Compton scattering on complex materials [Elektronische Ressource] : an investigation on the electronic structure of  alkali-metal doped Si-clathrates / vorgelegt von Martin Volmer
117 pages
English

Compton scattering on complex materials [Elektronische Ressource] : an investigation on the electronic structure of alkali-metal doped Si-clathrates / vorgelegt von Martin Volmer

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117 pages
English
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Compton Scattering on Complex Materials-an investigation on the electronic structureof alkali-metal doped Si-clathratesDISSERTATIONzur Erlangung des Doktorgrades derNaturwissenschaftendes Fachbereiches Physik der Universit¨at Dortmundvorgelegt vonMartin Volmer2006Table of contents IIIContentsTable of contents IIIIntroduction 11 Theory of Compton scattering 51.1 Inelastic x-ray scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 The non-relativistic double differential scattering cross-section . . . . . 61.3 The dynamic structure factor . . . . . . . . . . . . . . . . . . . . . . . 81.4 Impulse Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5 The Compton profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.6 The free electron gas model . . . . . . . . . . . . . . . . . . . . . . . . 141.6.1 Electron-electron correlation . . . . . . . . . . . . . . . . . . . . 141.7 The asymmetry of Compton profiles and limitations of the ImpulseApproximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.8 Relativistic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Models for the theoretical treatment of Compton profiles 192.1 The Hartree-Fock approximation . . . . . . . . . . . . . . . . . . . . . 192.2 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.1 The Khon-Sham equations . . . . . . . . . . . . . . . . . . . . . 212.2.

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Publié par
Publié le 01 janvier 2006
Nombre de lectures 69
Langue English
Poids de l'ouvrage 2 Mo

Extrait

ComptonScatteringonComplexMaterials
-aninvestigationontheelectronicstructure
ofalkali-metaldopedSi-clathrates

DISSERTATION

zurErlangungdesDoktorgradesder
Naturwissenschaften
desFachbereichesPhysikderUniversita¨tDortmund

vorgelegtvon

MartinVolmer

2600

Tableofcontents

Contents

III

TableofcontentsIII
Introduction1
1TheoryofComptonscattering5
1.1Inelasticx-rayscattering..........................5
1.2Thenon-relativisticdoubledierentialscatteringcross-section.....6
1.3Thedynamicstructurefactor.......................8
1.4ImpulseApproximation...........................10
1.5TheComptonprole............................12
1.6Thefreeelectrongasmodel........................14
1.6.1Electron-electroncorrelation....................14
1.7TheasymmetryofComptonprolesandlimitationsoftheImpulse
Approximation...............................16
1.8Relativisticeects..............................17
2ModelsforthetheoreticaltreatmentofComptonproles19
2.1TheHartree-Fockapproximation.....................19
2.2DensityFunctionalTheory.........................20
2.2.1TheKhon-Shamequations.....................21
2.2.2Approximationsfortheexchange-correlationfunctional.....23
3Siliconclathrates25
3.1Thestructureofclathrates.........................25
3.1.1ThestructureIsiliconclathrate..................28
3.1.2ThestructureIIsiliconclathrate.................30
3.2Synthesisofsiliconclathrates.......................32
3.3Propertiesandresearch...........................33
4Comptonscatteringonsiliconclathrates37
4.1ComptonscatteringatbeamlineID15BattheESRF..........37
4.1.1SetupA:StandardComptonscatteringsetupusing60keVin-
cidentphotonenergy........................38

VI

Tableofcontents

4.1.2SetupB:Dispersioncompensatingsetupat90keV
incidentphotonenergy.......................40
4.2Dataanalysis................................42
4.2.1Firstanalysisofthedata......................43
4.2.2The’glitch’oftheRowlandspectrometer.............43
4.2.3Energydependentcorrections...................44
4.2.4ThetotalenergycorrectionfactorsforsetupAandsetupB..46
4.2.5Multiplescattering.........................48
4.2.6AsymmetryoftheComptonspectraandnormalization.....49
4.3Comptonprolesofthevalenceelectrons.................52
4.3.1Analysisofthereferencematerials.................52
4.3.2Alkali-metaldopedsiliconclathrates...............58
4.4AmorphoussilicondioxideinK7.6Si46andNa8Si46............62
4.4.1X-rayRamanscatteringatthesiliconL-edgeofalkali-metal
dopedsiliconclathrates.......................62
4.4.2DeterminationoftheSiO2contributiontothemeasuredComp-
tonproles.............................68
5InterpretationoftheextractedComptonproles73
5.1Thealkali-metalguestasafreeatom...................73
5.2ComparisonoftheextractedComptonproleswithDFTspectra...75
5.2.1Sodiumdopedsiliconclathrate..................75
5.2.2Potassiumdopedsiliconclathrate.................76
5.2.3InuenceoftheassumedSiO2content..............78
5.2.4Conclusions.............................79
5.3Chargetransfer...............................80
5.3.1Electrondensityofstates......................80
5.3.2Mullikenpopulationanalysis....................82
5.3.3Conclusions.............................83
6Summaryandoutlook85
ADiractionpatternsofsiliconandsiliconclathrates87
Literaturei
ListofFiguresxi
Publicationsxv
Acknowledgementsxvii
EidesstattlicheErkla¨rungxix

Introduction

1

Insearchofmoreeectivethermoelectricmaterialstheconceptofaphononglassand
anelectroncrystal(PGEC)isatthecenterofrecentresearch[Fujita2006,Gao2005,
Slack1995].Itsuggestsmaterialspossessingelectronicpropertiesassociatedwith
agoodsemiconductorsinglecrystalwhilehavingathermalconductivitynormally
foundinamorphousorglass-likematerials.Thegureofmeritofagoodthermoelec-
tricmaterialisdenedbythequantityZ[Goldsmid1986].Itisoftendisplayedasa
dimensionlessquantityZTwithTbeingtheabsolutetemperature:ZT=S2/T.
HereSistheSeebeckcoecient,theelectricalconductivityandthetotalthermal
conductivity.Itwasinthemid1990s,whengroup-IVclathratesreenteredthefocusof
scienti

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