Towards a methodology for bulk sample neutron activation analysis

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JournalofTaibahUniversityforScience10(2016)235–241

Availableonlineatwww.sciencedirect.com

ScienceDirect

Towards

a

methodology

for

bulk

sample

neutron

activation

analysis

Mohsen

A. Abou

Mandour

a

,

Alya

Badawi

a

,

Nader

M.A.

Mohamed

b

,

Adel

Emam

c,∗

a_Nuclear_and_Radiation_Engineering_Department,_Alexandria_University,_Alexandria,_Egypt b_Egyptian_Atomic_Energy_Authority,_ETRR-2,_Cairo,_Egypt

c_Scientiﬁc_and_Technical_Consultation_Ofﬁce_(SATCO),_Cairo,_Egypt

Availableonline19June2015

Abstract

Themainchallengeinlargesampleneutronactivationanalysis(LSNAA)isthedeterminationofneutronself-shieldingandgamma

rayself-attenuationcorrections.Afterthesecorrectionsaredetermined,theanalysisproceedsasinnormalneutronactivationanalysis

(NAA),asifthesamplewereinfinitelysmall.Inthispaper,thesecorrectionsarecalculatedusingtheMCNPcodefordifferent

standardsamplegeometrieswithdifferentdiameters.ModellingstudiesforLSNAAusinganexternalneutronbeamwereperformed.

Ananalyticalformulaforthecorrectionfactorsforneutronself-shieldingandgammarayself-attenuationisderived.Thecorrection

factorsaswellasfluxparametersarecalculatedanalytically.TheanalyticalformulaisverifiedusingtheMCNPcode.Allofthe

calculatedparametersweretabulatedandgraphed.Fromthecalculateddata,otherunknownmaterialparameterscouldbeobtained

basedontabulateddataorgraphs.Thismethodisadirectandeasymethodtoperformlargesampleneutronactivationanalysis

withoutcomplexcalculations.Inaddition,fortheuserwhodoesnothavegoodexperiencewithcodessuchasMCNP,she/hecan

usethechartorthetabulatedinformationtodefinetheirunknownsamplewiththerequiredinformationfortheLSNAAexperiment.

theCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Largesampleneutronactivationanalysis;Neutronself-shieldingcorrections;Gammarayself-attenuationcorrections;NAA

1. Introduction

Allof the multielementalanalysismethods (instru-mental neutron activation analysis (INAA)) [1], and inductively coupled plasma atomic emission spec-trometry(ICP-AES),inductivelycoupledplasmamass spectrometry(ICP-MS)[2],etc.involvestudyingasmall portion of material (a few milligrams of solids or a

∗_{Corresponding}_author._Tel.:₊₂₀_1017048622.

E-mailaddress:[email protected](A.Emam). PeerreviewunderresponsibilityofTaibahUniversity.

http://dx.doi.org/10.1016/j.jtusci.2015.04.009

few millilitres of liquids) (see Table 1). The current trend is to use even smaller test samples, such as in totalreflectionX-rayfluorescence(XRF)spectrometry, solid-stateatomicabsorptionspectrometry(AAS),and laser-ablationICP[3].

TheobtainedinformationinthecaseofXRFisfrom the surface layers, whichrepresent a few milligrams, makingtheuseofquantitieslargerthanrequiredto pre-parethetargetmeaningless[4].

Thelimitationtothesizeofthesampleisoneofthe biggestproblemsfacingtheanalystwhendealingwitha largesample.Forexample,soils,rocks,plantmaterial, etc.canbemoreeasilyandrepresentativelysampledat quantities on the orderof hundreds of grams to kilo-gramsthanatquantitiesoflessthan1gbecauseasample isconsideredas“representative” onlyifit canpresent

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Table1

Sizesofthesamplesandanalyticalportionshandledinseveralmultielementanalysistechniques[4].

Analysistechnique Solidmaterialmassusedorpreparedtotestportion Volumeusedastestportion Atomicabsorptionspectroscopy(AAS)gasfurnace Typically1–2gdissolved; 10–20␮L

Atomicabsorptionspectroscopy(AAS)flame Maximumapproximately10g 1–2mL

Inductivelycoupledplasmaspectroscopy(ICP) Typically1–2gdissolved;maximumapproximately10g Approximately500␮L X-rayfluorescencespectroscopy(XRF) 10g

Instrumentalneutronactivationanalysis(INAA) Typicallyapproximatelyupto500mg;insomecases,up to30g

1–50mL

theaveragepropertiesofthematerial,environment,or populationtowhichitbelongs.

Representativenessisaprioripreservedwhen(i)the samplingis performed accordingto specific, certified norms or when (ii) a truly homogeneous material is sampled[4].

2. Largesampleneutronactivationanalysis

A few phenomena require more attention in large sampleneutronactivationanalysis(LSNAA)thanin nor-malNAA(whichusessamplesvaryingfrommicrograms toamaximumof0.5g)becausethesephenomenausually haveonlyaninsignificantimpactonthedegreeof accu-racyoftheresultsinnormalNAAA[5].Inlargesamples, e.g.,ofkilogramsize,neutronabsorptionandscattering result insubstantialself-shielding, causingdepression oftheneutronfluxatthecentreofthesamplecompared totheperiphery.Neutronself-thermalisationmaycause substantial changes in the neutron spectrum through-outthesampleifthesamplematerialalsocontains,for example,hydrogen.

Similarly, the gamma-radiation of the activation products deep inside in the sample will be more stronglyabsorbedandscatteredbeforeleavingthe sam-plethan the radiationresulting from, e.g., thesurface of the sample; moreover, the absorption and scatter-ingincreaserapidlyatlowergamma-rayenergies.This effectisdenotedasgamma-rayself-attenuation. Addi-tionally, a sample of 1kg cannot be considered as a more-or-less“pointsource”duringcountingatnormal sample–detectordistancesof,e.g.,10–30cm,resulting inacorrespondingdifferentresponseofthedetectorfor thegamma-radiation.

Other methods for standardisation have been pro-posed as well; these methods are primarily based on aprioriavailable informationonthe (gross) composi-tionoftheobject,e.g.,using MonteCarlosimulations

[6]orneutrontransportcodes[7](“fixedpointiteration method”).Degenaar[8]developedamethodinwhichno aprioriinformationisusedandtheneutronself-shielding

isestimatedonthebasisoftheattenuationand scatter-ingof theneutronbeam measuredoutsidethesample. BaasdevelopedamethodforNeutronActivation Analy-sisofInhomogeneousLargeSamples.Inthismethod,he consideredthelargesampleasalargenumberofsmall samples,andthesamedetectorareaisdividedintosmall portionstobeinlinewithhisassumedsubsamples[9].

OthermethodshavealsobeenproposedforPrompt Gamma Neutron ActivationAnalysis (PGNAA) using isotopicneutronsources,suchas252Cfor241Am(Be)

[10] and Pu–Be [11]. PGNAA is used for analysing largesolidsamples,includingirregularlyshaped mete-orite samples[12,13].Archaeological objects,such as bronzes,wereanalysedbythismethod[14].

2.1. Largesampleneutronactivationanalysis calculations

ThebasicmeasurementequationofNAAbywhich themassoftheunknownelementiscalculateddirectly demonstratesthefactthat thetechniquedoesnotseta prioriconstraintsonthemassofthesampleanalysed:

A0=∅thσeffN AVθm M (1−e −λtir_)e−λtd(1−e −λtm₎ λ γε (1)

whereA0istheareaoftherelevantpeakinthe

gamma-ray spectrum, ∅th is the thermal neutron fluence rate

(cm−2s−1), σeff is the effective absorption cross

sec-tion(cm2),NAvisAvogadro’snumber(mol−1),θisthe

isotopicabundance.misthemassoftheirradiated ele-ment(g),Mistheatomicmassnumber(gmol−1),λis thedecayconstantoftheradioisotopeformed(s−1),tir istheirradiationduration(s).

Eq.(1)couldbeusedinLSNAAasinEq.(2)after calculatingtheratioof

• Theneutronself-shieldinginsidethesample, • Thegamma-rayself-attenuationinsidethesample.

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Fig.1.Schematicformodelledsamples. A0=∅thσeffNAVθm M (1−e −λtir_)e−λtd(1−e −λtm₎ λ γεfn,γ (2) wherefn,γistheneutronandgammaattenuationfactor.

There are many approaches for these calculations, varying from pure theoretical modelling [5], Monte Carlo modelling [15], and modelling using a priori available information about the test sample composi-tion to actual empirical estimations of the correction factors.Modellingmayevenbeavoidedwhen,e.g.,for routineapplications,arepresentativewell-characterised (largesample)standardorevenareferencematerialis available.Thesestandardisationmethodsarefurther dis-cussedbelow.Theanalysesaremainlyfocusedonraw materialanalysis.

The scope of this study involves calculating both ratiosforneutronandgammaself-attenuationforalarge sample.

2.2. Neutronself-shieldingcalculation

Inthisstudy,MCNP5MonteCarlocodemodelling wasusedfor3differentsamplesizesforseveralmaterials andmixtures.Cylindersof5-,15-,and20-cmdiameter and a fixed 15-cm height are modelled [16].Table 2

shows the different materials analysed. The material compositionisasper[17].

A high intensity strength 1E+8neutron beam was used as showninFig. 1. The effectof sample height isnot consideredinthisstudy.The modelledsamples are rotated and moved up and down during irradia-tion/countingtoreducetheeffectsofinhomogeneity.

Inthisstudy,theETRR-2Radiographybeam param-etersareconsideredinourmodel[18],whichcouldbe appliedinthefuture.Additionally,thebeamparameters couldbeusedforsampleirradiation/countingtoprovide

Table2 Analysedmaterial. Material Densityρ(g/cm3₎ Inconel-600 8.43 Concrete,iron-Portland 5.0 St.steel304 8.02 Steel,carbon 7.82 Waterliquidatemixture 1.8 Waterliquidatemixture 1.4 Concrete,ferro-phosphorus 4.8 Titaniumdioxide 4.26 Waterliquidatemixture 1.2

Water 1.0

Ferroussulphate(standardFricke) 1.024 Waterliquidatemixture 0.9 Galliumarsenide 5.31

Masonite 1.3

Waterliquidatemixture 0.7 Ordinaryconcrete 2.3 Ordinaryconcrete 2.0 Waterliquidatemixture 0.5 Commercialenricheduranium 18.9 Depleteduranium 18.9 Naturaluranium 18.9 Heavysandmixturematerial 4.0 Naturallead 11.4 Heavysandmixturematerial 3.5

Granite 2.729

Glass,lead 6.220

Heavysandmixturematerial 3.0 Heavysandmixturematerial 2.8 Heavysandmixturematerial 2.6 Heavysandmixturematerial 2.4 Heavysandmixturematerial 2.2 Sandmixturematerial 2.0 Sandmixturematerial 1.9 Sandmixturematerial 1.7 Sandmixturematerial 1.5

someinformationabouttheinternalsamplecomposition andhomogeneity,asshowninFig.2.

Tworatioswerecalculatedfordifferentsample diam-etersandforthedifferentmaterials:(1)theratiobetween theaveragefluxoverthesampletotheinletfluxand(2) theratiobetweentheoutletfluxtotheinletflux.Those tworatiosareplottedinFigs.3–5forsamplediameters of20cm,15cm,and5cm,respectively.

Note that the relationships in the three figuresare nearly smooth, except for the sudden drop for three points.These3pointsareforcommercialenriched ura-nium,depleteduranium,andnaturaluranium.

The reason for thisdrop is the high probabilityof fissionforthese3materials,whichmeansthattwo reac-tions(n,f)and(n,γ),shouldbetakenintoaccountinthis case.

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Fig.2.Schematicoftheirradiationandtomographyfacility(vertical cross-section).

Fig.3. Relationshipbetweentherelativeaveragefluxandtherelative outletfluxfor20-cmsamples.

Fig.4. Relationshipbetweentherelativeaveragefluxandtherelative outletfluxfor15-cmsamples.

Fig.5.Relationshipbetweentherelativeaveragefluxandtherelative outletfluxfor5-cmsamples.

Fromthethreefigures,anunknownaveragethermal flux over the unknown large samples could be ana-lysed,andmoreinformationcouldbeobtainedaboutthe unknownlargesampleincomparisonwithourprepared MCNPresulttablesand/orgraphs.

Theaverageremovalmacroscopiccrosssectionr foreachmaterialiscalculatedasafunctionofaverage fluxratiotoinputflux,asgiveninEq.(3)[16]:

Φav Φin = 1−e− r∗D r∗D (3)

whereФavistheaveragenormalisedfluxoverasample

(calculatedbyMCNP5).Фin isthe inputneutronflux

on the surface of a sample (known). D is the sample thickness/diameter(known).ristabulatedfor differ-entmaterialsamplesforthermalneutronsofenergyof 0.025eV,aspresentedinTable3(calculatedbyMCNP5 andEq.(3)).

2.3. Gammaandneutronself-attenuation calculation

For samples with a very large diameter, the self-attenuation for gammaradiation shouldbeconsidered after theirradiation.The sampleisrotated andmoved up and down during the measurement infront of the detector,asshowninFig.6.

The detector was calibrated with a point source locatedatthesamedistancefromthesamplesurface.A leadshieldwitha2-cmorificeisused.Theorifice diam-eterisapproximately1/10ofthesamplediameter.The sampleisconsideredasaslabsample.Theprobability

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Table3

0.025eVrfordifferentmaterialsamples(uncertainty±0.5%).

Materialdensityρ(g/cm3₎ r/20cm(cm−1) r/15cm(cm−1) r/5cm(cm−1) Inconel-600,rho=8.43g/cc 0.7773 0.7969 0.8936 Concrete,iron-Portland,rho=5.0g/cc 0.4656 0.5091 0.7399

St.steel304 0.5246 0.5462 0.5844

Steel,carbon,rho=7.82g/cc 0.5016 0.5251 0.5164 Waterliquidmixturerho=1.8g/cc 0.3113 0.3571 0.6146 Waterliquidmixturerho=1.4g/cc 0.3396 0.2967 0.6273 Concrete,ferro-phosphorus,rho=4.80g/cc 0.2806 0.3106 0.4793 Titaniumdioxidedensity=4.26E+00g/cc 0.2509 0.3555 0.438 Waterliquidmixturerho=1.2g/cc 0.2216 0.2671 0.4369

Waterrho=1.0g/cc 0.2836 0.2379 0.4151

Ferroussulphate(standardFricke),rho=1.024g/cc 0.1931 0.2373 0.3907 Waterliquidmixturerho=0.9g/cc 0.1926 0.2234 0.4151 Galliumarsenide,rho=5.310g/cc 0.1791 0.2973 0.3626 Masonite,rho=1.30g/cc 0.1619 0.206 0.4786 Waterliquidmixturerho=0.7g/cc 0.1521 0.1945 0.3252 Ordinaryconcreterho2.3g/cc 0.1412 0.1805 0.2979 Ordinaryconcreterho2.0g/cc 0.1303 0.1679 0.2962 Waterliquidmixturerho=0.5g/cc 0.126 0.1643 0.394 Commercialenricheduranium,rho=18.90g/cc 0.1434 0.2282 0.322 Depleteduranium,rho=18.90g/cc 0.1643 0.1886 0.3163 Naturaluranium,rho=18.90g/cc 0.1307 0.1757 0.328 Heavysandmixturematerialrho=4.0g/cc 0.0932 0.1205 0.1928 Naturalleadrho=11.4g/cc 0.0906 0.1169 0.186 Heavysandmixturematerialrho=3.5g/cc 0.0943 0.1122 0.1745

Granite,rho=2.729 0.0874 0.1157 0.1699

Glass,lead,rho=6.220 0.0907 0.1134 0.1674 Heavysandmixturematerialrho=3.0g/cc 0.0811 0.1029 0.155 Heavysandmixturematerialrho=2.8g/cc 0.0783 0.0989 0.1468 Heavysandmixturematerialrho=2.6g/cc 0.0754 0.0946 0.1384 Heavysandmixturematerialrho=2.4g/cc 0.0723 0.0902 0.1297 Heavysandmixturematerialrho=2.2g/cc 0.069 0.0854 0.1209 Sandmixturematerialrho=2.0g/cc 0.0654 0.0804 0.1118 Sandmixturematerialrho=1.9g/cc 0.0632 0.0773 0.1073 Sandmixturematerialrho=1.7g/cc 0.0596 0.0722 0.0975 Sandmixturematerialrho=1.5g/cc 0.0552 0.0662 0.0876

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Table4

Calculatedgamma/neutroncorrectionfactor.

Sample(nucleiofinterest) Eγ(MeV)probability[19] MonteCarlocalculated factor(±8E−05)

Analyticalcalculatedfactor Deviation%

H2O(H2) 2.223 4.26E−01 4.0783E−01 −4.303

SiO2(Si) 1.78 8.21E−01 8.41E−01 2.466

SiO2(Si) 3.53 4.07E−01 4.18E−01 2.654

HCl(Cl) 0.786 8.50E−02 8.81E−02 3.744

HCl(Cl) 0.788 1.25E−03 1.31E−03 4.667

HCl(Cl) 1.952 4.90E−02 5.08E−02 3.556

Fig.7.Averagegammafluxinsidetherotatingsample.

of non-escape for gamma radiation is calculated. An elementwithδxisselected,asshowninFig.7.

Eachneutronof irradiation isassumed toinduce a (n,γ)reaction.Thefluxdistributioninsidethesampleis assumedtobeexponential.Asthesamplerotatesduring irradiationandcounting,thegammaradiationwill suf-ferfromself-attenuationinsidethesample.Therelative numberof absorbedtoproducedgamma(f_n,γ)willbe calculated[16]: fn,γ= _D O a∗A∗Φine− rx∗(1−e−μ(D−x))dx _D O a∗A∗Φine− rx_dx (4) whereaistheaveragegammamacroscopicabsorption cross-section.Фin isthe neutronsource intensity.Ais

thesamplearea.μistheaverageremovalgammacross section.Disthesamplethickness/diameter.

ByperformingtheintegrationinEq.(4),thefraction ofself-absorbedgamma,orthecorrectionfactorfn,γ of thecounted gammainthe detector,iscalculatedas in Eq.(5)[16]: fn,γ= (1−e− rD/ r)+(e−μD−1/ r−μ){e−( r−μ)D−1} (1−e− rD/ r)v∈ (5)

where␯ is the peak branchingratio. Єis the detector efficiency.

ThederivationofEq.(5)isfoundinRef[16]. Eq.(5)verificationwasperformedusingtheMCNP5 code.Astandardsamplewithathicknessof10cmand

with known percentages of impurities (single energy peak is selected inourcase study (H2O,HCl,SiO2))

as well as the High purity germanium detector with cylindricalgeometryweremodelled[16].Thedetector efficiency was 100% for the HPGe detector. The dis-tance between the sample and the lead shield orifice wasassumedtobe15cm,andthedistancebetweenthe detectorandtheleadshieldorificewasassumedtobe zero.

The Fm4 tally card was used to calculate the total

numberofinteractionsforacertainmaterialinthe sam-ple.Thetotalnumberofinteractionsisassumedtobe the sameas the numberof gammaphotons produced. Thetotalnumberofatomsofeachmaterialvolumewas calculated,normalisedinbarns.Thecountednumberof photonsinthedetectorforeachmaterialwascalculated. Theerrorwasfoundtobeintherangeof±(4–7)%for allelementsstudied.

ThecorrectionfactorwascalculatedusingMCNPand wascomparedtotheresultofEq.(5),aslistedinTable4.

2.4. Proposedprocedure

ForperformingLSNAAonanunknownsample,each samplewasprocessedusingthefollowingprocedure:

1. Measurementofthenaturalradioactivityinthelarge sampleattheposition(xo,yo,zo)infrontofthe detec-torpriortoirradiation.Correctionforthebackground mustbeapplied.

2. Measurementofthelinearattenuationcoefficientof the large sample as a function of the gamma-ray energy(usingEq.(3)).Correctionmustbeperformed forgamma-raysemittedfromthenaturalradioactivity insidethelargesampleandfromthebackground.

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3. Measurement of the spectrumof the irradiated big sampleattheposition(xo,yo,zo)infrontofthesame detector, subtracting the photopeak areas resulting fromthenaturalradioactivityinthelargesample(step 2)andfromthebackground.

4. Calculationoftheneutronparameters,theinletflux ФinandtheoutletinletfluxФout,forthelargesample,

from the external flux monitors, whichwere posi-tionedaroundthesampleduringirradiation. 5. Determinationoftheaverageflux(Фav/Фin)overthe

samplefromFigs.3–5.

6. Determinationof r fromTable3 orourprepared charts.

7. Calculationofthecorrectionfactorforgammausing theanalyticalformulaofEq.(5).

8. Comparisonofthemeasuredandthecalculated cor-rectionfactors.

3. Conclusions

The neutron self-shielding correction factor is cal-culated using MCNP and is tabulated and graphed to be used for unknown samples. The gamma-ray self-attenuation correction factor is calculated analytically.

Bothcorrections canbe usedfor the calculationof multielemental analysis for largesamples. The above methodologyisadirectandeasyapproachtoperform largesample neutronactivationanalysiswithout com-plexcalculations. Additionally,the userwhodoes not haveexperiencewithcodessuchasMCNPcanusethe chartorthetabulatedinformationtodefinetheunknown samplewiththerequiredinformationforher/his exper-iments.

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