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DETERMINATIONOFTHESITESYMMETRYOFNi(0)ANDFe(0)ATOMS ISOLATEDINSOLIDKRYPTONMATRIXVIAMAGNETICCIRCULARAND MAGNETICLINEARDICHROISMSPECTROSCOPY BY KARENL.JENSEN ADISSERTATIONSUBMITTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2003 Idedicatethiscompositiontomymother,DoloresEyring,atruly remarkablewomanwhoseloveforherchildhasbeenconsistentlydemonstrated inbothwordanddeed.Iwishalsotosimultaneouslydedicatethisworktothe memoryofmybestfriendinthislife,SteveBerman. ACKNOWLEDGMENTS Iwishtothankmycommitteeadvisor, MartinVala,Ph.D.,forhis incredible supportandinvolvementinmyacademicpursuits.Similarly,Iwouldliketorecognize the tremendous assistance, guidance, and hospitality extended to me by both Bryce Williamson,Ph.D. (oftheUniversityofCanterbury,Christchurch,NewZealand)and Jean-ClaudeRivoal,Ph.D.(oftheLaboratoired'OptiquePhysique,Paris,France). RussellPierce,theresidentchemistrydepartmentelectronicstechnician,isalso deservingofmyappreciation.Histenaciousassistanceintroubleshooting,designing,and repairingthecomplexelectronicsofoursystemenabledustokeepprogressingforward.I alsoamindebtedforthegracioushelpofDennisRoser,whoprovidedbackuprelieffor thedataacquisitionduringthemanylongperiodsofuninterruptedexperimentsalong withmanypositiveprofessionalandsociableencountersduringouryearsofworking together. IthankmysisterDonnaforhersupportovertheyears,andespeciallywishto thankmyclosefriendsAnitaBermanandRhondaJohnsonfortheconstancyoftheir friendship. in TABLEOFCONTENTS page ACKNOWLEDGMENTS iii LISTOFTABLES vi LISTOFFIGURES viii ABSTRACT xiv CHAPTERS 1 INTRODUCTION 1 History 1 PreviousFeandNiWork 9 ExtensiontoMLD 11 MagneticSaturation 12 StatementofProblem 13 2 THEORYOFMAGNETICCIRCULARANDMAGNETICLINEAR DICHROISM 21 ProductionofCircularlyPolarizedRadiation 21 MagneticCircularDichroism 26 MagneticLinearDichroism 37 3 SATURATIONTHEORYOFMCDANDMLDFORORIENTATIONALLY AVERAGEDSYSTEMS 47 MCDandMLDintheNonlinearRegime 47 DevelopmentofCrystalFieldHamiltonian 53 FullStateEigenvectors 59 Laboratoryvs.MolecularReferenceFrame 60 EulerTransformation 61 ApplicationofEulerTransformtoMCD/MLDEquations 66 Wigner-EckartTheorem 67 FinalReducedExpressionsforMCDandMLD 69 NumericalAnalysis 71 IV 8 4 THEMCDANDMLDSPECTRAOFFe(0)ATOMSINKRYPTONMATRIX 77 Introduction 77 ElectronicStateAssignmentsviaComplementaryMCD/MLDSpectroscopy 81 Experimental 81 Results 85 Discussion 86 DeterminationofSiteGeometryviaMagneticSaturationTechniques 87 Experimental 87 DataReductionandRefinement 91 Results 94 Discussion 116 Summary 129 5 THEMCDANDMLD OFNi(0)ATOMSINARGONANDKRYPTON MATRICES 196 Introduction 196 ElectronicStateAssignmentsofNi(0)inArgon 199 Experimental 199 Results 200 Discussion 208 MCDandMLDSaturationSpectroscopyofNi(0)inaKryptonMatrix 209 Experimental 209 DataReductionandRefinement 211 Results 213 3D3GroundStateConfigurationofNi(0) 213 3F4GroundStateConfigurationofNi(0) 21 Discussion 225 Summary 229 6 CONCLUSIONS 274 APPENDIX MATHEMATICALMODELINGSOFTWAREINC++ 283 LISTOFREFERENCES 309 BIOGRAPHICALSKETCH 315 LISTOFTABLES Table E§ge 3-1. BasissetvectorsforJ=3groundstateinoctahedral,tetragonal,andtrigonal crystalfieldsymmetries 55 3-2. BasissetvectorsforJ=4groundstateinoctahedral,tetragonal,andtrigonal crystalfieldsymmetries 56 3-3. CrystalfieldenergiesforJ=3andJ=4atomicstatesinoctahedral,tetragonal, andtrigonalsymmetries 57 3-4. Crystalfieldmatrixforoctahedral,tetragonal,andtrigonalsymmetriesinthe |JM)basis 58 4-1. MLDandMCDparametricexpressionsfortheintensityandsignofatomic transitionsforAJ=1,0,-1 78 4-2. MCDandMLDbandpositionsandassignmentsforFe(0)atomsisolatedina kryptonmatrixforthe5D4groundstateconfiguration 85 4-3. Freeatomandoctahedralrefinementparametersforthesimultaneously-refined MCDandMLDexperimentaldatasets 96 4-4. Freeatomandoctahedralrefinementparametersfortheindividually-refined MCDandMLDexperimentaldatasets 98 4-6. Tetragonalrefinementparametersfortheindividually-refinedMCDandMLD experimentaldatasets 99 4-7. Tetragonalrefinementparametersforthesimultaneously-refinedMCDandMLD experimentaldatasets 100 4-8. Tetragonalrefinementparametersfortheindividually-refinedMCDandMLD experimentaldatasetsatdifferentstartingvaluesofthecrystalfield parameters113 4-9. OctahedralrefinementparametersfortheMCDandMLDexperimentaldatasets determinedfromRMSvs.Pplotsforthelowestenergyconfigurationover250 thetaincrements 115 vi 4-10. RelativetransitionintensitiesfromthegroundstateJ=4Zeemansublevelsto theexcitedstateJ'=3Zeemansublevels 118 5-1. Gaansdpshigansse,aabnsdorpprteidoinctpeodsirteiloantsi,veoibnsteernvsietdieasrfgoornMmaCtDrixanMdCMDLaDndbaMndLsDfoprosNiitions atomswitha3D3groundstate 201 5-2. Gasphaseabsorptionpositions,observedargonmatrixMCDandMLD positions,signs,andpredictedrelativeintensitiesforMCDandMLDbandsfor Niatomswitha3F4groundstate 204 5-3. RelativeintensitiesforthepredictedMCDandMLDgasphasetransitions between339and352nm 206 5-4. Freeatomrefinementparametersforthe3D3MCDandMLDexperimentaldata sets 214 5-5. Octahedralrefinementparametersforthe3D3MCDandMLDdatasets 215 5-6. Tetragonalrefinementparametersforthe3D3MCDandMLDdatasetsreduced bycontinuousscalingofthemagnetizationdata 215 5-7. Tetragonalrefinementparametersforthe3D3MCDandMLDdatasetsreduced bycontinuousscalingofthemomentsdata 216 5-8. Trigonalrefinementparametersforthe3D3MCDandMLDdatasetsreducedby continuousscalingofthemagnetizationdata 217 5-9. Trigonalrefinementparametersforthe3D3MCDandMLDdatasetsreducedby continuousscalingofthemomentsdata 217 5-10. Freeatomrefinementparametersforthe F4MCDandMLDexperimentaldata setsforNi(0)atomsinKr 221 5-11. Octahedralrefinementparametersforthe3F4MCDandMLDexperimentaldata setsforNi(0)atomsinKrusingoneincrementfornumericalthetaintegration fromOtorc/2 221 5-12. Octahedralrefinementparametersforthe3F4MCDandMLDexperimentaldata setsforNi(0)atomsinKrusing250incrementsfornumericalthetaintegration over ton/2 222 5-13. Octahedralrefinementparametersforthe3F4MCDandMLDexperimentaldata setsforNi(0)atomsinKrusing1000incrementsfornumericalthetaintegration over tonil 222 Vll LISTOFFIGURES Figure ESge 1-1. TheMCD/MLDapparatus 15 1-2. ConfigurationforMCDexperiment 16 1-3. Zeemansplittingandallowedtransitionsforcircularlyandlinearlypolarized radiationinamagneticfieldBforanondegenerategroundstate 17 1-4. Zeemansplittingandallowedtransitionsforcircularlyandlinearlypolarized radiationinamagneticfieldBforadegenerategroundstate 18 1-5. Zeemansplittingandallowedtransitionsforcircularlyandlinearlypolarized radiationinamagneticfieldBforanondegenerategroundstatetotwo nondegenerateexcitedstates 19 1-6. ConfigurationforMLDExperiment 20 2-1. Configurationofpolarizingfilterandphotoelasticmodulator 41 2-2. Principleofphotoelasticmodulation 42 2-3. Componentsofelectricandmagneticwavepropagationthroughaphotoelastic modulator 43 2-4. OriginationofFaradayA term 44 2-5. OriginationofFaradayC term 45 2-6. OriginationofFaradayB term 46 3-1. MCDdependenceonBandT 72 3-2. NormalizedBoltzmannpopulationdistributionforFe(0)infreeatom5D4ground stateatvarioustemperatures(T°K)andmagneticfieldstrengths(BTesla) 73 3-3. Octahedralsymmetrysites 74 3-4. LowersymmetrymodelsofMX12system 75 viu . 3-5. RelationofmolecularxyzreferenceaxestolaboratoryXYZaxesviaEuler angles <|),9,and\\i 76 4-1. SplittingofFe(0)byspin-orbit(SO)andoctahedralcrystalfield(CF) perturbations 133 4-2. DiagramofAirProductsclosed-cycleheliumcryostat 134 4-3. DiagramofOxfordsuperconductingsplit-coilmagnet/liquidheliumcryostat....135 4-4. ExpandedViewofOxfordInstrumentsmagnet/cryostatcoldfinger 136 4-5. PlanviewoffurnaceandKnudsencellassemblyforgeneratingatomicbeam 137 4-6. Temperaturecalibrationdatacurvesderivedfromamomentsanalysis 138 4-7. Superfluid4Hevaporpressurecalibration 139 4-8. Carbon-Glassthermistorcalibration 140 4-9. AbsorptionspectrumofFe(0)atomsisolatedinKrmatrix 141 4-10. Magneticcirculardichroism(MCD)spectrumofFe(0)atomsisolatedinKr matrix 142 4-11. Magneticlineardichroism(MLD)spectrumofFe(0)atomsisolatedinaKr matrix 143 4-12. Fe(0)atomsinKrfreeatomMCDvs.Bexperimentalandtheoreticalplots 144 4-13. Fe(0)atomsinKrfreeatomMLDvs.B2experimentalandtheoreticalplots 147 4-14. Fe(0)atomsinKroctahedralMCDvs.Bexperimentalandtheoreticalplots 150 4-15. Fe(0)atomsinKroctahedralMLDvs.B2experimentalandtheoreticalplots 153 4-16. Fe(0)atomsinKrtetragonalMCDvs.Bexperimentalandtheoreticalplots 156 4-17. Fe(0)atomsinKrtetragonalMLDvs.B experimentalandtheoreticalplots 159 4-18. Fe(0)atomsinKrtrigonalMCDvs.Bexperimentalandtheoreticalplots 162 4-19. Fe(0)atomsinKrtrigonalMLDvs.B2experimentalandtheoreticalplots 165 4-20. RMSvs.DOCTplotsforactualMCDandMLDrefinementsat1.61K 168 4-21 RMSvs.DOCTplotsforactualMCDandMLDrefinementsat4.22K 169 IX 4-22. TheresultsofastructuredincrementingoftheD0CTvaluesat1.74and4.22K forMCDandMLD 170 4-23. ResultsofstructuredincrementingofD0CTperformedonallthedatasets between4.22Kand1.48Kforoctahedralgeometry 171 4-24. SuperimposedgraphsfortheMCDplotsofFigure4-23foreasiercomparison..174 4-25. SuperimposedgraphsfortheMLDplotsofFigure4-23foreasiercomparison..175 4-26. Tsohleutrieosnulftosrotfhein4c.r2e2meKntainndg1a.l7o4ngKoMneCdDimaenndsiMoLnD(FidTaEtTa)soeftsthetetragonal 176 4-27. Plotsofstructuredincrementingoveralldatasetsfortetragonalsymmetry 177 4-28. SimultaneousplotsofMCDrefinementdataforallgeometriesbasedon ninuimteiarlicstaalrltyinignpteagrraamteitnegrtsheotfaFoive^r1n=ilVi™n1on=eBst™epf=or1o.0c0tafhoerdtreatlrsagyomnmaeltarnydand trigonalsymmetry 180 4-29. SimultaneousplotsofMLDrefinementdataforallgeometriesbasedon numericallyintegratingthetaoverp/2inonestepforoctahedralsymmetryand initialstartingparametersofFi™1"=F2TET=B™T=1.00fortetragonaland trigonalsymmetry 181 4-30. SplittingofFe(0)byspin-orbit(S)andtetragonalcrystalfield(CF) perturbations 182 4-31. Fe(0)atomsinKrtetragonalMCDvs.Bexperimentalandtheoreticalplots. Initialinputparameterstominimizationroutine:Fi =F2 =B =0.05....183 4-32. Fe(0)atomsinKrtetragonalMLDvs.B2experimentalandtheoreticalplots. Initialinputparameterstominimizationroutine:Fi =F2T =B =0.05....186 4-33. SimultaneousplotsofMCDrefinementdataforallgeometriesbasedon ninuimteiarlicstaalrltyinignpteagrraamteitnegrtsheotfaFov^er1r=c/F22iTnETon=eRstepf=or0.o0c5tafhoerdtreatlrsagyomnmaeltarnydand trigonalsymmetry 189 4-34. SimultaneousplotsofMLDrefinementdataforallgeometriesbasedon ninuimteiarlicstaalrltyinignpteagrraamteitnegrtsheotfaFoiv^er1n=/2F2iTnETon=eBst1*epf=or0.o0c5tafhoerdtreatlrsagyomnmaeltarnydand trigonalsymmetry 190 4-35. PlotsofstructuredincrementingoftheMCDandMLDdataunderoctahedral symmetryprocessing250stepsofthetanumericalintegrationfrom totc/2 191

Determination of the site symmetry of ni (0) and fe(0) atoms isolated in solid krypton matrix via magnetic circular and magnetic linear dichroism spectroscopy PDF

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