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Microscopic model for chemical etchability along radiation damage paths in solids

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Microscopic model for chemical etchability along radiation damage paths in solids

    Microscopic model for chemical etchability

    along radiation damage paths in solids Availableonlineatwww.sciencedirect.com

    t

    

    

    :ScienceDirect

    NuclearScienceandTechniques19(2008)174-177

    Microscopicmodelforchemical

    damagepaths

    NUCLEAR

    SCIENCE

    AND

    TECHNIQUES

    etchabilityalongradiation

    insolids

    MukhtarAhmedRANA

    PhysicsDivision,DirectorateofScience,PINSTECH,PO.Nilore,Islamabad,Pakistan AbstractItwouldbeveryinterestingtodevelopapictureaboutremovalofatomsfromtheradiationdamagedpaths

    orlatentnucleartracksandundamagedbulkmaterialintrackdetectors.Here,theoryofchemicaletchingisdescribed

    brieflyandanewmodelforchemicaletchingalongradiationdamagedpathsinsolidsisdevelopedbasedonbasic

    scientificfactsandvalidassumptions.Dependenceofchemicaletchingonradiationdamageintensityandetching

    conditionsisdiscussed.Anewparameterforetchingalongradiationdamagedpathsisintrodu

ced,whichisusefulfor

    investigationofrelationshipbetweenchemicaletchabilityandradiationdamageinasolid.Re

    sultsanddiscussion

    presentedherealealsousefulforfurtherdevelopmentofnuclearwasteimmobilization.

    KeywordsRadiationdamage,Chemicaletchability,Fissionfragments,Nucleartrackdetecti

    ontechnique,Nuclear

    wasteimmobilization,Nanofabrication

    CLCnumbersTL815.7.077

    1Introduction

    Chemicaletchingoflatenttracks,damaged

    cylindricalzonescreatedbymovingchargedparticles insofids,isanimportantprocedureintrackdetection technique.Comparisonofremovalofatomsinthese damagedzonesandinthebulkmaterialmayprovide usefulinformationabouttrackformation.Itisalso helpfulinunderstandingradiationdamagetomaterials, whichhasapplicationsinnuclearwaste

    immobilizationLandionsimplantationin

    semiconductorsLetc.Anumberofresearchershave

    studiedtrackformationmechanism[3-61andother involvedprocesses,e.g.,annealingand

    etching[1o-l21ofnucleartracks.

    Nucleartracketching

    involvesanumberofparameters,ofwhichetching temperature.concentrationoftIleetchantandrelative chemicalreactivityofdamagedandbulkmaterialare significant.Intrackdetectiontechnique,asuitable etchantandproperetchingconditionsareessentially needed.TheycaninfluencetheinterpretationoftIle E-maihmukhtm'.ahmcdrana@manchester.ac.uk;marana@pi~tech.org.pk

Receivedlle:2007.12.O2

    experimentaldataaboutanuclearreaction,cosmicray measurementorradiationdosimetry.

    Itisalwaysusefultodevelopamathematical relationshipbetweenparametersinvolvedinaprocess likechemicaletchingoflatenttracksforanalysisand interpretationofexperimentaldata.Hereanattemptis madetodevelopamodelforchemicaletchingof latenttracksstartingwitIltheatomicscalepictureof theetchingprocess.nlemathematicalrelationship developedforetchingatatomicscaleistIlen transformedintoarelationshipofobservableetching parameters.JustificationfortIleassumptionsusedin doingsoisgiven.Inthenextsection,theoryofetching isdescribedverybrieflyfollowedbyasection containingtIlemathematicalderivationofamodelfor chemicaletchingoflatenttracks.Experimentaldata areanalyzedusingtheproposedmode1.Discussion aboutsignificanceandapplicationofmodeland conclusionsaregiveninthelastsection.

NO.3MukhtarAhmedRANAeta1./Microscopicmodelforchemicaletchabilityalongradiat

    ion......175

    2Amodelforchemicaltracketching

    phenomenon

    2.1Physicalpicture

    Theparallelprocessesoccurringduringchemical etchingarediffusionofetchingmoleculestothe etchingfrontinthenarrowtrackandtransportationor diffusionofetchproductsoutofnarrowchannels.

    Especiall~atthestRrtoftrackformation,theetchant flowintoananometersizedtrackchannelis complicated.Itmightbeoneofthereasonsforetch inductiontimewhichisthedelayinthefirst appearanceoftrackatmicrometerscale.Temperature oftheetchanthasastrongimpactondiffusionof etchingmoleculesandtransportationofetchproducts. Fig.1showsaschematicofthetypicalsituationof chemicaletchingofalatentnucleartrackinasolid, whichisawelldefinedtypeofradiationdamage,

    utilizingtheetchingschemesbyDitlov3andSchulz

    t以【l4].

    Molecules

    Fig.1Pictorialrepresentationofetchingprocessofanion induceddamageinadlelectricsolid.Thispictureisafurther developmen

    

    tofchemicaletchingsc-heme-srbyDiflov[and

    Schulzetal.

    Maximizationofpreferentialtracketchingfora particletrackwiththecomponentofdepositedenergy densityusedtocausedisorders

    =

    ,

    determiningtheratiooftracktobulketchingcross sectiono/oforagivendetectormaterial,along thetrackispossiblebytheoptimisationof(a)the etchantselection,whichdeterminestheactivation energyofetching,(b)concentrationoftheetchant, themeasureofconcentrationofetching

    molecules/atomsintheetchant,(c)thetemperature oftheetchant,themeasureofattemptfrequencyV,and (d)introductionofpropermagnitudeofstirringor turbulenceintheetchant,rotationoroscillation frequencyqoftheetchant.Thefunctionofstirringis toremoveetchproductsoutofgrowingtracksandto keconcentrationandtemperatureoftheetchant uniform.Thestirringorpumping(say,millilitreper secscale)oftheetchingsolutionfromandtoetching bathshallintroducesteadyoscillatoryorrotational flowwithintheetchingbath.

    2-2Mathematiealmodel

    Theratiooftracketchcrosssectiontobulketch crosssectionisgivenby

    /=g(.,)(1)

    where--b

    Ind

    istheaveragebindingenergyofatomsin

    thebulkdetectormateria1.Thebulkandtracketch crosssectionsaredefinedas

    and

    蔫一bb

    tt一鲁

    (2)

    (3)

    whereNandNarenumbersofatomsinbulkof

    volumeandtrackvolumematerials,

    whereasaistheareaofthelatentdamagedtrailof radiation;Nandarenumbersofatoms

    removedinetchingtimeintervalrperunitvolumeof

    etchingfrontwiththicknessequaltothedepth(or forbulkandtracketching,respectively)atwhich theattemptfrequencyvtorl,bhasanonzero

    value.

    E

    =ottdvtefdV

    t,e

    =

    c孥势簧警

    Theetchabifityisproportionaltocrosssection rationgiveninaboveequation.So,

    ,

    176NUCLEARSCIENCEANDTECHNIQUESV_o1.18 S=v,lv~?o-:/(6)

    J

    d~vb(

    -ZTZ,,

    睁警(7)

    whereandale,respectively,trackandbulk etchrates,Kisconstantofproportionality.Parameters oraleveryimportantanddependon

    chemicalreactionkineticsandporosityofthelatent tracks.

    c畿静簧e警?

    Forvariousradiationsandthesametargetand etchingconditions,willbeconstant.

    Theterm''reducedetchrate"wasdefinedforthe purposeofanalysisandcomparisonbetweendifferent trackdatasetsasithasweakerdependenceonetching

    conditionscomparedwitIltracketchrate.Now,itis realizedthatreducedetchrateisnotquiteindependent ofetchingconditions.Eq.(7)showsthatdependence ofreducedetchrateontemperatureisconsiderable duetodirectdependenceoftermexp[(EfEfmon temperature,whemasratioofbulktotrackattempt frequencies?/vtmightalsodependupontemperature. ItisclearfromEq.(7)thatthereisnodirect dependenceofSonconcentrationoftheetchant.The tracketchrateinEg.(8)stronglydependson temperatureandconcentrationoftheetchant. AnewparameterSTcalledhereas''temperature normalizedreducedetchrate"isdefinedas =

    ST=Se(9)

    Usingthisdefinition,Eq.(7)maybewrittenas, 孥睁Nob,

    Ifaveragevaluesofactivationenergiesofbulk andtracketchingareknownforarangeofions,the STwillbeaverysuitableparameterforanalysisofa trackdatasetandcomparisonofdifferentdatasets. 3Experimentalmethodandresults

    CR39dete~orsfromPershoreMouldings(UK) wereirradiatedwithfissionfragmentsof2Cfusing 2geometryplacingdetectorsamplesdirectlyon252Cf sourceholder,asshowninFig.2a.Theirradiated detectorswereetchedinNaOHsolutionof

    concentration1-7mol?attemperatures5080.C

    for45rainafterwhichtracklengthmeasurements weremade.AnothersetofCR.39detectorswas

    irradiatedwitIlfissionfragmentsandetchedfor3h undersimilarconditions.Vationinsetvaluesof etchingtemperaturewasnotmorethan-+1.C.Fig.2b showstheetchingprocedtileofirradiatedCR.39 detectors.Detailsaregiveninourpreviouspaper presentinginitialresults[15.

    CR.39

    

    ChemicaI

    etchantl

    ;

    :_djl龇酾l寰?Rg

    Fig.2.Diagramshowing(a)

    etchingprocedureoffission

    detectors.

    exposuregeometryand(b)

    fragmentirradiatedCR-39

    Afterchemicaletching,lengthsanddiametersof fissionfragmenttracksinCR-39detectorswere measuredusingaLeitzDA?.IrX22EBoptical

    microscope.T_mcklengthswerecorrectedforbulketch rate.Tracklengthmeasurementsyieldedfission fragmenttracketchrateswhereasbulketchrateswere measuredusingtrackdiametervariationmethod. Averagediametervalueof25mostcircularfission fragmenttracks(selectedoutof125measurements) wasusedfordeterminationofbulketchrateunder differentetchingconditions.Detailsaregiven elsewheret16.

    Fig.3showsthetemperaturedependenceof

    traditionallyusedreducedetchrateSandthatofnewly introducedparameterSr=Sexp[(inthe

    proposedmodelinSection2,whichistemperature normalisedreducedetchrate,overawiderangeof etchantconcentrationf17mol?IINaOHwater

    solution).Experimentalresultsinthisfigureclearly demonstratethatthedependenceof.ontemperature ismuchweakerthanthatofS.Foranalysisand comparisonofnucleartracketchingresultsfrom

NO-3MuldatarAhmedRANAeta1./Microscopicmodelforchemicaletchabilityalongradi

    ation......177

    differentetchingconditions,andpossiblyfrom differentlaboratoriesforthesalTledetector,thenew parameterSTwillprovidemorereliableandconclusive pictureofphysicalprocessesinvolved.

    256

    128

    64

    c,)

    32

    16

    6O65707580

    Temperature/.C

    Fig.3DependenceofSrontemperatureisveryweak comparedwitllthatofS.

    4Discussionandconclusion

    Alongtheradiationdamagedpaths,atomic

    bindingenergyanddensity【】inthetargetmaterialis

    lowered,resultinginpreferentialetchingalong

    radiationdamagedpaths(nucleartracks).Intensityof preferentialetchingdependsonintensityofradiation damageandetchingconditions.Forreliableanalysis ofrelationshipbetweenchemicaletchabilityand intensityofradiationdamageinthetargetmaterial,an experimentresultsbasedetchingparameterPis essentiallyrequired,showingideallynodependence onetchingconditions,asgivenbelow:

    P(T,C)=P(11)

    whereTandCareetchanttemperatureand

    concentration.Followingthismotivation,anew parameterSrfornucleartracketchingisdiscovered, whichshowsveryweakdependenceonetching

    temperature.So,useofSroverSwillbeveryuseful forenhancingchemicaletchabilityofradiation damagedpathsornucleartracks.Definitionofnew parameterincludesactivationenergiesoftrack andbulketching,whichwillhelpunderstandingthese importantetchingenergeticsrelatedparametersduring analysisofexperimentaldatabasedonthisnew parameter.Themicroscopicmodeldescribing chemicaletchabilityoflatenttracksdevelopedhereis supportedbyexperimentalresultsandwillbehelpful inunderstandingradiationdamageandpossiblymicro andnanofabricationofchannelsusingsingleions81.

    Acknowledgment

    FinancialsupportfromHigherEducation

    CommissionofPakistanunderPostDoctoral

    FellowshipProgram200708isgratefully

    acknowledged.

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