangles indicate INAA result too high or too low, out of the range shown

216 Table 5 INAA results of elements Se and Hg, in micrograms per kilogram

Element

NIST value

From RCM, #20

From all of the other participants

Se

Reference value: 99±4 Certificate value: 39.9±0.7

98.5±6.3

130±20 (#3); 113±10 (#4); 130±30 (#8); 17±2 (#13a); 69.6±6.6 (#16) 29±7 (#3); 3.5±0.3 (#16)

Hg

the samples should be accurately determined first, so that an accurate interference correction on the Hg determination can be performed to get a reliable Hg result. The nuclide 75Se has five main gamma-lines (121.1, 136.0, 264.7, 279.5, and 400.7 keV) available for INAA, but four of them suffer from interferences. Only the 400.7 keV line is practically free of interference, but it has a low emission intensity (11%), resulting in low INAA sensitivity. The ICM is able to overcome this problem, because samples can be measured at the closest position. Then not only is the counting efficiency for the 400.7 keV line much higher, but the apparent intensity of the weak 400.7 keV line is also enhanced by the sum effect of the cascade gamma-lines of 121.1+279.5 keV and 136.0+264.7 keV. At the 0 cm position of a 30% HPGe detector, the sum effect factor is 2.06, i.e., the apparent intensity of this line is doubled, allowing the acquisition of a good 400.7 keV peak in a reasonable counting period. The Se and Hg results of the ICM are given in Table 5, together with the INAA results reported by all of the other participants. [7] The quality of the ICM results is notable. Additional benefits from the ICM The ICM simplified experimental work. The samples and standards or flux monitors should be measured only once at a far counting distance. Thereafter, the samples may be counted at any detector and/or at any suitable position; standards or monitors no longer need to be measured. If the internal comparator is determined independently, the sample may be irradiated and measured alone. High deadtime counting is permitted, because the dead-time correction – an important source of errors in k0-INAA using external comparators – does not influence the ICM results. The turn-out time may be shortened. To reach the same detection limit for a specific element, the required counting time is much shorter at the 0 cm position. Because measurements of flux monitors (Au-Al) at closer positions are not required anymore, delay due to waiting for 198Au decay to measurable activity is avoided. This delay could be 3 weeks long in experiments with a long irradiation period in high flux [10]. When an independent technique is used to determine the internal comparator, this method may be used for the INAA of materials suffering from thermal self-shielding. The internal comparator undergoes the same degree of thermal neutron self-shielding as all of the other components in the test portion. The ICM of glass, having a large quantity of B and/or Cd, is an example (Lin and Fuss, 1997, personal communication). The effective thermal to epi-

39.1±2.8

thermal flux ratio in the test portion should be estimated when it has a very large quantity of strong thermal neutron absorber(s) like in the INAA of boron carbide (B4C) [14]. Highly thermalized neutron flux (f>1000) will be the best for sample irradiation. In this case, the contribution from the epithermal neutrons will be negligible, even for reactions with high resonance to thermal neutron crosssection ratio (Q0), consequently the estimation of the effective thermal to epithermal neutron flux ratio in irradiated sample can be omitted. In conclusion, the ICM offers reliable INAA results for samples with an irregular geometry and/or measured at the closest position from the Ge detector. When an independent technique is applied for determining the internal comparator, the ICM may be used in the INAA of materials suffering from a thermal neutron self-shielding problem. In this case, attention should be paid to a possible change of the thermal to epithermal neutron flux ratio in the analyzed samples. The ICM is particularly suitable for the routine INAA of a large number of samples because the experimental work is simplified and the turn-out time or throughput can be improved. In contrast to the internal standard method or the standard addition method, the ICM is capable of reporting multiple elements and does not alter the analyzed samples, thus avoiding the risk of contamination. To apply the ICM, the k0-method must be installed and the analytes, including the internal comparator, should be homogeneously distributed in the test portion. Acknowledgements The authors deeply thank Dr. D. Alber (HahnMeitner-Institut, Berlin, Germany) for her kind assistance in sample irradiation and Dr. N. Berryman for her kind help in preparation of the manuscript.

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13. Lin X, Henkelmann R (2003) Investigation of the error sources in barium determination by INAA. Presented at the Fachgruppentagung 2003 der GDCh-Fachgruppe Nuklearchemie und 19 Seminar Aktivierungsanalyse, Munich 14. Lin X, Henkelmann R, Lierse v Gostomski C (2003) Determination of impurities in boron carbide by neutron activation analysis. In: Fachgruppentagung 2003 der GDCh-Fachgruppe Nuklearchemie und 19 Seminar Aktivierungsanalyse 2003, Munich