Numerical and practical exercises in thermoluminescence PDF
Preview Numerical and practical exercises in thermoluminescence
Numerical and Practical Exercises in Thermoluminescence Vasilis Pagonis George Kitis Claudio Furetta Numerical and Practical Exercises in Thermoluminescence With110Figures VasilisPagonis GeorgeKitis DepartmentofPhysics NuclearPhysicsLaboratory McDanielCollege AristotleUniversityof WestminsterMD21157 Thessaloniki USA Thessaloniki54006 Greece ClaudioFuretta DepartmentofPhysics UniversityofRome, LaSapienza Rome00185 Italy Cover illustration: Typical thermoluminescence glow curves for first and second order kinetics. The equations for the glow curves are also shown. Figures are drawn by the authors. MathematicaisaregisteredtrademarkofWolframResearch,Inc LibraryofCongressControlNumber:2005926338 ISBN-10:0-387-26063-3 e-ISBN0-387-30090-2 ISBN-13:978-0387-26063-1 Printedonacid-freepaper. (cid:1)C 2006SpringerScience+BusinessMedia,Inc. Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permissionofthepublisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet,NewYork, NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Use in connection with any form of information storage and retrieval, electronic adaptation, computer software,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,evenifthey arenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyare subjecttoproprietaryrights. PrintedintheUnitedStatesofAmerica. (TB/SBA) 9 8 7 6 5 4 3 2 1 springer.com Idedicatethisbooktomywife,MaryJoBoylan,whoseconstant encouragementandsupportmadethisbookpossible. VasilisPagonis Idedicatethisbooktomywife,Φωτεινη,andmymentor, ProfessorStephanosCharalambous. GeorgeKitis I am very grateful to my wife, Maria Clotilde, for her loving supportofmyscientificwork. ClaudioFuretta Preface Thermoluminescence (TL) is a well-established technique widely used in dosi- metricanddatingapplications. Althoughseveralexcellentreferencebooksexistwhichdocumentboththethe- oreticalandexperimentalaspectsofTL,thereisagenerallackofbooksthatdeal withspecificnumericalandpracticalaspectsofanalyzingTLdata.Manytimesthe practicaldetailsofanalyzingnumericalTLglowcurvesandofapplyingtheoretical modelsaredifficulttofindinthepublishedliterature. The purpose of this book is to provide a practical guide for both established researchersandfornewgraduatestudentsenteringthefieldofTLandisintended tobeusedinconjunctionwithandasapracticalsupplementofstandardtextbooks inthefield. Chapter1laysthemathematicalgroundworkforsubsequentchaptersbypresent- ingthefundamentalmathematicalexpressionsmostcommonlyusedforanalyzing experimentalTLdata. Chapter2presentscomprehensiveexamplesofTLdataanalysisforglowcurves followingfirst-,second-,andgeneral-orderkinetics.Detailedanalysisofnumer- ical data is presented by using a variety of methods found in the TL literature, withparticularemphasisinthepracticalaspectsandpitfallsthatresearchersmay encounter.Specialemphasisisplacedontheneedtouseseveraldifferentmeth- ods to analyze the same TL data, as well as on the necessity to analyze glow curvesobtainedunderdifferentexperimentalconditions.Unfortunately,theliter- aturecontainsmanypublishedpapersthatclaimaspecifickineticorderforaTL peakinadosimetricmaterial,basedonlyonapeakshapeanalysis.Itishopedthat thedetailedexamplesprovidedinChapter2willencouragemorecomprehensive studies of TL properties of materials, based on the simultaneous use of several differentmethodsofanalysis. AlthoughthesubjectofTLcurvefittingandglowcurvedeconvolutionisbeyond thescopeofthisbook,thereadersmayfindthespreadsheetexamplesinChapter 2 useful and easily adaptable for implementing simple curve fitting algorithms. ThesealgorithmsarebasedontheexperimentallymeasurablemaximumTLpeak heightandthecorrespondingtemperature(I andT ).Intheexamplesgiven,the M M activation energy E acts as the adjustable parameter in the computerized curve vii viii Preface fittingprocedure.Severalofthesecurvefittingspreadsheetexamplescanalsobe foundintheauthors’website. Chapter 3 presents for the first time in the TL literature detailed numerical examplesofseveralcommonlyusedtheoreticalmodels,aswellasseveralcom- parativestudiesofanalyticalexpressionsusedforkineticanalysisofTLdata.The mainthrustofthischapteristoillustratehowtosolvethedifferentialequations describing the traffic of carriers during the various TL processes in the crystal. AfewsimpleexamplesofsolvingthebasicdifferentialequationsofTLusinga spreadsheetaregivenmostlyforillustrativeandeducationalpurposes.Themain bodyofthischapterconsistsofagradualpresentationofincreasinglycomplexTL modelsusingtheprogramMathematica. We have found this programming environment to be very efficient, versatile, andeasytoworkwith,oncethebasicstructureandprogrammingstylehavebeen mastered.Weemphasizeinparticularthetransparentnatureofthenumericalinte- gratingtechniquesusedinMathematica,whichareparticularlysuitedforsolving systemsof“stiff”differentialequationsthatarecommonintheoreticalTLwork. TheMathematicanumericalintegrationcodeisverystableandefficient,withrare occasional numerical instabilities. All examples given in this book have typical running times of 1–2 min on a desktop computer. Several of the Mathematica examples given in this book can also be found in the authors’ website for easy referenceanddownload. InChapter4,wegivenumericalexercisesrelevanttotheTLdoseresponseof dosimetricmaterials.Themodelsdescribedinthischapteraretakendirectlyfrom the published TL literature in order to facilitate direct comparison of the results with the original papers. As much as possible, we have kept the same symbols and mathematical notation as the original papers for easy cross-reference. The Mathematicaprogramsaregivenina“modular”formconsistingofasmallcore of subroutines performing separate tasks, which can be easily adopted by the readersforavarietyofdifferentpurposes. A very important class of TL models is presented, namely models based on competitionduringirradiationprocess,competitionduringtheTLheatingprocess, aswellasmodelscontainingcompetitionduringbothirradiationandheating.The lastexerciseinChapter4presentsanumericalexampleofhowthesuperlinearity andsupralinearitycoefficientsg(D)and f(D)canbecalculatedfromexperimental TLversusdosecurves. In Chapter 5, we present a variety of exercises dealing with practical aspects of several phenomena commonly encountered in the study of TL materials. A group of four numerical exercises deal with the accuracy and reproducibility of measurementsperformedusingTLdosimeters(TLDs).Inparticular,weshowhow thestatisticalaccuracyandreproducibilityofTLdatacanbegreatlyimprovedby using individual correction factors for each TLD. The next two exercises deal withthecommonlyobservedphenomenonofthermalquenchingandcomprisea detailedsimulationofthermalquenchingeffectsonthemeasuredTLglowcurves andontheinitialrisetechnique.Thenextgroupoftwoexercisesdealswithaspects ofthemathematicalformalismusedinenvironmentalTLdosimetry. Preface ix TwoextensiveexercisesinChapter5concernwiththeimportantbutsomehow underutilized technique of the TL-like presentation of phosphorescence decay curvesandwiththepracticalaspectsofhowtocorrectexperimentalTLdatafor temperature lag effects between the heating element in TL equipment and the sampleitself. Astutereaderswillnoticetheabsencefromthisbookofanyexercisesdealing withdatingapplicationsofTL.Wedecidedthatsuchexerciseswerebeyondthe specificscopeofthisbookandreferthereaderstothereviewpapersintheannotated bibliography,aswellastothemonographsdedicatedtothisimportanttopic. Perhaps, one of the most useful aspects of this book is the inclusion of an annotatedbibliographyonTLtopics.Tothebestofourknowledge,therehasbeen no other published annotated bibliography in the TL literature, and we believe thatthiswillbeanimportanttoolforbothestablishedTLresearchersandpersons startingaresearchprojectinthisfield. Althoughitisnotpossibletogiveacomprehensiveannotatedbibliography,we haveprovidedcharacteristicexamplesofpublishedarticlesinthevarioustopics coveredinthisbook.SeveralreviewarticlesofgeneralinterestonTLhavealso beenincludedinourlistings;thesecanserveasimportantintroductorymaterial forthevarioustopics. Our choices of papers and monographs in the annotated bibliography were dictatedbyourdesiretoguidethereadertowardfewcharacteristicandcomplete examplesofTLdataanalysis,ratherthanprovidingacompletelist. AnAppendixisprovidedwithexamplesofthemostbasiccommandsinMath- ematicaforreferencepurposes,althoughitcanonlycoverthemostrudimentary aspectsofthispowerfulprogrammingenvironment. November9,2005 VasilisPagonis GeorgeKitis ClaudioFuretta Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi 1. ExpressionsforEvaluatingtheKineticParameters . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 SimpleThermoluminescenceModel . . . . . . . . . . . . . . . . . . . . . . . 1 ExpressionsforFirst-,Second-,andGeneral-OrderTLKinetics. . . . . . 2 MethodsofAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 InitialRiseMethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 MethodsofAnalysisEmployingtheWholeTLGlowCurve. . . . . . . 12 PeakPositionMethodsofAnalysis. . . . . . . . . . . . . . . . . . . . . . . 13 MethodsofAnalysisBasedontheTemperatureattheMaximum . . . 13 MethodsofAnalysisBasedonVariousHeatingRates. . . . . . . . . . . 13 IsothermalDecayMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 MethodsofAnalysisBasedontheShapeoftheGlowCurve . . . . . . 17 CurveFittingMethods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 TheSeriesApproximationtotheTLIntegrals. . . . . . . . . . . . . . . . 19 ComputerizedCurveFittingProcedures . . . . . . . . . . . . . . . . . . . 20 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2. AnalysisofThermoluminescenceData. . . . . . . . . . . . . . . . . . . . . . 23 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Exercise2.1:AnalysisofaFirst-OrderTLPeak . . . . . . . . . . . . . . 24 Exercise2.2:HeatingRateMethodforFirst-OrderKinetics. . . . . . . 35 Exercise2.3:IsothermalMethodforFirst-OrderKinetics . . . . . . . . 39 Exercise2.4:AnalysisofaSecond-OrderTLPeak. . . . . . . . . . . . . 42 Exercise2.5:IsothermalMethodforSecond-OrderKinetics. . . . . . . 53 Exercise2.6:AnalysisofaGeneral-OrderTLPeak . . . . . . . . . . . . 58 Exercise2.7:InfluenceoftheBackgroundontheResultsofthe InitialRiseMethod . . . . . . . . . . . . . . . . . . . . . . . . 70 xi xii Contents Exercise2.8:Studyofthe15%RuleofThumbfortheInitialRise Technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Exercise2.9:ErrorAnalysisforPeakShapeMethods. . . . . . . . . . . 74 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3. SimpleTLModels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Exercise3.1:NumericalIntegrationofFirst-OrderEquation. . . . . . . 80 Exercise3.2:TheOne-Trap-One-RecombinationCenterModel . . . . 82 Exercise3.3:CalculationofGlowPeaksUsingMathematica . . . . . . 86 Exercise3.4:TheOTORModelinMathematica . . . . . . . . . . . . . . 91 Exercise3.5:TheIMTSModelinMathematica . . . . . . . . . . . . . . 96 Exercise3.6:AnalyticalExpressionsforFirst-OrderKinetics. . . . . . 99 Exercise3.7:AnalyticalExpressionsforSecond-OrderKinetics . . . . 102 Exercise3.8:AnalyticalExpressionsforGeneral-OrderKinetics. . . . 104 Exercise3.9:ComparativeStudyoftheAccuracyofAnalytical ExpressionsforFirst-OrderTLGlowPeaks . . . . . . . . 104 Exercise3.10:ComparativeStudyoftheAccuracyofAnalytical ExpressionsforGeneral-OrderTLGlowPeaks . . . . . 108 Exercise3.11:NumericalStudyofMixed-OrderKinetics . . . . . . . . 111 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4. TLDoseResponseModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 OverviewofNonlinearDoseResponseofTLMaterialsand Terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Exercise4.1:TheFillingofTrapsinCrystalsDuringIrradiation . . . . 122 ListingofProgramforExercise4.1 . . . . . . . . . . . . . . . . . . . . . . 126 Exercise4.2:CompetitionDuringExcitationModel. . . . . . . . . . . . 128 ListingofProgramforExercise4.2 . . . . . . . . . . . . . . . . . . . . . . 131 Exercise4.3:SuperlinearityModelwithCompetitionDuringBoth ExcitationandHeating. . . . . . . . . . . . . . . . . . . . . . 132 ListingofProgramforExercise4.3 . . . . . . . . . . . . . . . . . . . . . . 136 Exercise4.4:The f(D)andg(D)Functions. . . . . . . . . . . . . . . . . 138 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 5. MiscellaneousApplicationsofThermoluminescence. . . . . . . . . . . . . 144 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 ReproducibilityofTLDSystems. . . . . . . . . . . . . . . . . . . . . . . . . . 144 DefinitionsforReferenceandFieldDosimeters. . . . . . . . . . . . . . . 146 Exercise5.1:LowerDetectionLimit, D . . . . . . . . . . . . . . . . . 148 LDL Exercise5.2:ReproducibilityMeasurements. . . . . . . . . . . . . . . . . 149 Exercise5.3:IndividualCorrectionFactors,S . . . . . . . . . . . . . . . 151 i Contents xiii Exercise 5.4:RelativeStandardDeviationVersusDose . . . . . . . . . 152 Exercise 5.5:DoseMonitoringinaNuclearMedicine Department . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Exercise 5.6:DeterminationoftheSelf-DoseinaTLMaterial . . . . 155 Exercise 5.7:SimulationofThermalQuenchinginTLMaterials . . . 156 Exercise 5.8:TheEffectofThermalQuenchingontheInitial RiseMethodofAnalysis. . . . . . . . . . . . . . . . . . . . 162 Exercise 5.9:TL-LikePresentationofPhosphorescenceDecay Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Exercise5.10:TemperatureLagCorrections. . . . . . . . . . . . . . . . . 171 Exercise5.11:StudyoftheIntegralsAppearingintheExpressions forFirst-andGeneral-OrderTLKinetics . . . . . . . . . 174 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 AnnotatedBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Appendix:ABriefIntroductiontoMathematica. . . . . . . . . . . . . . . . . . 200 AuthorIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 SubjectIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
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