Ph.D. Thesis --- Peter Matus

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INFLUENCE OF LOCAL C60 ORIENTATION ON ELECTRONIC PROPERTIES OF A3C60 COMPOUNDS Ph.D. Thesis PÉTER MATUS Supervisors HENRI ALLOUL GYÖRGY KRIZA directeur de recherche scientific advisor Laboratoire de Physique Research Institute for Solid State Physics des Solides, Université Paris-Sud and Optics, Hungarian Academy of Sciences Orsay, France Budapest, Hungary RESEARCH INSTITUTE FOR SOLID STATE PHYSICS AND OPTICS of the Hungarian Academy of Sciences BUDAPEST 2006
  • relaxation rate
  • interactions between
  • interactions between nuclear
  • sodium spin lattice
  • line splits
  • na nmr
  • local c60
  • spin
  • spins
Publié le : lundi 26 mars 2012
Lecture(s) : 55
Tags :
Source : dept.phy.bme.hu
Nombre de pages : 98
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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, Katalin
Kamarás, Gergely Zaránd, Bertrand Deloche and Tito Williams contributed to
thiswork.
My thanks go to the number of colleagues I have been fortunate to work
with and to receive support from. They are: Véronique Brouet, Julien Bobroff,
Philippe Mendels, Alexander V. Dooglav, Philip M. Singer, Tito Williams,
Bernadette Sas, Mónika Bokor and György Lasanda. I cannot thank enough
László Németh, Ágnes Pallinger, Ildikó Pethes, Safia Ouazi, David Bono and
JeydipDaswithwhomIhavehadtheprivilegetobeaPh.D.student. Theywent
theextramileformesomanytimes.
Special thanks to Imre Bakonyi, the head of Metal Physics Department, for
the inexpressible value of his endurance and energy as he took part in the
incrementaldevelopmentofmywork.
I would further like to express my gratitude to my local thesis examiners of
myinstituteSándorPekkerandFerencSimonforthethoroughreviewofthetext
aswellastheirinsightfulcommentsatthepresentationrehearsalofmythesis.
viACKNOWLEDGEMENT vii
I am forever indebted to György Kriza and Tito Williams for continuously
improving the language of the thesis. The manuscript-reading work of Imre
Bakonyi, Katalin Dorottya Gyo˝ri, Eniko˝ Hulej, and Ferenc Balázs Kis must also
beremembered.
MyappreciationisduetheBlondelfamilyforcreatingaperfectenvironment
for the very short year spent in France, which now seems more like holiday
than hard work. I am very pleased for the various types of help and support of
Alexander V. Dooglav in the integration period. During the time of writing the
dissertationthefamiliesofGáborGyo˝riandPéterGyo˝riwentsomanytimesout
oftheirwaysothatIcouldenjoythepeaceandtranquilityneededsoastofitall
thatIhadresearchedontogether.
Last, but not at least I thank my family without whose solid background of
patienceandloveIwouldnotbeabletostandheretoday.Abstract
We have investigated sodium containing Na AC fullerene superconductors2 60
(A = Cs, Rb, and K) by nuclear magnetic resonance (NMR) spectroscopy. The
23NaNMRspectrum,Knightshift,spin-lattice(T )andspin-spin(T )relaxation1 2
times have been measured in the temperature range of 10 to 400 K. Spin-echo
doubleresonance(SEDOR)resultsarealsopresentedat80K.
23Weshowthatthe Naspectrumlinesplitsintotwolinesatlowtemperature
in all the three compounds investigated. The splitting occurs at 170 K for A =
Cs. For A = Rb and K the splitting is between 80 K and room temperature.
This is the first observation of line splitting in fullerene superconductors with
simple cubic ground state. SEDOR experiments prove that the two spectral
components originate from the same phase. We explain the spectral splitting as
well as the temperature dependence of the spin-lattice and spin-spin relaxation
times by a dynamic site exchange. The rate of the exchange process is found to
be temperature activated in the range 125 to 299 K with an activation energy of
3300K.
From a detailed analysis of several NMR properties, we show that the
site exchange is caused by the reorientation of the C molecule between two60
different orientations. Assuming no correlation between the orientations of
neighboringmolecules,wedeterminetheconcentrationoforientationaldefects.
The defect concentration we infer is in good agreement with neutron scattering
results[Prassidesetal.,Science263,950(1994)].
In the light of our findings we revisit the problem of a similar spectral
splitting in A C superconductors with face centered cubic structure, and3 60
provideaunifiedpicturefortheinterpretationofthelinesplitting.
We also show that the sodium spin lattice relaxation rate 1/(T T) follows a1
different temperature dependence than the expected Korringa law. We explain
23the temperature dependence of the Na Knight shift and relaxation rate by the
23effectoflibrationalphononsontheelectrondensityatthe Nanuclei.
viii

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