Fluorine dynamics in BaF_1tn2 superionic conductors investigated by NMR [Elektronische Ressource] / von Patryk Gumann

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• Physik

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• Publié par: technischen_universitat_darmstadt
• Publié le: 01 janvier 2008
• Nombre de lectures: 24
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

FluorinedynamicsinBaF superionic2
conductorsinvestigatedbyNMR
VomFachbereichPhysik
derTechnischenUniversita¨tDarmstadt
zurErlangungdesGrades
einesDoktorsderNaturwissenschaften
(Dr. rer. nat.)
genehmigteDissertation
von
M.Sc. PatrykGumann
ausSkarzysko-Kamienna,Polen
Referent: Prof. Dr. FranzFujara
Korreferent: Prof. Dr. BerndStu¨hn
TagderEinreichung: 16.10.2007
TagderPru¨fung: 17.12.2007
Darmstadt2008
D172Contents
Contents 2
1 Introduction 3
2 FastIonicConductors 5
2.1 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 LatticeDefectsinIonicCrystals . . . . . . . . . . . . . . . . . 9
2.2.1 TheFormationofLatticeDefects . . . . . . . . . . . . 10
2.3 CrystalGrowth . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 PhaseDiagram . . . . . . . . . . . . . . . . . . . . . . 17
2.4 SolidElectrolyteswithFluorite Structure . . . . . . . . . . . 19
2.4.1 Fluorite Structure . . . . . . . . . . . . . . . . . . . . . 19
2.4.2 TransportMechanisms . . . . . . . . . . . . . . . . . . 23
2.4.3 StateoftheArt . . . . . . . . . . . . . . . . . . . . . . 24
3 EssentialAspectsofSolidStateNMRTheory 29
3.1 ThePhenomenonofNuclearMagneticResonance . . . . . . 29
3.2 ClassicalTreatmentoftheRelaxation . . . . . . . . . . . . . . 30
3.3 QuantumMechanicalTreatment . . . . . . . . . . . . . . . . 32
3.3.1 TheDensityMatrixRepresentation. . . . . . . . . . . 32
3.3.2 CoherencesandPopulation . . . . . . . . . . . . . . . 33
3.3.3 EssentialAspectsofthePerturbationTheory . . . . . 34
3.4 NuclearSpinHamiltonian . . . . . . . . . . . . . . . . . . . . 35
3.4.1 ZeemanInteraction . . . . . . . . . . . . . . . . . . . . 35
3.4.2 Dipole-DipoleCoupling . . . . . . . . . . . . . . . . . 35
3.4.3 TheChemicalShift . . . . . . . . . . . . . . . . . . . . 37
3.4.4 QuadrupolarCoupling . . . . . . . . . . . . . . . . . 38
3.5 CorrelationFunctionsandSpectralDensities . . . . . . . . . 39
3.6 ExamplesofRelaxationProcesses . . . . . . . . . . . . . . . . 40
3.6.1 RelaxationviaDipole-DipoleCoupling . . . . . . . . 40
3.6.2 Dipole-DipoleCouplingtoQuadrupolarSpinSystem 40
1CONTENTS
4 ExperimentalTechniques 47
4.1 NMR-Lineshape . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1.1 SignalProcessing . . . . . . . . . . . . . . . . . . . . . 49
4.1.2 Magic-AngleSpinning . . . . . . . . . . . . . . . . . . 52
4.1.3 Multiple-PulseSequences . . . . . . . . . . . . . . . . 56
4.2 Field-CyclingSpectroscopy . . . . . . . . . . . . . . . . . . . 62
4.2.1 HighTemperatureProbeHead . . . . . . . . . . . . . 64
4.3 StaticFieldGradientNMR . . . . . . . . . . . . . . . . . . . . 65
4.3.1 HahnEcho . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.2 SolidEcho . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.3 StimulatedEcho . . . . . . . . . . . . . . . . . . . . . 67
5 MeasurementsandAnalysis 71
5.1 DiffusionMeasurements . . . . . . . . . . . . . . . . . . . . . 71
5.1.1 AgingEffect . . . . . . . . . . . . . . . . . . . . . . . . 72
5.1.2 InfluenceofTrivalentImpurities . . . . . . . . . . . . 73
5.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2 LineshapeAnalysis . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.1 InfluenceofDoping . . . . . . . . . . . . . . . . . . . 83
5.2.2 MASMeasurements . . . . . . . . . . . . . . . . . . . 84
5.2.3 TheoreticalAnalysis . . . . . . . . . . . . . . . . . . . 85
5.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.3 RelaxationMeasurements . . . . . . . . . . . . . . . . . . . . 91
5.3.1 BPPModel . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3.2 Non-ExponentialCorrelationFunction . . . . . . . . 99
5.3.3 ModelofTwoDifferentSublattices . . . . . . . . . . . 100
5.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.4 ResultsandDiscussion . . . . . . . . . . . . . . . . . . . . . . 106
6 Summary 111
7 Zusammenfassung 113
Bibliography 117
ListofFigures 125
Acknowledgements 131
2Chapter1
Introduction
Thefirstobservationsofhighionicconductivitywithinthesolidstatehad
already been performed in 1833 by M. Faraday [1–4] yet, to date, no uni-
versal”explanation”ofthenatureofthesuperionicconductorsexists.
Thefundamentalunderstandingofthisphenomenonhasprovidedone
ofthemajorchallengesinthefieldofcondensedmatterscience. Theexper-
imental and theoretical approaches to the study of conduction processes
are often very complicated [6]. Nevertheless, a clearer picture of the be-
havior of superionic materials has emerged within the past few decades.
Thesolidstatematerialsexhibitahighionicconductivity,eitherofcations
−3 −1 −1oranions,whichiscomparabletomoltensalts(intheorderof10 Ω cm )
[7]. However,becauseofthe hugevarietyinmaterials,neitherthe critical
temperature of the transition into the superionic phase, nor the critical
valueoftheionicconductivity canbedefined. Thematerialsdescribedin
thiswork,forexample,shownosharptransitionintothesuperionicphase
but undergo a gradual change of ionic conductivity. Numerous applica-
tionsofthesematerialscanbefoundrangingfromgassensors,electrodes,
fuelcells,toscintillatorsetc.[5].
ThegoalofthisworkwastoutilizethepotentialthatthedifferentNMR
techniques offered for investigating BaF -type superionic conductors and2
in this way learn more about the structure and fluorine dynamics at dif-
ferenttimeandlengthscales.
Magic-anglespinningandtemperature-dependentlineshapemeasure-
ments,especiallyonhighlydopedBa La F samplesdesignedtoclar-1−x x 2+x
ify the debate of the structure, were of imperative interest. Field cycling
(FC) data supported by theoretical analysis shed light on the movement
of the interstitial and original ions on the micro-scale. In contrast to FC
NMR,StaticFieldGradient(SFG)measurementswereintendedtoexplore
the macro-scale and to give some information about the temperature de-
3Introduction
pendentdiffusioncoefficients.
Thisworkconsistsoffivemainchapters: chapter2tochapter6. Ashort
introduction to fastionic conductors andto the structure of Ba La F1−x x 2+x
with its deviations is given in chapter 2. The background of NMR and
theories for understanding and analyzing the experimental data are de-
scribed in chapter 3. Experimental techniques and a description of spec-
trometers used, as well as the pulse sequences used for different experi-
mentalpurposesarepresentedinchapter4. Inchapter5theexperimental
results are discussed in detail in order of the complexity of experiments
anddataanalysis. Chapter6summarizesthewholework.
4Chapter2
FastIonicConductors
In the past 60 years huge efforts, both experimental and theoretical, have
beenmadeinordertoexplainanddescribethenatureoffluorinedynam-
ics in rare earth fluorides [7,12–14]. Many materials having superionic
propertieswerediscovered. Someofthemandtheirionicconductivity,are
illustratedinfigure2.1. Itcanreadilybeseenthatnotonlycrystallinema-
(a) t (°C)
100 01000 300
1
α–AgI
α
β Rb Ag I
4 5
β
α
-1
PbSnF
4LuF
3
β
-3
α CuI PbF2
γ
-5
β−AgI
BaF2
2 31 4
3 -1 -1
10 ×T (K )
Figure 2.1: Arrhenius diagram of conductivity for a variety of fast ionic
conductors [15]. In the left bottom corner data for BaF are shown. The2
LaF dataarenotpresentedonthisdiagrambutinthe temperature range3
3 3 −1 −1of from 1.8*10 to 3.0*10 xT /K the conductivity of LaF isbetween-53
−1 −1and-3lnσT(Ω cm K)[116].
5
-1 -1
ln σT (Ω cm K)FastIonicConductors
terials are exhibiting fast ionic conduction, but also polycrystalline ones,
ceramics, glasses, and polymers [7]. In fact, since the first observation of
superionicity [2], the types of materials found to act as solid electrolytes
are so numerous that various schemes for their classification into cate-
gories have been suggested. Categorization based on the form of their
Arrheniusplotsofconductivity[10],thenatureofthechargecarrier[7],as
wellasonstructuralaspects[16]haveallbeenproposed.
Despite the diversity of the types of compounds which display fast
ionicconduction,thereareseveralcharacteristicsthatmost,ifnotall,such
substances possess. Since ionic transport and the dynamic properties of
solid electrolytes are determined by the interaction between the crystal
lattice ions, the common traits of this class of substances are most easily
thunderstood whenone considers the binding energyE of ai mobile ioni
inacrystallattice.
2X X Xr +r −r qq e α qi j ij i j j i2E = A exp[ ]+e − (2.1)i ij 4ρ r 2 rij ijj j j
where:
r andr aretheionicradiiofmobileionsiandstationaryionsji j
r istheinter-atomicdistanceij
A isthemultiplicativefactordependentuponiontypesij
ρ is a constant, andq,q are the fractional charge of the mobile and fixedi j
ionspecies,respectively
thα isthepolarizabilityofthej stationaryatomj
Various interaction potentials having appeared in literature serve as the
basis for theoretical calculations [19] and are more or less similar to the
energyofalatticeioninanearlyworkofFlygareandHuggins[17].
Consideringequation2.1,generalizationsconcerningfactorswhichtend
to minimizeE andapriori enhance the conductivity of the mobile ions,i
can be made. It is well documented that those compounds in which the
mobile species pos