# ASTM E481-16

Designation: E481 − 16Standard Test Method forMeasuring Neutron Fluence Rates by Radioactivation ofCobalt and Silver1This standard is issued under the fixed designation E481; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers a suitable means of obtainingthe thermal neutron fluence rate, or fluence, in well moderatednuclear reactor environments where the use of cadmium, as athermal neutron shield as described in Test Method E262,isundesirable because of potential spectrum perturbations or oftemperatures above the melting point of cadmium.1.2 This test method describes a means of measuring aWestcott neutron fluence rate (Note 1) by activation of cobalt-and silver-foil monitors (See Terminology E170). The reaction59Co(n,γ )60Co results in a well-defined gamma emitter havinga half-life of 1925.28 days (1).2The reaction109Ag(n,γ)110mAgresults in a nuclide with a complex decay scheme which is wellknown and having a half-life of 249.76 days (1). Both cobaltand silver are available either in very pure form or alloyed withother metals such as aluminum.Areference source of cobalt inaluminum alloy to serve as a neutron fluence rate monitor wirestandard is available from the National Institute of Standardsand Technology (NIST) as Standard Reference Material 953.3The competing activities from neutron activation of otherisotopes are eliminated, for the most part, by waiting for theshort-lived products to die out before counting. With suitabletechniques, thermal neutron fluence rate in the range from 109cm−2·s−1to3×1015cm−2·s−1can be measured. For thismethod to be applicable, the reactor must be well moderatedand be well represented by a Maxwellian low-energy distribu-tion and an (1/E) epithermal distribution. These conditions areusually met in positions surrounded by hydrogenous moderatorwithout nearby strongly absorbing materials. Otherwise, thetrue spectrum must be calculated to obtain effective activationcross sections over all energies.NOTE 1—Westcott fluence rate 5v0*0`n~v!dv.1.3 The values stated in SI units are to be regarded as thestandard.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:4E170 Terminology Relating to Radiation Measurements andDosimetryE177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE181 Test Methods for Detector Calibration and Analysis ofRadionuclidesE261 Practice for Determining Neutron Fluence, FluenceRate, and Spectra by Radioactivation TechniquesE262 Test Method for Determining Thermal Neutron Reac-tion Rates and Thermal Neutron Fluence Rates by Radio-activation Techniques3. Significance and Use3.1 This test method uses one monitor (cobalt) with a nearly1/v absorption cross-section curve and a second monitor(silver) with a large resonance peak so that its resonanceintegral is large compared to the thermal cross section. Thepertinent data for these two reactions are given in Table 1. Theequations are based on the Westcott formalism ((2, 3) andPractice E261) and determine a Westcott 2200 m/s neutronfluence rate nv0and the Westcott epithermal index parameterr=T/T0. References (4, 5, and 6) contain a general discussionof the two-reaction test method. In this test method, theabsolute activities of both cobalt and silver monitors aredetermined. This differs from the test method in the referenceswherein only one absolute activity is determined.3.2 The advantages of this test method are the elimination ofthree difficulties associated with the use of cadmium: (1) the1This test method is under the jurisdiction ofASTM Committee E10 on NuclearTechnology and Applications and is the direct responsibility of SubcommitteeE10.05 on Nuclear Radiation Metrology.Current edition approved Oct. 1, 2016. Published October 2016. Originallyapproved in 1973. Last previous edition approved in 2015 as E481 – 15. DOI:10.1520/E0481-16.2The boldface numbers in parentheses refer to references listed at the end of thistest method.3Standard Reference Material 953 is available from National Institute ofStandards and Technology, U.S. Dept. of Commerce, Washington, DC 20234.4For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1perturbation of the field by the cadmium; (2) the inexactcadmium cut-off energy; (3) the low melting temperature ofcadmium. In addition, the reactivity changes accompanying therapid insertion and removal of cadmium may prohibit the useof the cadmium-ratio method. However, the self-shieldingcorrections remain important unless the concentrations ofcobalt and silver are small. Studies indicate that the accuracy ofthe two-reaction method for determination of thermal neutronfluence is comparable to the cadmium-ratio method (14).3.3 The long half-lives of the two monitors permit thedetermination of fluence for long-term monitoring.4. Apparatus4.1 NaI(Tl) or Germanium Gamma-Ray Spectrometer (us-ing a multichannel analyzer)—For the NaI(Tl) technique andthe germanium technique, see Test Methods E181.4.2 Precision Balance.4.3 Digital Computer.5. Materials and Manufacture5.1 The two monitors required for this test method arecobalt and silver. Although these two materials are availablecommercially in very pure form, they have been used (15)alloyed with aluminum (≤1 % cobalt and ≤1 % silver) tominimize the self-shielding effect and to permit insertion intoa high thermal-neutron fluence rate (1015cm−2s−1) facility (6,16). Typical alloys contain 0.1 % silver or cobalt in aluminum)see 6.1 and 8.1).5.2 The uncertainties and nonuniformity of alloy concentra-tions must be established by one or more different testmethods. These might include chemical and activationanalysis, or spectrometry. The purity of the aluminum matrixshould also be established.5.3 Whenever possible, the alloys should be tested forinterfering impurities by neutron activation.5.4 The method of encapsulating the monitors for irradia-tion depends upon the characteristics of the facility in whichthe measurements are to be made. The monitors have essen-tially the same chemical characteristics as pure aluminum;therefore, an environment in which aluminum would not beadversely affected would be generally satisfactory for thealloys. However, the low mechanical strength of the monitorsrequires in many instances that it be encapsulated or shieldedfrom physical disturbances by some type of container. Alumi-num cans or tubing are satisfactory for many cases of interest,but for hostile environments, stainless steel or vanadium maybe preferable. Perturbation due to the presence of the containermust be accounted for, especially in the case of stainless steel.The container should be constructed in such a manner that itwill not create a significant flux perturbation and that it may beopened easily, especially if the monitors must be removedremotely.6. Westcott Neutron Fluence Convention6.1 The Westcott neutron fluence convention is designedprimarily for calculations involving reactions rather than thoseinvolving scattering or diffusion. It states that the reaction rateper atom present, R, is equal to the product of an effective crosssection, σˆ, with the Westcott neutron fluence φw= nv0, wheren = the neutron density, including both thermal and epithermalneutrons, cm−3, and v0= 2200 m/s.Thus:R 5 φwσˆ 5 nv0σˆ (1)The true equation for reaction rate is given by the equation:R 5 *0`n~v!vσ~v!dv (2)where:n(v) = neutron density per unit velocity,v = neutron velocity, andσ(v) = cross section for neutrons of velocity v.TABLE 1 Recommended ConstantsSymbol ParameterCobalt (60Co) Silver (110mAg)ValueAReference ValueAReferencet1/2Half-life 1925.28 (14) days (1) 249.76 (4) days (1)A Abundance of parent isotope 100 % (59Co) (1) 48.161 (8) % (109Ag) (1)σaAbsorption 2200 m/s cross section for target59Co and109Ag37.233b±0.16%B,C91.0b±1% (7)σ02200 m/s cross section for formation of60Co and110mAg 37.233b±0.16%B,C4.12 (10) (8)S0Correction factor which describes the departure of thecross section from the 1/v law in the epithermalregion1.80[59Co(n,γ)60Co]D18.1(7)[109Ag(n,γ)110mAg](8)I0Resonance Integral 75.421b±0.77%[59Co(n,γ)60Co](9)E67.9 (31) b[109Ag(n,γ)110mAg](8)σ2Effective absorption cross section for product nuclide(reactor spectrum)2b (10) 82 b (11)GthThermal neutron self-shielding factor Table 3 (12) 1−4/3R^a(4)G resResonance neutron self-shielding factor Table 3 (12) Fig. 1Fg Correction factor which describes the departure of thecross section from 1/v law in thermal region1.0 (2) See Table 4 (2)AThe numbers in parenthesis following given values are the uncertainty in the last digit(s) of the value; 0.729 (8) means 0.729 ± 0.008, 70.8(1) means 70.8 ± 0.1.BA 2200 m/s cross section (E = 0.0253 eV, T = 20°C) was taken from the sources indicated in Ref (9).CCross section uncertainty data is taken from Ref (7), the cross section comes from the other reference.DCalculated using Eq 10.ECross section uncertainty comes from covariance data provided in the cross section source. The other reference indicates the source of the cross section.FIn Fig. 1, Θ =4ErkT/AΓ2= 0.2 corresponds to the value for109Ag for T = 293 K, ^r=N0σr, max. σr, max=29999 barn at 5.19 eV (13) .E481 − 162Therefore, the effective cross section is defined by theequation:σˆ 5 *0`n~v!vσ~v!dv/nv0(3)The neutron spectrum assumed by Westcott has the form:n(v)=n(1 − f)Pm(v)+nfPe(v), where Pmand Peare theMaxwellian and epithermal density distribution functions nor-malized so that: *0`Pm~v!dv5*0`Pe~v!dv51. The quantity f is thefraction of the total density, n, in the epithermal distribution.The epithermal distribution is assumed proportional to 1/E perunit energy interval. This distribution is terminated by a cut-offfunction at a suitable lower limit of energy. Based on the abovespectrum, one obtains the following relation for the effectivecross section:σˆ 5 σ0~g1rs! (4)where:σ0= cross section of 2200 m/s neutrons,g = a measure of the departure of the cross section from 1/vdependence in the thermal region,s =S0=T/T0, a factor which describes the departure of thecross section from the 1/v law in the epithermal region,including resonance effects, andr = a measure of the proportion of epithermal neutrons inthe reactor spectrum.More specifically:r 5 f=πµn/4 (5)where:f = fraction of the total density in the epithermaldistribution, andµn= a factor chosen to give the proper normalization to theepithermal density distribution. A suitable factor forwater moderated systems is 5 (2).6.2 Limitation of the Westcott Convention—Sufficient con-ditions for the applications of the Westcott convention are that:(a/ξ(s,0.1 (6)and:T/Tm,1.07 (7)where:∑a= macroscopic absorption cross section averaged over allmaterials affecting spectrum,ξ = average logarithmic energy decrement per collision,∑s= macroscopic scattering cross section averaged over allmaterials affecting spectrum,T = neutron temperature, K, andTm= temperature of the moderator, K.If as a result of neutron captures (for example, in the fuel)the quantity ∑a/ξ∑sbecomes too great or if the neutrontemperature T is too great relative to the moderator temperatureTm, the Maxwell spectrum hypothesis fails and the truespectrum must be calculated and the effective cross sectiondetermined with this spectrum.6.3 The conventional 2200 m/s thermal neutron-fluencerate, φ0, and the epithermal fluence-rate parameter, φe,asdefined in Test Method E262, can be obtained from theWestcott neutron-fluence rate, φw, and the Westcott epithermalindex, r =T/T0, by means of equations Eq 8 and Eq 9:φ05S1 24 r=πµnDφw(8)φe52=πr ŒTT0φw(9)6.4 In Eq 8, it is necessary to estimate the neutrontemperature, T, in order to obtain the value of r from the indexr=T/T0. Provided inequality (Eq 7) is satisfied, only slighterror is introduced by assuming T=Tm, the moderatortemperature.6.5 Although the Ag109(n,λ)Ag110mS0value in Table 1 is ameasured value, S0can be calculated by the following equa-tion:S052=πI“0σ052=πSI0σ02 2g ŒE0ECdD (10)where:I“0= resonance integral excess over the 1/v cross sectionvalue, cm2,σ0= 2200 m/s cross-section value, cm2,I0=resonance integral, *ECd`σ~E!EdEE0= 0.0253 eV, andECd= 0.55 eV.7. Procedure7.1 Decide on the size and shape of the monitors to beirradiated, taking into consideration the size and shape of theirradiation space. The mass and exposure time are parameterswhich can be varied to obtain a desired disintegration rate fora given neutron fluence rate level. To facilitate the convergenceof the two activity equations for the fluence rate and theepithermal index, the concentration of the alloys should bechosen so that the ratio of the disintegration rates is on theorder of one.7.2 Weigh the samples to a precision of 61.0 % (1S %) asdefined in Practice E177.7.3 Irradiate the samples for the predetermined time period.Record the power level and any changes in power during theirradiation, the time at the beginning and end of the irradiation,and the relative position of the monitors in the irradiationfacility.7.4 A waiting period is necessary between termination ofthe exposure and start of counting when using Co-Al andAg-Al monitors. This allows the 0.62356 days (17) half-life24Na which is formed by fast-neutron reactions on27Al or bythermal-neutron captures by23Na impurities to decay belowlevels at which its radiations may cause interferences. It issometimes advisable to count the samples periodically andfollow the decay of the portions of the activities due to the24Na. The length of the waiting period can be reduced by theuse of a germanium detector.E481 − 1637.5 With the gamma-ray spectrometer, analyze the silversample for110mAg and the cobalt sample for60Co. Obtain thenet count rate in each full-energy gamma-ray peak of interest,that is, 657.7623 keV or 884.684 keV for110mAg, 1332.501keV for60Co (see Test Methods E181). See Table 2 for gammaradiations of110mAg.8. Calculation8.1 Calculate the activities of110mAg and60Co in disinte-grations per second.8.2 AWestcott 2200 m/s neutron fluence rate, nv0,orφwandtheWestcott epithermal index parameter, r =T/T0are related tothe measured activities of the silver and cobalt monitors by thefollowing equation:A 5 N0λBFGσˆ1φwti(11)where:A = measured activity at the end of the exposure time,disintegrations/