Patrick M. Granti University of California Iwine. 92664
I
The Experimental Determination of Thermal Neutron Flux in the Radiochemistry Curriculum
T h e past several years have seen the advent of numerous research reactors in America (I) and throughout the world ( 2 ) . As a result. these research and educational instruments have become accessible to an increasing number of investigators. In addition to serving the institutions a t which they are sited, nuclear readors are also often available to qualified personnel a t other institutions in the surrounding vicinities. Besides having applications in many areas of chemistry, reactors are finding use in teaching and research in physics, engineering, biology, archeology, geology, medicine, and many other scientific fields (3-10). At the University of California, Iwine, the Chemistry Department operates a light-water moderated Mark I TRIGA nuclear reactor manufactured hv General Atomic (11). Present licensing allows continuous steady-state operation to 250 kW and repetitive pulsing to 900 MW, and the reactor is used extensively in the radiochemistry program a t UCI. Instruction has been conducted a t both the undergraduate and graduate levels, in addition to a U S . Atomic Energy Commission-suonsored Summer Institute in Radiation and ~ a d i o c h e m i s t ;for ~ high school and college teachers. Lahoratories have been associated with the undermaduate course and the Summer Institute, and the experimekd determination of the reactor's thermal neutron flux has proven to he a versatile practical exercise in that its theoretical basis can be suitably varied to match the students' level of proficiency. Experimental The neutron flux determination of various irradiation positions in Irvine's reactor is accomplished by means of an activation technique. In a typical experiment,portions of a high purity gold-aluminumalloy flu wire (such as that available from Reactor Experiments, Inc.) are cleaned, accurately weighed, and mounted for irradiation in standard sample containers-TRIGA tubes or pneumatic transfer rabbits. Two wires are irradiated in every specimen container, one hare and one surrounded by a cadmium neutmn filter of0.05-cm thickness. The gold monitors are irradiated far 15 min, with the reactor operating at full power (250 kW)and the cooling water maintained at 20'C. In one study, a total of 22 wires were analyzed in 11 separate sample containers, and distribution among the various irradiation terminals in the reactor core was accomplished (see figure:and Ret (11)). Four TRIGA tubes sampled the lower rotary rack location (bottom oosition of a counled TRIGA-tube arraneement).and four sampled ;he upper location (top prsition of the mn&m arrangement,. 'The four irradiation poaitiona werc spaced equ~d~stnntly in the lazy auvan, and the rusan was mated during neutron bomhardmenr to ensure constant fluence (time-integratedflux) in the various samplea. Of the three remainingcontainers, TRIGA tubes probed the central thimble upper and lower positions, while a polyethylene rabbit monitored the pneumatic transfer terminus. After irradiation, the flux wires were set aside for several days to bv the fast-neutron induced 27Al( n.a.) allow the 15-hr 24Nakeneratad ... >*Nareaction, t o decay u, h,w &tiwry Ievele. The wirex were then annlyred for the 411.8 krV. 95.47% abundant (12) gamma ray of 2.G9fi-dny '*aAudemy on a Gnl.iJ apectromeier system. Since abrolute radioactivity assessments are required for flux determinations by the activation method, a constant-geometrycounting position on the spectrometer was effieieney-calibrated and well-characterized through the use of standardized gamma-ray reference sources. The 198Auactivities at the end of the irradiation could thereforehe cal~
'Present address: Nuclear Chemistry Grmp CNC-11, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545.
u
40-POSITIOh
ROTARY RACK Fa INSIDE GRAPHI'
@
. BORATED GRAPHITE CONTROL ROD . CENTRAL THIMBLE IRRADIATION FACILITY
REFLECTOR
PNEUMATIC TRANSFER TERMINUS OTHER POSITIONS IN THE CORE ARRAY ARE GENERALLY FILLED WITH ENRICHED- URANIUM FUEL- MODERATOR ELEMENTS A N D GRAPHITE D U M M Y ELEMENTS.
Core configuration of lrvina's TRlGA nuclear reactor.
d a t e d from the decay-corrected, experimental counting rates by means of the equation (1) Addps) = Ao'(cps)/f I, in which c is the total photopeak efficiency and I, is the gamma intensity (0.9547) of the 411.8 keV quantum. Computational Methods After the experimental determination of the lg8Auabsolute disintegration rates o i t h e irradiated wires, the thermal neutron flux can he calculated from these data in different ways. T h e comoutational techniaues involve emnirical knowledge of quanti'ties known as c a d k u m ratios. ~ e f i n e das the ratio of adivitv induced hv all neutrons to that induced hv neutrons with energy greate;than 0.5 eV only, the cadmium ratio is obtained by a direct comparison of the disintegration rates of the bare and cadmium-covered flux monitors a t a given irradiation uosition. The cadmium foil selectivelv absorbs neutrons ofiess than -0.5 eV kinetic energy while allowing those of higher energy to pass through. Thede~rminatio~~ofnrtrtron flux by nucleivacti~~ation has as its hasis the well-known activation equation (1.31 An = Nlr+ (1- e-"2) (2) I n this relationship, A. is the activity a t the end of the irradiation, in disintegrations per second (dps), of the induced radioisotope of interest ('98Au); N is the number of target nuclei available in the sample for the production of this nu-
Volume 54. Number 11. November 1977 / 707
elide; u is the cross section or probability of reaction for the particular nuclear reaction of interest [Ig7Au(n,y)lg8Au],in units of em2; C$ is the neutron flux to which the sample is exposed, in nlcm2 sec; X is the decay constant of the radioactive species formed ('98Au); and ti is the duration of the irradiation. N is related to the weight ( w ) of an element in grams via eqn. (3), in terms of Avogadro's number and the atomic weight (M)of the element. If the cross section has heen expressed, as it usually is, for one particular isotope of the element, then the fractional isotopic abundance ( f ) of the specific stable nuclide which undergoes the nuclear reaction of interest must also he included N = (6.022 X 10Z3)wfIM (3) One prescription for calculating the 2200 mhec or "conventional" thermal neutron flux density is that given by the International Commission on Radiation Units and Measurements (ICRU) (14). The activation rates of isotopic ahsorhers in a moderated neutron spectrum are independent of the neutron temperature providing their cross sections exhibit l/u hehavior in the energy region of interest. For species which do not observe the l/u law in the thermal region, however, a suitahle modification of the activation equathn is called for. The ICHL' recommends the Westcott formulation (1.5) as the correction of choice. Westcott's method assumes that the neutron spectrum consists of two distinct components-a Maxwellian distribution corresponding to a temperature T(OK) and a 1IE epithermal constituent with a low energy cut-off. An effective cross section, d, is then chosen for use in the flux calculation such that 2 = &(T) t rs(T)]
(4)
where T denotes neutron temperature and a0 is the cross section a t neutron enerw .. Eo = 0.0253 eV. The g and s parameters allow for cross-section deviations from 1/11hehavior in the Maxwellian and epi-Maxwell~anenergy -~ reglons, respeetively, and both are fuhctions of the neutron temperature. In the special case of llv absorbers, g = 1and s = 0, and the necessary condition that 8 reduces to uo is obtained. For lgSAu activation a t 20°C, the ICRU lists (14) a g value of 1.005 and an s value of 17.3; uo is tabulated as 98.8 b. The index r is a characteristic of the particular moderating assembly employed and depicts the relative strength of the 1/E epithermal component. An experimental determination of the cadmium ratio ( R c ~allows ) a calculation of the r value for gold through the equation (15) ~
Rca =
+
+ TIT^)^/^]-'
rs
(5)
Here.. To.. = 293.6OK (20.4'C) and K is a coefficient dependent upon the neutron source and cadmium thickness. Fori).O5-cm thick filtersand an isotropic neutron distrihurion, K isgiven (15)as 2.0728. The activation equation then becomes A. = N84(l - e-AiO (6) and the conventional flux density (C$o)is calculated from
-
AoNV[oo(g+ rs)](l e-AiO (7) A. is experimentally measured as described previously, N is given by the weight of the flux wire, 8 is determined through the cadmium ratio assessment, and the saturation factor, (1 - e-\' ), is set by the neutron irradiation time. Another orocedure. much simoler than the ICRU method. for calculat& the 2200 mlsec ieutron flux from radioacti: vation techniques is recommended by the American Society for Testing and Materials (ASTM) (16, 17). In the ASTM method, C$o is computed via the formula $0 =
A0
-
40=~oo(~ e-"a)'=
708 / Journal of Chemical Education
Red -1 (8)
Conventlonal Flux Densltles Available In the Mark I TRlGA Nuclear Reactor al the Unlverslty of Calltornla, lrvlne Durlng Full-Power (250 kW). Steady-State Operation Deviation of Ca6 iCRU 4, ASTM 4, ASTM 4, Core mium (n/cm2s) (n/cm2s) From IrradiationPosition Location Ratio ( ~ 1 0 ' ~ )( ~ 1 0 ' ~ )lcRU40(%) Rotary RackReflector 3.0' 0.7Z8 0.718 1.4* Lower Rotary RackReflectw 3.1' 0.50' 0.49. 2.0. Upper Pneumatic Transfer M i n g 1.7 1.67 1.62 3.0 5.71 5.49 3.9 Central Thimble- Position A1 1.5 Upper 3.23 3.05 5.6 Central Thimble- Poshion A l 1.4 Lower Average of four determinationo.
where all of the terms are as defined above. Elementary algebraic manipulation of the cadmium ratio factor in this equation shows that it is simply modifying the flux obtained from the unperturbed activation equation (eqn. (2)) by the thermal percentage of the total neutron flux. That is thermal flux - thermal flux (9) fit.* -- - I _ Rr4 thermal T re-onancc flux mul flux The ASTM. therefore, advocates the use of a scheme which is experimen~allyidentical to the ICRL' method hut which does not rewire the same amount of theoretical sophistication and comple~its.If is thus more suitablr for introductory levels of instruction. A separate measurement 118)of the effective neutron temperature in the moderator assembly under investigation is also not necessitated by the ASTM method. Results and Dlscusslon From the same counting data ohtained for the irradiated eold-aluminum flux wires, two different calculations for the Eonvemiond flux density were performed. One employed eqn. (7) of the ICRU method while the other utilized eqn. (8) of the AS'I'M method, and the results are presented in the table. The flux values obtained at L'CI are in good agreement with those ~ - ~ouoted - - ~ hv other TRlCA reactors (19). . . Variations of the duplicate results from the rotary rack samples were 5 i 4% in all instances. and the numbers calculated bv the ASTM convention were consistently lower than those oitained with the ICRU recommendations. The discre~ancvwas observed to vary inversely with the cadmium ratio,-however, and agreement was actually quite good a t the well-moderated rotary rack facility. I t seems, therefore, that for gold activation anyway, flux determinations of well-thermalized irradiation facilities may he reasonably made with the simpler ASTM computational technique. 1; may also be possible to extend the method to more poorly moderated core positions by using flux monitors, such as cobalt, which give much larger cadmium ratios than gold. Acknowledgment The author gratefully acknowledges the advice and guidance of G. E. Miller and F. S.Rowland during the course of this study. This work was supported by the United States Atomic Energy Commission, Contract AT-(04-3)-34, Agreement No. 126. Literature Cltad ~
A~~~~~~~
~. ~
~
(1) "Nudear Resftors Built, Being Built, or Planned in the United State8 aaof June 30, 1975,"TID.8200-R32. National Technical information Service. U.S.Dept, of Cammerrr, SpringAeld.Virginia22151.
(2) "Power and Research Reactors in M e m b r statea," International Atomic EneIgy Agency, Vienna, 1974. (31 Maicr-Leibnitn, H., end Springer, T., Ann. Re". Nucl. Sei., 16,201(1966). (41 "Neutron Sources and Applications."CONF-710402. Savannah River Laboratory, Aiken,South Camlins, 1971.
(5) Siluer,S.."R8dioaetivcNuelidesinMedicin~andBiology,"3rd Ed.. Leaand Febiger,
Philadelphia, 1968. (6) "Nuclm Techniques in Environmental Pollution,'.
lnt~mationslAtomic Energy
Agency. Vienna, 1971. (7) Perlman, I.,Asaro, F., and Miehel, H. V.,Ann. Re". Nuel. h i . , 22,383 (1972). (8) lanihan, J. M. A..Thomean.S. J., and Guinn, V. P., (Edilom), "Advances in Activation Analysia,"Vol. 2. A c a d c m i c P ~New ~ ~ ~York. , 1972. (9) "Nuclear Techniques for M i n e d Eiplomtim and Exploitation." Intarnstiond Atomic E n e w Agency, Vienna. 1971. (10) Blahd, W. H.."Nuclear Medicine," 2nd Ed.. MeCraw-Hill, New York, 1971. (11) Schnurer. G. T.. and McMain, A. T.. Refemnee (4). Vol. 11, p. 1-1 to 1-9. (12) Ms7tin.M. J.,DRNL-514,1976,p.48. (13) Guinn,V. P..in ' l k a t i s e on AmlyticalChemistry. Part I.Theory and Prsctiee,.'Val. 9, (Editors: Kolthoff. I. M.. andEluing. P. J.), Wiley.Intaraeienee. New York. 1971.
PP. 5585-5590: Kruger, P.. '"Principles of Activation Analysis," Wiley.lnterseience, NewYork, 197I.pp.3M7. (10 "Neutron Fluenee, Neutron Spectra and Kerma," ICRU Report 13. IntDrnationel Commiarion on Redistion Unitsand Measurements, Washington. D.C.. 1969. (15) Westeott, C. H., Walker. W. H.,and Alexander, T. K.,Proc. Second lnlsr. Conf on Peoreful Uses of Atomic Energy, Genauo. 16.70 (1958). (16) "Standard Method tor Measuring Neutron Flux by Radioactivation Techniques," ASTM Method E261, in AnnvolBook of ASTMStandards, Part 30,AmericsnSocietv for Testinrand Materisls. Philadelohis. Pa.. 1970. (171 "Standard ~ ~ t forh Measuring 2 ~ h e r m a~i e u l ~ oFlux " by Radloactivation Teehniques," ASTM Method E 262, in Annuol Book of ASTM Stondorda, see Rat lifil. .~. (1) Sehmid, L.C.. and Stinmn. W. P., N u d Sci. En#, 7,477 (1980). (19) M0rrinon.G. H.,snd Potter, N.M.,Anal. Cham., 44,839(19721.
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