Ph.D. Thesis --- Peter Matus

INFLUENCEOFLOCALC ORIENTATION60
ONELECTRONICPROPERTIESOFA C3 60
COMPOUNDS
Ph.D.Thesis
PÉTERMATUS
Supervisors
HENRIALLOUL GYÖRGYKRIZA
directeurderecherche scientificadvisor
LaboratoiredePhysique ResearchInstituteforSolidStatePhysics
desSolides,UniversitéParis-Sud andOptics,HungarianAcademyofSciences
Orsay,France Budapest,Hungary
RESEARCHINSTITUTEFORSOLIDSTATEPHYSICSANDOPTICS
oftheHungarianAcademyofSciences
BUDAPEST
2006SincewhatmaybeknownGodisplaintothem,
becauseGodhasmadeitplaintothem.
Forsincethecreationoftheworld
God’sinvisiblequalities
—Hiseternalpoweranddivinenature—
havebeenclearlyseen,
beingunderstoodfromwhathasbeenmade.
ROMANS 1,19–20Contents
Contents i
ListofFigures iii
ListofTables v
Acknowledgement vi
Abstract viii
Kivonat ix
1 Introduction 1
2 Theworldoffullerenes 3
2.1 ThebuckminsterfullereneC . . . . . . . . . . . . . . . . . . . . . . 360
2.1.1 ThemolecularstructureofC fullerene . . . . . . . . . . . . 360
2.1.2 Fullerite,thecrystallineformoffullerene . . . . . . . . . . . 5
2.1.3 Fullerenecompounds . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Alkalifulleridesalts. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 A C superconductors . . . . . . . . . . . . . . . . . . . . . 113 60
3 Nuclearmagneticresonancespectroscopy 15
3.1 PhysicalbackgroundofNMR . . . . . . . . . . . . . . . . . . . . . . 16
3.1.1 Nuclearspintransition . . . . . . . . . . . . . . . . . . . . . . 16
3.1.2 Nuclearmagnetization . . . . . . . . . . . . . . . . . . . . . . 17
3.1.3 Larmorprecession . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.4 Relaxationalprocesses . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Pulsesequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.1 Spin-echo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.2 Measurementofthespin-latticerelaxationtime . . . . . . . 23
3.3 InteractionsinNMRspectroscopy . . . . . . . . . . . . . . . . . . . 24
3.3.1 Interactionsbetweennuclearspins . . . . . . . . . . . . . . . 25
3.3.2 Quadrupolarinteraction . . . . . . . . . . . . . . . . . . . . . 26
3.3.3 Interactionsbetweenelectronsandnuclearspins . . . . . . . 26
3.4 Spin-echodoubleresonance . . . . . . . . . . . . . . . . . . . . . . . 28
iCONTENTS ii
4 Experimental 30
4.1 Samplepreparationandcharacterization . . . . . . . . . . . . . . . 30
4.2 NMRapparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.3 Measurementsetup,dataprocessing . . . . . . . . . . . . . . . . . . 35
4.3.1 SEDOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5 Results 40
5.1 LinesplittingintheNMRspectra . . . . . . . . . . . . . . . . . . . . 40
235.1.1 NaNMRspectraofNa CsC . . . . . . . . . . . . . . . . . 402 60
235.1.2 NaNMRspectraofNa RbC andNa KC compounds . 422 60 2 60
235.1.3 NaNMRlinewidthinNa CsC . . . . . . . . . . . . . . . 452 60
05.2 IsthedetectedT peakintrinsic? . . . . . . . . . . . . . . . . . . . . 46
5.2.1 NMRlineshiftsinNa CsC . . . . . . . . . . . . . . . . . . 462 60
5.2.2 Spin-echodoubleresonanceexperiments . . . . . . . . . . . 47
0 135.3 ComparisonofT spectralweightand Clinewidth . . . . . . . . 49
5.4 Relaxationrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.4.1 Spin-spinrelaxation . . . . . . . . . . . . . . . . . . . . . . . 50
5.4.2 Spin-latticerelaxation . . . . . . . . . . . . . . . . . . . . . . 50
6 Discussion 52
6.1 Orientationalorderingtransition . . . . . . . . . . . . . . . . . . . . 52
6.2 Tetrahedrallinesplitting . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.3 Influenceofquadrupolarinteractiononthelineshape . . . . . . . . 55
6.4 SodiumsiteexchangeduetoC reorientations . . . . . . . . . . . . 5760
236.4.1 NaNMRspectrum . . . . . . . . . . . . . . . . . . . . . . . 57
6.4.2 Spin-spinrelaxation . . . . . . . . . . . . . . . . . . . . . . . 59
6.4.3 Spin-latticerelaxation . . . . . . . . . . . . . . . . . . . . . . 61
6.4.4 Dynamicalcrossover . . . . . . . . . . . . . . . . . . . . . . . 63
6.5 TheinfluenceoflibrationsonT relaxationrates . . . . . . . . . . . 651
06.6 T–T splittingduetoC orientationalenvironments . . . . . . . . 6960
6.6.1 TheoriginofsplittinginNa AC . . . . . . . . . . . . . . . 692 60
06.6.2 T–T probleminA C withmerohedraldisorderrevisited . 733 60
7 Conclusion 78
Bibliography 80
Ownpublications 87ListofFigures
2.1 StructureofaC molecule . . . . . . . . . . . . . . . . . . . . . . . 460
2.2 C bondlengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
2.3 ElectronicstructureofC andbandstructureofK C . . . . . . . 660 3 60
2.4 Twostandardorientations: merohedraldisorder . . . . . . . . . . . 7
2.5 Nearestneighborfullereneconfigurations . . . . . . . . . . . . . . . 8
2.6 Twoexamplesoffullerenecompounds . . . . . . . . . . . . . . . . . 9
2.7 InterstitialsitesinfcchostlatticeofC . . . . . . . . . . . . . . . . 1060
2.8 StructureofalkaliC compounds . . . . . . . . . . . . . . . . . . . 1160
2.9 Latticeconstantdependenceofsupercond. transitiontemperature . 12
02.10 FirstobservationofT–T splitting . . . . . . . . . . . . . . . . . . . . 13
3.1 Precessionofmagneticmomentin B rffield(rotatingframe). . . . 181
3.2 Precessionofmagneticmomentin x–yplanein B field . . . . . . . 180
3.3 Relaxationalprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4 Spin-echopulsesequence . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5 Saturationrecoverypulsesequence . . . . . . . . . . . . . . . . . . . 24
3.6 Inversionrecoverypulsesequence . . . . . . . . . . . . . . . . . . . 24
3.7 SEDORpulsesequence . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1 Na CsC magnetizationbySQUID . . . . . . . . . . . . . . . . . . 312 60
4.2 SamplecharacterizationbyusingNMRspectra . . . . . . . . . . . . 32
4.3 Blockdiagramofhome-builtNMRspectrometer . . . . . . . . . . . 33
4.4 NMRprobehead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.5 FIDandNMRspectrumat100K . . . . . . . . . . . . . . . . . . . . 36
4.6 Decayofreducedmagnetizationin T measurement . . . . . . . . . 371
4.7 Decayoftransversemagnetizationin T measurement. . . . . . . . 382
235.1 NaNMRspectraofNa CsC . . . . . . . . . . . . . . . . . . . . . 412 60
235.2 NaNMRspectraofdifferentNa AC salts . . . . . . . . . . . . . 432 60
5.3 NMRspectratakenbydifferentcoolingrates . . . . . . . . . . . . . 44
235.4 FWHMlinewidthof NaNMRspectruminNa CsC . . . . . . . 452 60
235.5 Temperaturedependenceof NaNMRlineshiftsinNa CsC . . 462 60
5.6 SEDORfractionsat80K . . . . . . . . . . . . . . . . . . . . . . . . . 47
0 135.7 TemperaturedependenceofT spectralratioand Clinewidth . . 49
235.8 Temperaturedependenceof Naspin-spinrelaxationrate . . . . . 50
iiiLISTOFFIGURES iv
5.9 Temperaturedependenceofsodium1/(T T)relaxationrate . . . . 511
236.1 NaNMRspectrumofNa CsC fromSaitoetal. . . . . . . . . . . 532 60
6.2 DisplacementofsodiumionsinNa AC compounds . . . . . . . . 542 60
236.3 Naspectrumtogetherwithlinefitsat100K . . . . . . . . . . . . . 55
6.4 MeasuredandsimulatedNMRspectraofNa CsC . . . . . . . . . 582 60
6.5 Spin-spinrelaxationratewithfit . . . . . . . . . . . . . . . . . . . . 60
6.6 Arrheniusplotofspin-latticerelaxationrate . . . . . . . . . . . . . . 61
6.7 Spin-latticerelaxationrateswithfits . . . . . . . . . . . . . . . . . . 63
1/26.8 1/(T T) displayedasafunctionoflineshift . . . . . . . . . . . . 661
6.9 MeasuredlineshiftsfittedwithEinsteinmodel . . . . . . . . . . . . 68
+6.10 LocalC orderaroundtetrahedralintersticesfromNa ions . . . . 7160
6.11 Relativedeviationofthesecondmoment . . . . . . . . . . . . . . . 75
¯6.12 FullereneconfigurationsaroundaTsiteinthe Fm3mstructure . . . 76ListofTables
6.1 Exchangeparameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.2 LocalC configurations . . . . . . . . . . . . . . . . . . . . . . . . . 7260
6.3 Relativedeviationofthesecondmoment . . . . . . . . . . . . . . . 75
¯6.4 C configurationsaroundatetrahedralsitein Fm3mstucture. . . . 7660
vAcknowledgement
Although this dissertation bears my name on the front, if it were not for the
selflessnessofahostofpeopleIwouldnothavebeenabletoreachthispointof
mylifeonmyown. Letmeexplicitlyrefertosomeofthemhereandnowwitha
remarkthatthelistwillnotbeexhaustive.
FirstandforemostIwouldliketoexpressmyextraordinarygratitudeforthe
patience, counsel and leadership of my two mentors, György Kriza and Henri
Alloul. Their ability to ask the right question at the right time and to verbalize
theirthoughtswithprofoundprecisionchangedmeinnumerousways.
I am very grateful for the collaboration with László Forró and his group
in Lausanne who provided us high quality samples prepared by Slaven Garaj.
Theircontributionwasindispensableforthisthesis.
Consultationswithx-rayandneutronscatteringexpertshavebeenparticular-
lyusefulwhensolvingsomeoftheproblemspointedoutinthethesis. Fortheir
willingness to help my gratefulness goes to Gábor Oszlányi, Kosmas Prassides
and Roger Moret. The comments and remarks on NMR by Kálmán Tompa,
AndrásJánossyandCharlesSlichteralwaysencompassedmorethanIexpected
butneverlessthanwhattheproblemdemanded.
I am very grateful for the many ways Gyöngyi Pergerné Klupp