A Technique for the Evaluation of Systematic Errors in the Activation Analysis for Oxygen with 14-MeVNeutrons S. S. Nargolwalla, M. R. Crambes, and J. R. DeVoe National Bureau of Standards, Washington, D . C. 20234 In comparative 14-MeV neutron activation analysis of oxygen, the neutron and gamma ray attenuation differences in the sample and standard introduce systematic errors. A quantitative evaluation of these attenuation processes in a wide range of matrices and for three sample diameters is given. The experimentally determined correction factor, in each case, shows an exponential dependence on the calculated difference between the appropriate attenuation coefficients for sample and standard. Within the range of sample diameters tested, preliminary data indicate that the slope of each calibration line is linearly dependent on the sample diameter. For comparable diameters, the magnitude of the slope for neutron attenuation is approximately ten times greater than for gamma attenuation. These calibration lines are used to predict attenuation correction factors for the determination of oxygen in other matrices. Some typical analyses of Standard Reference Materials, corrected for attenuation, illustrate the high degree of accuracy and precision obtained.
IN THIS ANALYSIS TECHNIQUE 14 MeV neutrons which are generated by the nuclear reaction 3H(d,n)4He produce 16N in the sample by the reaction lE0(n,p)16N. I6N has a halflife of 7.2 seconds and emits a 6.1-MeV gamma ray. In this analysis, two important systematic errors occur. One is the attenuation of the 14 MeV neutrons within the sample during the irradiation, and the other is attenuation of the gamma rays by the sample during the radiation detection. To evaluate these systematic errors, it is necessary to have knowledge of and control over all random errors within the analysis process. Serious variability with time in the spatial neutron flux distribution around the tritium target has been observed. To decrease this source of random error a dual sample-biaxial rotating assembly (1) similar to that described by Mott and Orange (2) and Wood, Jessen, and Jones (3) was used. Equivalency of the two sample positions and a precision determined only by counting statistics was realized with the assembly designed in our laboratory (1). Several experimental procedures described by other authors and amplified in this report have resulted in improvement in precision (4-8).
The work of Anders and Briden ( 4 ) provided sufficient incentive to initiate an investigation of these systematic errors. The attenuation process for both 14 MeV neutrons and 6.1 (1) F. A. Lundgren and S. S . Nargolwalla, ANAL.CHEM.,40, 672 (1968). (2) W. E. Mott and J. M. Orange, ANAL.CHEM., 37, 1338 (1965). (3) D. E. Wood, P. I-. Jessen, and R. E. Jones, Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Feb. 1966. (4) 0. U. Anders and D. W. Briden, ANAL.CHEM.,36,287 (1964). (5) F. C. Burns, G. L. Priest, and H. F. Priest, Society of Applied Spectroscopy, Chicago, June 1966. (6) B. L. Twitty and K. M. Fritz, Zbid. (7) R. F. Coleman, Analyst, 87, 590-593 (1962). (8) K. Perry, G. Aude, and J. Laverlochere, Symposium on Trace Characterization-Chemistry and Physics, National Bureau of Standards, Washington, D. C., Oct. 1966, Paper 54. 666
ANALYTICAL CHEMISTRY
MeV gamma rays can be expressed as a simple exponential absorption law.
f
-
e-cd
fa f
=
E
=
fa =
(1)
neutron flux (n c n r 2sec-l) or gamma intensity (photons/ sec) after traversing the effective attenuation sample thickness (d, cm) represents the proportionality constant in the differential expression (dfldd) = - cf)-e.g. absorption coefficient (cm-l) neutron flux (n cm-* sec-l) or gamma intensity (photons/ sec) without sample attenuation present
Of course, the use of such a generalized expression for both the interaction of neutrons and that of gamma rays is not possible, and separate meanings for E will be required. However, the principle of only a single interaction of the neutron or photon with a nucleus or atom in the sample which is correctly represented by Equation 1 applies for these processes under consideration. It should be noted that the term effective attenuation sample thickness is used. This implies the experimental nature of the E and d, for it is difficult to evaluate the values of e which pertain to specific samples. This is particularly true of the pertinent cross section for neutron attenuation. For the purpose of generating a correction factor, we have assumed that Equation 1 is a valid description of the fundamental attenuation process. Suitable correction factors can be generated with d taking the form of an empirical constant. 14-MeV Neutron Attenuation. It is extremely important that the appropriate attenuation coefficients be used in describing the exponential behavior of the attenuation process. In view of the mechanisms involved in the attenuation process, we have considered the concept of the total removal cross section as a more accurate measure for the matrix attenuation of 14-MeV neutrons than that of the total macroscopic cross section. The earlier study ( 4 ) assumes a total macroscopic cross section in describing this process, even though correction factors were generated with a n experimental geometry that would seem to approximate a measurement of removal cross section. The absorption coefficient, e, of Equation 1 now can take the more usual meaning of cross section:
where
V
=
volume of sample (cm3>
(9) A. F. Avery, D. E. Bendall, J. Butler, and K. T. Spinney, U.K. At. Energy Authority, AERE-R-3216, 1960.
u ~ (=~microscopic )
Wi
Mi No
ZR
= = = =
removal cross section of element i, (cm2/atom), the values for ( ~ ~ ( $are 1 available in the literature (9) weight of element i in the sample (gram) atomic weight of element i (g/gram-atom) Avogadros Number 6.03 X 1023 (atoms/g-atom) total macroscopic removal cross section of the sample for 14-MeV neutrons (cm-l)
Gamma-Ray Attenuation. In the case of gamma ray attenuation, the E of Equation 1 takes the more usual meaning of the total linear attenuation coefficient, po (cm-'),
the conditions of irradiation, primarily caused by the time difference between the sequential counts. We now wish to correct the experimentally measured radioactivity terms by multiplying them by an attenuation correction factor, y, which is equal tofo/f(Equation 1). Because identical standards are used, ysl = ys2, and we then obtain a corrected oxygen content ( Wrox)
W'OX
Rz YX
= Wo3 -
Ri ys3
(7)
Substituting Equation 6 into 7 gives
(3) From Equation 1 we have where
(5)f
(9) =
pi
=
pi
=
mass attenuation coefficient for element, i, (cm2/ gram). In the treatment for gamma-ray attenuation in the particular case of oxygen analysis, it is assumed that the mean energy approximates 6.0 MeV. The literature values for the mass attenuation coefficients were used (IO). photon linear attenuation coefficient for element, i (cm-l) W,/V = partial density of element i (gram/cm3)
Total Attenuation Correction Factor. It is evident that the left side of Equation 1 is the correction factor required for removal of the systematic errors due to the indicated absorption processes. Therefore, it is necessary to devise an experimental procedure for evaluating not only these factors, but also to provide some indication for validation of Equation 1 itself. Our main consideration is to calculate the amount of oxygen in a sample (Wax) by comparing its induced radioactivity (A,) with the weight (wO3)and radioactivity (Ass) of a standard.
where the subscripts on the values of E are the same as those for the radioactivity parameter ( A ) above. Wox is evaluated by experimentally measuring the parameters of Equation 6. This result is compared to materials whose oxygen content is known to high accuracy. For a given diameter of sample, an experimentally measured volume and weight, and a macro constituent analysis, the appropriate values of E are calculated from Equations 2 and 3. A plot of Wax/ W',, c's. the attenuation coefficient differences, which shows exponential behavior, would indicate validity of Equation 9. The slope of a straight line on a semilogarithmic plot would be the attenuation sample thickness (4. From the experimentally established relationship, attenuation correction factors for other samples could be predicted and applied to obtain an accurate result. Only one additional problem remains. When the above described experiment is performed, the product of the two correction factor ratios is obtained. The proper generalized equation is
(4)
In order to establish the constancy of experimental corrections caused by the sample irradiation system ( I ) (e.g., the samples are irradiated simultaneously but counted sequentially), two standards of identical macro constituent composition and weight (SIand S2) are placed in the sample rotator at positions 1 and 2 , respectively. It is understood that the sample to be analyzed (X)is to be placed in position 1 and S3 in position 2 of the rotator. (Otherwise remeasurement of SI and S p using reversed order will be necessary.) If we define
where Asl and A S 2 refer to the radioactivity induced in Si and S p ,respectively, Equation 4 becomes
where R1 is thought of as a correction factor resulting from (10) "X-Ray Attenuation Coefficient from 10 keV to 100 MeV," National Bureau of Standards Circular 583, U. S. Government Printing Office, Washington, D. C.
Therefore, in order to evaluate the individual attenuation processes, we select materials for which one of the correction factor ratios vanishes-e.g., p 0 , ~ 3= p o , ~ . After d, is evaluated and a correction curve for neutron attenuation established, the gamma attenuation factor and dy can be easily determined from Equation 9. EXPERIMENTAL
Equipment. The fast neutron activation facility at the National Bureau of Standards consists of a CockcroftWalton neutron generator rated at 500 pA beam current, dual sample pneumatic system with a rotating sample assembly ( I ) , sequence programmer, and a detector system consisting of two 4-inch X 3-inch NaI(T1) detectors coupled to a 400-channel pulse height analyzer. A schematic drawing of the general layout is shown in Figure 1 . The sample preparation apparatus is a simple hand operated device which permits uniform compacting of the samples in a nitrogen atmosphere. The irradiation capsules used were two-dram polyethylene vials (Olympic Plastics, Los Angeles) molded in nitrogen. A change in the sample diameter was achieved by centrally locating a vertical polyethylene tube of appropriate diameter inside the two-dram vial. In this tube the sample was compacted by means of a hand operated plunger device with replaceable heads of the VOL. 40, NO. 4, APRIL 1968
667
I
~~
~
NEUTRON
400 CHANNEL ANALYZER
SEOUENCE PROGRAMMER
SEND /RECEIVE
- N2 SUPPLY
Figure 1. Schematic design of pneumatic transfer system
Table I.
Neutron Attenuation Correction Factors and Calculated Absorption Data
Sample diameter = 1.45 cm; Sample volume = 7.78 cc; X" = 0.8 cm; Slope (d) 3.9113 i 0.09013bcm; Intercept 0.9987 i. 0.00174c
Sample Standard no. 1 (C0OH)z CadPOdz Ti02 C8Hi206
i
Standard no. 2 (COOHI2 NHzCHzCOOH Hz0 Nylon
0.0265
e--lrax 0,9790
Neutron attenuation correction factor 1.oooOi 0.00666d
0.0120
0.0175 0.0365 0.0258
0.9861 0.9712 0.9796
1.1248 f 0.01782 1.0728 i 0.01669 1.0597 + 0.02121
O.oo00 -0.0039 -0.0266 -0.0285
0,0272 0.0232 0.0271 0.0287
0.9785 0.9818 0.9792 0.9773
1.oooO f 0.00666 0.9811 i 0.01183 0.9000 i 0.01081 0.8921 f 0.00981
Sample wt (8) 8.3613
Z R (cm-l) 0.0507
A Z R (cm-l) O.oo00
P O (cm-9
4.9112 10.0425 i . 6463
0.0180 0.0327 0.0387
0.0327
8,5727 6.7891 7.7780 8.3800
0 I0520 0.0559 0.0786 0.0805
0.0180
Sample diameter = 0.95 cm; Sample volume = 3.34 cc; X" = 0.48 cm; Slope ( d ) 2.3111 i 0.25791 cm; Intercept 0.9958 i. 0.00562
i
Standard (C0OH)z Ca3(P0& Ti02 C6HI206 Ca3(P04)ze
4.8408 2.4103 4.5988 3.6888 2.4103
0.0684 0.0275 0.0349 0.0435 0.0275
O.oo00 0.0409
0.0335 0.0244 -0.0409
0.0358 0,0355 0.0379 0.0290 0.0355
0.9900 0.9940 0.9891 0.9910 0.9940
Loo00 & 0.00611 1.1038 i 0.01212 1.0523 i 0.01264 1.0480 i 0.02112 0.8943 + 0.01433
Sample diameter = 0.64 cm; Sample volume = 1.46 cc; X" = 0.32 cm; Slope ( d ) 1.5146 i. 0.25193 cm; Intercept 0.9984 i. 0.00381
i
Standard (C0OH)z CadPOdz TiOz CGHLZOB Hz0 a
1.9983 1.0651 2.0142 1.5259 1.4660
0.0644 0.0277 0.0349 0.0410 0.0785
O.oo00 0.0366 0.0295 0.0234 -0.0143
0.0355 0,0202 0.0391 0.0273 0.0263
0.9912 0.9960 0.9894 0.9920 0,9930
1.oooO i 0.00666 1.0714 =k 0.02064 1.0440 f 0.01562 1.0170 f 0.01631 0.9747 i.0.01282
Values of X are assumed to be approximately 0.5 sample diameter.
* Weighted standard error of the slope based on the number of points indicated for each sample diameter (least squares analysis).
Weighted standard error of the intercept based on the number of points indicated for each sample diameter (least squares analysis). Weighted mean standard error of the weighted mean of 6 determinations. Caa(P04)zused as the standard and run against (COOH), N.B. AZR for samples listed under Standard no. 1 were obtained by subtracting Z R (sample) from Z R (Standard no. 1). AZR for samples listed under Standard no. 2 were obtained by subtracting Z R (sample) from Z R (Standard no. 2). c
d
5
668
ANALYTICAL CHEMISTRY
Table 11. Gamma Attenuation Correction Factors and Calculated Absorption Data Sample diameter = 1.45 cm; Sample volume = 7.78 cc; Slope ( d ) 0.3985 =t 0.01334" cm; Intercept 1.0000 + 0.019226
Sample Standard no. 2 (COOH),
Fez03 Biz03d
PbO
Sample wt. (g)
la (cm-1)
AMO(cm-9
Z R (cm-l)
Neutron attenuation correction factor (least square fit of data in Table I)
8.5727 10.6367 36.0505 36.7996
0.0272 0.0397 0.1936 0.2001
O.oo00 -0.0123 0.1662 -0.1729
0.0520 0.0303 0.0523 0.0491
1.oooO 1.0820 1.0010 1.0100
Sample diameter
i
Standard (C0OH)z Fez03 Bi203 PbO Bi203C
r
=
Gamma attenuation correction factor 1.oooO f 0.00666~ 0.9864 f 0.02274 1.0680 i 0.01031 0.9331 i 0.01094
0.95 cm; Sample volume = 3.34 cc; Slope (d) 0.2614 =k 0.05542 cm; Intercept 0.9930 =t 0.00831
4.8408 5.6209 20.2324 17.6078 20.2324
0.0358 0.0607 0.3162 0.2231 0.3162
Sample diameter = 0.64 cm; Sample volume
O.oo00 - 0.0249
-0.2804 -0.1873 0.2555 =
0.0684 0.0373 0.0684 0.0548 0.0684
1.oooO 1.0740 1.oooO 1.0320 1.0740
1.oooO f 0.00611 0.9741 f 0.01032 0.9360 i: 0.01184 0.9310 i 0.00902 1.0499 i 0.01661
1.46 cc; Slope ( d ) 0.1237 41 0.02741 cm; Intercept 1.0038 i 0.00363
Standard
1.9983 0.0335 0.oooO 0.0644 1.oooO 1.oooO i 0.00666 2.8143 0.0693 -0.0356 0.0426 1.0340 0.9904 f 0.01441 8.1791 0.2914 -0.2577 0.0630 1.0020 0.9789 i 0.01224 Bi203 0.9781 =IC0.01503 PbO 8.0812 0.2334 -0.1997 0,0573 1.0100 PbOf 8.0812 0.2334 0.0147 0.0573 1.0230 1.0367 f 0.01482 Weighted standard error of the slope based on the number of points indicated for each sample diameter (least squares analysis). * Weighted standard error of the intercept based on the number of points indicated for each sample diameter (least squares analysis). Weighted mean standard error of the weighted mean of 6 determinations. Bi203 used as the standard and run against (C0OH)z. e Bi203used as the standard and run against Fe203. f PbO used as the standard and run against FeZOa. N. B. A I J was ~ obtained by subtracting po (sample) from p o (standard). (C0OH)z
Fez03
E
appropriate sizes. During sample preparation great care was taken t o compact small amounts of the powder with uniform pressure. The irradiation assembly has been discussed in detail in another publication ( I ) . Experimental Procedure. SAMPLESELECTION.For the determination of the neutron attenuation correction factors, a series of samples was carefully selected. The basic requirements of low moisture content, homogeneous fine powder, and high purity could be satisfied by only a few oxygen containing compounds. As indicated above, an additional requirement was that the calculated total gamma-ray mass absorption coefficient for each compound, compacted in the irradiation container, be approximately the same. Table I gives a list of compounds with their calculated coefficients. It is seen that although the gamma absorption differences between the compounds is negligible, the neutron attenuation coefficient differences are quite large. This difference was obtained by including organic materials with high carbon and hydrogen content. For the gamma attenuation studies, samples were selected on the basis of weight which would give substantial differences between the calculated total mass absorption coefficient of the sample and standard. In all cases the materials were dried and the results corrected for moisture content. The gamma absorption coefficients of these samples of 1.45-cm diameter are summarized in Table 11. Absorption data for sample diameters 0.95 and 0.64 cm can be computed in a similar manner. It should be noted that the sample length in each case was kept approximately constant. SAMPLE PREPARATION. The importance of this operation cannot be sufficiently stressed. The general procedure involves the loading of 250-500 rng of sample at a time, into
the vial and compacting this with the pressure device at a pressure of 30 lb/in2. I n all cases no void space was allowed. The capsules were heat sealed and stored in a nitrogen atmosphere. ANALYTICAL TECHNIQUE.The procedure consisted of simultaneously irradiating a sample and a standard (oxalic acid) for about 40 seconds and sequentially counting in the multiscaler mode gammas of energies between 4.8-8.0 MeV ( I ) . The counting time for the sample was 20 seconds and 24 seconds for the standard. A reproducible delay period of four seconds before initiation of the first count (sample) and before initiation of the second count (standard) was necessary for transfer and then exchange of the capsules, respectively. Nitrogen pressure was used to transport the capsules in the pneumatic system. During irradiation nitrogen at 5 lb/in* was allowed to flow into the rotating irradiation sample assembly. The samples were spun during counting by a vortex created by air at 15 lb/in2 entering through a point about '/z inch below the arrester pin located at the counting station in a manner similar to that described in reference (4). The counts were integrated for the sample and standard sample counts and the ratio (Rz)determined. In the same standard counts manner two identical standards were irradiated and the ratio standard #1 counts - ( R J determined. The weights of S1 and standard 12 counts S2 are the same within the precision of the analytical balance. These ratios were used in the computation of the attenuation correction factors as indicated above. A remote station machine digital computer facility was used in the computation. VOL 40, NO. 4, APRIL 1968
669
Figure 2.
14.5-MeV neutron attenuation correction factor calibration curve
Once the neutron attenuation correction factors had been determined the samples in Table I1 were run against a standard. The ratios obtained in these cases were corrected for neutron attenuation from the predetermined correction factor relationship. The corrected values for the oxygen content of these samples were compared with the true content and the gamma attenuation correction factor relationship determined. The entire procedure was repeated for 0.95- and 0.64-cm diameters. RESULTS AND DISCUSSION
The neutron attenuation effect for a typical sample diameter of 1.45 cm is illustrated in Figure 2. The gamma attenuation for the same diameter is plotted in Figure 3. The straight lines drawn on the semilog coordinates of the figures are a result of a least squares analysis. The results of the least squares analysis for all samples with their standard errors are given in Tables I and 11. The least squares calculations were performed on a computer using a code based on the Gram-Schmidt Orthonormalization process. Although the data can be fitted to the equation, the magnitude of the correction factor does not preclude the possibility
that the data can be fitted to a straight line. In addition, the assumption that the correction factors are multiplicative is supported by the fact that the correction factor curve for gamma ray absorption was generated from knowledge of the neutron absorption curve (see Equation lo). Attempts to use total neutron cross section data with our experimental data resulted in no simple relationship resembling that obtained in this work. Therefore, the use of the removal cross section receives credence. It is clear that the straight line functions should intercept the origin (0,l point). From Tables I and I1 one can be 95 confident that the true line goes through the origin in all cases studied. If we assume that Equation 1 holds, the slope of the line represents the experimentally determined effective attenuation sample thickness. It can be observed that the effective attenuation sample thickness as seen by the neutron beam is significantly larger than the actual sample diameter. Adjustment of the values used for the total removal cross section could reduce this difference without jeopardizing the fundamental relationship (Equation l). However, for the purpose of evaluating correction factors for neutron attenuation, the use of highly accurate quantities for total removal cross sec-
(pobtd)-p@mple))cm-' Figure 3. 6-MeV gamma attenuation correction factor calibration curve
670
ANALYTICAL
CHEMISTRY
Table 111. Results Oxygen Analysis in Standard Reference Materials
Sample
Sample diameter, cm
Oxygen content5>b certified or other method
No. of det.
SRM 163 1.45 1365 i 190 ppmC 8 Steel SRM 1090 0.64 484 i 28 ppm 6 Ingot Iron SRM 1091 0.64 131 i 16ppm 14 Stainless steel SRM 143b 1.45 26.63ze 8 Cystine f l 8 SRM 143b 1.45 26.63ze Cystine #2 Error is twice standard error of the average. * As per NBS certificate. c Five determinations by Vacuum Fusion Technique. d At sensitivity limit with available neutron flux. e Content by difference assuming 100% purity of this microchemical standard.
tion is not necessary, nor does the effective attenuation sample thickness need have physical meaning. On the other hand the slope of the gamma attenuation lines are about % the mean sample thickness of about 0.8 cm. This is readily understood when one considers the fact that all gammas of 6.0 MeV can undergo a scatter event and still possess sufficient energy to trigger the lower level discriminator. It is expected that for monoenergetic gamma counting, the attenuation sample thickness would approach the mean sample thickness (approximately 1/2 sample diameter). Gamma ray attenuation coefficients taken from the literature can be considered less apt to be different for this experimental system than for neutron attenuation coefficients in view of the geometrical considerations. Additional attenuation studies with other gamma energies and positron emitters appear to bear out this conclusion. It is expected however, that positron emitters must be treated as a special case in which consideration will have to be given to the attenuation of the positron energy as well as the 0.511-MeV annihilation photons in the sample. Preliminary data indicate that within the range of sample diameters studied, Linear interpolation between these diameters allows generation of the appropriate correction factors. Correction factors for any matrix are obtained by calculating the total removal cross section and total linear gamma attenuation coefficient for a given diameter of sample and substituting into Equation 9 using the appropriate d, from Tables I and 11. Use of approximate macro constituent analysis--e.g., i 5 relative standard deviation single determination-is satisfactory for these purposes. The above described technique has been used for the analysis of a series of Standard Reference Materials and the results are compared to the certified results in Table 111. It can be seen
14 MeV neutron activation analysis Error" Statistical Oxygen content (Counting) Experimental 1498 ppm
35 ppm
39 ppm
479 ppm
28 ppm
30 ppm
147 ppmd
30 ppm
32 ppm
26.28%
0.58%
0.60%
26.22%
0.45z
0.47%
that the precision of the activation analysis method is limited only by that imprecision caused by counting statistics and that the differences between the observed mean and the certified value are well within two times the standard error of the mean. For a given neutron generator, sample size, sample irradiation device, and gamma-ray detection system (including geometry of components) it is possible to generate an experimental exponential relationship that will allow the evaluation of systematic errors caused by absorption processes which will allow the application of correction factors for matrices that have not been measured experimentally. It should be emphasized that the attenuation sample thickness must be evaluated for each irradiation facility. This technique can be adapted to the analysis of other light elements such as nitrogen, aluminum, silicon, phosphorus, and fluorine, and future work will report on the necessary conditions for evaluating the systematic errors for these elements. ACKNOWLEDGMENTS
The cooperation of our colleagues J. Suddueth, P. Black, and Miss S. Birkhead is greatly appreciated. The assistance of Lloyd A. Currie and David Hogben with the statistical interpretation of the data is also gratefully acknowledged. RECEIVED for review September 19, 1967. Accepted January 11, 1968. In order to specify adequately the procedures, it has been necessary occasionally t o identify commercial materials and equipment in this report. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best available for the purpose.
VOL. 40, NO. 4, APRIL 1968
671
