Modeling the generation, distribution and transport of point defects in oxide mixed ionic-electronic conductors

228 Pages·2001·9.5 MB·English

by  Duncan, Keith L., 1968-

MODELINGTHEGENERATION,DISTRIBUTIONANDTRANSPORTOFPOINT
DEFECTSINOXIDEMIXEDIONIC-ELECTRONICCONDUCTORS
BY
KEITHL.DUNCAN
DISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHE
UNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHE
REQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
2001
ACKNOWLEDGMENTS
I would like to thank my advisor. Dr. Eric D. Wachsman, for his support,
encouragementandfacilitationofmygraduateresearch. Underhistutelage,Ihavecomea
longwayintheburgeoningfieldofsolidstateelectrochemistryandhavebeenequippedto
goevenfarther. Iamalsogratefultomycommitteemembers.Dr.R.T.Dehoff,Dr.R.
Hummel,Dr.M.Orazem,Dr.W.SigmundandDr.S.Sinnott,formakingthemselves
accessiblefordiscussionandforchallengingmetoexpandthehorizonsofmyresearch.
Iwouldliketothankmyfamily. MywifeNicoleandsonMatthewhavegivenme
tremendoussupportthroughtheordealsofdoctoralresearch. Theyallowedmetotake
themfromtheircontentedlifeinJamaicaandtheyenduredmuchhardshiptohelprealize
myambitions. Moreover,theyenabledmetoretainabalancedperspective,helpingmeto
smellafewrosesalongthejourney. Imustalsoexpressmysincereappreciationforthe
effortsofmymother,MerdeanBennett,asingleparentwhogaveallshecould,often
undertryingconditions.
Finally,IthankGodwhothroughhisHolySpiritandthesavinggraceofJesus,His
son,shepherdedmethroughtheyears. Godhasblessedmeincountlessway. Heblessed
mewiththisopportunitytostudy. Hemadeawaywheretherewasnone. Heprovided
mewiththebestsituationinwhichtothrive. MayallofmylifebetoHishonorand
glory. AdmajoremDeigloriem.
11
TABLEOFCONTENTS
E2ge
ACKNOWLEDGMENTS
ii
LISTOFTABLES vi
LISTOFFIGURES vii
KEYTOSYMBOLSANDABBREVIATIONS xi
ABSTRACT xvi
CHAPTERS
INTRODUCTION
1 1
1.1 MixedIonic-ElectronicConductors 1
1.2 ApplicationsofOxideMixed-IonicElectronicConductors 2
1.3 ResearchChallengesandOpportunities 4
1.4 MajorAssumptionsUsedinModelDevelopment 7
1.5 Summary 11
2THERMODYNAMICSOFOXIDEMIXEDIONIC-ELECTRONIC
CONDUCTORS 12
2.1 Introduction 12
2.2 PreviousModels 14
2.2.1 BrouwerApproach 14
2.2.2 OxygenPartialPressureasaFunctionofDefectConcentration 15
2.2.3 NumericalMethods 16
2.3 DefectGeneration 17
2.3.1 DefectEquationsandChargeNeutrality 17
2.3.2 RelationshipsamongEquilibriumConstants 24
2.3.3 RelationshipsbetweenSmallPolaronConcentrations 27
2.3.4 ModelingtheFunctionalDependenceofDefectConcentrationonPq2 30
2.3.5 GeneralizedEquationsforDefectConcentrationDependenceonPq2 38
2.3.6 ResultsandDiscussion 40
2.4 CaseStudy:Acceptor-DopedCeria 47
22..44..12 FEuvnacltuiaotnianlgDtheepeMnadgennitcuedoefoDfeftheectEqCuoinlciebnrtiruamtiCoonnsotnanPtq,2Kr 4583
2.4.3 TransportProperties:Conductivity,TransferenceNumberandFlux 64
iii
2.4.4
DefectAssociation 69
2.5 Summary 76
3 SPATIALDISTRIBUTIONANDTRANSPORTOFDEFECTS
INOXIDEMIXEDIONIC-ELECTRONICCONDUCTORS 77
3.1 Introduction 77
3.2 ReviewofPreviousModels 79
3.3 GeneralEquations 83
3.3.1 TransportPropertiesandLaws 83
3.3.2 Current-VoltageRelationshipsinanSOFCorElectrocatalyticReactor 88
3.3.3 Open-circuitConditionsandEffectiveTransferenceNumber 91
3.4 ModelingDefectDistributionandTransportinMIECsbyAssuminga
LinearElectricField(V2<f>=0):TheLinearPotentialModel 94
3.4.1 GeneralDevelopmentoftheLinearPotentialModel 95
3.4.2 AmbipolarDiffusioninOpen-CircuitConditions 98
3.4.3 EstimatingtheMagnitudeoftheEquilibriumConstantsKrandKm 101
3.5 BoundaryConditions:DefectConcentrationsattheBoundaries 103
3.5.1 ExpressionsfortheDefectConcentrationsattheBoundaries 103
3.5.2 EffectofPotentialDifferenceontheEquilibriumConstants 104
3.6 ResultsandDiscussionfortheLinearPotentialModel 109
3.6.1 SpatialDistributionofDefects:DefectConcentrationProfiles Ill
3.6.2 AverageDefectConductivityandEffectiveIonicTransferenceNumber....120
3.6.3 DefectFluxDensityandCurrentDensity 125
3.6.4 Efficiency 132
3.7 ModelingDefectDistributionandTransportinMIECswithoutAssuming
aLinearElectricField:TheNon-LinearPotentialModel 134
3.7.1 GeneralDevelopmentoftheModel 134
3.7.2 LimitingCases 138
3.7.3 AverageConductivityandEffectiveTransferenceNumber 140
3.8 ResultsandDiscussionfortheNon-LinearPotentialModel 142
3.8.1 Flux,Current,Conductivity,TransferenceNumberandEfficiency 142
3.8.2 SpatialDistributionofDefectsandPotential 146
3.9 ExperimentalVerificationoftheModel(inOpen-CircuitConditions) 149
3.10Summary 163
4BILAYEREDMEMBRANES 166
4.1 Introduction 166
4.2 BilayerModel 170
4.2.1 Open-CircuitConditions 170
4.2.1.1 “Thermodynamic”approach 171
4.2.1.2 “Transport”approach 174
4.2.2 Closed-CircuitConditions 180
4.3 Summary 187
IV
5 CONCLUSIONS 190
APPENDICES
A EVALUATINGTHE“EQUILIBRIUMCONSTANTS”(K-ANDK+)FORTHE
SMALLPOLARONFORMATIONREACTION 194
B DEFECTGENERATIONFORMULAEFOROXYGENINTERSTITIALSAND
CATIONVACANCIES 198
C MODELINGTHEACCOMMODATIONOFCUBICBISMUTHOXIDEIN
THEFLUORITESTRUCTURE 200
REFERENCES 202
BIOGRAPHICALSKETCH 207
v
LISTOFTABLES
Table page
2-1 TypicaldopantconcentrationsandunitcellvolumesincommonoxideMIECs 22
2-2 Summaryofdefectequationsforfluoritesandperovskites 25
2-3 Proportionalityrelationshipsbetween(dominant)defectconcentrationsandPo2
foreachBrouwerregime 43
22--4 ComparisonbetweenthedominantdefectspairsoftheBrouwerapproachand
3- thedominantdefecttriadsofthepresentmodel 44
2-5 ValuesoftheconstantsusedinthenumericalsolutionofSDC’sdefectequations..49
2-6 Calculatedvaluesof0andKrforSDCfromtheuncorrected<f>ocdataof
Godickemeieretal.[44,45] 57
2-7 Calculatedvaluesof0andKrforSDCfromthecorrectedOocdataof
Godickemeieretal.[44,45] 58
8 CalculatedvaluesofKrfromthermogravimetrydataofKobayashietal.[47] 60
1 Calculatedvaluesof0andKrforSDCfromthecorrectedd>ocdataof
Godickemeieretal.[44,45] 102
3-2 CalculatedvaluesofKr,Km,lion,andd>app 110
3-3 ValuesofKrandDe/Dyusedtofitthemodeltoexperimentaldata 157
vi
LISTOFFIGURES
1-
2F-igure page
1-1 SOFCPowergeneration 2
2 Overarchingtheoreticalframeworkofthisstudy 8
1 Unitcellof(a)thefluoritestructureand(b)theperovskitestructure 13
2-2 ReactionsbetweentheoxygensublatticeofanoxideMIEC(fluoritestructure)
andanexternalgasphase 18
2-3 DefectconcentrationdependenceonPq2forafluorite-structuredMIEC 41
2-4 DefectconcentrationdependenceonPq>2foraperovskite-structuredMIEC 42
2-5 SmallpolaronconcentrationdependenceonPo2forafluorite-structured
MIEC 45
2-6 SmallpolaronconcentrationdependenceonPo2foraperovskite-structured
MIEC 45
2-7 Variationofnon-stoichiometrywithPq2forafluorite-structuredMIEC 46
2-8 Variationofnon-stoichiometrywithPo2foraperovskite-structuredMIEC 47
2-9 DefectequilibriumdiagramofSDCobtainedthroughnumericalsolutionofits
defectequations 50
2-10 DefectequilibriumdiagramofSDCintheregionofinterest(reducedfrom
Figure2-9) 51
2-11 ComparisonofSDC’sDEDobtainednumerically(solidsymbols),fromthe
model(lines),andfromPoratandTuller[11](opensymbols) 53
2-12 Modeleda(P)fittedtoexperimentaldatafromEguchietal.[49]forSDC 66
Vll
d 5
2-13 AnoxideMIECinanarbitraryPq2gradient 67
2-14 Oxygenfh\x,jo2{P),througha1mmthickMIEC 69
22--15 Dependenceofcy0(o)andcsp-(0)onPq2with(symbols)andwithout(lines)
theeffectofdefectassociation 73
3-
2-16 Oxygenpartialpressuredependenceofcy0,csp-,cji,Cd2andc3 74
17 EffectofKrontheformationofdefectassociates 75
1 EquivalentcircuitdiagramofanSOFCinclosed-circuitconditions 89
3-2 AmbipolardefectfluxinanSOFCinopen-circuitconditions 99
3-3 EffectofAOonthereactionprofileoftheexternalequilibriumreaction
betweenanMIECandagasphase 105
3-4 Oxygenvacancyconcentrationprofilesinanrz-typeMIECwithfixedBDCs...112
3-5 Electronconcentrationprofilesinan«-typeMIECwithfixedBDCs 113
3-6 Oxygenvacancyconcentrationprofilesinap-typeMIECwithfixedBDCs 114
3-7 Holeconcentrationprofilesinap-typeMIECwithfixedBDCs 11
3-8 Oxygenvacancyconcentrationprofilesinanrc-typeMIECwithpotential
dependentBDCs 116
3-9 Electronconcentrationprofilesinan«-typeMIECwithpotentialdependent
BDCs 116
3-10 Oxygenvacancyconcentrationprofilesinap-typeMIECwithpotential
dependentBDCs 117
3-11 Holeconcentrationprofilesinap-typeMIECwithpotentialdependent
BDCs 117
3-12 Comparisonofthespatialdistributionofoxygenvacanciesandelectronsinan
n-typeMIEC(SDC)withpotentialdependentBDCs 119
3-13 Comparisonofthespatialdistributionofoxygenvacanciesandholesina
p-typeMIEC(ESB)withpotentialdependentBDCs 120
3-14 Averageconductivityandeffectivetransferencenumberofann-typeMIEC....121
viii
3-15 Averageconductivityandeffectivetransferencenumberofap-typeMIEC 122
3-16 Defectfluxdensityinan«-typeMIEC(SDC) 126
3-17 Defectfluxdensityina/?-typeMIEC(ESB) 127
3-18 Defectcurrentdensityinan«-typeMIEC(SDC) 130
3-19 Defectcurrentdensityinap-typeMIEC(ESB) 131
3-20 Currentandpowerefficiencyofann-typeMIEC(SDC) 133
3-21 Currentandpowerefficiencyofap-typeMIEC(ESB) 133
—
3-22 Defectfluxdensityinanrc-typeMIEC Non-LinearPotentialModel 143
—
3-23 Defectcurrentdensityinann-typeMIEC Non-LinearPotentialModel 143
3-24 Averagedefect—conductivityandeffectivetransferencenumberinann-type
MIEC(SDC) Non-LinearPotentialModel 145
—
3-25 Oxygenvacancyconcentrationprofileinan«-typeMIEC Non-Linear
PotentialModel 146
—
3-26 Electronconcentrationprofileinan«-typeMIEC Non-LinearPotential
Model 147
3-27 Compari—sonofthespatialdistributionofvacanciesandelectronsinan«-type
MIEC Non-LinearPotentialModel 148
3-28 Spatialdistributionofpotentialinan«-typeMIEC 149
3-29 Setupofthefuelcellapparatus 150
3-30 Open-circuitvoltageversusOsensorat800°C 151
3-31 Open-circuitvoltageversusOsensorat750°C 152
3-32 Open-circuitvoltageversus<bSensorat700°C 153
3-33 Open-circuitvoltageversusOsensorat650°C 154
3-34 Open-circuitvoltageversusQ>Sensorat600°C 155
3-35 Open-circuitvoltageversus sensorat550°C 156
ix
3-36 Open-circuitvoltageversus0?sensorat500°C 157
33--37 PlotsofKrandDe/Dyversusreciprocaltemperature 158
4-
3-38 ComparisonoftheSDC-gasandSDC-Pt-gasinterfaces 159
39 Open-circuitvoltage,<f>ocversusOsensor(<&th)at800°Cwithout“fitting” 164
1 Conceptualrepresentationofabilayeredsolidoxidemembrane 167
4-2 ThicknessratiodependenceoninterfacialPo1inopen-circuitconditionsat
800°C 176
4-3 ThicknessratiodependenceoninterfacialPo2inopen-circuitconditionsat
500°C 178
4-4 ThicknessratioversuspotentialdifferenceacrosstheESBlayerinclosed-circuit
conditionsat800°C 184
4-5 ThicknessratioversuspotentialdifferenceacrosstheESBlayerinclosed-circuit
conditionsat500°C 185
4-6 OxygenvacancyconcentrationversuspotentialacrosstheESBlayer 187
x