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RadiogenicIsotopeGeology ThirdEdition
Thethirdeditionof RadiogenicIsotopeGeology examinesrevolutionarychangesingeochemicalthinkingthathave occurredoverthepast15years.ExtinctnuclidestudiesonmeteoriteshavecalledintoquestionfundamentalgeochemicalmodelsoftheEarth,whilenewdatingmethodshavechallengedconventionalviewsofEarthhistory.Atthesame time,theproblemofglobalwarminghasraisednewquestionsaboutthecausesofpastandpresentclimatechange. Inthenewedition,theseandotherrecentissuesareevaluatedintheirscholarlyandhistoricalcontext,soreaderscan understandthedevelopmentofcurrentideas.Controversialtheories,newanalyticaltechniques,classicpapers,and illustrativecasestudiesallcomeunderscrutinyinthisbook,providinganaccessibleintroductionforstudentsand criticalcommentaryforresearchers.
AlanP.Dickin isProfessorofGeologyatMcMasterUniversity.
“TheDickintextprovidesanexcellentintroductiontoradiogenicisotopegeochemistry.Ireadapreviouseditioncoverto-coverduringpreparationforthegeneralknowledgeexamsingraduateschool,andIstillsuggestthatgraduate studentsdothesameinpreparationfortheirexams.Itcontinuestobeakeyreferenceforteachingandintheclassroom andinthelaboratory.”
–
MatthewJackson,UniversityofCalifornia,SantaBarbara
“IsotopegeochemistryishugelyinfluentialinthedevelopmentofnewapproachesandideasintheEarthsciences.New datachallengemodelsfortheformationoftheEarth,theevolutionofthecontinentalcrust,andclimatechange.An understandingofthebasicprinciplesofisotopegeologyisimportantinawiderangeofthesciences,andthiswelcome thirdeditionof RadiogenicIsotopeGeology buildsonthesuccessofthepreviouseditions.Itisscholarlyandaccessible, anditcombinesanalltoorarehistoricalcontextwithacomprehensiveintroductiontoawiderangeofradiogenic isotopetechniques.Writtenbyoneoftheworld’smostrespectedauthorsinthisfield,thistextbookwillbeinvaluable forundergraduateandgraduatecourses,anditisanexcellentreferencetextforscientistsinotherfields.”
– ChrisHawkesworth,UniversityofBristol
“Forteachersandstudentsinbothlow-andhigh-temperaturegeochemistrywhoneedreadyaccesstogeochemical conceptsandtechniques,AlanDickinoffersanup-to-date,well-writtenmedium-leveltextbookonisotopegeochemistry. Apleasant,handy,andusefulbookforyourshelf.”
– FrancisAlbarède,EcoleNormaleSupérieuredeLyon
RadiogenicIsotopeGeology ThirdEdition
AlanP.Dickin
McMasterUniversity
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Informationonthistitle:www.cambridge.org/9781107099449 DOI: 10.1017/9781316163009
C AlanP.Dickin2018
Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress.
Firstpublished1995
Secondeditionpublished2005
Thirdeditionpublished2018
PrintedintheUnitedStatesofAmericabySheridanBooks,Inc.2018
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloging-in-Publicationdata
Names:Dickin,AlanP.,author.
Title:Radiogenicisotopegeology/AlanP.Dickin,McMasterUniversity.
Description:[2018edition].|Cambridge:CambridgeUniversityPress,2018.| Includesbibliographicalreferencesandindex.
Identifiers:LCCN2017023083| ISBN 9781107099449(alk.paper)
Subjects:LCSH:Isotopegeology.|Radioactivedating.|Geochemistry.| Paleoclimatology.|Environmentalarchaeology. Classification:LCCQE501.4.N9D532017|DDC551.9–dc23 LCrecordavailableathttps://lccn.loc.gov/2017023083
ISBN 978-1-107-09944-9Hardback
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Additionalresourcesforthispublicationatwww.cambridge.org/dickin3 CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracy ofURLsforexternalorthird-partyinternetwebsitesreferredtointhispublication anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate.
ToMargaret andtothememoryofStephenMoorbath, isotopepioneer
ContentsinBrief 7IsotopeGeochemistryofContinentalRocks.................
8OsmiumIsotopes....................................
PrefaceandAcknowledgements
1NucleosynthesisandNuclearDecay.........................
1.1TheChartoftheNuclides.............................1
1.2Nucleosynthesis....................................2
1.2.1 StellarEvolution................................ 3
1.2.2 StagesintheNucleosynthesisofHeavyElements...........
1.3RadioactiveDecay..................................6
1.3.1 IsobaricDecay.................................
1.3.2 AlphaandHeavyParticleDecay......................
1.3.3 NuclearFissionandtheOkloNaturalReactor.............
1.4TheLawofRadioactiveDecay.........................10
2.1ChemicalPurification...............................13
2.1.1 IonExchangeSeparation..........................
2.1.3
2.1.4
2.1.5
2.2IonSources......................................16
2.2.1
2.3Mass-dependentFractionation........................19
2.3.1 MassFractionationinTIMS........................ 19
2.3.2 MassFractionationinMC–ICP–MS...................
2.4MagneticSectorAnalysis............................22
2.4.1 IonOptics................................... 22
2.4.2 Detectors.................................... 24
2.4.3 DataCollection................................
2.5IsotopeDilution...................................26
2.5.1 AnalysisTechnique..............................
2.5.2 DoubleSpiking................................
2.5.3 Pb–TlDoubleSpiking............................
2.6MC–ICP–MSSolution-basedApplications.................28
2.6.1 Hf–W......................................
2.6.2 Lu–Hf......................................
2.6.3 U–Th......................................
2.6.4 Pb–Pb......................................
2.6.5 Sm–Nd.....................................
2.7LA–ICP–MS.......................................30
2.7.1 U–Pb......................................
2.7.2 Lu–Hf......................................
2.8IsochronRegressionLineFitting.......................32
2.8.1 TypesofRegressionFit........................... 32
2.8.2 RegressionFittingwithCorrelatedErrors............... 32
2.8.3 Errorchrons..................................
2.8.4 ProbabilityofFit...............................
2.8.5 Isoplot.....................................
2.9ProbabilityDensity... ..............................35
2.9.1 DetritalZirconDistributions....................... 35
2.9.2 IsochronDataDistributions........................ 36
3TheRb–SrMethod..................................... 40
3.1TheRbDecayConstant..............................40
3.2DatingIgneousCrystallization... .....................41
3.2.1 SrModelAges................................. 42
3.2.2 TheIsochronDiagram........................... 42
3.2.3 EruptedIsochrons.............................. 43
3.2.4 MeteoriteChronology............................ 44
3.3DatingMetamorphicSystems.........................45
3.3.1 MineralandWhole-RockIsochrons................... 45
3.3.2 BlockingTemperatures........................... 47
3.4DatingOreDeposits................................48
3.5DatingSedimentarySystems..........................49
3.5.1 Shales...................................... 50
3.5.2 Glauconite................................... 51
3.6SeawaterEvolution.................................52
3.6.1 MeasurementoftheCurve......................... 52
3.6.2 TheCretaceous–TertiarySeawater Curve...................................... 54
3.6.3 SeawaterSrandGlacialCycles...................... 55
3.6.4 ModellingtheFluxes............................ 56
3.6.5 QuantifyingtheHydrothermalFlux.................. 58
3.6.6 TheEffectsofHimalayanErosion.................... 60
3.6.7 GlacialCycles................................. 61
3.6.8 StableSrIsotopesinSeawater...................... 62
4TheSm–NdMethod.................................... 67
4.1Sm–NdIsochrons..................................67
4.1.1 Meteorites................................... 67
4.1.2 PrecambrianMaficRocks......................... 68
4.1.3 High-GradeMetamorphicRocks..................... 70
4.1.4 GarnetGeochronology........................... 70
4.2NdIsotopeEvolutionandModelAges...................72
4.2.1 ChondriticModelAges........................... 72
4.2.2 DepletedMantleModelAges....................... 73
4.2.3 NdIsotopeMapping. ........................... 75
4.3ModelAgesandCrustalProcesses......................78
4.3.1 SedimentarySystems............................ 79
4.3.2 Meta-SedimentarySystems........................ 79
4.3.3 Meta-IgneousSystems............................ 80
4.3.4 PartiallyMeltedSystems.......................... 81
4.4TheCrustalGrowthProblem..........................82
4.4.1 CrustalAccretionAges........................... 82
4.4.2 SedimentProvenanceAges......................... 83
4.4.3 ArcheanDepletedMantle......................... 84
4.4.4 EarlyArcheanCrustalProvinces..................... 86
4.5NdintheOceans..................................88
4.5.1 ModernSeawaterNd............................ 88
4.5.2 TheOceanicNdParadox.......................... 89
4.5.3 AncientSeawaterNd............................ 90
4.5.4 TertiarySeawaterNd............................ 91
4.5.5 QuaternarySeawaterNd......................... 92
5LeadIsotopes... 99
5.1U–PbIsochrons...................................99
5.1.1 U–PbIsochronsandDecayConstants................. 100
5.1.2 UraniumIsotopeComposition..................... 100
5.1.3 U–PbIsochronsandTimescaleCalibration............. 101
5.2U–PbConcordiaDating.............................102
5.2.1 LeadLossModels.............................. 103
5.2.2 AirAbrasionandDirectEvaporation................. 104
5.2.3 ChemicalAbrasionandAnnealing.................. 105
5.2.4 ConcordiaAgesandDecayConstants................. 107
5.2.5 InheritedZircon.............................. 108
5.2.6InSitu Analysis.............................. 109
5.2.7 AlternativeU–PbDatingMaterials.................. 111
5.3Pb–PbDating....................................112
5.3.1 TheAgeoftheEarthandPbParadox................. 113
5.3.2 MeteoriteDatingandtheTotalPbIsochron............. 115
5.4Pb(Galena)ModelAges.............................118
5.4.1 TheHolmes–HoutermansModel.................... 118
5.4.2 ConformableLeads............................. 119
5.4.3 Open-SystemPbEvolution........................ 120
5.4.4 Plumbotectonics.............................. 121
5.5Whole-RockPbandCrustalEvolution..................122
5.5.1 ArcheanCrustalEvolution........................ 122
5.5.2 Paleo-IsochronsandMetamorphicDisturbance........... 124
5.5.3 ProterozoicCrustalEvolution...................... 124
5.6EnvironmentalPb.................................125
5.6.1 AnthropogenicPb............................. 126
5.6.2 PbasanOceanographicTracer.. 127
5.6.3 Paleo-SeawaterPb............................. 129
6IsotopeGeochemistryofOceanicVolcanics................. 134
6.1IsotopicTracingofMantleStructure...................134
6.1.1 ContaminationandAlteration..................... 134
6.1.2 DisequilibriumMelting.......................... 135
6.1.3 MantlePlumes............................... 136
6.1.4 PlumPuddingMantle........................... 137
6.1.5 MarbleCakeMantle............................ 138
6.1.6 MantleConvectionandViscosity.................... 139
6.2TheNd–SrIsotopeDiagram..........................140
6.2.1 TheMantleArrayandOIBSources.................. 140
6.2.2 BoxModelsfortheMORBSource.................... 141
6.2.3 Nd–142andEarlyEarthDifferentation............... 143
6.3PbIsotopeGeochemistry............................144
6.3.1 Pb–PbIsochronsandtheLeadParadox................ 145
6.3.2 TheKappaConundrum 146
6.3.3 TheThirdLeadParadox......................... 149
6.4MantleReservoirsinIsotopicMultispace................150
6.4.1 TheMantlePlane.............................. 151
6.4.2 TheMantleTetrahedron......................... 151
6.5IdentificationofMantleComponents..................154
6.5.1 DepletedOIBSources........................... 155
6.5.2 EMII...................................... 155
6.5.3 EMI...................................... 156
6.5.4 HIMU..................................... 158
6.5.5 TheDUPALAnomaly........................... 159
6.6IslandArcsandMantleEvolution.....................159
6.6.1 Two-ComponentMixingModels.................... 159
6.6.2 Three-ComponentMixingModels................... 161
7IsotopeGeochemistryofContinentalRocks................. 167
7.1MantleXenoliths.................................167
7.1.1 MantleMetasomatism.......................... 168
7.2CrustalContamination.............................170
7.2.1 Two-ComponentMixingModels.................... 171
7.2.2 MeltinginNaturalandExperimentalSystems........... 172
7.2.3 InversionModellingofMagmaSuites. 174
7.2.4 PhenocrystsasRecordsofMagmaEvolution. 178
7.2.5 LithosphericMantleContamination................. 178
7.3PetrogenesisofContinentalMagmas...................179
7.3.1 Kimberlites,CarbonatitesandLamproites.............. 179
7.3.2 AlkaliBasalts................................ 181
7.3.3 FloodBasalts................................ 183
7.3.4 PrecambrianGranitoids......................... 185
7.3.5 PhanerozoicBatholiths.......................... 187
8OsmiumIsotopes.................................... 194
8.1OsmiumAnalysis.................................194
8.2TheRe–OsandPt–OsDecaySchemes...................195
8.2.1 TheReDecayConstant.......................... 195
8.2.2 MeteoriteIsochrons............................ 196
8.2.3 DatingOresandRocks.......................... 197
8.2.4 OsNormalizationandthePt–OsDecayScheme.......... 198
8.3MantleOsmium..................................199
8.3.1 TheBulkSilicateEarth.. 199
8.3.2 LithosphericMantle............................ 200
8.3.3 PrimitiveUpperMantle......................... 201
8.3.4 AsthenosphericMantle.......................... 202
8.3.5 EnrichedMantlePlumes......................... 204
8.3.6 SubductionZones............................. 205
8.3.7 TheCoreOsmiumSignature....................... 206
8.4PetrogenesisandOreGenesis........................206
8.4.1 TheBushveldComplex.......................... 207
8.4.2 TheStillwaterComplex.......................... 208
8.4.3 TheSudburyIgneousComplex..................... 209
8.5SeawaterOsmium................................210
8.5.1 OsmiumIsotopeEvolution........................ 210
8.5.2 OsFluxesandResidenceTimes..................... 212
8.5.3 QuaternarySeawaterOsmium..................... 213
9TheLu–Hf,Ba–La–CeandK–CaSystems 218
9.1Lu–HfGeochronology..............................218
9.1.1 TheLuDecayConstantandCHURComposition.......... 218
9.1.2 DatingMetamorphism.......................... 220
9.2ModernMantleReservoirs...........................221
9.2.1 DepletedMantle.............................. 221
9.2.2 EnrichedMantle.............................. 223
9.3AncientHfEvolution..............................226
9.3.1 EarlyWork.................................. 226
9.3.2 DetritalZircon............................... 227
9.3.3 HfModelAges................................ 228
9.3.4 ArcheanDepletedMantle........................ 229
9.4SeawaterHafnium................................230
9.5TheLa–CeandLa–BaSystems........................232
9.5.1 La–BaGeochronology........................... 232
9.5.2 La–CeGeochronology........................... 232
9.5.3 CeIsotopeGeochemistry......................... 233
9.5.4 SeawaterCeriumGeochemistry..................... 234
9.6TheK–CaSystem.................................235
10K–Ar,Ar–ArandU–HeDating........................... 240
10.1TheK–ArDatingMethod............................240
10.1.1 AnalyticalTechniques........................... 240
10.1.2 InheritedArgonandtheK–ArIsochronDiagram......... 242
10.1.3 ArgonLoss.................................. 244
10.2The 40 Ar–39 ArDatingMethod........................244
10.2.1 40 Ar–39 ArMeasurement......................... 244
10.2.2 IrradiationCorrections.......................... 245
10.2.3 StepHeating................................ 246
10.2.4 ArgonLossEvents............................. 247
10.2.5 ExcessArgon................................ 249
10.2.6 39 ArRecoil.................................. 250
10.2.7 DatingPaleomagnetism.. 251
10.2.8 LaserMicroprobeDating......................... 252
10.3TimescaleCalibration..............................254
10.3.1 MagneticandAstronomicalTimescales.. 254
10.3.2 IntercalibrationofDecayConstants.................. 257
10.4Thermochronometry..............................259
10.4.1 ArrheniusModelling........................... 259
10.4.2 ComplexDiffusionModels........................ 261
10.4.3 K-FeldsparThermochronometry.................... 265
10.5U–Th–HeDating..................................268
10.5.1 ProductionandAnalysis......................... 268
10.5.2 AnnealingBehaviour........................... 269
10.5.3 CosmogenicHeliumPaleothermometry................ 269
11NobleGasGeochemistry............................... 274
11.1Helium........................................274
11.1.1 MassSpectrometry............................. 274
11.1.2 HeliumProductioninNature...................... 275
11.1.3 TerrestrialPrimordialHelium..................... 277
11.1.4 The‘Two-Reservoir’Model........................ 279
11.1.5 HeliumBoxModels............................ 281
11.1.6 CrustalandMantleHelium....................... 282
11.1.7 OceanicSedimentsandInterplanetaryDust............ 283
11.2Neon..........................................285
11.2.1 NeonProduction.............................. 285
11.2.2 PrimordialNeonintheEarth...................... 285
11.2.3 Sub-SolarNeon............................... 287
11.2.4 AtmosphericNeon............................. 288
11.2.5 NucleogenicNeon.............................. 289
11.3Argon.........................................289
11.3.1 TerrestrialPrimordialArgon...................... 290
11.3.2 AtmosphericContamination...................... 291
11.3.3 Argon-38................................... 293
11.4Krypton........................................294
11.5Xenon.........................................295
11.5.1 IodogenicXenon.............................. 295
11.5.2 FissiogenicXenon............................. 296
11.5.3 RadiogenicXenonReservoirs...................... 298
11.5.4 Non-RadiogenicXenon.......................... 299
11.5.5 TheBarium–XenonSystem....................... 300
12U-SeriesDating... 306
12.1SecularEquilibriumandDisequilibrium ................306
12.2AnalyticalMethods................................307
12.2.1 EarlyWork.................................. 308
12.2.2 MassSpectrometry............................. 308
12.2.3 Half-Lives................................... 309
12.3Daughter-ExcessMethods...........................309
12.3.1 234 UDatingofCarbonates........................ 309
12.3.2 234 UDatingofFe–MnCrusts...................... 311
12.3.3 230 ThSedimentDating.......................... 313
12.3.4 230 Th–232 Th.................................. 314
12.3.5 230 ThSedimentStratigraphy...................... 315
12.3.6 231 Pa–230 Th.................................. 317
12.3.7 210 Pb...................................... 319
12.4Daughter-DeficiencyMethods........................321
12.4.1 230 Th:Theory................................ 321
12.4.2 230 Th:Applications............................. 322
12.4.3 230 Th:DirtyCalcite............................. 324
12.4.4 231 Pa...................................... 326
12.5U-SeriesDatingofOpenSystems......................326
12.5.1 231 Pa–230 Th.................................. 326
12.5.2 ESR–230 Th.................................. 328
13U-SeriesGeochemistryofIgneousSystems.. 333
13.1GeochronologyofVolcanicRocks.....................334
13.1.1 TheU–ThIsochronDiagram...................... 334
13.1.2 U–Th(Zircon)ModelAges........................ 335
13.1.3 Ra–ThIsochronDiagrams........................ 336
13.1.4 Ra–ThModelAges............................. 337
13.2MagmaChamberEvolution..........................337
13.2.1 TheThIsotopeEvolutionDiagram................... 338
13.2.2 Short-LivedSpeciesinMagmaEvolution. 341
13.3MantleMeltingModels.............................342
13.3.1 MeltingUnderOceanRidges...................... 343
13.3.2 TheEffectofSourceConvection..................... 344
13.3.3 TheEffectofMeltingDepth....................... 347
13.3.4 TheEffectofSourceComposition.................... 348
13.3.5 CrustalMeltingandContamination................. 350
13.4Short-LivedSpeciesandMeltingModels.................351
13.4.1 226 RaandMeltingModels........................ 351
13.4.2 231 PaandMeltingModels........................ 353
13.4.3 SourcesofContinentalMagmas.. .................. 354
13.5SubductionZoneProcesses..........................355
13.5.1 U–ThinArcMagmas... 355
13.5.2 Ra–ThinArcs................................ 357
13.5.3 U–PainArcs................................. 358
14CosmogenicNuclides 363
14.1Carbon-14......................................363
14.1.1 EarlyWork.................................. 363
14.1.2 Closed-SystemAssumption........................ 365
14.1.3 InitialRatioAssumption......................... 366
14.1.4 Dendrochronology............................. 367
14.1.5 BayesianAnalysis............................. 369
14.1.6 Pre-HoloceneCalibration......................... 369
14.2RadiocarbonandClimateChange.....................372
14.2.1 RadiocarbonintheModernOceans.................. 372
14.2.2 Glacial/HoloceneVentilationAges................... 373
14.2.3 CausesofClimateChange........................ 376
14.3AcceleratorMassSpectrometry.......................378
14.3.1 PrinciplesofAcceleratorMassSpectrometry. 378
14.3.2 RadiocarbonDatingbyAMS...................... 379
14.4Beryllium-10... .................................380
14.4.1 10 BeintheAtmosphere.......................... 380
14.4.2 10 BeintheOceans............................. 381
14.4.3 10 BeinSnowandIce........................... 384
14.4.4 10 BeProductionandClimateCycles.................. 385
14.4.5 10 BeinSoilProfiles............................. 386
14.4.6 10 BeinMagmaticSystems 387
14.5Chlorine-36.....................................390
14.6Iodine-129......................................393
14.7 InSitu CosmogenicNuclides.........................394
14.7.1 MeteoriteTerrestrialResidenceAges.................. 394
14.7.2 Al–BeTerrestrialExposureAges.................... 395
14.7.3 Al–BeBurialAges............................. 396
14.7.4 Al–Be–NeAges............................... 397
14.7.5 Chlorine-36ExposureAges........................ 398
15ExtinctRadionuclides... 407
15.1Introduction....................................407
15.1.1 NuclideProductionandDecay..................... 407
15.1.2 CelestialObjectsandAges........................ 407
15.1.3 Parent–DaughterPairs.......................... 409
15.2StableIsotopes...................................409
15.2.1 CosmicBuildingBlocksoftheEarth.................. 410
15.2.2 SolarSystemIsotopeHeterogeneity.................. 410
15.3ExtantActinides..................................411
15.4Iodine–Xenon....................................412
15.4.1 TheXe–XeCorrelationDiagram.................... 412
15.4.2 TheDeterminationof‘Delta’...................... 413
15.4.3 Pu–Xe..................................... 414
15.4.4 I–XeChronology.............................. 415
15.5Al–Mg.........................................415
15.5.1 26 AlintheAllendeMeteorite...................... 416
15.5.2 DeterminationofDelta.......................... 416
15.5.3 Al–MgEarlyNebularChronometry.................. 417
15.5.4 Testingthe‘Canonical’Model...................... 418
15.6Short-LivedSpeciesinPlanetaryDifferentiation...........419
15.6.1 Pd–Ag..................................... 419
15.6.2 Mn–Cr.................................... 420
15.6.3 Fe–Ni..................................... 421
15.6.4 Hf–W..................................... 423
15.6.5 Hf–WSolarSystemChronometry................... 424
15.6.6 RevisitingtheGiantImpactModel.................. 426
15.7TheSm–NdSystem................................427
15.7.1 EarlyWork.................................. 427
15.7.2 ChondritesandtheBulkEarth. 429
15.7.3 The 142 NdConundrum .......................... 429
15.7.4 SCHEMorChondriticMoon....................... 430
15.7.5 142 Nd,CoreSulphideandE-Chondrites................ 432
15.7.6 142 NdintheArcheanEarth....................... 433
15.8TheCurium–Uranium–(Nd)System....................433
15.9SpallogenicExtinctNuclides.........................435
15.9.1 Be-10...................................... 435
15.9.2 Ca–K..................................... 436
15.10Conclusions.....................................437
16Fission-TrackDating..................................
16.1TrackFormation..................................444
16.2TrackEtching....................................446
16.3CountingTechniques..............................446
16.3.1 PopulationMethod............................ 447
16.3.2 ExternalDetectorMethod........................ 447
16.3.3 Re-EtchingandRe-Polishing....................... 448
16.3.4 LA–ICP–MS................................. 449
16.3.5 AutomatedTrackCounting....................... 449
16.4DetritalPopulations...............................449
16.5TrackAnnealing..................................451
16.6UpliftandSubsidenceRates.........................452
16.7TrackLengthMeasurements.........................454
16.7.1 ProjectedTracks(Semi-Tracks)...................... 455
16.7.2 ConfinedTracks............................... 456
16.7.3 TrackWidths................................ 457
16.7.4 cAxisProjection.............................. 458
16.7.5 ForwardandInverseModelling.................... 459
16.8PressureEffects..................................462
PrefaceandAcknowledgements Thepastfifteenyearshaveseenaquietrevolutioninisotopegeochemistry,asaonce-arcanefieldinvolving‘extinct’ radionuclidesinmeteoriteshascalledintoquestionfundamentalgeochemicalmodelsoftheEarthitself.Atthesame time,increasingpublicawarenessoftheproblemofanthropogenicglobalwarminghasfocusedattentionontheroleof isotopegeochemistryinmonitoringpastandpresentinfluencesonclimatechange.
Thethirdeditionof RadiogenicIsotopeGeology attempts toplacetheseandotherrecentdevelopmentsinscientific thinkingintheiroverallscholarlycontext.
Theapproachtothesubjectmatterishistorical,forthree mainreasons.Firstly,togiveanimpressionofthedevelopmentofthoughtinthefieldsothatthereadercanunderstandtheoriginofpresentideas;secondly,toexplainwhy pasttheorieshavehadtobemodified;andthirdly,topresent ‘fallback’positionslestcurrentmodelsberefutedatsome futuredate.Thisapproachembodiesthescholarlyprinciple thatknowledgeoftheclassicworkinthefieldisthestarting pointforcurrentresearch.
Thetextisalsoparticularlyfocussedonthreetypesofliterature.Firstly,itattemptstogiveaccurateattributionof newideasormethods;secondly,itreviewsclassicpapers whichhavebecomestandardsintheirfield;andthirdly,it presentscasestudiesthathaveevokedcontroversyintheliterature,asexamplesofalternativedatainterpretations.
Theorganizationofthebookallowseachchaptertobe arelativelyfree-standingentitycoveringonesegmentofthe fieldofradiogenicisotopegeology.However,thereadermay benefitfromanunderstandingofthethread,which,inthe author’smind,linksthesechapterstogether.
Chapter1introducesradiogenicisotopesbydiscussing thesynthesisanddecayofnuclideswithinthecontextof nuclearstability.Decayconstantsandtheradioactivedecay lawareintroduced.
Chapter2providesanexperimentalbackgroundtomany ofthechaptersthatfollowbydiscussingthedetailsofmass spectrometricanalysis(TIMSandICP–MS),alongwithadiscussionofisochronregressionfitting.
Thenextthreechaptersintroducethethreepillarsof lithophileisotopegeology,comprisingtheSr,NdandPb isotopemethods.Emphasisisplacedontheirapplications togeochronologyandtheirevolutioninterrestrialsystems. Chapter3coverstheRb–Srsystem,sincethisisoneof thesimplestandmostbasicdatingmethods.Chapter4 coverstheSm–Ndsystem,includingtheuseofNdmodel agestodatecrustalformation.Chapter5examinesU–Pb geochronologyandintroducesthecomplexitiesofterrestrial Pbisotopeevolutioninastraightforwardfashion.Eachchapterendswithanexaminationoftheseisotopesasenvironmentaltracers,focussingparticularlyontheoceans.
Chapters6and7applySr,NdandPb,asgeochemicaltracers,tothestudyofoceanicandcontinentaligneousrocks. Thisisappropriate,becausetheseisotopesaresomeofthe basictoolsoftheisotopegeochemist,whichtogethermay allowunderstandingofthecomplexitiesofmantleprocesses andmagmaticevolution.Thesemethodsaresupplemented inChapters8and9byinsightsfromtheRe–Os,Lu–Hfand otherlithophileisotopesystems,whicharisefromtheirdistinctchemistry.
Chapter10completesthepanoplyoflong-livedisotopic datingsystemsbyintroducingtheK–Ar,Ar–ArandU–He methods,includingtheirapplicationstomagneticandthermalhistories.ThisleadsusnaturallyinChapter11tothe considerationofraregasesasisotopictracers,whichgive uniqueinsightsintothede-gassinghistoryoftheEarth.
Chapter12introducestheshort-livedisotopesoftheuraniumdecayseries,coveringclassicalandrecentdevelopmentsinthedatingofQuaternary-agesedimentaryrocks. ThispreparesusforthecomplexitiesofChapter13,which examinesU-seriesisotopesastracersinigneoussystems. Short-livedprocessesinmantlemeltingandmagmaevolutionarethefocusofattentionhere.
Chapter14examinesthemostimportantofthecosmogenicisotopes.Theserepresentavastandgrowingfieldof chronologyandisotopechemistry,whichisespeciallypertinenttoenvironmentalgeoscience.Inparticular,theradiocarbonmethodisavitaldatingtoolinarchaeologyanda traceroftheocean–atmospheresysteminvolvedinclimate change.
Chapter15representsacomprehensivereviewofthe ‘extinctnuclide’systemsinmeteoritesthathaverecently raisedquestionsaboutthecosmiccontextofterrestrialgeochemistry.Thisoverviewdealswithallofthemajorextinct nuclidepairs,anddiscussestheirsignificancefortheorigins ofthesolarsystemandtheEarth.
Lastly,Chapter16examinesthespecializedfieldof(radiogenic)fissiontrackanalysis,originallydevelopedasaregular datingmethod,butincreasinglyappliedtothermalhistory analysis.
Thetextisgatheredaroundalargenumberofdiagrams, manyofwhichareclassicfiguresfromtheliterature.Igratefullyacknowledgethemanyauthorswhoseoriginaldataand diagramsformthebasisforthesefigures.Authoracknowledgementforallfiguresourcesisgivenwithinindividual figurecaptions,andcorrespondingtitles,journalnames,volumesandpagesarecontainedinthelistofcitedreferences attheendofeachchapter.
AlanP.Dickin McMasterUniversity
Chapter1 NucleosynthesisandNuclearDecay 1.1TheChartoftheNuclides Inthefieldofisotopegeology,neutrons,protonsandelectronscanberegardedasthefundamentalbuildingblocksofthe atom.Thecompositionofagiventypeofatom,calledanuclide,isdescribedbyspecifyingthenumberofprotons(atomic number, Z)andthenumberofneutrons(N)inthenucleus.Thesumoftheseisthemassnumber(A).Byplotting Z against N forallofthenuclidesthathavebeenknowntoexist(atleastmomentarily),thechartofthenuclidesisobtained(Fig.1.1).In thischart,horizontalrowsofnuclidesrepresentthesameelement(constant Z)withavariablenumberofneutrons(N).These areisotopes.
Fig.1.1 Chartofthenuclidesincoordinatesofprotonnumber Z,againstneutronnumber N.( ) = stablenuclides;( ) = unstable nuclides;( ) = naturallyoccurringlong-livedunstablenuclides;( ) = naturallyoccurringshort-livedunstablenuclides.Some geologicallyusefulradionuclidesaremarked.Smoothenvelope = theoreticalnuclidestabilitylimits.Foramoredetailednuclidechart, seeAppendix1.
Abotalof264stablenuclidesareknown,whichhave notbeenobservedtodecaywithavailabledetectionequipment.Thesedefineacentral‘pathofstability’,coloured blackinFig.1.1.Oneithersideofthispath,thezig-zag outlinedefinesthelimitsofexperimentallyknownunstable nuclidescompiledbyHansen(1987).Thesespeciestendto undergoincreasinglyrapiddecayasonemovesoutoneither sideofthepathofstability.Thesmoothouterenvelopesare thetheoreticallimitsofnuclidestability(‘driplines’)beyond whichpromptdecayoccurs.Thismeansthatthesynthesis anddecayofanunstablenuclideoccursinasingleparticle interaction,givingitazeroeffectivelifetime.
Asworkprogresses,thedomainofexperimentallyknown nuclidesshouldapproachthetheoreticalenvelope,ashas alreadyoccurredfornuclideswith Z < 20(Thoennessen, 2013).Thishasbeenachievedoverthepast60yearsusing heavyionaccelerators(e.g.Darmstadt)tomakeexoticspecies bycollision.Becauseofthecurvatureofthepathofstability(Fig.1.1),itwasrelativelyeasytopopulatetheprotonrichsideofthepathofstability,sincethesespeciescanbe madebyfusionoflighterelements.Speciesontheneutronrichsidearemadebybombardingtargetmaterialwith 238 U, creatingunstableheavyatomswhichimmediatelyundergo fissiontoproduceveryneutron-richproducts(e.g.Geissel etal.,2003).Knowledgeabouttheseunstablenucleiwill improveourunderstandingofthenucleosyntheticr-process whichoccursinsupernovae(ThoennessenandSherrill, 2011).
Asmallnumberofunstablenuclideshavesufficiently longhalf-livesthattheyhavenotentirelydecayedtoextinctionsincetheformationofthesolarsystem.Afewother short-livednuclidesareeithercontinuouslygeneratedinthe decayseriesofuraniumandthorium,orproducedbycosmic raybombardmentofstablenuclides.Thesenuclides,andone ortwoextinctshort-livedisotopes,plustheirdaughterproducts,aretherealmofradiogenicisotopegeology.Thosewith half-livesover0.5MaaremarkedinFig.1.2.Nuclideswith half-livesover1000Gadecaytooslowlytobegeologically useful.Observationshowsthatalloftheotherlong-livedisotopeseitherhavebeenorarebeingappliedingeology.
1.2Nucleosynthesis Arealisticmodelforthenucleosynthesisoftheelements mustbebasedonempiricaldatafortheir‘cosmicabundance’.Truecosmicabundancescanbederivedfromstellar spectroscopyorbychemicalanalysisofgalacticcosmicrays. However,suchdataaredifficulttomeasureathighprecision, socosmicabundancesarenormallyapproximatedbysolarsystemabundances.Thesecanbedeterminedbysolarspectroscopyorbydirectanalysisofthemost‘primitive’meteorites,carbonaceouschondrites.Acomparisonofthelatter twosourcesofdata(RossandAller,1976)demonstratesgood agreementformostelements(Fig.1.3).Exceptionsarethe volatileelements,whichhavebeenlostfrommeteorites,and theLi–Be–Bgroup,whichareunstableinstars.
Fig.1.2 Unstablenuclideswithhalf-lives(t1/2 )over0.5Ma,in orderofdecreasingstability.Geologicallyusefulparentnuclides aremarked.Someverylong-livedradionuclideswithno geologicalapplicationarealsomarkedinbrackets.
Itiswidelybelieved(e.g.Weinberg,1977)thatabout30 minutesafterthe‘bigbang’,thematteroftheuniverse(in theformofprotonsandneutrons)consistedmostlyof 1 H and22–28%bymassof 4 He,alongwithtracesof 2 H(deuterium)and 3 He.Hydrogenisstillbyfarthemostabundantelementintheuniverse(88.6%ofallnuclei)andwith helium,makesup99%ofitsmass,butnaturallyoccurring heavynuclidesnowexistuptoatomicweight254orbeyond
Fig.1.3 Comparisonofsolarsystemabundances(relativeto silicon)determinedbysolarspectroscopyandbyanalysisof carbonaceouschondrites.AfterRingwood(1979).
Fig.1.4 Plotofabsolutemagnitudeagainstspectralclassof stars.Hatchedareasshowdistributionsofthethreemainstar groups.Thepostulatedevolutionarypathofastarofsolar massisshown.
(Fig.1.1).Theseheaviernucleimusthavebeenproducedby nucleosyntheticprocessesinstars,andnotinthebigbang, becausestarsofdifferentageshavedifferentcompositions whichcanbedetectedspectroscopically.Furthermore,stars atparticularevolutionarystagesmayhavecompositional abnormalities,suchasthepresenceof 254 Cfinsupernovae. Ifnucleosynthesisoftheheavyelementshadoccurredinthe bigbangthentheirdistributionwouldbeuniformaboutthe universe.
1.2.1StellarEvolution PresentdaymodelsofstellarnucleosynthesisarebasedheavilyonaclassicreviewpaperbyBurbidge etal.(1957),inwhich eightelement-buildingprocesseswereidentified(hydrogen burning,heliumburning, α,e,x,r,sandp).Differentprocesseswereinvokedtoexplaintheabundancepatternsof differentgroupsofelements.Theseprocessesare,inturn, linkedtodifferentstagesofstellarevolution.Itistherefore appropriateatthispointtosummarizethelife-historyof sometypicalstars(e.g.Iben,1967).Thelengthofthislifehistorydependsdirectlyonthestellarmass,andcanbe tracedonaplotofabsolutemagnitude(brightness)against spectralclass(colour),referredtoastheHertzsprung–Russell orH–Rdiagram(Fig.1.4).
Gravitationalaccretionofastarofsolarmassfromcold primordialhydrogenandheliumwouldprobablytakeabout 1Matoraisethecoretemperaturetoca.107 K,when nuclearfusionofhydrogentoheliumcanbegin(Atkinson andHoutermans,1929).Thisprocessisalsocalled‘hydrogen burning’.Thestarspendsmostofitslifeatthisstage,asa ‘mainsequence’star,whereanequilibriumissetupbetween energysupplybyfusionandenergylossintheformofradiation.FortheSun,thisstagewillprobablylastca.10Ga,but
Schematicevolutionofalargestarshowing nucleosyntheticprocessesalongitsacceleratinglife-historyin responsetoincreasingtemperature.Timeismeasured backwardsfromtheendofthestar’slifeontheright.After Burbidge etal.(1957).
averylargestarwith15timestheSun’smassmayremainin themainsequenceforonly10Ma.
Whenthebulkofhydrogeninasmallstarhasbeenconvertedinto 4 He,inwarddensity-drivenforcesexceedoutward radiationpressure,causinggravitationalcontraction.However,theresultingriseincoretemperaturecausesexpansion oftheouterhydrogen-richlayerofthestar.Thisformsahuge low-densityenvelopewhosesurfacetemperaturemayfallto ca.4000K,observedasa‘redgiant’.Thisstagelastsonlyone tenthaslongasthemainsequencestage.Whencoretemperaturesreach1.5 × 107 K,amoreefficienthydrogen-burning reactionbecomespossibleifthestarcontainstracesofcarbon,nitrogenandoxygeninheritedfromoldergenerations ofstars.ThisformofhydrogenburningiscalledtheC–N–O cycle(Bethe,1939).
Atsomepointduringtheredgiantstage,coretemperaturesmayreach108 K,whenheliumfusiontocarbonis ignited(the‘heliumflash’).Furthercorecontraction,yieldingatemperatureofca.109 K,followsasheliumbecomes exhausted.Atthesetemperaturesanendothermicprocessof α-particleemissioncanoccur,allowingthebuildingofheaviernuclidesuptomass40.However,thisquicklyexpends theremainingburnablefuelofthestar,whichthencoolsto awhitedwarf.
Moremassivestars(ofseveralsolarmasses)haveadifferentlife-history.Inthesestars,greatergravitationallyinduced pressure–temperatureconditionsallowthefusionofhelium tobeginearlyintheredgiantstage.Thisisfollowedbyfurthercontractionandheating,allowingthefusionofcarbonandsuccessivelyheavierelements.However,aslighter elementsbecomeexhausted,gravitationallyinducedcontractionandheatingoccurataneverincreasingpace(Fig. 1.5),untiltheimplosionisstoppedbytheattainmentof neutron-stardensity.Theresultingshockwavecausesa
Fig.1.5
Fig.1.6 Schematicdiagramofthecosmicabundancesofthe elements,highlightingthenucleosyntheticprocesses responsibleforformingdifferentgroupsofnuclides.After Burbidge etal.(1957).
supernovaexplosionwhichendsthestar’slife(e.g.Burrows, 2000).
Intheminutesbeforeexplosion,whentemperatures exceed3 × 109 K,veryrapidnuclearinteractionsoccur.Energeticequilibriumisestablishedbetweennucleiandfreeprotonsandneutrons,synthesizingelementslikeFebythesocallede-process.Thesupernovaexplosionitselflastsonlya fewseconds,butischaracterizedbycolossalneutronfluxes. Theseveryrapidlysynthesizeheavierelements,terminating at 254 Cf,whichundergoesspontaneousfission.Productsof thesupernovaexplosionaredistributedthroughspaceand laterincorporatedinanewgenerationofstars.
1.2.2StagesintheNucleosynthesisof HeavyElements Aschematicdiagramofthecosmicabundancechartisgiven inFig.1.6.Wewillnowseehowdifferentnucleosynthetic processesareinvokedtoaccountforitsform.
Theelement-buildingprocessbeginswiththefusionof fourprotonstoone 4 Henucleus,whichoccursinthree stages: 1
where Q istheenergyoutputand t1/2 isthereactiontimeof eachstage(thetimenecessarytoconsumeonehalfofthe reactants)forthecentreoftheSun.Thelongreactiontime forthefirststepexplainsthelongdurationofthehydrogenburning(mainsequence)stageforsmallstarsliketheSun. Theoverallreactionconvertsfourprotonsintoonehelium nucleus,twopositronsandtwoneutrinos,plusalargeoutputofenergyintheformofhigh-frequencyphotons.Hence thereactionisverystronglyexothermic.Althoughdeuteriumand 3 Hearegeneratedinthefirsttworeactions above,theirconsumptioninthethirdaccountsfortheir muchlowercosmicabundancethan 4 He.
Ifheavierelementssuchascarbonandnitrogenare presentinastar,thecatalyticC–N–Osequenceofreactions canoccur,whichalsocombinesfourprotonstomakeone heliumnucleus:
TheC–N–Oelementshavegreaterpotentialenergybarriers tofusionthanhydrogen,sothesereactionsrequirehigher temperaturestooperatethanthesimpleproton–proton(p–p)reaction.However,thereactiontimesaremuchshorter thanforthep–preaction.ThereforetheC–N–Oreactioncontributeslessthan10%ofhydrogen-burningreactionsina smallstarliketheSun,butisoverwhelminglydominantin largestars.Thisexplainstheirmuchshorterlifespaninthe mainsequence.
Heliumburningalsooccursinstages:
He + 4 He ↔
The 8 Benucleusisveryunstable(t1/2 < 10–15 s)andinthe coreofaredgianttheBe/Heequilibriumratioisestimatedat 10–9 .Howeveritslifeisjustlongenoughtoallowthepossibilityofcollisionwithanotherheliumnucleus.(Instantaneous three-particlecollisionsareveryrare.)Theenergyyieldofthe firststageissmall,andthesecondisactuallyendothermic, butthedecayofexcited 12 C∗ tothegroundstateisstrongly exothermic,drivingtheequilibriumtotheright.
TheelementsLi,BeandBhavelownuclearbindingenergies,sothattheyareunstableatthetemperaturesof107 K andabovefoundatthecentreofstars.Theyaretherefore bypassedbystellarnucleosyntheticreactions,leadingtolow
cosmicabundances(Fig.1.6).Thefactthatthefivestableisotopes 6 Li, 7 Li, 9 Be, 10 Band 11 Bexistatallhasbeenattributed tofragmentationeffects(spallation)ofheavycosmicrays (atomicnucleitravellingthroughthegalaxyatrelativistic speeds)astheyhitinterstellargasatoms(Reeves,1974).This istermedthex-process.
Problemshavebeenrecognizedinthex-processmodel forgeneratingthelightelementsLi,BeandB,sincecosmicrayspallationcannotexplaintheobservedisotoperatios oftheseelementsinsolarsystemmaterials.However,Casse etal.(1995)proposedthatcarbonandoxygennucleiejected fromsupernovaecangeneratethesenuclidesbycollision withhydrogenandheliuminthesurroundinggascloud. ThisprocessisbelievedtooccurinregionssuchastheOrion nebula.ThecombinationofsupernovaproductionwithspallationofgalacticcosmicrayscanexplainobservedsolarsystemabundancesofLi,BeandB.
Followingthesynthesisofcarbon,furtherheliumburningreactionsarepossible,toproduceheaviernuclei:
12 C + 4 He → 16 O + γ (Q =+7 15MeV )
16 O + 4 He → 20 Ne + γ (Q =+4 75MeV )
20 Ne + 4 He → 24 Mg + γ (Q =+9.31MeV ) .
Interveningnucleisuchas 13 Ncanbeproducedbyadding protonstothesespecies,butarethemselvesconsumed intheprocessofcatalytichydrogenburningmentioned above.
Inoldredgiantstars,carbon-burningreactionscan occur:
12 C + 12 C → 24 Mg + γ (Q =+13 85MeV ) → 23 Na + 1 H (Q =+2.23MeV ) → 20 Ne + 4 He (Q =+4 62MeV )
Thehydrogenandheliumnucleiregeneratedintheseprocessesallowfurtherreactionswhichhelptofillingaps betweenmasses12and24.
Whenasmallstarreachesitsmaximumcoretemperature of109 Ktheendothermic α-processcanoccur:
20 Ne + γ → 16 O + 4 He (Q =−4.75MeV ) .
Theenergyconsumptionofthisprocessiscompensatedby stronglyexothermicreactionssuchas:
20 Ne + 4 He → 24 Mg + γ (Q =+9 31MeV ) , sothattheoverallreactiongeneratesapositiveenergybudget.Theprocessresemblesheliumburning,butisdistinguishedbythedifferentsourceof 4 He.The α-processcan buildupfrom 24 Mgthroughthesequence 28 Si, 32 S, 36 Arand 40 Ca,whereitterminates,owingtotheinstabilityof 44 Ti.
Themaximumtemperaturesreachedinthecoreofa smallstardonotallowsubstantialheavyelementproduction.However,inthefinalstagesoftheevolutionoflarger
stars,beforeasupernovaexplosion,thecoretemperature exceeds3 × 109 K.Thisallowsenergeticequilibriumtobe establishedbyveryrapidnuclearreactionsbetweenthevariousnucleiandfreeprotonsandneutrons(thee-process). Because 56 Feisatthepeakofthenuclearbindingenergy curve,thiselementismostfavouredbythee-process(Fig. 1.6).However,theotherfirst-seriestransitionelementsV,Cr, Mn,CoandNiinthemassrange50to62arealsoattributed tothisprocess.
Duringthelastfewmillionyearsofaredgiant’slife,a slowprocessofneutronadditionwithemissionofgamma rays(thes-process)cansynthesizemanyadditionalnuclides uptomass209(seeFig.1.7).Twopossibleneutronsources are:
The 13 Cand 21 Neparentscanbeproducedbyprotonbombardmentofthecommon 12 Cand 20 Nenuclides.
Becauseneutroncaptureinthes-processisrelatively slow,unstableneutron-richnuclidesgeneratedinthisprocesshavetimetodecayby β emissionbeforefurtherneutron addition.Hencethenucleosyntheticpathofthes-process climbsinmanysmallstepsupthepathofgreateststability ofproton/neutronratio(Fig.1.7)andisfinallyterminatedby the α decayof 210 Pobackto 206 Pband 209 Bibackto 205 Tl.
The‘neutroncapturecross-section’ofanuclideexpresses howreadilyitcanabsorbincomingthermalneutrons,and thereforedetermineshowlikelyitistobeconvertedto ahigheratomicmassspeciesbyneutronbombardment. Nuclideswithcertainneutronnumbers(e.g.50,82and126) haveunusuallysmallneutroncapturecross-sections,makingthemparticularlyresistanttofurtherreactionandgivingrisetolocalpeaksinabundanceatmasses90,138and 208.Hence, N = 50,82and126areempiricallyreferredtoas neutron‘magicnumbers’.
Incontrasttothes-process,whichmayoccuroverperiodsofmillionsofyearsinredgiants,r-processneutronsare addedinveryrapidsuccessiontoanucleusbefore β decay ispossible.Thenucleiarethereforerapidlydriventothe neutron-richsideofthestabilityline,untiltheyreachanew equilibriumbetweenneutronadditionand β decay,representedbythehatchedzoneinFig.1.7.Nuclidesmovealong thisr-processpathwayuntiltheyreachaconfigurationwith lowneutroncapturecross-section(aneutronmagicnumber).Atthesepointsa‘cascade’ofalternating β decaysand singleneutronadditionsoccurs,indicatedbythenotched laddersinFig.1.7.Nuclidesclimbtheseladdersuntilthey reachthenextsegmentofther-processpathway.Nuclides withneutronmagicnumbersbuildtoexcessabundances,as withthes-process,buttheyoccuratproton-deficientcompositionsrelativetothes-processstabilitypath.Therefore, whentheneutronfluxfallsoffandnuclidesontheladders undergo β decaybacktothestabilityline,ther-processlocal abundancepeaksaredisplacedabout6–12massunitsbelow
Fig.1.7 Neutroncapturepathsofthes-processandr-processshownonthechartofthenuclides.Hatchedzoneindicatesthe r-processnucleosyntheticpathwayforaplausibleneutronflux.Neutron‘magicnumbers’areindicatedbyverticallines,andmass numbersofnuclideabundancepeaksaremarked.AfterSeeger etal.(1965).
thes-processpeaks(Fig.1.6).Ther-processisterminatedby neutron-inducedfissionatmass254,andnuclearmatteris fedbackintotheelement-buildingprocessesatmassesofca. 108and146.Thus,cyclingofnuclearreactionsoccursabove mass108.
Becauseoftheextremeneutronfluxpostulatedforthe r-process,itsoccurrenceisprobablylimitedtosupernovae. However,BlakeandSchramm(1976)proposedtheexistenceofaprocessthatoccurredatintermediateneutron fluxesbetweenthes-andr-processes,whichtheycalled the‘n-process’.Thiscouldoccurwhenneutronaddition onlyslightlyexceedsratesof β decay.Althoughneglected formanyyears,phenomenasimilartothen-processhave receivedconsiderationinsomerecentmodellingofsupernovaoutflows(Meyer,2005;Wanajo,2007;PanovandJanka, 2009).
Theeffectsofr-ands-processsynthesisoftypicalheavy elementsmaybedemonstratedbyanexaminationofthe chartofthenuclidesintheregionofthelightrareearths (Fig.1.8).Thestep-by-stepbuildingofthes-processcontrasts withthe‘rainofnuclides’producedby β decayofr-process products.Somenuclides,suchas 143 Ndto 146 Ndareproduced bybothr-ands-processes.Some,suchas 142 Ndares-only nuclides‘shielded’fromthedecayproductsofther-process byinterveningnuclides.Others,suchas 148 Ndand 150 Nd arer-onlynuclideswhichlieoffthes-processproduction pathway.
Severalheavynuclidesfrom 74 Seto 196 Hglieisolatedon theproton-richsideofthes-processgrowthpath(e.g. 144 Sm inFig.1.8),andarealsoshieldedfromr-processproduction. Inordertoexplaintheexistenceofthesenuclidesitisnec-
essarytopostulateap-processbywhichnormalr-andsprocessnucleiarebombardedbyprotonsatveryhightemperature(>2 × 109 K),probablyintheouterenvelopeofa supernova.
1.3RadioactiveDecay Nuclearstabilityanddecayisbestunderstoodinthecontextofthechartofnuclides.Ithasalreadybeennoted thatnaturallyoccurringnuclidesdefineapathinthechart ofthenuclides,correspondingtothegreateststabilityof
Fig.1.8
Partofthechartofthenuclidesintheareaofthe lightrareearthstoshowp-,r-ands-processproductnuclides. AfterO’Nions etal.(1979).
Fig.1.9 Theoreticalstabilitylimitsofnuclidesillustratedona plotof N/Z againstmassnumber(A).Lowerlimitsfor α emissionareshownfor α energiesof0,2and4MeV.Stability limitsagainstspontaneousfissionareshownforhalf-livesof10 Gaandzero(instantaneousfission).AfterHanna(1959).
proton/neutronratio.Fornuclidesoflowatomicmass,the greateststabilityisachievedwhenthenumbersofneutrons andprotonsareapproximatelyequal(N = Z),butasatomic massincreases,thestableneutron/protonratioincreases until N/Z = 1.5.Theoreticalstabilitylimitsareillustrated onaplotof N/Z againstmassnumber(A)inFig.1.9(Hanna, 1959).
Thepathofstabilityisinfactanenergy‘valley’into whichthesurroundingunstablenuclidestendtofall,emittingparticlesandenergy.Thisconstitutestheprocessof radioactivedecay.Thenatureofparticlesemitteddepends onthelocationoftheunstablenucliderelativetotheenergy valley.Unstablenuclidesoneithersideofthevalleyusually decayby‘isobaric’processes.Thatis,anuclearprotonisconvertedtoaneutron,orviceversa,butthemassofthenuclide doesnotchangesignificantly(exceptforthe‘massdefect’ consumedasnuclearbindingenergy).Incontrast,unstable nuclidesatthehighendoftheenergyvalleyoftendecayby emissionofaheavyparticle(e.g. α particle),thusreducing theoverallmassofthenuclide.
1.3.1IsobaricDecay DifferentdecayprocessesindicatedonFig.1.9canbestbe understoodbylookingatexamplesectionsofthechart ofnuclides.Figure1.10showsapartofthechartaround theelementpotassium.Thediagonallinesindicateisobars (nuclidesofequalmass)whicharedisplayedonenergysectionsinFig.1.11andFig.1.12.
Nuclidesdeficientinprotonsdecaybytransformationof aneutronintoaprotonandanelectron.Thelatteristhen expelledfromthenucleusasanegative‘β’particle(β ), alongwithananti-neutrino(ν).Theenergyreleasedbythe
Fig.1.10 Partofthechartofthenuclides,incoordinatesof atomicnumber(Z)againstneutronnumber(N)intheregion ofpotassium.Stablenuclidesareshaded;thelong-livedunstable nuclide 40 Kishatched.Diagonallinesareisobars(linesof constantmassnumber, A).
transformationisdividedbetweenthe β particleandthe anti-neutrinoaskineticenergy(Fermi,1934).Theobserved consequenceisthatthe β particlesemittedhaveacontinuousenergydistributionfromnearlyzerotothemaximum decayenergy.Low-energy β particlesareverydifficulttoseparatefrombackgroundnoiseinadetector,makingthe β decay constantofnuclidessuchas 87 Rbverydifficulttodetermine accuratelybydirectcounting(Section3.1).
Inmanycasesthenuclideproducedby β decayisleftin anexcitedstatewhichsubsequentlydecaystotheground statenuclidebyareleaseofenergy.Thismayeitherbelost asa γ rayofdiscreteenergy,ormaybetransferredfrom thenucleustoanorbitalelectron,whichisthenexpelled
Fig.1.11 Asimpleenergysectionthroughthechartof nuclidesalongtheisobar A = 38showingnuclidesandisomers. DatafromLedererandShirley(1978).
Fig.1.12 Energysectionthroughthechartofnuclidesalong isobar A = 40.Isomersareomittedforsimplicity.Fornuclides withmorethanonedecaymechanismthepercentageof transitionsbydifferentdecayroutesisindicated.Datafrom LedererandShirley(1978).
fromtheatom.Inthelattercase,nuclearenergyemission inexcessofthebindingenergyoftheelectronistransferred totheelectronaskineticenergy,whichissuperimposedasa linespectrumonthecontinuousspectrumofthe β particles. Themeta-stablestates,or‘isomers’oftheproductnuclide aredenotedbythesuperscript‘m’,andhavehalf-livesfrom lessthanapico-secondupto241years(inthecaseof 192m Ir). Many β emittershavecomplexenergyspectrainvolvinga groundstateproductandmorethanoneshort-livedisomer, asshowninFig.1.11.Thedecayof 40 Clcanyield35differentisomersof 40 Ar(LedererandShirley,1978),buttheseare omittedfromFig.1.12forthesakeofclarity.
Nuclidesdeficientinneutrons,e.g. 38 K(Fig.1.11),may decaybytwodifferentprocesses:positronemissionandelectroncapture.Bothprocessesyieldaproductnuclidewhich isanisobaroftheparent,bytransformationofaprotontoa neutron.Inpositronemissionapositivelychargedelectron (β+ )isemittedfromthenucleusalongwithaneutrino.As with β emission,thedecayenergyissharedbetweenthe kineticenergyofthetwoparticles.Afterhavingbeenslowed downbycollisionwithatoms,thepositroninteractswithan orbitalelectron,wherebybothareannihilated,yieldingtwo 0.511MeV γ rays(thisformspartofthedecayenergyofthe nucleartransformation).
Inelectroncapturedecay(EC)anuclearprotonistransformedintoaneutronbycaptureofanorbitalelectron,usuallyfromoneoftheinnershells,butpossiblyfromanouter shell.Aneutrinoisemittedfromthenucleus,andanouter orbitalelectronfallsintothevacancyproducedbyelectron
capture,emittingacharacteristicX-ray.Theproductnucleus maybeleftinanexcitedstate,inwhichcaseitdecaystothe groundstateby γ emission.
Whenthetransitionenergyofadecayrouteisless thantheenergyequivalentofthepositronmass(2me C2 = 1.022MeV),decayisentirelybyelectroncapture.Thereafter, theratio β+ /ECincreasesrapidlywithincreasingtransition energy(Fig.1.12),butasmallamountofelectroncapture alwaysaccompaniespositronemissionevenathightransitionenergies.
Itisempiricallyobserved(Mattauch,1934)thatadjacent isobarscannotbestable.Since 40 Arand 40 Caarebothstablespecies(Fig.1.10), 40 Kmustbeunstable,andexhibitsa brancheddecaytotheisobarsoneitherside(Fig.1.12).
1.3.2AlphaandHeavyParticleDecay Heavyatomsabovebismuthinthechartofnuclidesoften decaybyemissionofan α particle,consistingoftwoprotons andtwoneutrons(He2+ ).Thedaughterproductisnotanisobaroftheparent,andhasanatomicmassreducedbyfour. Theproductnuclidemaybeinthegroundstate,orremain inanexcitedstateandsubsequentlydecayby γ emission.The decayenergyissharedbetweenkineticenergyofthe α particleandrecoilenergyoftheproductnuclide.
TheUandThdecayseriesareshowninFig.12.1.Because theenergyvalleyofstableproton/neutronratiosinthispart ofthechartofthenuclideshasaslopeoflessthanunity, α decaystendtodrivetheproductsofftotheneutron-richside oftheenergyvalley,wheretheyundergo β decay.Infact β decaymayoccurbeforethecorresponding α decay.
Atintermediatemassesinthechartofthenuclides, α decaymayoccasionallybeanalternativetopositronorelectroncapturedecayforproton-richspeciessuchas 147 Sm. However, α decaysdonotoccuratlowatomicnumbers becausethepathofnuclearstabilityhasa Z/N slopeclose tounityinthisregion(Fig.1.1).Anysuchdecayswould simplydriveunstablespeciesalong(parallelto)theenergy valley.
Anexoticmodeofradioactivedecaywasdiscoveredinthe 235 Uto 207 Pbdecayseries(RoseandJones,1984),whereby 223 Radecaysbyemissionof 14 Cdirectlyto 209 Pbwithadecay energyof13.8MeV.Howeverthismodeofdecayoccurswith afrequencyoflessthan10 9 ofthe α decayof 223 Ra.
1.3.3NuclearFissionandtheOklo NaturalReactor Thenuclide 238 U(atomicno.92)undergoesspontaneousfissionintotwoproductnucleiofdifferentatomicnumber,typicallyca.40and55(ZrandCs),alongwithvariousother particlesandalargeamountofenergy.Becausetheheavy parentnuclidehasahighneutron/protonratio,thedaughterproductshaveanexcessofneutronsandundergoisobaricdecayby β emission.Althoughthefrequencyofspontaneousfissionof 238 Uislessthan2 × 10 6 thatof α decay, inheaviertransuraniumelementsspontaneousfissionisthe
principalmodeofdecay.Othernuclides,suchas 235 U,may undergofissioniftheyarestruckbyaneutron.Furthermore, sincefissionreleasesneutronswhichpromotefurtherfissionreactions,achainreactionmaybeestablished.Ifthe concentrationoffissilenuclidesishighenough,thisleads toathermonuclearexplosion,asinasupernovaoratomic bomb.
Inspecialcaseswhereanintermediateheavy-element concentrationismaintained,aself-sustainingbutnonexplosivechainreactionmaybepossible.Thisdepends largelyonthepresenceofa‘moderator’.Energetic‘fast’neutronsproducedbyfissionundergomultipleelasticcollisions withatomsofthemoderator.Theyaredeceleratedinto‘thermal’neutrons,havingvelocitiescharacteristicofthethermalvibrationofthemedium,theoptimumvelocityforpromotingfissionreactionsinthesurroundingheavyatoms. Onenaturalcaseofsuchanoccurrenceisknown,termed theOklonaturalreactor(Cowan,1976;Naudet,1976).
InMay1972, 235 Udepletionswerefoundinuraniumore enteringaFrenchprocessingplantandtracedtoanore depositatOklointheGabonRepublicofcentralAfrica.In spiteofitsapparentimprobability,thereisoverwhelming geologicalevidencethatthe 235 Udepletionswerecausedby theoperationofanaturalfissionreactorataround1.8Ga.It appearsthatintheEarlyProterozoic,conditionsweresuch thattheseriesofcoincidencesneededtocreateanaturalfissionreactorwereachievedmoreeasilythanatthepresent day.
Uraniumdispersedingraniticbasementwasprobably erodedandconcentratedinstream-bedplacerdeposits. Itwasimmobilizedinthisenvironmentastheinsoluble reducedformduetothenatureofprevailingatmospheric conditions.Withtheappearanceofblue-greenalgae,the firstorganismscapableofphotosynthesis,theoxygencontentoftheatmosphere,andhenceriverwater,probablyrose, convertingsomereduceduraniumintomoresolubleoxidizedforms.Thesewerecarrieddown-streaminsolution. Whenthesolubleuraniumreachedariverdeltaitmusthave encounteredsedimentsrichinorganicooze,creatinganoxygendeficiencywhichagainreducedandimmobilizeduranium,butnowatamuchhigherconcentration(upto0.5% uraniumbyweight).
Afterburialandcompactionofthedeposit,itwassubsequentlyuplifted,foldedandfractured,allowingoxygenated groundwaterstore-mobilizeandconcentratetheoresinto veinsover1mwideofalmostpureuraniumoxide.Hencethe specialoxygenfugacityconditionsobtainingintheProterozoichelpedtoproduceaparticularlyconcentrateddeposit. However,itsoperationasareactordependedonthegreater 235 Uabundance(3%)atthattime,comparedwiththepresent daylevelof0.72%,reducedby α decayintheinterveningtime (half-life = 700Ma).
InthecaseofOklo,lightwater(H2 O),musthaveacted asamoderator,andthenuclearreactionwascontrolledby abalancebetweenhotwaterlossbyconvectiveheatingor boiling,andreplacementbycoldgroundwaterinflux.Inthis
Nd,Oklooreandreactorfissionproductwaste.Datafrom Cowan(1976).
waytheestimatedtotalenergyoutput(15000mega-watt years,representingtheconsumptionofsixtonsof 235 U)was probablymaintainedatanaverageofonly20kWforabout 0.8Ma.
Geochemicalevidencefortheoccurrenceoffissionis derivedfirstlyfromthecharacteristicelementalabundances offissionproducts.Forexample,excessconcentrationsof rareearthsandotherimmobileelementssuchasZrare observed.Alkalimetalandalkalineearthswereprobably alsoenriched,buthavesubsequentlybeenremovedbyleaching.Secondly,thecharacteristicisotopeabundancesofsome elementscanonlybeexplainedbyfission(Raffenach etal., 1976).
TheNdisotopecompositionoftheOklooreisverydistinctive(Fig.1.13). 142 Ndisshieldedfromisobaricdecayof theneutron-richfissionproducts(Fig.1.8)sothatitsabundanceindicatesthelevelofnormalNd.Aftercorrectionfor anenhancedabundanceof 144 Ndand 146 Ndduetoneutron capturebythelarge-cross-sectionnuclides 143 Ndand 145 Nd, OkloNdhasanisotopiccompositioncloselyresemblingthat ofnormalreactorfissionproductwaste(Fig.1.13).
Evidenceforasignificantneutronfluxisalsodemonstratedbytheisotopesignaturesofactinideelements.For example,theabundantisotopeofuranium(238 U)readilycapturesfastneutronstoyieldanappreciableamountof 239 U, whichdecaysby β emissionto 239 Npandthen 239 Pu(Fig. 1.14).Thelatterdecaysby α emissionwithahalf-lifeof24ka toyieldmore 235 U,contributinganextra50%tothe‘burnable’fuel,asina‘fast’breederreactor(‘fast’referstothe speedoftheneutronsinvolved).Becausethefissionproducts of 239 Puand 235 Uhavedistinctisotopicsignatures,itisdeterminedthatverylittle 239 Puunderwentneutron-induced
Fig.1.13 Barchartsoftheisotopecompositioninnormal
Fig.1.14 Nuclearreactionsleadingto‘breeding’of transuraniumelementfuelintheOklonaturalreactor.
fissionbeforedecayingto 235 U.Hence,thelowfluxandprolongedlifetimeofthenaturalreactorarededuced.
1.4TheLawofRadioactiveDecay Therateofdecayofaradioactiveparentnuclidetoastable daughterproductisproportionaltothenumberofatoms, n presentatanytime t (RutherfordandSoddy,1902):
where λ istheconstantofproportionality,whichischaracteristicoftheradionuclideinquestionandiscalledthe decayconstant(expressedinunitsofreciprocaltime).The decayconstantstatestheprobabilitythatagivenatomofthe radionuclidewilldecaywithinastatedtime.Thetermdn/dt istherateofchangeofthenumberofparentatoms,andis negativebecausethisratedecreaseswithtime.Rearranging equation[1.1],weobtain:
Thisexpressionisintegratedfrom t = 0to t,giventhatthe numberofatomspresentattime
0is
whichcanalsobewrittenas:
Ausefulwayofreferringtotherateofdecayofaradionuclideisthe‘half-life’, t1/2 ,whichisthetimerequiredforhalf oftheparentatomstodecay.Substituting n = n0 /2and t = t1/2
intoequation[1.5],andtakingthenaturallogofbothsides, weobtain:
Thenumberofradiogenicdaughteratomsformed, D
,is equaltothenumberofparentatomsconsumed:
but n0 = n eλ t (fromequation[1.5]);sosubstitutingfor n0 in equation[1.7]yields:
Ifthenumberofdaughteratomsattime t = 0is D0 ,thenthe totalnumberofdaughteratomsaftertime t isgivenas:
Thisequationisthefundamentalbasisofgeochronological datingtools.
Intheuraniumseriesdecaychains,thedaughterproductsofradioactivedecay(otherthanthethreePbisotopes) arethemselvesradioactive.Hencetherateofdecayofsucha daughterproductisgivenbythedifferencebetweenitsproductionratefromtheparentanditsowndecayrate:
where n1 and λ1 aretheabundanceanddecayconstantof theparent,and n2 and λ2 correspondtothedaughter.
Butequation[1.5]canbesubstitutedfor n1 inequation [1.11]toyield:
Thisequationisintegratedforachosensetofinitialconditions,thesimplestofwhichsets n2 = 0at t = 0.Then:
ThistypeofsolutionwasfirstdemonstratedbyBateman (1910)andisnamedafterhim.Recently,Catchen(1984) examinedmoregeneralinitialconditionsfortheseequations,leadingtomorecomplexsolutions.
1.4.1Uniformitarianism Whenusingradioactivedecaytomeasuretheageofrockswe mustapplytheclassicprincipleofuniformitarianism(Hutton,1788),byassumingthatthedecayconstantoftheparentradionuclidehasnotchangedduringthehistoryofthe Earth.Itisthereforeimportanttooutlinesomeevidencethat thisassumptionisjustified.
Thedecayconstantofaradionuclidedependsonnuclear constants,suchas a ( = elementarycharge2 /Plank’sconstant/velocityoflight).Shlyakhter(1976)arguedthattheneutroncapturecross-sectionofanuclideisverysensitively dependentonnuclearconstants.Becauseneutronabsorbers (suchas 143 Ndand 145 Nd)inthe1.8GaOklonaturalreactor
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