Table Of ContentNumerical 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
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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
