demonstrate the practical usefulness and accuracy of the fluorescence method. The x-ray method is rapid and the result is obtained automatically with the composition analysis by the LAMA program. It does not require previous knowledge or even a good estimate of the thickness because any initial value, even if it is wrong by an order of magnitude, will give the correct answer although the computing time will be slightly increased.
CONCLUSION It has been shown that x-ray fluorescence analysis associated with computer calculations can now respond to the growing need of the thin film technology for a rapid, nondestructive, and precise method of determination of the composition and mass thickness of thin film materials. Only thick standards are required and they can be pure element or complex compounds. The accuracy of the analyses is similar to that of atomic absorption spectroscopy or of electron probe microanalysis of thick specimens. The thickness values also compare very well with the interferometry values. If the thickness of a film is known from interferometry for example, the method provides for the calculation of the average density which is an important characterization parameter and may vary from one film to another.
ACKNOWLEDGMENT We are grateful to C. R. Guarnieri and R. E. Richardson for thin film specimen preparation and interferometer measurements, J. Eldridge and M. H. Lee for specimen
preparation and rate-monitor data, D.F. Kyser for the electron microprobe results, and B. L. Olsen of the IBM T. J. Watson Research Center, Yorktown Heights, N.Y., for the atomic abosrption spectroscopy results.
LITERATURE CITED J. W. Criss and L. S. Birks, Anal. Chem., 40, 1080 (1968). D. Lagultton and M. Mantler, Adv. X-Ray Anal., 20, in press. F. Claisse, Rep. R.P. 327, Ministry of Mines, Quebec, P.Q., Canada, 1956. B. J. Mitchell and F. N. Hopper, Appl. Spectrosc., 20, 172 (1966). F. Claisse and M. Quintin, Can. Spectrosc., 12, 129 (1967). S. D. Rasberry and K. F. J. Heinrich. Anal. Chem., 48, 81 (1974). R. Tertian and P. Vi0 le Sage, X-Ray Spectrom., 5, 73 (1976). R. Rousseau and F. Claisse, X-Ray Spectrom., 3 , 31 (1974). R. Jenkins, J. F. Croke, R. L. Niemann, and R. G. Westberg, Adv. X-Ray Anal., 18, 372 (1975). C. E. Austen and T. W. Steeie, Adv. X-Ray Anal., 18, 368 (1975). J. Sherman, Spectrochlm. Acta, 7, 283 (1955). J. Sherman, Spectrochim. Acta, 14, 466 (1959). T. Shiraiwa and N. Fujino, Jpn. J. Appl. Phys., 5 , 866 (1966). G. Pollai, M. Mantler, and H. Ebel, Spectrochlm. Acta, Parts, 28, 747 (197 1). F. H. Chung, A. J. Lentz, and R. W. Scott, X-Ray Spectrom.,3, 172 (1974). K. Hirokaw, T. Shimanuki, and H. Got& Fresenius’ 2.Anal. Chem., 190, 309 (1962). Katsumi Ohno, personal communication. D. Laguitton, IBM Rep. RJ 1938 (1977); submitted for publication. J. V. Gilfrich and L. S.Birks, Anal. Chem., 40, 1077 (1968). K. F. J. Heinrich, Anal. Chem., 44, 350 (1972). W. Parrish, T. C. Huang, and G. L. Ayers, Trans. Am. Ciyst. ASSQC. 12, 55 (1976). P. A. Albert and C. R. Guarnieri, J. Vac. Scl. Techno/., 13, 138 (1977). J. W. Coiby, Adv. X-Ray Anal., 11, 287 (1968).
RECEIVED for review February 23, 1977. Accepted April 7, 1977.
Gamma-ray Activity Determination in Large Volume Samples with a Ge-Li Detector Alessandra Cesana and Mario Terrani * Istituto di Ingegneria Nucleare-Politecnico di Milano, Milan, I f a h
A method for the determlnatlon of the y-ray actlvlty of large volume sources is described and dlscussed. The efficiency of the detector Is expressed as the product of an Intrinsic, a geometrlcal, and a self-absorption factor. The first and the second terms are determined experimentally whlle the last Is evaluated theoretlcally. The method has been applied to the determination of the y speclflc activity of natural potassium and natural lanthanum. For potassium a value of 3.21 f 0.01 y / s g of K was obtained, whlle for 13’La the partial half-llves for the photons of 789.1 and 1435.8 keV turned out to be 3.68 f 0.14 X 10” y and 1.99 f 0.03 X 10l1 y, respectlvely.
The main difficulty connected with the measurement of the y activity of large samples is the determination of the counting
efficiency. The use of standards which is the procedure more often encountered, is pratical only when the samples are similar in density and chemical composition (e.g., in the determination of fallout activity) but it can be a problem to find an appropriate set of standards ( I ) when the sample characteristics are widely varying such as, for instance, in the determination of uranium and thorium in rocks. On the other hand, total efficiency calculations are reliable for NaI(T1) detectors, while it is a general opinion that for 1156
ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
Ge-Li detectors the uncertainties on the exact extent of the active volume significantly limit the accuracy. Greater uncertainties are connected to the computation of the peak to total ratio so that full energy peak efficiency (FEP) calculations can easily be wrong by several per cent. Perhaps the more convenient procedures are based partly on measured and partly on calculated quantities (1). The method described below, which is currently used in our laboratory, has proved to be satisfactory. The FEP efficiency eeXt of the extended and self-absorbing source is expressed as: eext =
fF?Pa
where t is the F E P efficiency of a point source situated a t a given position on the axis of the detector; Fg is the ratio between the FEP efficiency of the extended source (supposed non-absorbing) and the point source; and Fa is the ratio between the FEP efficiences of two identical extended sources: absorbing/not absorbing. The first two terms are determined experimentally, while Fa is calculated.
EXPERIMENTAL Counting Device and Sample Dimensions. The y-ray spectroscope is a coaxial Ge-Li detector (32 cm3of volume) coupled to a multichannel analyzer. The detector dimensions are: radius, 1.91 cm; height, 2.98 cm; radius of the p-type core, 0.5 cm. The crystal is enclosed in an aluminum cap 2 mm thick. The distance
a
I
I
5
10 Simple T h i c k n e s s l c m )
b
Figure 2. Source to detector arrangement: (a) source, (b) absorber, and (c) detector
Table I. Total Efficiency Values for a 3-inch NaI(TI) detectora
i
3-inch
SourceTotal efficiency 7-ray detector enerev. distance. Our Ref, Ref. -keV cm. results 2 3 I
10
Figure 1. (a) Relative counting rate (C,) and (b)relative statistical error (l/&J vs. sample thickness
81'
212' llOOb
81'
between its upper face and the cap (not accurately known in our case) is about 1.5 cm. The samples, in powder or liquid form, are enclosed in containers of Plexiglas 1mm thick, having a radius of 2.2 cm (actually determined by the dimensions of the shield) and 3.3 cm high. This height has been chosen such that beyond it no significant improvement in counting statistics can be expected. This can be seen from Figure l a which shows the variation of the counting rate C, (calculated with the procedure described below) vs. the sample thickness for a sample consisting of an igneous rock having a density of 2.5 g/cm3 and for a y-ray energy of 1 MeV, and from Figure l b which shows the variation of the relative statistical error 1/1& vs. the sample thickness. Determination of Absorption Factor Fa.F, was calculated as the ratio of the total efficiency of an absorbing and nonabsorbing source. Total efficiency was defined according to others (2-4) as the fraction of photons emitted from the source that interacts with the crystal. The value of F, calculated in this way is the same as that defined in the introduction within the limit of validity of the hypothesis (well justified by experiments, see, e.g., Ref. 4) that the peak to total ratio a t a given energy is a quantity characteristic of the crystal. The calculations were carried out as follows: 1) The detector and the source are divided in cells. The first as shown in Figure 2, the second in the most convenient way according to its geometric shape. 2) The efficiency for each cell of the source is calculated according to the expression:
ei = Ce-@'d'e-CLadze-@3~3(1- e - @ f i i , A x ) 3 j
X
4n
where the summation is extended over the detector volume and
212' 1100'
5500' 320' 662b 1330b 4440' 6100'
0.5 0.5 0.5 3 3 3 3 10
10 10 10 10
0.435 0.404 0.229 0.143 0.123 0.0701 0.0526 0.0251 0.0201 0.0165 0.0134 0.0132
0.435 0.403 0.228 0.145 0.123 0.0702 0.0526 0.0247 0,0198 0.0162 0.0130 0.0130
0.0250 0.0190 0.0164 0.0127 0.0138
a The source is placed on the crystal axis; the absorpPoint tion coefficients for NaI are taken from Ref. 4. source. ' Disk source (3-inch diameter).
pl,p2, p3, and p3/
are, respectively, the total absorption coefficient of the source, the absorber, and the detector with and without coherent scattering included; d l , d2, d3, Ax are the path length in the source, the absorber, from the upper face of the detector to the center of the upper face of the jth cell, in the jth cell, respectively. As2, = (AA cos b , ) / R 2where AA is the area of the upper face of the cell in the detector; 8 , the angle between the photon direction and the normal to the face of the cell, R = dl + dz + da. 3) Total efficiency is given by: text= Ccf,where f, is the ratio between the volume of the ith cell and the volume of the source and the summation is extended over the source volume. With this definition of text,the calculation can be easily carried out by a desk computer for a number of simple geometric forms of the source; on the other hand some approximations are introduced in particular in the computation of the solid angles. A Fortran program was written for a minicomputer (LABEN 701) and, in order to ascertain the reliability of our approximations, some values of the total efficiency of a 3-inch X 3-inch NaI(T1) crystal were calculated and compared with those obtained by other authors ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
1157
~~
-
Fa
Table 11. Photopeak Efficiency Values of Our Ge-Li Detector for Point Sources. Source to Detector Distance d 4.5 cm
a
5
9
P (6)
E,
(photons/disint.)
142' 15gb 192" 329' 412d 487' 816' 1099' 1292' 1368e 1596' 2754e
8.5 x 10-3 7.3 x 10" 2.80 X lo-' 2.0 x 10-I 9.47 x lo-] 4.67 X lo-' 2.28 X lo-' 5.65 X lo-' 4.32 X lo-' 1 9.60 X 10" 1
~
~b . 47sc.
c
1
4
0
~
d~
1 9 8 ~
E 1
0.0210 0.0186 0.0140 0.00696 0.00499 0.00391 0.00216 0.00151 0.00128 0.00119 0.000987 0.000516 ~ e . 24Na,
0.9
08
0.7
\ 800 0.6
500
\ 0.5
(see Table I). It was found that this method is unsatisfactory at very low energy values when the source to detector distance is very small; the results improve rapidly as the source to detector distance and/or the energy increase and can be considered very good in a wide range of distances (25 mm) and in a range of energy sufficient to cover all the cases of interest. The absolute values of the efficiencies calculated for our Ge-Li detector may nevertheless be inaccurate owing to the uncertainties regarding the dimensions of the detector and the detector to its envelope distance; it is, however, reasonable to suppose that the calculated values of F, (€absorb~ng/€not-absorbing) be accurate since the errors in efficiency partially cancel in the ratio. For instance, for a sample having a density of 3 g/cm3, the standard composition of an igneous rock (5) and a t a photon energy of 300 keV, the dependence of F, on the source-to-detector distance was estimated to be only 0.5%/cm. F, vs. sample density is shown in Figure 3 for a number of y-ray energies. Even in this case the sample composition was supposed to be that of an igneous rock and the absorption coefficients were taken from Ref. 4. Determination of Geometrical Factor Fg. Fgdepends upon the energy and the distances: point source-detector and extended source-detector. In order to achieve the maximum sensitivity, the extended source was situated directly on the aluminum cap covering the detector. Calculations as a function of energy and point source to detector distance ( d ) show that the energy dependence of FBis very small and vanishes above d E 4.5 cm. On the contrary, the dependence upon distance is very strong. Since this parameter, as stated above was not accurately known in our case, Fgwas measured. The determination was made using the and 1596 keV emitted in the decay photons of 131,328,487,816,
300
'
150
04
0.3
0.2
01
0
Flgure 3. Dependence of Fa on density and y-energy
of I4'La. We made use of the relation:
Fg=
ce c*F a
where C, is the FEP counting rate for a point source; C, is the FEP counting rate after the source has been dissolved in water to a volume such as to fill our extended source containers; and F, is the absorption factor for water calculated as described above. The distance between the point source and the detector was d = 4.5 cm. The results obtained, according to our calculations did not show any significant dependence on energy; thus we assumed Fgconstant for E > 131 keV. The value obtained was Fg = 1.41 f 0.02.
Table 111. Results of Some Determinations of Low Level y-activity of Large Samples Sample (mass) Pitchblende (83 8)
E, keV
Present work'
1001
0.145 i. 0.002
9
(U,O, content) %
KI
1460
La203 148 &!) ~
3.21 r 0.01
789.1
3.68 t 0.14 1Ol1
1435.8
1.99 r 0.03 10"
I,
From other authors 0.142 i. 0.002 0.136 i 0.001 0.137 t 0.002 0.149 t 0.003 0.136 i 0.003 3,25i 0.07 3.25 i 0.06 3.25 i. 0.07 4.7 I1.5 10" 3.5 i 0.3 10" 2.83 r 0.04 10" 2.34 * 0.37 10" 1.64 i. 0.06 10" 1.66 t 0.02 10"
Ref.
From IAEA certificate
(10) (11) (8) 110)
( 1 1j
(partial half life (8) of ],*La, y ) a The quoted error is the standard deviation between different determinations, It does not include the errors assdciated with ei, Fa, F g , chemical purity, etc. 1158
ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
Figure 4. Full-energy peak efficiency vs. energy for a point source situated on the axis of the detector; source to detector distance ~ 4 . 5 + cm. The full line corresponds to the equatlon: e = 5.74 X 0.0231
e-0.01176
X E
Determination of e. A conventional technique was used. Relative FEP efficiences were determined in the range 142-1596 keV using the nuclides and at the energy values listed in Table 11. The experimental points were fitted to the expression E =
u E - ~+ ce-dE
( E > 142 keV)
(1)
To convert the curve obtained to an absolute one, our Ge-Li detector was intercalibrated with a 3-inch X 3-inch NaI(T1) a t the energy values: 159 keV (47Sc),412 keV (19*Au),1368 keV and 2754 keV (24Na).The results are shown in Figure 4 together with the line resulting from the best fit to Expression 1. The mean per cent deviation of the points from the line was 1.3%.
RESULTS AND DISCUSSION The degree of accuracy attainable with this method can be deduced from the results of the tests described below.
a) Uranium Content in an IAEA Standard Uranium O r e (reference sample S-8,0.141% U308). The analysis was based on the determination of the intensity of the 1001 keV y-ray emitted in the decay of 234mPawith an equilibrium intensity of 8.28 yldisintegration of 238U(12). A sample having a mass of 83 g was analyzed 3 times; the counting time of each run was about 62 h.
b) Specific Activity of Natural Potassium. The sample consisted of 88 g of KI 99.9% pure, it was analyzed 3 times ( t , = 24 h). c ) Specific Activity of Natural Lanthanum. The sample consisted of 48 g of LazO3, 99% pure. Even in this case the analysis was repeated 3 times (t,= 48 h). In the decay of 138La,two photons are emitted having energies 788 f 1and 1436 f 1keV (10). In the present measurement the energies have been redetermined by comparison with: 352.0 keV (‘I4Pb); 609.3, 1120.0, 1765 keV (‘14Bi) and 1460.7 keV (40K). The result was 789.1 f 0.5 and 1435.8 f 0.4 keV, respectively. The second y-ray is free from interferences while the first may interfere with the photons of 786 keV, 785 and 793 keV emitted from the daughters of 226Raand ‘“Ra, respectively, and the photon of 786 keV emitted in the decay of the 234mPa daughter of 238U. Our sample was then analyzed for 226Ra, 228Ra,and U content. Its contamination turned out to be 6.2 pCi of 226Ra,5.7 NCi of ‘“Ra, and 4 ppm of U, with a resulting correction on the 789 keV photon counting rate of .=2 7’0. The results of these tests are reported in Table I11 and compared with those from other authors. As can be seen, a t least for the samples of U and K for which a sound comparison is possible, the agreement is satisfactory. The proposed method is relatively simple and requires in principle the knowledge of the absolute intensity of only a point source of a convenient radionuclide. The way in which the efficiency has been expressed implies the advantage that only Fa depends on the nature of the sample for a given geometry; moreover, in the energy region where the Compton cross-section dominates the absorption coefficient, measured in cm2/g, is a slow varying function of the atomic number, Le., a t a given energy Fa is, in practice, only a function of the sample density. In other words for energies above -400 keV, the curves of Figure 3 can be used, irrespective of the sample chemical composition, without a significant loss in accuracy. LITERATURE CITED (1) S. Morsy and S. K. Youssef, Int. J . Appl. Radiat. Isotopes, 27, 343 ( 1976). (2) R. L. Heath, “Scintillation Spectrometry”, Vol. 1, IDO-16880-1 (1964). (3) M. Belluscio, R. De Leo, A. Pantaleo, and A. Vox, Nucl. Instrum. Methods, 118, 553 (1974). (4) C. E. Crouthamei, “Applied GammaRay Spectometry”, 2nd ed.,Pergamn Press, Oxford, 1970. (5) “Handbook of Chemistry and Physics”, 46th ed., Chemical Rubber Company, Cleveland, Ohlo, 1965. (6) “Atomic Data and Nuclear Data Table”, VoL’13, No. 2-3, Academic Press, New York, (1974). (7) H. Leutz, G. Schulz, and H. Wenninger, Z . Phys., 187, 151 (1965). (8) A. W. De Ruyter, A. H. W. Aten, Jr., A. Van Dulmen, C. Krol-Koning, and E. Zuidema, Physica, 32, 991 (1966). (9) A. Azman, A. Moljk, and J. Pahor, Z . Phys., 208, 234-2 (1968). (10) J. L. Ellis and H. E. Hall, Jr., Nucl. Phys. A , 179, 540 (1972). (11) R. N. Glover and D. E. Watt, Phil. Mag., 49 (1957). (12) R. Gunnink and J. F. Tinney, in “Analytical Methods in the Nuclear Fuel Cycle”, SM-149/29, Vienna, 1972, 373 pp.
RECEIVED for review December 7, 1976. Accepted April 1, 1977.
ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
1159
