Anal. Chem. 1982, 84, 2360-2371
2966
Use of Spherical Targets To Minimize Effects of Neutron Scattering by Hydrogen in Neutron Capture Prompt y-Ray Activation Analysis Elizabeth A. Mackey’pt a n d Glen E. Gordon*
Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742 Richard
M.Lindstrom
Inorganic Analytical Research Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 David
L.Anderson
Division of Contaminants Chemistry, U.S. Food and Drug Administration, Washington, D.C. 20204
For hydrogenous targets that are thinner than they are W, eiement wnsitivitks (counts*~-”g-~)for determining concentrations of elements by neutron capture prompt w a y actlvatlon analysis (PGAA) are enhanced relathre to sendtivities obtained from measurements on nonhydrogenous materials. Them enhancwmto are causedmainly by d a d k neutron scattering by H, whkh changes the average neutron fluonce rate within the matrix. The magnitude of the effect depends on the macrorcopic scattering and abrorptlon Cross uctkns and on the dze, shape, and orientatlon of the target with respect io the neutron beam. s.nrltMtks Increaw linearly with H denrlty for thin targets of constant size and shape and ako vary with target shape. Theorotkai work was &own that element unsitlvitks for hydrogonow targets in the form of spheres are b a d affected by neutron scattering. Metwere d . v W for creating rdkl @teres and for containing liquids in spherical shapes. Eknwnt wndtMtkr weredot~forspheresanddlaksofseveralhydmgmom materials. For H, B, Ci, K, Br, and Cd, 80ndtMu.r for 8phOres were found to be l e u affected by neutron scatt.rlng. Exwptlonr were Sm and Gd sendtlvltb measured in llqukk containod In quartz globes.
INTRODUCTION For neutron capture prompt y-ray activation analysis
(PGAA), the sensitivity for a given element (where sensitivity is the slope of the analytical response curve, counts-s-l.mg-9 depends on the average neutron fluence rate (4) within the target. Therefore, determinations of element concentrations are valid only if 4 is the same for the standard and unknown matrix, or if appropriate correction factors are used to account for any differences. Assuming that the incident fluence rate (4i) is constant, the two processes that affect the average fluence rate within the target are neutron absorption and neutron scattering. In matrices containing large concentrations of absorbing nuclides, a decrease in the overall fluence rate is due to neutron absorption within the target. This self-shielding effect is well understood theoretically and, for simple geometries, can be corrected by application of an t Present address: Inorganic Analytical Reeearch Division, Chemical Scienceand Technology Laboratory, National Instituteof Standards and Technology,TechnologyAdministration,US.Departmentof Commerce. t Deceased.
0003-2700/92/03%4-238%$03.00/0
absorption law.’ The effects of neutron scattering on the average fluence rate cannot, in general, be accounted for by simple correction factors. For several target shapes, results obtained using the University of Maryland and National Institute of Standards and Technology (UM/MST) PGAA facility213showed that when hydrogen, a strong scatterer, is present in the matrix, element sensitivities are enhanced relative to those obtained from nonhydrogenous materials. As the neutron beam at this facility is well thermalized, the Sensitivity enhancements are unlikely to be significantly affected by inelastic neutron scattering or neutron moderation. Theoretical work using Monte Carlo methods to calculate the probability for neutron absorption within a scattering matrix has shown that these enhancementa are largely the result of elastic ecattering.495 Elastic neutron scatbringaffecta absorption reaction rates (or sensitivities) by altering the average distance traveled by the neutrons within the target or, equivalently stated, by altering the average neutron fluence rate. The magnitude of the effect is dependent on the size and shape of the target and on the density of the scattering and absorbing nuclides comprising the matrix. Depending on the size and shape of the target, absorption reaction rates maybe either increased or decreased relative to t h w obtained from materials possessing much smaller scattering cross sections. Thisproblem has been studied experimentally using the UWNIST PGAA facility%*and theoretically using Monte Carlo methods.4~5Results from Monte Carlo calculations for disks showed the same trends that were observed experimentally.6 Similar enhancement effecta were recently reported by researchers at the Center for Nuclear Reeearch in Strasbourg,France, but thoee authors attribute the enhancementa to inelastic scattering.’ Researchers using the UM/NIST facility obtain accuracy in the analpieof hydrogenous materials by carefully matching the target shape and matrix of test materials and standards. (1) Fleming, Ronald F. Znt. J. A pl. Rodiat. Zsot. 1983,33,1289-1268.
(2) Mackey, Elizabeth A.; Gorgn, Glen E.; Lindatrom, Richard M.; Anderson, David L. Anol. Chem. 1991,63,288-292. (3) Mackey, Elizabeth A. PLD. Theab, University of Mnryland, Department of Chemistry a d Biochbmirtry, 1991. (4) Copley, John R D.; Stone,Craig A. Nucl. Znutrum.Methob Phy8. Res. 1989, A281,593-604. (5) Copley,John R. D. N w l . Znutrum.M e t h o b m y 8 . Res. 1991,A307, 389-397. (6) Mackey, Elizabeth A.; Copley, John R. D., submitted to J. Rodioanol. Nuel. Chem. (7) Trubert, Didier; Dupletre, G.; AbM, Jean-Chles Znt. J. Rodiat. Appl. Zsot. 1991,42A, 699-705. Q 1992 Amarkan Chemical Socbty
ANALYTICAL CHEMISTRY, VOL. 64, NO. 20, OCTOBER 15, 1992
For example, Anderson e t al.8 described a procedure for the analysis of hydrogenous materials in which element standards of varying H concentrations are used to determine element sensitivities as a function of the mass of H, to yield accurate results from analyses. Enhancements due to other scatterers commonly present in biological materials, e.g. C, N, 0, have not been observed in PGAA measurements, probably becauseof the lower scattering crms sections of these elements. In previous study, we showed that the use of spheres largely eliminates the effects of neutron scattering on H sensitivity.2 In that study, only one element in one matrix (paraffin) was determined. Hydrogen sensitivities remained constant over the range of sphere sizes measured, whereas sensitivities for disks of the same material (over the same range of mass) showed increasing sensitivity with decreasing disk thickness. Theoretical work has shown that, for targets having a given scattering and absorption cross section, sensitivities for spheres should be least affected by neutron To determine if the use of spheres would eliminate enhancements for elements in addition to H in other matrices, we have measured sensitivities for several elements in various hydrogenous materials. For this work, methods were devised for preparing solid spheres and for containing liquids in quartz spheres. Element sensitivities were measured for both liquid and solid materials that had been studied in other geometries so that comparisons could be made and the magnitude of the effects of scattering could be assessed.
2387
Figure l.Stainless steel die usedto prepare l.27cm-diameter spheres from powders and spheres of THAM, SRM 1577a. and SRM 1632a formed using this die.
EXPERIMENTAL SECTION Test Sample Preparation. A seriesof disks of constant 1.27cm diameter and varying thicknesses and a series of spheres of varying diameters were prepared from each of the following substances: urea [6.71'"0 (w/w) HI, tris(hydroxymethy1)aminomethane [THAM, 9.15% (w/w) HI, NIST Standard Reference Material (SRM) 1570 spinach leaves [5.57'I"0 (w/w) HI, SRM 1577a bovine liver [6.98% (w/w) HI, SRM 1632a bituminous coal [3.85% (w/w) HI. Disks were formed from powders of each substance with a commercial stainless steel die and hydraulic press. For each material, up to 14 disks were prepared ranging in thickness from approximately 1to 12 mm. Spheres of the same materials were formed using steel dies. Six dies, capable of forming spheres of diameters 4.76,6.35,7.94, 9.53,11.1, and 12.7 mm, were designed and fabricated at NIST. The dies were made by first machining steel into two cylinders that were oil-hardened to withstand the pressures necessary for formingsolid spheresfrom powders. A hemisphere was hollowed into the end of each cylinder by electric discharge machining with carbon electrodes. The two cylinders and a push rod fit into a sleeve so that when the two pieces of the die met to form a sphericalcavity, the push r o d was flush with respect to the top of the sleeve (Figure 1). Due to difficulties in compressibility or in obtaining uniform density with the use of these dies, some materials were first formed into disks using the standard 1.27cm-diameter disk-shaped die (described above), carved into roughly spherical shapes using a scalpel and, finally, smoothed into spheres using those dies capable of forming spheres. This procedure often resulted in spheres with diameters not equal to the internal diameter of the die and thus allowed for a greater number of diameters than six (the number of dies). Spheres of urea, THAM, and SRM 1632awere created in this manner. The diameter of each spherewas measured and the density calculated to ascertain the degree of uniformity over the range of sphere sizes used. The average densities of the spheres were 2-4% less than those of the disks of the same material, the exception being average densities for THAM for which the sphereswere 5% more dense than thedisks. Relativestandard deviationsof the densities of spheres for each material were about 2-3 % . All targets were packaged in bags formed from 0.0025-cm-thick Teflon film. Hollow,sphericalfused-quartz containers, prepared at the glass shop at NIST, were used for irradiation of liquids (Figure 2). (8)Anderson, David L.;Cunningham, W.C.;Mackey, Elizabeth A. Biol. Trace Elem. Res. 1990,27, 613.
Flgure 2. Quartz globes used to contain IiquM matrices and two solM 1.27cm-diameter spheres (THAM and SRM 1570).
External diameters were measured with a micrometer, and internal diameters (5.40, 7.!54,8.22, 10.1, 11.7 mm) were determined based on the volume of H2O that each could contain. Differences between the external and internal diameters yielded approximate thicknesses of the walls of the globes which ranged from 0.5 to 0.7 mm. Irradiation of empty globes (blanks)showed that the quartz was slightly contaminated with B, and to a lesser extent with Na, but were otherwise very clean. The count rates for B and Na measured in the globe blanks were about 2-3 times greater than the count rates obtained during irradiation of Teflon bag blanks. Data from measurements on materials containing B were corrected for the presence of B and Na in the quartz. The globes were filled using a syringe and placed in Teflon bags to facilitate positioning in the neutron beam. For these experiments, sensitivities for eight elements in 100% H20, four elements in 100% DzO, and five elements in 50% solutions of H20 and D20 were measured. Compositions of the 25 solutions are listed in Table I. PGAA Method, Data Reduction, and Analysis. Most experiments were carried out at a reactor power of 20 MW, which corresponds to a neutron fluence rate at the target position of
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 20, OCTOBER 15, 1992
Table I. Compounds and Element Concentrations for Stock Solutions 1-8 solution
1 2a 2b 2c 3 4 5
6 7a 7b
7c 8a 8b
element
H
B B B
c1 K c1 Br Cd Sm Sm Sm Gd Gd
compound
(Hz0) HsBOa &Boa HBBOa NaCl KC1 KCl NaBr CdCl2 SmzOs in 1M HNO3 SmzOa in 1M HNOa SmzOain 1M HNOs GdZOa in 2 M HCl GdgOa in 2 M HCl
solution A (m /mL) B 2 0
111.9 5.291 1.334 0.533 58.68 90.59 82.15 119.9 0.577 0.561 0.927 1.961 0.272 0.541
solution B (mg/mL)
D~O
solution C
(m /mL) H~%/D~o 50.74
5.462 1.097 0.483 58.75
P
P
58.69
0.523
0.576 0.588
0.205
0.331 .
&."_I,
0
approximately 3.3 X 108 cm-26-l.O Disks were placed at an angle of 45O to the neutron beam, and the y-ray spectra were obtained during irradiations. The UM/NIST PGAA facility is described in detail e l s e ~ h e r e . ~Targets J~ were suspended in the central, uniform portion of the neutron beam. Liquids, urea and tris(hydroxymethy1)aminomethane (THAM), were irradiated for 130 min, and the SRMs were irradiated from 5 to 12 h, depending on the counting statistics desired. y radiations over an energy range of approximately 100 keV to 8 MeV were observed using a germanium detector (27% efficiency relative to a 7.6- X 7.6-cm NaI crystal) with a Nuclear Data (ND) 16K-channel analog-todigital converter (ADC). The ADC was connected to a ND9900 Workstation through a ND Ethernet multichannel analyzer. Data reduction was accomplished using a VAX 11/730 computer. Nuclear Data programs PEAK and PILEUP and a code, SUM, written by one of us (Lindstrom) were used for data reduction. All data were corrected for the effects of the pileup of pulses at high count rates,I1for temporal variations in neutron fluence rate, and for neutron self-shielding1except where noted otherwise. ATi foil (12.7-mmdiameter,139.8mg) was irradiated, and its y-rays were observed before and after irradiations to monitor temporal variations of the neutron fluence rate. Over a typical 5-week fuel cycle, the fluence rate varied by f1.5%. Additional corrections were applied to H and B data to account for the presence of these elements in the background. When measured during the irradiation of a Teflon bag blank, neutron capture reactions in the shielding materials produce background equivalent to approximately 4 mg of H and 0.5 pg of B at the target position. When scattering materials are irradiated, these count rates are enhanced as a result of the increased number of neutrons that are scattered into the surrounding shielding and support structures.3J2
RESULTS AND DISCUSSION Solid Disks and Spheres. Element sensitivities were measured for disks and for spheres of five hydrogenous materials: urea, THAM, SRM 1632a bituminous coal, SRM 1570 spinach leaves, and SRM 1577a bovine liver. Sensitivities for H were measured in all materials, sensitivities for K were measured in the three SRMs, and sensitivities for six additional elements were measured in SRM 1632a. For urea and THAM,H sensitivities were calculated using the nominal H concentration; for the SRMs, element sensitivities were calculated using the certified values, when available. Ele(9) Failey, Michael P.; Anderson, David L.; Zoller, William H.; Gordon, Glen E.; Lindstrom, Richard M. Anal. Chem. 1979,51, 2209-2221.
(10)Anderson,David L.; Failey,MichaelP.;Zoller,William H.; Walters, William B.; Gordon, Glen E.; Lindstrom, Richard M. J.Radioanal. Chem. 1981, 63, 97. (11)Lindstrom, Richard M.; Fleming, Ronald F. Proceedings of the 4th International Conference on Nuclear Methods in Environmental and Energy Research; Vogt, J. R., Ed.; University of Missouri; Columbia, 1980; p 25. (12) Anderson, David L.; Mackey, Elizabeth A., submitted to J. Radioanal. Nucl. Chem.
I
I
300
.
I
600
.
I
900
P
-
I
1200
Mass (mg)
.
I
1500
-
I
1800 I
Flgurs 3. Hydrogen sensttlvtties measured In disks (0)and spheres (0)of THAM.
Table 11. Average H and K Sensitivities for Spheres of Urea, THAM, Paraffin, and SRMs 1570, 1577a, and 1632a H sensitivity K sensitivity number (countS.s-1. (countad material of spheres m d mg-9 SRM 1570 6 1.170 f 0.033 0.183 f 0.0062 SRM 1577a 13 1.307 0.017 0.189 f 0.0067 SRM 1632a 12 1.312 f 0.028 0.182 f 0.0096 THAM 8 1.160 f 0.013 urea 6 1.180 f 0.009 paraffin 12 1.180 f 0.014 Uncertainties represent one standard deviation of the average sensitivity. 0
merits for which these materials were not certified include H for all SRMS and B, Si, C1, Sm, and Gd for SRM 1632a; concentrations for these elements were taken from a compilation of literature values.13 Generally, measurements on disks showed the same trends that have been previously observed for disks of paraffin and of SRM 1571 orchard leaves,2 Le., element sensitivities increased with increasing disk thickness over the range of 0-2 mm and beyond 2 mm decreased with increasingthickness. On the average, element sensitivities measured in disks of 2and 12-mm thickness (of the same material) differed by about 15%. For most materials, the sensitivities for disks for which thicknesses were approximately equal to the diameter (Le., targets for which the shapes were closest to spherical) agreed best with those for spheres. Sensitivitiesfor H in disks and spheres of THAM are shown in Figure 3. For spheres of all sizes, sensitivities remained constant within the errors shown which include the Uncertainties associated with counting statistics, background subtraction, and fluence-rate normalization factors. Similar results were obtained for H sensitivities from measurements on the other materials; as shown in Table 11, H sensitivities for spheres of a given material were constant within 1 2% Average sensitivities in spheres of urea, THAM, and SRM 1570 spinach leaves agree within one standard deviation of the average value. However, average H sensitivity values were greater for SRMs 1577a and 1632a than for the other materials, probably due to insufficient drying of these
.
(13) Gladney, Ernest S.; Burns, C. E.; Perrin, D. R.; Roelandte, I.; Gills, Thomas E. National Bureau ofStandards Special PublicationNo. 260-88; U.S.Government Printing Office: Washington, DC, 1984; p 9.
ANALYTICAL CHEMISTRY, VOL. 64, NO. 20, OCTOBER 15, 1992
materials. (The disks and spheres were stored in a desiccator over P205; however, the powdered SRMs were not dried prior to forming disks and spheres.) Similar results were obtained from measurements of K sensitivities in disks and spheres of the three SRMs. Average values for K sensitivity in spheres, listed in Table 11, are the same (within uncertainties listed) as those measured in a solid disk of KNOB,0.185 f 0.002 counts-s-1.mg-l. That the value of the average K sensitivity for spheres is the same within error as that measured in a nonhydrogenous disk-shaped standard indicates that the use of spheres eliminated sensitivity enhancement. Enhancements have not been observed for matrices containing other (weaker) scatterers such as C, N, or 0. For example, B sensitivities measured in a graphite matrix (100% C) and in a D2O matrix (20% D and 80% 0) were the same within the errors of the method.8 Sensitivitiesfor H and B in disks and spheres of SRM 1632a showed the same trends as those measured in other materials. Sensitivities for S, C1, K,Si, Ti, Sm, and Gd were alsomeasured in disks and spheres of SRM 1632a. For some of these elements, the trends were less clear due to the lower H concentration in this material (so that less enhancement was expected) and due to lower sensitivities (S, Si, K),or lower concentrations of the elements (Ti, Sm, Gd), causing uncertainties associated with counting statistics to be appreciable (12.5% ). However, the sensitivity averages and standard deviations of the averages for these elements were greater for disks than for spheres. Liquids Contained in Globes. We previously measured element sensitivities in liquid matrices to determine the magnitude of enhancement as a function of H concentration.2 Liquid H2O and DzO matrices provided a wide range of H concentrations and ensured homogeneity. For this work, aqueous solutions contained in quartz globes were used to determine whether the use of spheres would eliminate enhancementsfor liquids. Similar matrices were used (100% H20, 100% D20, and 50% H20/50% D2O) so that results from previous measurements on liquids contained in Teflon bags could be compared with results from spheres. Element sensitivities for B, C1, Cd, and Gd were measured in all three matrices; H and Sm sensitivities were measured in 100% H 2 0and in the 50/50 mixture, and those for K and Br were measured in 100% H2O. The values for the macroscopic absorption cross section, C,, ranged from approximately 0.01 to 0.25 cm-1. These values are defined as: C, = ZNi(uJi, where Ni is the number of atoms of element i per unit volume and u, is the cross section for neutron absorption. Values for the macroscopic scattering cross section, Z, are controlled largely by the amount of H present and are estimated by C, = ZNi(ua)i, using uB= 80b (the bound atom cross section) for H, and the free atom usvalues for all other elements.'* Values for E, ranged from approximately 5 cm-1 for 100% H2O solutions to 0.0004 cm-1 for 100% DzO solutions. The average sensitivity and standard deviation (for five spheres) for each element in each matrix are listed in Table 111. Results of measurements on aqueous boric acid solutions (contained in quartz globes) for three different H concentrations are compared in Figure 4 with those from previous measurements2 on boric acid solutions (ranging in H concentration from 0 to 11% ) contained in pillow-shaped Teflon bags. The three sensitivity values for spheres represent the average of the five spheres of different sizes measured for each value of H concentration (0,5.6, and 11.2% H), and the uncertainties shown represent one standard deviation of this average. The data shown for solutions contained in Teflon (14) Mughabghab, Said F., Divadeenam, Mundrathi, Holden, Nor"E., Eds.,Neutron Cross Sections; Academic Press: New York, 1981.
2360
Table 111. Sensitivities (countsd-mgl) for Elements Measured in Aqueous Solutions Contained in Quartz Globes ~~
element, soluE,(keV) tion
sensitivity in 100% H20 50% H20 100% DnO
standards0 (0% H) ~~
H (2223) B (477) C1 (787) Cl(787) K (770) Br (245) Cd (558) Sm(334) Gd(182)
1 2c 3 4
4 5 6 7a 8a
1.24 f 0.01 730.3 f 9.3 1.94f 0.04 2.01 f 0.05 0.195 f 0.010 0.298 f 0.007 219.2 f 3.2 851 f 4 1034f 17
1.18 f 0.02 732.2 f 8.7 715 f 9.1 714 f 14 1.91 f .01 1.9OfO.03 1.89f 0.03
0.185 f 0.002 . ..0.308 f 0.005 212.4 f 2.4 211.4 f 3.2 245 f 5 860 f 6 960f 14 948f8 ~~~
Nonhydrogenous standards used BIG, NaBr, NaCl, KCl, KN03, and CdClz in DzO;uncertainties represent the standard deviation of the average of as many as six measurements. (I
0
2
4
6
8
10
12
%H (wlv) Figure4. Boronsensitlvitles measured in borlc acid solutions contalned in Teflon bags (X) and in quartz globes (0).The dotted line represents the average sensitivity of the three values for the globes, 726 cps.
1050
. r L
c
,-I
I
h
0
2
4
6
8
1
0
1
2
%€I (w/v) Flguro 5. Gadollnlum sensitivity measured In aqueous solutions contained in Teflon bags (X) and in quartz globes (0). Data were corrected by fa.
bags represent single portions, and the uncertainties shown represent the propagated uncertainties associated with counting statistics and background subtraction. Sensitivities remained constant for spheres, as reflected by the small relative standard deviations in Table 111, but increased with increasing H concentration for the pillow-shaped bags. Similar results were obtained from measurementson aqueous solutions containing C1. However, Gd sensitivities measured in spheres showed enhancements similar to those measured in Teflon bags (Figure 5). Sensitivities were constant for the five spheres; the average of the five for each of the three matrices is plotted. Sensitivities for most elements (H, B, C1, K,Br, Cd) were constant over the range of sphere sizes studied (Table 111). For each of these elements, the standard deviation of the average of the five values (for a given matrix) is approximately
2370
ANALYTICAL CHEMISTRY, VOL. 64, NO. 20, OCTOBER 15, 1992
Table IV. Boron Sensitivities (countscl-mgl) for Several Aqueous Solutions of Varying B Concentrations Measured in Quartz Globes boric acid L B Sensitivity not corrected stock solution (cm-l) corrected bv f. by fa HzO matrix
920 900 880 860 840
820 800
-
0.0
0.2
0.4
0.6
0.8
solution 2a solution 2b solution 2c
I
I
0.2
.
.
.
.
0.4
0.6
0.8
1.0
Solution Mass (8)
702.0 f 9.24 730.9 i 7.32 739.8 i 6.57
Boron sensitivity at 0% H is 730 f 9 (countadmgl). (a)
0.0
759.5 f 9.12 753.4 i 2.70 750.6 f 5.67
1.0
Solution Mass (g)
I . ,
0.2475 0.0946 0.045
(b)
Figure 8. Samarlum (a) and hydrogen (b) SensRhrltIes measured in stock solution 7c. The upper curves In a and b represent data that were corrected by fa and the lower represent uncorrected data.
f 2 % ,which is greater than the uncertainties associated with counting statistics, but much less than the magnitude of sensitivity enhancements observed for nonspherical targets, up to 25%. The exceptions were Sm and Gd sensitivities measured in aliquots of solutions 7b and 7c, and 8b, respectively. Sensitivities for these elements increased with increasing sphere size (constantH concentration). Hydrogen sensitivities measured in these solutions showed the same trends as those of the analytes, Le., H sensitivities increased with increasing sphere size for three solutions containing Gd and Sm, but were constant for the solutions containing B, C1, or Cd. Results for Sm and H sensitivities measured in aliquota of solution 7c are shown in parts a and b of Figure 6, respectively. That the analyte and H sensitivities showed the same trends indicates that any change in the neutron distributions within these targets affects both elements in the same manner, regardless of differences in the absorption cross-section curves. However, sensitivities for these same elements (Sm and Gd) measured in solutions 7a and 8a, which were more dilute than solutions 7b and 7c, and 8b, were constant over the range of sphere sizes studied, suggesting that the effect might be dependent on the concentration of absorber. To determine whether the amount of absorber would affect sensitivities, B sensitivities were measured over a wider range of E,. Boron sensitivitieswere constant as a function of sphere size for each of three H20 solutions, and the average sensitivitiesfor each matrix were the same within 1.2 % (Table IV). These solutions were more strongly absorbing than solutions 7b, 7c, and 8b, for which sensitivity enhancements were observed, so the concentration of absorber is probably not the cause of the observed enhancements for Sm and Gd. Both Gd and Sm possess isotopes for which the absorption cross-section curves include broad (full widths at halfmaximum of about 0.08 eV), low-energy neutron capture resonances (at energies of about 0.03andO.l eV, respectively). No enhancements were observed for the ‘‘1/u” nuclides. A resonance might increase the effectiveabsorptioncross section
for that element, causing more self-shielding, or cause a decrease in the number of neutrons within a given energy range, i.e., spectral softening or hardening. However, any of these effects would decrease the average fluence rate within the target. We know of no mechanism by which the presence of isotopes possessing absorption resonances might increase sensitivities. Although all resonances enhance scattering as well as absorption, the scattering cross sections at thermal neutron energies are about 2 orders of magnitude smaller than the absorption cross sections; the contribution from Sm or Gd to the macroscopic scattering cross section for the solutions measured is negligible. The relative importance of any energy-dependent process depends on the details of the energy distribution of the neutron beam and the values of the relevant cross sections for that particular energy distribution. Copley and Stone4 have shown that elastic scattering alone can account for sensitivity enhancements of the magnitude observed at the UM/NIST PGAA facility. The extent to which inelastic scattering affects sensitivities is not known. The neutron beam at this facility is well thermalizedsso that inelastic scattering should not be a large factor in sensitivity enhancement. However, for elements that possess low energy neutron absorption resonances, changes in the energy spectrum of the neutron beam may be important. Further work is necessary to determine the energy spectrum of the neutron beam and the effect of any changes in the energy distribution on elementsensitivities for scattering matrices. Data shown in the preceding figures and tables have been corrected by a factor, fa, which accounts for the decrease in the neutron fluence rate caused by absorption within the target. (The measured count rates are divided by f a to correct for neutron absorption). The value of fa depends on the target shape and on the amount of absorber present. As defined in ref 1,for spheres, f a = 3 / x 3 [ x 2 / 2- 1+ (1 + %)e-.]where x = Car and r = sphere radius, and for disks the approximation f a = l/x[ 1- e-xl, where x: = Z,(t/cos 45) and t = disk thickness, was used. This factor is appropriate for pure absorbers, but does not accout for any changes in the average fluence rate caused by neutron scattering. The general correction factor that accounts for both scattering and absorption of neutron is f = 4/4ie5s6 (If the material is a pure absorber, then f = fa). Scatteringmay either increase of decrease the average neutron fluence rate, so the appropriate correction factor may be either greater or less than fa. Theory predicts that, all other factors being equal, spheres will be least affected by neutron scattering, but not necessarily ~ n a f f e c t e d .For ~ ~ most ~ of the solid spheres studied, element sensitivities were constant within h2%. These materials encompass a broad range of values for C, (from approximately 0.5-5 cm-l) but only a relatively small range of Ea values (approximately0.02-0.05 cm-l). Corrections for neutron self-shielding were typically 13%. To determine whether the correction factors required to account for both scattering and absorption cf, are greater or less than those required for pure absorbers Cfd, apparent correction factors, Le., the factors that would be required to
ANALYTICAL CHEMISTRY, VOL. 64, NO. 20, OCTOBER 15, 1992 1.05
I
+
0.85
0.0
0.1
0.2
0.3
2RZabs -0 7. SeH-ehkIdlng (X) and apparent (+) wrrectlOn factors for data obtained from measurmnte of B In boric acid solutions contahed
hquerttw-.
correct the measured sensitivity to the sensitivity obtained from measurements on nonhydrogenous materials, were compared with the calculated self-shielding factors (f3 for the aame targets. Results from measurements on boric acid solutions of varying concentrationscontained in quartz globes showed that the correction factors required for spheres that both scatter and absorb neutrona are greater than those required for purely absorbing spheres (Figure 7). (That is, because the value of the apparent correction factor is greater, the percent by which the values are corrected is less.) This finding indicates that, for spheres, neutron scattering counteracts the effects of neutron absorption; thus, the use of neutron self-shielding factors alone to correct data would overestimate the true correction factor that accounts for the effeda of both scattering and absorption. This finding is not consistent with theoreticalworkWhat predicts that correction factors for spheres that scatter and absorb will be less than those that only absorb.
CONCLUSIONS In general, to ensure accuracy in the analysis of hydrogenous materials (of any size or shape), analytical portions and standards should be matched with respect tqjize, shape, and matrix, where "matrix" refere to the concentrations of individual elements. Using this method, elementsensitivities for the (hydrogenous)standards and analytical portions will be enhanced relative to those obtained from nonhydrogenous standards, so that a new set of standards must be prepared for each type of matrix and target shape analyzed. Sensitivity enhancements were not observed in conjunction with other scatterers commonly present in biological materials (C, N, 0) so that, in most cases, it is sufficient to match portions and standards with respect to H concentration, size, and shape. To eliminate the need to prepare a different set of standards for each matrix, spheres may be employed as, in many cases, the use of spheres will eliminate sensitivity enhancements. (16)Reynolds, Samuel A,;Mullins, W.Thomae. Znt.J. Appl. Radiat. h o t . 1983, 14, 421.
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For materials that are both strongly scattering and absorbing (especially hydrogenous materials containing large amounts of Gd or Sm), standards and analytical portions should be closely matched with respect to element composition (aswell as size and shape). Although measurements using instrumental neutron activation analysis (INAA) were not performed for this work, enhancement of INAA sensitivities for hydrogenous materials have been reported twice, and those investigators attributed the observed enhancements to neutron moderation.7J5 Accordingto theory, little or no enhancementshould be observed for INAA or for in-reactor PGAA in which irradiations in a nearly isotropic neutron field are used.5 Theoretical work495 and comparison of theoretical and experimentaldata6indicate that the sensitivityenhancements observed using the UM/NIST PGAA facility are large the result of elastic neutron scattering by H. However, it is unlikely that the anomalous results from measurements on spheres containing Sm and Gd solutions can be accounted for by this model. As discussed above, these results suggest a possible role of low-energy neutron absorptions resonances, which are quite strong in both elements, but a mechanism by which the presence of a resonancemight increase sensitivities for all elements in the matrix is not known.
ACKNOWLEDGMENT We gratefully acknowledge the cooperation of the NIST reactor staffduringtheseexperiments. WethankDickTurner of the NIST machine shops for his time and effort in the fabrication of the dies used for creating solid spheres and Jeff Anderson of the NIST glass shop for his time and effort in creating the quartz globes. We also wish to thank John R. D. Copley for his interest and advice in this work. This work was supported in part by the National Institute of Standards and Technology through Grant/Cooperative Agreement 70NANB9H0903 to the University of Maryland. This work was taken from the dissertation submitted by E.A.M. to the Graduate School of Arb and Sciences at the University of Maryland in pahial fulfillmentof the requirementsfor a Ph.D. degree in Chemistry. Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedures in adequate detail. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technologynordoes it implythat the materials or equipment identified are necessarily the best available for the purpose. Contributions of the National Institute of Standards and Technology are not subject to copyright.
RECEIVED for review February 25, 1992. Accepted June 30, 1992. Registry No. THAM, 77-86-1; H,1333-74-0; B,7440-42-8; C1,7782-50-5;K,7440-09-7;Br,7726-95-6;Cd,7440-43-9;Sm, 7440-19-9;Gd, 7440-54-2;urea, 57-13-6;quartz, 60676-86-0; neutron, 12586-31-1.
