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Atomic-level properties of thermal barrier coatings: Characterization of metal- ceramicinterfaces

Christensen, Asbjørn; Jarvis, E.A.A.; Carter, E.A.

Published in:Chemical Dynamics in Extreme Environments

Publication date:1999

Document VersionEarly version, also known as pre-print

Link back to DTU Orbit

Citation (APA):Christensen, A., Jarvis, E. A. A., & Carter, E. A. (1999). Atomic-level properties of thermal barrier coatings:Characterization of metal- ceramic interfaces. In R. A. Dressler, & C. Ng (Eds.), Chemical Dynamics in ExtremeEnvironments (pp. 490-546). Advanced Series in Physical Chemistry

https://orbit.dtu.dk/en/publications/38772214-a435-49d4-b528-59ee1ee01896

Chapter 1

ATOMIC-LEVEL PROPERTIES OF THERMAL BARRIER

COATINGS :CHARACTERIZATION OF METAL-CERAMIC INTERFRACES

AsbjornChristensen,Emily A. AscheandEmily A. Carter

Departmentof ChemistryandBiochemistryBox951569Universityof California, LosAngelesLosAngeles,California 90095-1569,USA

1. INTRODUCTION AND CHAPTER OVERVIEW

Thischapterconsidersbasicresearchrelatedto theextremeenvironmentof an aircraft engineand the use of Thermal Barrier Coatings(TBC’s)to amelioratethe effects of extremetemperaturecycling on metal enginecomponents.Thefailureof theseTBC’s is aserioustechnologicalproblem;onethat,if solved,shouldgreatlyincreasethefuel efficiency andoperatinglifetimes of airplaneengines. TheseTBC’s are comprisedof ceramics,with favorably low thermalconductivity, depositedon the enginemetals.Accordingly, we areconcernedwith thecharacterizationof Metal-Ceramic(M/C) interfacesatafundamental level. In thischapter, weattempttoprovideanoverview of experimentaltechniquesfor characterizingM/C interfaces.However, sincewearetheorists,muchof thereview is focusedonprovidingadetailed,critical analysisof theoreticalmethodsin usetodayto studysuchsystems.Wealsogiveexamplesfrom ourown modelingat theatomiclevelthathasyieldedsomeinsightsinto theinterfacialbehavior of TBC’s.

Let us outline the problemcausedby the extremecombustionenviron-ment. The ideal enginewould operateat very high temperatureswithoutfailurein orderto havethehighestfuel efficiency. Typically, thecombustiongasis heldat temperaturesabove 1370

�C, while themetalsuperalloys that

constitutethe enginecomponentshave melting pointsrangingfrom 1230-1315

�C! Thismakesit imperative to eithercoolthemetalcomponents(e.g.,

by drilling holesandflowing coolair) or to provide thermalprotectionfrom

1

2 AsbjornChristensen,EmilyA. AscheandEmilyA. Carter

thecombustiongas.1 Ideasfor optimizingthecoolingtechniquesandenginemetalalloy compositionsreacheda point of diminishingreturnsat least10yearsago.2 Hence,engineerslooked to ceramicmaterialsas a meansofproviding a thermalbarriercoatingthatwill: (i) extendthe life of gastur-binecomponents,(ii) reducecoolingrequirements(therebydecreasingfuelconsumption),or (iii) allow for anincreasein gasinlet tempratures(therebyincreasingthrust).3

Ceramicsarethermalinsulatorsthat canprovide the thermalbarrierde-sired. The challengeof working with suchceramicsis that typically theyhave completelydifferent thermochemicalpropertiesfrom the materialtowhich they areexpectedto adhere,namelya metallic alloy. As a result,theusualthermalcycling that suchM-C interfacesundergo tendsto stresstheseinterfacesto thepointof fractureandspallation(chipping-off).1 It hasbeensuggestedthat researchis neededto try to connectthesemacroscopicphenomenato microscopicproperties,in orderto make progressin under-standinghow to designthe bestM/C junction.4,5 In particular, the exactnatureof the interfaceat the atomic level is poorly characterized;the ex-actmechanismshave yet to be identifiedby which the interfaceis formed,stressed,fractured,andspalled.Furthermore,it remainsunclearwhatrolesoxidationandtemperatureplay in stabilizingor destabilizingthe interface.Gainingan atomic-level understandingof thesemechanisms,shouldhelpelucidateways to optimize the M/C couple: simultaneouslymaximizingthermalinsulationandminimizingspallation.

This chapterinitially exploresthe TBC from an experimentalpoint ofview. In Section2 of this chapter, we presenta detaileddescriptionof theTBC structureandcomposition.We explore thetypical chemicalmake-upof a TBC, the formation of the thermally grown oxide, and the physicalmethodsusedin TBC fabrication. Section3 lists a numberof the experi-mentaltechniquesusedto characterizefunctionalTBC’sandexplainssomeexperimentalcharacterizationof ideal interfaces.Section4 investigatestheproblemof TBC spallation. This includesidentifying likely perpetratorsof spallation,describingproposedspallationmechanisms,looking at somefeaturesthatcomplicatespallationstudies,andexpoundingon the issueofadhesion. We also mentionsomeof the techniquesusedfor measuringstress,fracture,andspallationat the endof this section. After looking atTBC’s from anexperimentalstandpoint,we turn our discussionto presentapplicabletheory. Wedescribeatomisticmodelingapproachesin Section6andhow thosecanbeappliedto M/C interfaces.This includesexploringtheuseof clusterandslabmodels,the ideaof interfacestoichiometry, andtheproblemof latticemisfit. Wethenconsidertheavailableabinitio techniquesfor modelingM/C interfaces.This is broken down to morespecificmeth-

Atomic-levelpropertiesofthermalbarrier coatings: characterizationofmetal-ceramicinterfraces 3

odsincludingquantumchemicalapproaches,densityfunctionaltheory, theapproximationof theHarrisfunctional,andtight bindingschemes.Wealsopresentresultsobtainedfrom anumberof densityfunctionaltheorystudies,including our own, aswell as tight binding predictions. Section7 and8review theorydesignedto handlelarger systemsthanarecomputationallyfeasiblewith the ab initio techniques.Finally, we offer brief conclusionsthat attemptto look to the future for waysof enhancingunderstandingofandoptimizationof thermalbarriercoatings.

2. CREATING A TBC SYSTEM

2.1. Commonly UsedMaterials

WhencreatingaTBC, generallya topcoatandabondcoatlayermustbedeposited.Thetop coatservesasthe insulatorandthebondcoatmediatescontactbetweenthe top coatandmetalalloy substrate.The nickel-based“superalloy” substrateis a realpotpourri of elements,consistingof Ni, Co,Cr, Mo, Al, Ta, Ti, C, Zr, andB (wherethenon-Ni elementsarepresentatthe few to hundredthsof a weight percentlevel.)6 Yttria-StabilizedZirco-nia (YSZ) is a favoredtop coatmaterial. Purezirconiahasrelatively highstrength,wearresistance,andfracturetoughness.Likewise, it exhibits anextremelylow thermalconductivity. In fact,excludingPyrex glass,thether-malconductivity of zirconiais lower thanany otherengineeringceramicbyover anorderof magnitude.6 In practicalterms,this propertyallows evenathin zirconiafilm (lessthanonemillimeter thickness)to potentiallyreducethe temperatureof the underlyingalloy several hundreddegreesCelsius.7

Furthermore,thelinearthermalexpansioncoefficientandelasticmodulusofzirconia(especiallythetetragonalphase)arewell-matchedtoseveral popularnickel-basedsuperalloys, comparedto possiblealternative ceramics.Thesepropertiesareessentialto coatingsurvival duringthermalcycling.7–9 Unfor-tunately, zirconiaalsoexhibits polymorphismasa functionof temperature,primarily betweenthemonoclinic,tetragonal,andcubicphases.Althoughthepolymorphismcanbeexploitedto inhibit crackpropagationvia volumechangesthat occurupontransformation,7,10,11 unregulatedpolymorphismcanbe detrimentalto TBC functionality. As a result, other cubic oxidesareaddedto controlor eliminatepolymorphism.Partial stabilizationof thetetragonalphaseacrossthe relevant temperaturerangeaffords somephasecontrol yet preservesthevaluableinhibition of stress-inducedmicro-crackpropagation.Greaterthan8.5 mole percentY � O� dopantproducesfully-stabilizedcubiczirconiawhile a 2-8.5percentY � O� concentrationcreatesa partially stabilized(tetragonal)form;12 similarly, addingCeO� , CaO,orMgO cangeneratestabilizedzirconia.13–16 Conversely, usingTiO � asthe


stabilizingoxideis lesseffectivethantheotheroxidesstudied.17,18 However,TiO � addedtoY � O� orCeO� stabilizedZrO� hasbeenshown toproducezir-coniapolycrystalswith favorableproperties.19,20 Althougha percentageofthepartiallystabilizedZrO� tendstoremainin themonoclinicphasethrough-out thermalcycling, the initially formedcubicphaseconvertsto tetragonalafterthermaltreatmentin air.21,22 Despitethefavorablepropertiesof aYSZtopcoat,thedifferencein thermomechanicalpropertiesbetweena YSZ topcoatanda metal-alloy substrateis enoughto requiretheintroductionof anintermediatelayer. Thisbondcoatis importantfor adhesionandgradingthethermalexpansionmismatchbetweenthetop coatandsubstrate.A typicalbondcoatcontainsnickel, chromium,aluminum,andyttrium, with nickelasthe primary elementfor nickel-alloy substrateapplications.With otheralloys, it is sometimesdesirableto useiron or cobaltin placeof thenickelin thebondcoat.23,24

2.2. Formation of the Thermally Grown Oxide

A third layer presentin a TBC is the ThermallyGrown Oxide (TGO).Bond coat oxidation can reduceTBC adhesionto the substrate. In mostcases,theoxidationproductsbegin to form evenprior to topcoatdeposition.It is standardpractice,in zirconiafilm creationchambers,to supplyoxygento ensurestoichiometryof the zirconia layer. Moreover, the bond coatcontinuesto be oxidizedoncethezirconialayer is in place,sincezirconiareadilyconductsoxygenionsat high temperature.25 Accordingly, theTGOlayer betweenthe bond coat and top coat thickenswith thermalcycling.Althoughthis layeris generallythin comparedto theTBC layer, it canleadto largestressesin thesystemduetosignificantthermalexpansionmismatchof theTGO andbondcoat.

The growth of the TGO falls into two primary regimes. Fast initialgrowth of non-protective oxidesis followedby continuousprotective scalegrowth, largelycontrolledbydiffusion. Theprimaryprotectivescaleformedwith bondcoatoxidationis alumina,Al � O� . For a bondcoatcomposedofNiCrAlY, the oxidation also producesNi(Cr,Al) � O� spinels,Y � O� , NiO,AlYO� , and Al � Y � O �� bandsorientedperpendicularto the bond coat.23In the initial oxidation stages,X-ray diffraction of a FeCrAlY bond coatindicatethatbothFeCr� O� andCr� O� form in thatsystem.24

Oxidescalestudiesarecomplicatedfurtherby thecoexistenceof variousoxidephases.For instance,atearlytimes,both

�-alumina,atransientphase

formedwhen � -aluminais heated,and -aluminaarepresent.Amorphousaluminatransformsthrougha seriesof metastablephasesuntil the morestable -aluminadominatesatlongoxidationtimes.26 Althoughthicknessesof the layersvary, somefairly typical valuesare250-500 m for the top


coat,100-150 m for thebondcoat(this variessincesomebondcoatsaredesignedfor surfaceroughnessandwith severalgradationlayers),andaboutanorderof magnitudelessthanthesefor thethermallygrown oxide.23 Fig. 1displaysa schematiccross-sectionof aTBC.

��Nickel Alloy

Bond Coat

Thermally Grown Oxide

m)YSZ Top Coat

(~100-150 µ m)

(~250-500

(~10-25 µ m)

µ

(macroscopic)

Figure 1 Cross-sectionof a TBC (notpicturedto scale)

2.3. Depositingthe TBC and Bond Coat

Severalmethodseffectively applythincoatingstosubstrates.Oneprocesscommonlyemployed for TBC fabricationis thermalplasmaspraying. Forthistechnique,thebondcoatis depositedwith low pressureplasmasprayingandtheZrO� topcoatis thencreatedusingatmosphericplasmaspraying.27A potentialproblemwith this methodis coatingfracturedue to weak in-terlamellaradhesion,resultingfrom discontinuitieswithin the solidifyingprocess.28 Accordingly, plasmasprayedcoatingstendto fail within theTBCitself. Alternatively, electron-beamphysical-vapordepositioncanbe usedfor TBC fabrication.Onedrawbackof thismethodispossiblespallation,viaseparationatthebondcoatinterfaceduringcooling.26 Nevertheless,success-ful coatingsof this typepossesscolumnarmicro-structure,supplyingsomeof thestresscompliancerequiredby theTBC. Furthermore,this methodissuitedfor creatinga gradedAl � O� -ZrO� layer. It is hopedthat a gradualtransitionfrom thebondcoatoxide to the top coatwould improve the lifeof the TBC;29 however, more work is neededto understandthe practicaleffectivenessof sucha layer.30 Sputterdepositionis anotherusefulmeansfor producingthin coatings.31,32 Eachdepositionmethodhasits own setofprosandcons,hencethisvarietyin fabricationtechniquescontinues.


3. CHARACTERIZING THE TBC

3.1. Characterization Techniques

Advancedcharacterizationmethodsarerequiredto gain a microscopic-level understandingof TBC’s. High-ResolutionTransmissionElectronMicroscopy (HRTEM) andScanningElectronMicroscopy (SEM) arefre-quentlyusedto explore thestructureof thecoatingsurfaceandthemetal-oxide interface.22,33,34 SEM alsoprovidesa qualitative thicknessmeasureof oxidegrowth. Thecoating’s porositycanbemeasuredby imageanalysistechniquesandmercuryporosimetry. Useof thelattercanposedifficultiessincelarge poresarefilled with mercuryprior to applyingpressure.Con-versely, imageanalysisis ineffective for measuringvery small poresandmicrocracks.35 X-ray diffraction providesa meansto determinethe oxidespeciesandphases.22 Likewise,field-emissionSEM andenergy dispersivespectroscopy aid in characterizingoxidationproducts.23 Microindentationtestsdeterminetheelasticmodulusof thepreparedcoatings;however, duetoinherentinhomogeneityin thecoatings,resultsfromthismethodmustbeap-propriatelyaveraged.35 Thermalconductivity measureshave beenprovidedby laserflashmethodsthat measurediffusivity andspecificheatmeasure-mentsfrom differentialscanningcalorimetry.36,37 Alternatively, diffusivityvaluescanbe obtainedwith a multipropertyapparatusthat measurestem-peraturegradients,samplegeometry, andheatflux.38 Thesingle-wavelengthpyrometermethodgathersspectraleffectiveemissivities. Althoughthermo-couplescouldalsobeused,thesingle-wavelengthpyrometertechniquehasthe superiorattributesof not requiringsurfacecontactduring temperaturemeasurements,immunitytoelectromagneticinterferencefromthesurround-ings,andno systemperturbationduringmeasurements.39 Theuseof AugerElectronSpectroscopy (AES),X-ray photoelectronspectroscopy (XPS),andAugerparameter( ’) analysisprovidemeansto explorethenickel-aluminainterfaceformation. Furthermore,thesetechniquesaresuitedfor determin-ing ionicity andgrowth mechanismsat metal-oxideinterfaces.40

3.2. Characterization of Ideal Interfaces

At hightemperatures,interdiffusionleadsto theformationof new phasesat theM/C interface.4 For example,Qin andDerby41 usedopticalandelec-tron microscopy to characterizethestrengthof Ni/ZrO � andNi/NiO/ZrO �interfaces.They foundthatthestrongestinterfaceswereformedby anneal-ing Ni/ZrO � in air, which allowed a thin layer of NiO to form that helpedadhesionto the ceramic. Qin andDerby alsostudiedthe formationof aninterfacebetweenZrO� and a Ni(Cr) alloy, wherea mixed oxide with aspinelstructurewasformedat the interface.42 Thereactionat the interface


appearedto beaccompaniedby local meltingafter interdiffusion,althoughit is not clearwhich elementswereactuallydiffusing. Wagneret al.43 ex-aminedchargeflow in aNi|ZrO� |Zr cell andshowedthatat 1273K with noappliedvoltage,oxygenionsmove from theNi to theZr electrode,formingNi � Zr andNi � Zr � at theNi electrodewhile reducingZrO� to Zr. At theZrelectrode,monoclinicZrO� forms. Thus,oxygenion diffusion appearstobeanimportantprocessby whichadhesiontakesplace.

As mentionedearlier, Al � O� (TGO) alsoforms at the TBC-bondcoat-superalloy junction.TrumbleandRühle44 showedbyTransmissionElectronMicroscopy (TEM) thatat1390

�C,pureNi doesnotformaspinel(NiAl � O� )

at theinterfacebetweenNi andAl � O� . However, even0.07percentoxygenin theNi will induceformationof a thin spinellayerat the interface(withnoNiO intermediaterequired),wherethekineticsappearto becontrolledbyoxygendiffusion. Shearstrengthmeasurementsby Loh et al.45 determinedthat,underconditionswherethespinelNiAl � O� is formed,fractureoccursalongthespinel-Niinterface.It is still controversialasto whetherformationof thespinelcompoundattheseinterfacesactuallyhelpsorhindersadhesion.Zhong and Ohuchi,46 using X-ray photoelectronspectroscopy, and laterBrydsonetal.,5 usingspatiallyresolvedtransmissionElectronEnergy LossSpectroscopy (EELS)andHigh ResolutionElectronMicroscopy (HREM),determinedthattheinterfacebetweenNi andAl � O� formsdirectNi-Al bondsunderreducingconditionsat high temperatures.They presentedevidencefor a Ni � Al phaseat the interface,which they suggestedwas formed byAl diffusion into the Ni, and that this phaseprovides a driving force fortheformationof Ni-Al bondsratherthanNi-O bonds.They suggestedthatformationof any spinelphasecontainingNi-O bondsneedsto beminimizedbecausethespinelis brittle, anexactly oppositeconclusionto that reachedby Qin andDerbyfor theNi-ZrO � interface.

In additionto M/C interactions,characterizationof ZrO� -Al � O� is inter-estingaswell, becauseof theAl � O� that formsbetweenthebondcoatandthe TBC. Aita andcoworkers have grown andcharacterizedwith HREMnanolaminatefilms thatalternatebetweenpolycrystallineZrO� andAl � O�layers. They have shown that ZrO� grows with the close-packed tetrag-onal(111)or monoclinic(11̄1) surfacesparallel to the substrate.47 Interest-ingly, werecentlycalculatedthosesurfacesto bethemoststablefor eachofthesetwo phases.48 They alsoobservedthattheamountof t-ZrO� increaseswith decreasingZrO� film thicknessand that the crystallitesgrow in thistetragonalphaseup to a critical thicknessof about6.0 nm, at which pointadditionalZrO� convertsthecrystalliteinto themonoclinicphase.49 In otherwork, they showed that the stress-inducedtransformationof tetragonaltomonocliniczirconiais limited to nanometer-scaleregionsin thesenanolam-


inates.50 In Section6.2.2.2,wediscussourown theoreticalrationalizationoftheseobservations.Theroleof aluminaseemsmerelyto confinethesizeofZrO� crystallitesformed. Our own calculationson ZrO� -Al � O� (discussedin Section6.2.2.2)areconsistentwith theseobservations.

4. TBC FAILURE

Differencesin crystalstructure,size,andthermalexpansioncoefficientsbetweenthetopcoat,bondcoat,andsubstrateintroducestraininto theTBC.The thermalexpansioncoefficient of the top coat is generallylower thanthatof thebondcoator thealloy substrate.As mentionedearlier, aproperlydesignedbondcoatserves asa gradedthermalexpansionlayer to reducethe straincausedby thermalexpansionmismatch. Unfortunately, thermalcycling in air enhancesthe mismatchand increasesstrain resultingfrominterfacial damageduring oxidation.24 With repeatedcycling, this straincontributesto coatingfailure.

4.1. Lik ely Culprits

TBC failure involves a numberof contributing factors. Obviously, thestrainsintroducedwith thermalcycling area major areaof concern. Thebuildup of the TGO, migration and segregation of the components,andphasetransitionsof theTGOandtopcoatmayeachcontributeto thecoatingfailure. Even the typeof porosityin thecoating,largely dependenton thecoatingprocedureused,can affect the coating lifetime. A greatdeal ofexperimentalwork connectedwith TBC’sexistsin theliterature.Ernstpub-lishedanexcellentreview thatcoversmany experimentsperformedbefore1995.4 Dueto inherentcomplexities of TBC’s,studiesto elucidatethefail-uremechanismsgenerallyconcentrateon only certainaspectscontributingto failure. Thesubtlerelationshipsof all thefactorsarenotfully understood;hence,furthermodelingandexperimentsareneededtogainamorethoroughunderstandingof presentweaknessesandpossiblefutureimprovements.

4.2. Spallation Mechanisms

Spallationis theprocessby whichtheTBC peelsoff of thesubstrate;andnaturally, after the coatinghasspalled,the continuousthermalprotectionlayerno longerexists. Likewise,thespalledfragmentscanblock gasflow,contaminateproducts,andpermitcorrosion.Thefailureof theTBC leadingto spallationappearscloselyrelatedto thedamageprocesswithin theTGOlayer. Unfortunately, dueto thehighly complex natureof theproblem,thereis limited understandingof how growth kineticsof theTGOandmicrocrackdamageaffect TBC lifetime. Threeprimaryscenarioshave beenproposed


for the spallationmechanism.51 The first of thesestatesthat a bucklingeffect canresultfrom planarcompressive stresseswithin theceramiclayer.It seemsthis is a plausiblemechanismprovided thereexists an interfacialdelaminationcrack, formed due to local conditionscreatingboth out-of-planeandsheartensions. Recentmicroscopy dataindicatespallationcanproceedvia this buckling mechanismwhen the delaminationcrack is atleastsixteentimesthe TBC thickness.51,52 However, for thick oxides,thebucklingmodeis notviable. Thosesystemsmayundergoasurfacewedgingeffect.53 Thissecondmodelreliesonthedevelopmentof athrough-thicknessshearcrack in the TBC due to compression.54 Finally, a more recentlyproposedmechanismdependsupon a void formationunderthe TBC andsubsequentfolding effects which may lead to cracking.55 This effect isalsoknown as“wrinkling” or “rumpling.” Naturally, in addition to voidsformedthroughthermalcycling, thepore-typesinitially createdin theTBCmayinfluencetheeventualspallationmode.Althougheachmodelappearsplausiblein its descriptionof the final spallationeffect, an understandingthat would elucidatedynamicevolution conditionsleadingto spallationisdesired.Fig. 2 displaysschematicdiagramsof thethreespallationmodels.

Wedging

Buckling

��

�� Wrinkling

Figure 2 SpallationMechanismsof theTBC

4.3. Complicating Featuresof Spallation

Althoughanunderstandingof spallationmechanismsis useful,it seemsTBC andsubstratedelaminationresultsfrom ahighly complex relationship,


which includesbondcoatoxidation,micro-crackevolution,andprogressivebuckling.51 Fracturesurfacescreatedby TBC spallationsuggestthatfailureoccursin theTBC-bondcoatinterfacial region.56 A piezospectroscopicstudyshows large failure regionsmay follow the oxide grain impressionsin thebondcoat,indicatingfailurewheretheTGO hasgrown into thebondcoatgrain boundaries.26 Certainmorphologicalinstabilitiesof the oxide-bondcoat interfacemay causethe fracturethat joins the failure regions. Theseinstabilitiescouldresultin local normalforcesacrossthe interfaceleadingto interfacialfracture.A similarphenomenonoccurswith spontaneousspal-lation aftercoolinga TBC to roomtemperature.Consequently, sub-criticalcrack growth may be hastenedby environmentalfactors. Propensityformoistureto enhancesuchcrackgrowth in metal-aluminainterfacesfurthersupportstheseideas.26,57,58 Using thermalplasmasprayingfor bondcoatdepositionmayresultin a layeredbondcoatwith irregularthickness.Sam-plespossessingthisdiscontinuityin bondcoatthicknessfailedafterthermaltreatmentunderan argon atmosphere,indicatingthat at leastonefactorinthermalspallationis increasedresidualstressontheYSZ afterthermaltreat-ment.21 Thus, althoughthe buildup of the TGO may play a large role inthe eventualTBC failure, an overall spallationmechanismencompassesavarietyof complicatingfeatures.51

4.4. Adhesion

Compositionof thesubstrateandbondcoataffectsadhesionof aluminaformedduring bondcoatoxidation. Of course,when the aluminaspalls,thezirconialayer is not maintained;so theTBC fails. Migration, segrega-tion, andstressgenerationarekey areasof concernin thethermallygrownoxide region. Migration of aluminumions from bondcoat to metal-alloysubstrateoccursdueto a concentrationgradient.Likewise,migrationfromthe substrateandbondcoat into the thermallygrown oxide region is alsoexpected. Actually, it appearsthat limited yttrium ion migration to thealuminaimprovesadhesion;25 however, contaminantsin the aluminagen-erally leadto additionalstresses,which decreaseadhesionduring thermalexpansion.59 Thehigh temperaturediffusionof bulk yttria ionsto theYSZsurfacedestabilizesthe top coat.60,61 This permitszirconiaphasetransfor-mationto monoclinic,62 resultingin anundesirablevolumeexpansionthatmaycontribute to spallation.Furthermore,anSEM studyshows bondcoataluminumcandiffuseinto theYSZ layer.39 Previously, it hasbeensuggestedthatbothneutralandionic aluminumdiffusion into theYSZ layer inducesspallation.63 Accordingly, diffusion-controlledmigration in the TBC maypromoteharmfulphasetransitionsandenhancethermalstresses.


Althoughaconcentrationgradient allowsmigrationviadiffusion, theoxy-genchemicalpotentialgradient,arisingduringoxidation,suppliesanotherdriving force. Studiesshow that this chemicalpotentialgradientpenetratesthe top coat, bond coat and into the metal substrate. It affects oxygen-reactive speciesin all theselayers,including thoseinitially in the form ofstableoxides,nitrides,carbidesandsulfides.64–67

Segregationto themetal-TGOinterfacealsoaffectsoxideadhesion.Forinstance,sulfur segregatesto this interface,which can prove detrimentalto TBC lifetime. The interfacial sulfur increasesthe thicknessof the oxi-dationlayer, decreasesadhesionof the oxide layer to the metal, increasestransformationof metastablealuminato thealphaphase,andenhancesporeformationat the interfaceandwithin theoxide layer. Increasedinterfacialrougheningand void formation results. The formation of voids is prob-lematic sincevoids act as stressconcentrationsiteswithin the oxidationlayer.65,68–72 De-sulfurizationof the sampleto lessthan1 ppm may helpprevent spallation.73–76 However, it is possiblethat the presenceof otherspecies(suchasY andZr) in thebondcoatandsubstratemaysupresstheharmfuleffectsof thesulfurandrenderde-sulfurizationunnecessary.25,65,77

Finally, scalestressescanresultfrom isothermallygeneratedgrowth stressduringtheoxideformationor from coolingstressdueto thermalexpansionmismatchduringthermalcycling.78

4.5. Measuresof Stress,Fracture and Spallation

In additionto experimentalmeansfor initially characterizingTBC sys-tems,anumberof techniquesareusefulfor investigatingstress,fracture,andspallation.Cr�� piezospectroscopy is anopticalmethod,sensitive to Cr��dopantsin thealumina,thatpermitsstudyof oxidationstressesthroughtheTBC. Prior to this technique,non-destructive studyof the oxide layer hadproven difficult due to the physicallocation of the alumina. Fortunately,zirconia is fairly transparentat the frequenciesof interest. As a result,this piezospectroscopictechniqueis ableto detectstressesandsomephasedifferenceswithin the oxide layer.79 Techniquesfor determiningfractureenergy includedoublecantilever-beamexperiments,80,81 four-pointbendingtests,82–84 andwedge-loadedpeeltests.83 Furthermore,laserspallationpro-videsa meansto measuretensilestrengthof themetal-oxideinterface.85–87

Pulsedlasers,usedashighshockgenerators,allow explorationof thespalla-tion processthroughsimulatedhigh pressureloading.88,89 A methodbaseduponThin LayerActivation(TLA) attemptsto directly measurespallation.TLA reliesonthecreationof radionuclidesin thesurfacelayerafterexposureto a high-energy beamof chargedparticles.90,91 Lossof activatedmaterialdue to spallationresultsin a decreased� -activity signal. Furthermore,it


is possibleto collect thespalledmaterial,allowing massquantificationthatprovides an additionalsensitive spallationmeasure.92 Recently, effectivemeasurementsof amplitudeandprofileof lasergeneratedstresspulseshavebeenmadeusingaDopplervelocity interferometersystemfor any reflector.An advantageof timeresolvedinterferometryis thatit allowstheresearcherto investigatedynamicbehavior of the materialby looking at damageef-fectson wave propagation.93 Dilatometryprovidesa quantitative meanstoexplore interfacial damagedue to oxidation, allowing thermalexpansionexperiments.24 Thestrainintroducedby thermalexpansionmismatchplaysa majorrole in TBC failure,sotechniquesfor exploring thermalexpansionarevery important.

5. THEORETICAL PREDICTION OF INTERFACE STABIL-ITY

Theoreticalmethodsoffer the opportunityto explore structure-propertyrelationshipsin ideal metal-ceramicinterfaces. Ultimately, improved un-derstandingof thecausalsequenceleadingto aparticularinterfacestructureandsetof propertieswould enablefurther optimizationof manufacturingparameters.Atomisticmodelingconstitutestheperfectlaboratoryin thisre-spect.Within thelimits of thespecificapproximationsusedfor interatomicinteractions,physicalpropertiesmayberesolved to arbitraryaccuracy andcompetingeffectsmaybeseparated.

Herewe will beconcernedmainly with the interfacestructuralstabilityand electronicstructure. One of the most important factorsdeterminingthe interfacestability is the interfacecohesive strength.Otherfactorsmaybe equallyimportantfor stability of the interface,dependingon theactualsituation,e.g. corrosionresistance,thermalexpansionandelasticmatchingof the metal and ceramic,the flexibility of the structureto releasestressbuildup during thermalcycling, stability towardsstructuraldegradationbyunwantedinterfacesegregationof certainelementsandundesirablemixedphaseformationat the interface. In this section,we give an overview ofstrategiesby whichtheorycanplayanimportantrolein helpingcharacterizesuchinterfaces. A recentandexcellent review on the theoreticalaspectsof the M/C interface was given by Finnis94 in 1996; we will thereforeconcentrateon laterdevelopmentsin theunderstandingof M/C interfaces.

6. ATOMISTIC APPROACHES

Thedisciplineof atomisticmodelinghasproliferatedtremendouslyoverthe pasttwo decades,dueto the increasedcapacityof moderncomputers.The basictrade-off in atomisticmodelingis always betweenaccuracy of


calculatedenergies and forcesand,on the other hand,size of the atomicensemblemeantto modela macroscopicsystem.The larger theensemblesize, the smaller is the influenceof miscellaneousfinite size effects onthe physical properties. However, the larger the systemsize, the moreapproximatetheatomisticdescriptionnecessarilybecomes.

Which tradeoff to choosedependson thesituation: somephysicalprop-ertiesareinsensitive to detailsin the interatomicpotentials.In suchcases,a modelpotentialwill provide essentiallyidentical resultsto the exact, aslongasthemodelpotentialreproducescertaincharacteristicquantitieslike,e.g.,elasticconstantsandbulk cohesive energies.

Physicalpropertiesmaybeinsensitive to detailsof theinteratomicpoten-tial for a variety of reasons.For exampleat low temperatures,the atomicsystemmay probea boundedregion of phasespace,mostoften the elas-tic regime aroundthe equilibrium state; and in this boundedregion, theinteratomicinteractionsmay be representedwell by a suitablemodelpo-tential. Someclassesof physicalproperties,like critical phenomena,areintrinsically insensitive to many detailsin theinteratomicpotentials,astheyarecontrolledby collective behavior. For otherphysicalphenomena,likemelting,effectsof fine detailsin the interatomicpotentialstendto averageout.

However, in othersituations,therewill beastrongsensitivity to detailsinthe interatomicpotential. This is thecasewhenthephysicsandchemistryis governedby rareevents,likecrossingactivationbarriersandthebreakingandforming of chemicalbonds.If thetransitionstateis not well character-izedandincludedcarefully in theparameterizationdatabasefor themodelpotential,the activation barrier is very likely to be describederroneouslyby themodelpotential,leadingto wrongtransitionrates.This is whereabinitio methodsareneeded.

In the sectionsbelow, the particularaspectsassociatedwith atomisticmodelingof M/C interfaceswill be reviewed alongwith applicablerecentwork donein thisfield.

6.1. Structural Models for M/C Interfaces

Atomisticapproachesneedastructuralmodelto representtherealsystem.In thissection,wewill brieflydiscussthemostcommonchoicesof structuralmodelsalongwith advantagesanddisadvantages,in orderto enablereadersunfamiliar with detailsto critically judgeresultspresentedin theliterature.We will then discussissuesinvolved in choosingthe structureof the in-terfacewhich involveslatticestoichiometryandmisfit. Themostcommonstructuralmodelsof M/C interfacesfall into two mainclasses:clusterandslabrepresentations.


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METAL

A B

METAL

CERAMIC

VACUUM

C

CERAMICCERAMIC

METAL

Figure 3 Schematicpictureof M/C interfacestructuralmodels.A : Clustermodelwith vacuumaroundit.B : DenseM/C interfaceunit cell, physicallycorrespondingto a superlatticeor sandwichstructure.C : Slabmodelwith vacuumbetweenperiodicimagesperpendicularto theinterface.Physi-cally, thestructurecorrespondsto M/C thin films. Thebordersof theperiodicallyreplicatedunit cellsin B andC areshown with bold lines.

6.1.1. ClusterModels Thesemodelsareusuallyconstructedby scoopingout a small representative region (seeFig.3A) containing5-30atomsfromthe real M/C interface. Clustermodelsemphasizechemistryas local byonly consideringa small“active” region. Unfortunately, someearlyclusterstudiesusedunrealisticallysmallclusters,which werepoorrepresentationsof the real interface they attemptedto model.95 In suchcases,importantlong-rangeeffectsaremissed.

Sometimestheceramicsideof theclusteris embeddedin anarrayof thenominalanionandcationpoint chargesin theproperstructure,to emulatethe real Madelungpotential in the ceramic- this definitely improves therealismof theclustermodel.96–100 A Green’s functionconstructedfrom theperfecthostcrystalhasalsobeenusedto embeda ceramiccluster.101 Analternative to anionandcationpoint chargesis embeddingtheclusterintoanarrayof overlappinganionandcationpseudopotentials,102,103 thustryingto capturesomeof the electron-electroninteractionwith the surroundingceramicmedium. A supplementto this is mechanicalembeddingof theclustervia forcefield interactionswith thesurroundingsubstratelattice,104

so-calledmolecularmechanics. The latter neglects the perturbationsininteratomicforceconstantscausedby metallicadsorptionandis likely to beratherinaccuratein thecaseof reconstructionor extensive relaxationsin theinterfaceregion.

Clustermodelshave othergenericfinite sizeeffects. Interfacesareoftengeometricallyfrustrated:for all metalatoms,thereis apreferredadsorption


site on the ceramicsurface. Whenonemetalatomoccupiesthat site, theneighboringmetal atom generallywill not be able to occupy an equallyfavorablesite,dueto thelatticemismatchbetweenmetalandceramic.Thisfrustrationeffect is not modeledproperly, if themetalsideof theclusteristoo small. Anotherfinite sizeeffect is that the electronicdensityof statesoscillatessignificantlywith theclustersize.105 This is critical neartheFermilevel, becausesuchoscillationsin thedensityof statesavailablefor bondingto the ceramicis likely to producepredictionsthat converge slowly withclustersize.106 Thiseffectmaybecounteredby “statepreparation”105 or byembeddingthemetalclusterin aperiodicmetalslab.107 Unfortunately, sincemany finite sizeeffectsconverge slowly with the clustersize,unmanage-ably largeclustersmayberequiredif notembeddedproperly. Furthermore,charged clustersareoften considered,due to the nonstoichiometryof theceramicpieceof thecluster. Otherwise,theanionsandcationswill not bein theproperchargestate,correspondingto theoverallneutralbulk ceramic.A back-of-the-envelope estimatesuggeststhat thenonphysicalpolarizationinducedby chargedfragmentsmaysubstantiallyaffect thechemicalpredic-tions. Theonesignificantadvantageof clustermodelsis that thepower ofab initio quantumchemicalmethodscanbeappliedandthereforesystemat-ically convergedresultsindependentof experimentcanbe obtained,albeitfor asmallpieceof themacroscopicsystem.Thiswill bediscussedin moredetailshortly.

6.1.2.SlabModels Thesemodelsarethepreferredgeometryin electronicstructuremethodsoriginatingfrom solid statephysics. Periodicboundaryconditionsareappliedto a unit cell representingtheM/C interface. There-fore, slab modelsare restrictedto coherentinterfaces,which meansthatperiodicityparallelto theinterfaceis present- thiscorrespondsto a“lockedin” interfacestructure.Of course,theperiodicitymayhavealongrepetitionlength,which maynot bemodeledproperlyin someperiodicslabcalcula-tions. Therearetwo typesof slabcells: thosethatdo not includea vacuumlayerandthosethatdo. Denseunit cells (Fig.3B)physicallycorrespondtosandwichstructureswith two M/C interfacesper unit cell. From an ener-getic point of view, this geometryis ratherrestrictive, becauseit requiressufficient symmetrysuchthat the interfacesare identical (in order for theinterfaceenergy to be uniquelydefined). Unfortunately, this requirementoftenrestrictstransverserelaxation,becausethesymmetry“locks” theM/Cinterface. On theotherhand,if symmetryis enforced,this unit cell hasnonetperpendiculardipolemoment,so thatunphysicalelectrostaticcouplingbetweenthe interfacesis avoided. It is also necessaryto make both themetalandceramiclayer thick enoughso that the interfacesdo not interact


via electronicstructureperturbationsor strain,in orderto havesuchamodelrealisticallyportrayasingleM/C interface.

A moregeneralinterfacegeometryis shown in Fig.3C.Physicallythiscorrespondsto aninfinite arrayof M/C thin film couplesseparatedby vac-uum. A salientpoint is that thevacuumlayersshouldbethick enoughthatadjacentM/C slabsdo not interact. Interactionis possiblein two ways:eithervia electronicwavefunctionoverlap in the vacuumor via Coulom-bic multipoles. The former interactionis usuallyvanishing,if more than8 10 9: of vacuumis present.The latter interactionis ratherlong-ranged,but fortunatelymethodshave beendevisedto electrostaticallydecoupletheslabs.108–110 Of course,it is requiredthatboththemetalandceramiclayersarethick enoughthattheinterfaceandsurfacesdonot interact.

Theslabgeometryalsosuffersfrom otherfinite sizeeffects. If theextentof theunit cell parallelto the interfaceis too small,artificial straineffectsare introduced,becausethe metal and ceramicare forced to be coherentby the periodic boundaryconditions. Of course,this may be eliminatedby enlarging the unit cell, which unfortunatelyleadsto very computer-intensive calculations,asis thecasewith theclustermodels. However fortheslabmodel,theoscillationsin theelectronicdensityof statesarenot asdramaticwhen varying the numberof atomsas in the casewith clusters.This is becausetheslabis infinite parallelto theinterface.This impliesthespectrumis continuous,andthemetalslabdoesnot have anartificial bandgap,unlike themetalcluster.

The artificial requirementof the unit cell periodicity perpendiculartotheinterfacemaybeavoided,if a Green’s functiontechniqueis used.Suchtechniqueshavebeenusedfor metal-metalinterfaces111 with highsymmetry,but no suchcalculationsfor M/C interfaceshave beenreportedyet to ourknowledge.

6.1.3. InterfaceStoichiometry If no experimentalevidenceis availableconcerningthe orientationof the metalandceramiccrystalswith respectto eachother for a coherentinterface,one needssomehow to produceareasonableguessasto how theparentcrystalsmaymatchupattheinterface.Thepossibilitiesareimmense,especiallyif theceramichaslow symmetry:first oneneedsto considerwhich facesfrom eachparentcrystalwill matchup. Symmetryconsiderationsareoften helpful at this point. Freeenergyconsiderationmightalsobeguiding: weaklyinteractingM/C pairsarelikelyto matchup on their low energy surfaces. Strongly interactingM/C pairsaremore likely to matchup on their high energy surfaces,becausethesegenerallycontainmoreunsaturatedatomsreadyfor bonding. However, ifa new reactionphaseforms at the interface, the situationbecomesmorecomplicated.If thebondingmechanismis dominantlyelectrostatic,image


theory, which we returnto later, predictsthemostpolarceramicsurfacetobind mosttightly to themetal,i.e., it hasthelargestwork of separation; .However, this doesnot meanthat polar interfacesaremoststablefrom athermodynamicalpoint of view; themoststableM/C interfacethat canbeformedbetweenthepair M andC is theonewith smallestfreeenergy, i.e.smallestinterfacetension�= :� A@ � ED ; DGFIH HKJMLNH (1)Thisis theDupŕerelation,generalizedto allow massexchange,e.g.,with theambientgasor with thebulk, atchemicalpotentials H . JMLNH is thechangeinabundanceof speciesO in theinterfaceregion on forming theinterface,and�= aresurfacetensionsof baremetalandceramic,respectively. Thus,becausea polar surfaceis energetically very unfavorable(theoretically�=>divergesfor aperfect,infinite polarceramicsurface),it maynotbefavorableto form an interface with a polar ceramictermination,even though theinterfacebinding is relatively strong. Anotherapproachfor guessingtheceramicterminationat the interfaceis to estimateanion/cation/metalbondcombinationsfrom the appropriatebulk phases. But no foolproof rulescanbe formulatedon how the ceramicis terminatedat the M/C interface.Stoichiometryis a complicatingaspectin this context, becauseit dependson the chemicalpotentialspresent;and the interface chemistrychangesdramaticallywith stoichiometry, aswe will discusslater.

6.1.4. Lattice Misfit Having settledon somemetalandceramicsurfacesthat we think will match,we must determinethe relative orientationandtranslationof thesesurfaceswith respectto eachother. Certaindirectionsinthemetalandceramicarelikely tobealignedfor astableinterface. Therewilloftenbemultipleminima,correspondingtodifferentlock-in possibilitiesforthecoherentinterface. Lastly, thesizeandshapeof the interfaceunit cellneedsto bedetermined,if weassumeacoherentinterface,which is implicitif periodic boundaryconditionsare applied. A realistic unit cell will ofcoursecorrespondto low strainon boththemetalandceramicside.

Thisvastnumberof possibilitiescallsfor asystematicprocedureto iden-tify asubsetof themostlikely interfacematchingsof theparentcrystals. Thissubsetwill thenbethestartingpoint for atomisticmodeling. Thequestionaboutunit cell sizeandshapeis relatively simpleto address.Many relatedproceduresbasedon linearelasticitytheoryandlatticestrainestimatesmaybeadopted.Thebasicsituationis sketchedin Fig. 4: anoverlayerunit cellA needsto bematchedtogetherwith asubstrateunit cell B. Matchingpairsof unit cellsare,in general,multiplesof primitivecellsin theinterfaceplanefor themetalandceramic,respectively.


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b22a

T

a1 b1

Ω

A A + B

Overlayer

B

Substrate

Figure 4 Schematicpictureof M/C interfacelatticematching.A : Arbitrary overlayerunit cell constitutedof many primitive cellsspannedby thevectorsZ\[^]�Z�_ .B : Arbitrary substrateunit cell constitutedof many primitive cellsspannedby thevectors` [a] ` _ .T : LineartransformationbetweenA andB.A+B : The“overlap” b betweencellsA andB.

The mostcrudeapproachto quantify the commensurabilityof the twogivenunit cellsis to assignamismatchfactorbasedon theoverlapbetweenthecellsA andB, i.e. @CcdD egf hiff jkf B f lmf (2)where f jkf P f lmf and f hif signify the areaof cell A, B and the overlap area,respectively. Thisquantityvanishes,if A n B andincreaseswith decreasingoverlap h , assketchedin Fig.4. Thusonewouldlike to chooseaninterfacematchingthatminimizes .

Anothergeometricalapproachwastakenby Bolding andCarter,112 whoconsideredthe matchingof orthogonalunit cells. By taking multiplesofeachunit cell a suitablenumberof times in eachdirection,an arbitrarilylow misfit might be achieved, in the sameway that an arbitrary irrationalnumbermight beapproximatedby a rationalnumber, if thenumeratoranddenominatoraresufficiently large. Morespecifically, they definedthestrainvariables o�pIq� @ r^s � Ditdu �tdu � (3)

Atomic-levelpropertiesofthermalbarrier coatings: characterizationofmetal-ceramicinterfraces 19owvyx� @ z{s � D}|~u �|u �wheres �P s �P u ��P u � arethelengthof thebasisvectorsspanningtheprimitiveunit cellsof whichA andB aremultiples,seeFig. 4. t P | P r P z areintegersgiving theunit cell enlargementalongeachbasisvector. ThenBolding andCarterproposedminimizing thequantity pIvMqx > @ � f o�pIq� f B~ � f o�vyx� f (4)which obviously is positive definiteandvanishesat perfectcoherency be-tweenA andB. Here ��P � areweightfactorsthatmight berelatedto theelasticpropertiesof metalandceramic.In Bolding andCarter’s case,theseweightfactorsweresetto unity.

A moregeneralapproachwouldbeto directlyconsidertheelasticenergyassociatedby deformingcell A into cell B soasto achievecoherency. If thisdeformationis designatedby the eAe lineartransformationmatrix l @ j (5)wherethematricesj and l containthevectorsspanningthe(almost)match-ing pair of metalandceramicunit cells, it is easyto show that the corre-spondingexact strain tensor and the correspondingelasticenergy isgivenby @ ce R D (6) @ ce Ma�} (7)It is importantto usetheexact straintensordefinition,Eq. (6), to achieverotationalinvariancewith respectto latticerotation;theconventionallinearstrain tensoronly provides differential rotational invarianceof in Eq.(7).113,114 A hierarchyof approximationsmaybeusedfor theelastictensor� . The most rigorousapproachis to transformthe bulk elastic tensor accordingto �I^� @ H a H xq x q (8)whereasummationconventionoversameindicesappliesand is therotationmatrix from interfaceto bulk crystalCartesianframes.113 However, it is notguaranteedthat a thin film hasthe sameratio betweenelasticconstantsasthe bulk crystal. Generally, six elastic constantsare inequivalent in 2Delasticitytheory, which follows from thepermutationalsymmetryof . Asanapproximationwe mayassumeonly �T� , � � and �T� arenonvanishing,which is true for cubicsymmetry. The lowestlevel of approximationis to


assumeisotropy, in which casethe relation \�¡� @ � � B e �T� appliesandonly a ratio, like � �¢\�T� , needsto beestimated.Theapproachassumesafixedsubstrate;themostsophisticatedprocedure

wouldbeto minimizetheelasticenergy @ £¤w ¡¥ �¦ B �¨§ ¦ q ¥¨© ¦ . Thisproperlyresultsin asmalloverallrescalingof theelasticenergies.However,dueto thephysicalsimplicity of this elasticmodel,it is doubtfulwhetherabetterdescriptionis obtainedunlessbothsubstrateandoverlayerarehighlyanisotropic. Further, if materialA is grown onto a bulk substrateB, it isunlikely thata transversaldeformationof thesubstratewould take placeinrealityanyway.

It is instructive to comparethis model to that of Bolding andCarter112

discussedabove, for the casewhereboth substrateandoverlayerhave or-thogonallattices(in the interfaceplane). If we multiply theoverlayerunitcell r P z{ times along s ��P s � and correspondinglythe substrateunit cell t P | timesalong u �P u � , thetransformationmatrix in Eq.(5)becomes pIvMqx @«ª p ¤ [q ¥ [ ¬¬ v ¤ _x ¥ _® (9)Inserting this into the strain tensorEq.(6), we get the harmonicenergy,Eq.(7),to secondorderin thestrainvariablesof Bolding andCarter, p¯v°qx @ ce �±�T�

o p²q� � B ce �³�T�o vyx� � B �±� � o p²q� o vyx� (10)

Comparedto the misfit factor of Bolding and Carter pIvMqx > , Eq.(4), thisexpressioncontainsacrosstermandscalesdifferentlyin thestrainvariables.Both expressionswill bezerofor perfectcoherency o � @ o � @ ¬ , but forcompetinginterface lock-in possibilities,one might expect Eq.(10) to bequalitatively moreaccurate.In conclusion,to find themostfavorableunitcell lock-ins for a given substrateandoverlayerlattice, from an elasticitypoint of view, we simply needto scanan expressionlike Eq.(10) in fourindices t P | P r P z{ to find a subsetof likely coherentinterfaceunit cells.This is easilydoneonacomputer.

In additionto theelasticenergy, of course,thechemicalinteractionen-ergy betweenmetal and ceramicmust be accountedfor. The possibilityof competitionbetweenelasticity and chemistryexists suchthat a ratherelasticallystrainedinterfacecombinationmay be morestablethanan un-strainedone,becausethestrainedonemayhavefavorablechemicalbondingbetweenmetalandceramicatomsattheinterface.Therefore,otherinterfacecombinationsthantheleaststrainedneedto beconsideredin general.

We now move on to discusshow onecanassessstructureandenergeticsof suchinterfacesfrom theory, startingfrom themostaccuratemodelsandendingwith themostapproximate.


6.2. Ab Initio Techniques

Firstprinciplestechniquescanbedistinguishedfromsemiempiricalmeth-odsin that they includequantummechanicaleffectsexplicitly usingexactor moderateapproximationsfor electronicexchangeandcorrelation.Gen-erally, explicit inclusionof quantummechanicaleffectsis computationallydemanding,which restrictsab initio methodsto small systems,typicallylessthan50inequivalentatomsonmodernworkstations(1999).Usingmas-sively parallelcomputers,up to 300inequivalentmaingroupatomscanbehandledab initio today. ´ In specializedcases,significantlymoreatomscanbehandledby so-calledµ¶ L abinitio techniques,wherethecomputationalloadscalesessentiallylinearly with thenumberof atomsL . For insulatingsystems,tightbindingcalculationshaveshownthatelectronicdensitymatrixmethods115–118maybeappliedsincetheelectronicdensitymatrixhasafiniterange,andsimulationswith 650atomson a modernworkstationhave beenreported.119Alternatively, divideandconquer120 andlocalizedwavefunctionapproaches121–124arewell suitedtoachieve µk L scalingfor insulatingsys-tems.If anartificialnonzerotemperatureis assumedfor theelectronsystem,densitymatrix117,125–127 andlocalizedwavefunctionapproaches128 arealsofeasiblefor metallicsystems,but imposinganonphysicalelectronictemper-ature- unlessit is removed by the endof thecalculation127 - is a dubiousapproximationfor systemswheretheelectronicdensityof stateshasmuchstructurearoundtheFermilevel, asin thecasefor transitionmetal/ceramicinterfaces.For free-electron-like bulk systems,Orbital-freeDensityFunc-tional Theoryinvolving kinetic energy densityfunctionalshasallowed thetreatmentof 8 6000symmetry-inequivalent metalatoms.129 The drawbackof this methodis that it is limited by the accuracy of the kinetic energydensityfunctional,which is not known exactly for many-electronsystems.Improving suchfunctionalsis, however, anactive areaof research.130–144

The restrictionon the numberof inequivalent atomsimplies that onlypropertiesinvolving short length scalescan be treatedaccurately, unlessthesepropertiesare consistentwith periodic boundaryconditions. Thisrestrictionis ratherseverein thecaseof a M/C interface,becausethe realinterfaceis oftentransverselyaperiodicandmaycontainlong-rangedstrainfieldsanddefectstructuresperpendicularto theinterface,whichwill requireanextremelylarge unit cell to model. Thusonly idealizedM/C interfaceshaving small unit cells may be treatedrealistically by ab initio methods.·Thedefinitionof theconceptabinitio is somewhatfluid, butusuallymeansessentiallyfreeof empirical

parameters.Beingab initio is generallyconsidereda quality stamp,but oneshouldbeawarethatsomeapproaches,whichareformallyparameter-free,e.g.Thomas-Fermidensityfunctionaltheoryorabinitiotight binding,fail miserablyoutsidelimited applicationranges.


Thisexcludesmany M/C combinationswith largelatticemismatchbetweenthe metalandthe ceramic,becausea small interfaceunit cell implies thateither the metal or the ceramicmust be strainedto an unphysicalextent,leading to unphysicalresultsinducedby the artificial periodic boundaryconditions. Still, for M/C interfaceswhere the natural lattice mismatchis low, ab initio studiesof idealizedM/C interfacesareinstructive, givingvaluableinsightsinto quantumeffectsat theinterface.Wenow discusswhathasbeenaccomplishedwith ab initio calculationsof idealizedinterfaces.

6.2.1.QuantumChemicalApproaches A moreprecisedescriptionfor thisclassis full wavefunctionmethods,wherethebasicvariableis thefull many-bodywavefunction.Themainproblemwith full wavefunctionapproachesisthatthecomputationalloadincreasesdrastically withthenumberof electronsL

. At theHartree-Fock level, the load increasesasL �^¸I� , andthescaling

withL

increasessteadily, the more completethe inclusion of electroniccorrelation. Sincerealisticmodelingof interfacesrequiresquite large unitcellsor largeclusters,very few full wavefunctionstudiesatandbeyondtheHartree-Fock level have beenreportedin the literature. The interactionofa Cu145 anda Pd146 atomwith a singleMgO moleculehave beenstudiedusingmultireferenceconfigurationinteraction.In bothcases,bindingof themetalto theO-atomin theMgO moleculewaspredictedasmoststable(i.e.a linearmolecule),with an“adsorption”energy of 2.28eV and2.65eV forCu andPd,respectively. This is in accordancewith thetrend,observed bylessaccurateelectronicstructuremethods,that metalatomsadsorbon topof theO atomson theMgO(001)surface.

Hartree-Fock studieshave beenundertaken for cluster modelsof theCu/MgO147 andNi/Al � O� 148 interfaces.Bothstudiesfind significantchargedonationfrom themetalatomto theoxideconductionstates.Hartree-Fockwith a posteorielectroncorrelationtaken from a free electrongas(HF-CC)154 in the supercellapproachhasbeenappliedto Ag/ -Al � O� 155 andAg/MgO(001).155,156 Ag wasfound to beweaklyboundto thecompletelyO-terminated -Al � O� (0001)surface,althoughsignificantcharge transferoccurred.In agreementwith densityfunctionalcalculations,HF-CCcalcu-lationsfind Ag physisorbedabove the O atomsin the MgO(001)surface.The adsorptionenergy above the O(Mg) site is 0.47(0.11)J/m� , in goodagreementwith the experimentalvalue,0.45 J/m� for a thick Ag film.157However, this numberis likely to be an averageof adsorptionof Ag overboth O and Mg in separatedomains,due to the (small) lattice misfit be-tweenAg andMgO. A principal problemwith the HF-CC methodis thatthea posteorifreeelectrongaselectroniccorrelationis not consistentwiththe exact exchangeenergy usedin the underlyingHartree-Fock method-importanterrorcancellationsbetweenexchangeandcorrelationarelost.158


Initial tests154 indicateda confidencelevel comparableto the bestdensityfunctionalmodelsfor exchangeandcorrelation,but theapproachneedstobetestedon moresystemsto seeif systematicerrorsexist. Relatedin spirit totheHF-CCmethodis theB3LYP159approach,whichevaluatestheelectronicexchange-correlationenergy asa weightedaverageof the exact exchangeenergy andtheelectrongasresultsfor theexchange-correlation energy. Theweighting parametersfor this averagewere determinedsemiempirically,which makes this approachaestheticallyunpleasant.However, for manymoleculesandfinite clustersthis approachhasdeliveredaccurateresults.An instructive studyhasappeared,160 which comparesthe adhesionof CuatomsonMgO(001)usingmany electronicstructuremethods,rangingfromvariousformsof densityfunctionaltheoryto post-Hartree-Fockapproaches.Here,the resultsof theB3LYP methodagreedratherwell with the resultsobtainedby thebestpost-Hartree-Fockapproach,whichestimatedthebind-ing energy of theCuatomonMgO(001)to 0.40 ¹ 0.05eV. This is probablythe most accuratetheoreticalestimateof this quantity today. This paperalsoillustratedquitedramaticallythesensitivity of the resultsto choiceofDFT functional,whichshouldsoundanoteof cautionregardingthegeneralapplicabilityandtransferabilityof currentimplementationsof DFT.

In summary, full wavefunctionmethodsarethe mostaccurateab initiomethods,if electroniccorrelationis accountedfor properlyand the basissetfor expansionof theelectronicwavefunctionis sufficiently complete–this might be difficult to judgeby a non-expert. Furthermore,if a clustermodelis used,it needsto beof sufficient sizeor beproperlyembeddedforconclusionsto berepresentative of anextendedM/C interface.

6.2.2. DensityFunctionalTheory For condensedphasesystems,DensityFunctionalTheory(DFT)158,161,162 methodsconstitutetheoptimalcompro-mise betweenaccuracy and efficiency of all ab initio methodsavailabletoday. The key point of DFT is to show that the exact quantummechan-ical total energy º is a functional only of the total electrondensity »²½¼ ,a 3-dimensionalfunction,which correspondsto the intractablemany-bodyelectronicwavefunction¾ , a3N-dimensionalfunctionwhereN is thenum-berof electrons.The total energy within DFT, E[ » ], is relatedto the totalenergy expressedin termsof ¾ , E(¾ ), asº ¾ ¿@ À ¾ f Á ¦ q ¦TÂ B ÁÃ f ¾ÅÄ B H � p@ Æ¦ q ¦¨Â » B Ã Â q ¥Ç H Â ¥ q » B Ã°È Â » ¯B H � p (11)@ º » In principle,DFT is thusaformally exactmeanfield theory. Here H � p is theionic kinetic energy,

Ã Â q ¥� H Â ¥ q is theclassicalmeanfield Coulombenergy


for ionic coresandchargedistribution » , ¦ q ¦¨Â representsthekineticenergyof the (noninteracting)electrons,and

Ã°È Â is a termdescribingloweringofelectron-electronrepulsionby correlatedelectronicmotion andelectronicexchange,aswell asa kinetic energy componentdueto electron-electroninteractions.

Ã°È Â in Eq. (11) is theonly termwhosefunctionalform is notknown exactly: themostcommonlyusedapproximationsto it todayaretheLocalDensityApproximation(LDA) andtheGeneralizedGradientApprox-imation(s)(GGA).149 A varietyof slightly differentGGA parameterizationshave beenproposedover theyears;150–153 indeedthechoiceof which GGAfunctionalto useis anonsystematicaspectof DFT calculations.

A slightly lower level of approximationthantheLDA is theX method,wherethecorrelationenergy is assumedto beproportionalto theexchangeenergy, for which the LDA uniform electrongasexpressionis used. TheX -approximationhasbeenusedfor many pioneeringmetal/ceramicmodelstudies. A consensushasdevelopedin the literature154,160,163–165 that theGGA onaverageis betterthantheLDA. But in certaincases,theGGA tendstoovercorrecttheLDA.166,167 Forionicsurfaces,asignificantloweringof thesurfaceenergy goingfrom LDA to GGA hasbeennoticedin somecases.168

Anothermajordrawbackof theLDA/GGA approximationsin thiscontext isthatthey arenotableto describestronglycorrelatedoxides,suchasmany 3dtransitionmetaloxides.169 Thesecaseswith breakdown of the LDA/GGAare due to two shortcomingsof the LDA/GGA. The first is the generalunderestimationof thebandgap,whichcanbetracedbackto adiscontinuityfeaturein theexchange-correlationpotentialasfunctionof electronfilling162

not capturedby theLDA/GGA. Thesecondis theself-interactionproblemin theLDA/GGA in whichelectronsartificially interactwith themselvesdueto theelectrongasapproximationfor theexchange-correlation energy. Thismay be remediedby consideringa self-interactioncorrection(SIC)170,171

schemeto theLDA/GGA, e.g. theLDA+U method.172

For insulatingmaterials,suchasceramics,this normally doesnot poseproblems,becausetheconductionbandis emptyandthebandgaperror isnot reflectedenergetically. However, for M/C interfacestheremaybesomereasonto worry, sincemixing betweenoxide conductionbandsandmetalstateswill influencethemagnitudeof adhesionandcharge transfer. Thesestatesmay becomefilled, dependingon the Fermi level on the metalside.Furtherresearchon this issueis warranted.

BecauseDFT-basedtechniqueshave the electronicdensity »²½¼ as thebasicvariable,thecomputationalloadscalesmoderatelywith thenumberofelectrons

L, µ¶ L �É¸I� . Thusthey areabletohandlesignificantly moreatomsthantraditionalquantumchemicalapproachesthatretainthefull electronic

many-body wavefunctionasthe basicvariationalquantity. This favorable


scalingcurrentlymakesDFT-basedtechniquesmostpromisingfor ab initiostudiesof M/C interfaces,and thereforewe will emphasizethis groupofmethodsin our review.

6.2.2.1. Applicationsof DFT to M/C Interfaces An increasingnumberof studiesusingself-consistentDFT-basedtechniqueshave beenreportedrecently. The most popularM/C interfaceamongtheoreticianshasbeenAg/MgO(001), due to its small unit cell and small lattice mismatchof3% and hencesimple epitaxial character. Furthermore,this interface iswell characterizedexperimentally. Generally, studiesbasedon electronicstructuremethodsagreethat this interfaceis characterizedby weakphys-ical rather than strongchemicaladhesion,with marginal charge transferto Ag, and the O-siteasmost favorableadsorptionsite.155,156,173–175 TheMgO(001)surfaceis stoichiometric(i.e., thereis an equalnumberof MgandO ionson thesurface)andO is nominally in theO�a¸ charge state.Asalsonotedby Finnis,94 it is interestingto observe the scatteringin adhe-sionenergiesobtainedby differentbasissetexpansions.For Ag adsorbedon top of O(Mg), theFull-PotentialLinearMuffin Tin Orbital (FP-LMTO)methodgives1.59(0.78)J/m� for 3 layersof Ag,176 theFull-PotentialLinearAugmentedPlaneWave (FLAPW) methodgives0.53(0.53)J/m� for 1 Aglayer,174 whereasaGaussian-basedLinearCombinationof Atomic Orbitalsrepresentationgives1.9(1.08)J/m� for 1 Ag layer.177 All of thesestudieswereperformedwithin theLDA, whichis notoriousfor its tendency towardsoverbinding.158 Thisoverbindingtrendis followedfor theAg/MgO system,confirmedby comparingto theexperimentalvalue0.45J/m� for a thick Agfilm.157 Again, this valueis likely to bean averageof alternatingdomainswith Ag adsorbedoverO andMg respectively, dueto misfit dislocationsin-ducedby strain.Thescatterin thetheoreticalresultsis notexplainedby theextentto whichrelaxationsin theinterfaceregionwereincluded;all authorsrelaxed theAg-O distance,andnoneincludedfull relaxationsin theoxide.TheFP-LMTO study176 relaxed theoxide planesperpendicularto thesur-face,theFLAPW studykept theoxidefrozen. ThefreeMgO(001)surfaceterminationdisplaysarumplingof theions;however, ourown DFT calcula-tions,178,179 whichfeaturefull relaxation,show thattheAg-film smoothstheMgO(001)surfacerumpling,sothattheoxidelayernearestto theinterfaceis flat. Furthermore,the oxide interlayerdistancesareasin bulk MgO towithin 0.005 9: . Fig. 5 displaysa repeatedunit cell from our calculationsof anAg layeron top of a MgO(001)surface.Thus,in this particularcase,thestructuralconstraintin theFLAPW studydid notaffect theresults.Thelargevariationsin theoreticalpredictionsremainsanunsatisfyingaspectofthesecalculations.


Figure 5 Ag/MgO(001)chargedensityplot cross-sectionalview.Thereareseven Ag siteson top of the layer of seven O sites. TheMg, with little valencecharge, appearfaintly beneaththe O sites. AnotherO layer andMg layer appearsat thebottom.Thecontourlinesat thetop of theboxarea resultof periodicboundaryconditions.

PolarM/C interfaceshave only beenstudiedsparsely. The polar (111)andnonpolar(100)Cu/MgOinterfaceswerecomparedin aslabcalculationwithin the LDA.180 As expectedfrom the imagemodel theory, the polarinterfacedisplayeda considerablyhigherwork of separation.In additiontheseauthorsfounda largerchargetransferandCu-MgOorbitalmixing forthepolarinterface.


Generally, ab initio methodshave foundthatmetalsadsorbat theO-siteof MgO(001)andthat theMg-sitecorrespondsto a local maximumon theadsorptionpotentialenergy surface(PES),but the accordendshere. ForAg/MgO(001),Honget al.177 andScḧonberger et al.176 find a corrugationof thePESof theorderof 50 % of thecohesive energy whereasLi et al.174

find anextremelyflat PESwith corrugationlessthan1 %. For comparison,for Pd/MgO(001),Goniakowski181 findsacorrugationof order20 %. Thuseventhoughthesesystemsappeareasyto study, thedisagreementuponevenqualitative featuresof theinteractionis ratherdisturbing.

It isaninterestingquestionwhether theGGAimprovestheagreementwithexperiments,asis oftenthecase,or evenchangestrendspredictedwithin theLDA. Weinvestigatedthisby calculatingtheAg/MgO(001)adhesionwithinboththeLDA andGGA, usingstate-of-the-artultrasoftpseudopotentials178

in a converged planewave basis. For Ag adsorbedon top of O(Mg), weobtainadhesionenergiesof 0.62(0.27)J/m� within theLDA and0.23(0.06)J/m� within the GGA. This indicatesthat the GGA overcorrectsthe LDAsomewhat, comparedto the experimentalvalue of 0.45 J/m� .157 Also, asensitivity on detailsof how theGGA functionalis parameterizedhasbeennoticed.160,182

Only recently have other M/C interface studiesappearedthat testedthe GGA in this context. Pacchioniand Rösch183 studiedNi and Cu onMgO(001) in a clustermodel. As might be expected,they found that NibindsmorestronglythanCu, dueto theopend-shellof Ni. In bothcases,the O-siteis favored. They found a significantlowering of the adsorptionenergy for Cu whenusingtheGGA, 0.65J/m� , comparedto thevalue2.54J/m� obtainedrecentlyin a clustercalculationusingtheLDA.184 PacchioniandRöschalsonotedthat in thesecasesmetal-metalbondswerestrongerthanmetal-substratebonds,thuspredictinga 3D (cluster)growth modeasopposedto layer-by-layer growth (wetting). A more systematicstudy oftransitionmetaladsorptiononMgO(001)usingGGA waspresentedby Yu-danov et al.,175 usinga clustermodel. Interestingly, they foundno obviouscorrelationbetweencohesionandd-bandfilling asindicatedby otherstud-ies. They foundthatsingleCu, Ag, Au, Cr, andMo atomsexhibitedweakinterfacebonds,whereasNi, Pd,PtandW atomsformedstrongbonds.ForAg/MgO, they obtained0.36J/m� , similar to ourfindingsfor acoherentAgmonolayer.

Square-planarM � clusteradsorptionfor M =(Ni, Cu,Pd,Ag) onMgO(001)hasbeenstudiedwithin theGGA.185 Althoughhereopenshell transitionmet-alsadsorbedstronger, metal-metalandmetal-oxidebondcompetitionwerefoundto becomplex. An extensive studyof Cu growth on MgO(001)wasperformedfor clusterswith 1-13Cuatoms.186 Hereagain,theauthorsfound


themetal-metalbondsstrongerthanthemetal-ceramicbonds,thusfavoringa 3D (cluster)growth mode. Relatively weak cohesionfor the Cu/MgOinterfaceis alsoexpectedon thebasisof the large latticemismatch(13 %)betweenthemetalandceramic.

Electronicstructurecalculationsof metal/Al� O� interfaceswereinitiatedbyJohnsonandPepper.187 They modeledthisinterfacewith ametal-AlOÊÌË ¸clusterusingtheX -method,with themetalatomadsorbedin anO-triangleemulatingahollow siteonaO�^¸ -terminatedsurface.Thisstudyconcludedthebondingbecameweaker asthetransition-metaladsorbatebecamemorenoble,whichwasexplainedin theconventionalorbitalmixingpicture,whereantibondinglevelsbecomefilled in therightsideof thetransitionseries.Thispicturewasessentiallyconfirmedby laterinvestigators.MostauthorsfocusontheO-terminated D Al � O� (0001)surface,whichisnonstoichiometric, asthesubstratefor metallicgrowth. Underoxygendeficientconditions,how-ever, it isnotclearthattheO-terminationisappropriatefor growthmodeling.GrazingincidenceX-ray scatteringdataindicatethatthe D Al � O� (0001)isAl-terminatedunderultrahighvacuum(UHV).188,189Furthermore,DFTcal-culationspredictthatthecharge-neutralO-terminated D Al � O� (0001)hasasignificantlyhighercleavageenergy190 thanAl-terminated D Al � O� (0001).Experimentally, whenNi wasdepositedon D Al � O� in UHV, noNi-O inter-actionwasdetectedby XPS.191 It is certainlyreasonableto considerNi-Albonds,sinceNiAl is a very stablealloy. In any case,discussionsaboutwhich Al � O� -substrateterminationat the cleanmetal/Al� O� interface ismostrelevantcanbesomewhatacademic,sincereactionphases,likespinels(MAl � O� ),192 areoften formedat the interface. Our point of view is thatmost structuralpossibilities,at this stage,are interesting,sincethey helpto furnish a generalunderstandingof the electronicstructureof the M/Cinterfaceundervariousconditions.

We have usedDFT to study the Ni/Al � O� interface. Thesecalcula-tions wereperformedwithin the planewave DFT codeVASP using ultra-soft pseudopotentials.178,193 Calculationswith oneand threelayersof -Al � O� depositedonto the Ni(111) surfacewere performed. Both Al andO terminationsof the -Al � O� (0001)surfacewereexamined. Fig. 6 dis-playsa repeatedview of a unit cell with relaxed atomiccoordinatesfor aNi(111)/Al� O� (0001) interfacecalculation. The lighter atomsin the toplayer correspondto aluminumand the darker atomsare oxygen. In theAl-terminated -Al � O� (0001)surfaces,it appearsthat interfacial bondingbetweenthe alumina and Ni substratedecreaseswith increasingAl � O�thickness.This effect may contribute to the increasedspallationobservedexperimentallywith thethickeningof theTGO.


C BO

A

Z

X

Y

4: 3_3_rel

Figure 6 Ni(111)/Al _ OÍ (0001)relaxedinterfacegeometryKruse et al.194,195 studiedNb monolayers(and multiple Nb layers to

simulatebulk-like properties)on theO-terminated D Al � O� (0001)surfaceandfound that Nb bondedto the hollow sitesabove the vacantoctahedralsites. Theseauthorsemphasizedthe importanceof ion relaxationswhencomparingcompetingadsorptiongeometries,afeatureoftenlackingin manyreportedstudies.

We have also undertaken studiesof the Ni/ZrO � interfaceagainusingultrasoftpseudopotentialswithin theVASPcode.178,196 Up to threelayersofcubicZrO� (111)were“deposited”ontotheNi(111)substrate.As wefound


for theNi/Al � O� interface,thework of separation(or adhesionstrength)isquite large for the first monolayer;and,asmoreZrO� is added,the intra-ceramicbondsincreasein strengthat theexpenseof theinterfacialbonding.Theadhesionstrengthis halvedby thetimethat3 layersof ZrO� arepresent.We find significantatomic distortionsat the interface and a suppressionof magnetismin the Ni layersnearestto the interface. The decreaseinadhesionasZrO� grows on Ni is consistentwith the needfor a bondcoatalloy, sinceourpredictionssuggestthick ZrO� films maynot readilyadhereto theNi-basedsuperalloy undertheTBC.

6.2.2.2.Aplicationsof DFT to Ceramics We have alsostudiedbulk ZrO�in the monoclinic,tetragonal,andcubic phasesaswell astheir associatedlow-index surfaceswithin theLDA to DFT.48 Wefoundthatthemoststablesurfacesof tetragonal(t)andmonoclinic(m)zirconia- thet(111)andm(1̄11)surfaces- are nearly degeneratein their surfaceenergies. This providesanexplanationfor thepreferentialstabilizationof t-ZrO� in smallparticles,wheresurfaceenergiesratherthanbulk cohesive energiesshoulddeterminethe preferredstructure. By usinga Wulff construction197 andknown ori-entationrelationshipsbetweenthe t andm phases,we showed that t(111)surfaceswill transformto half m(1̄11)andhalf m(111)surfacesuponphasetransformation.While the m(1̄11) surfacesarelow in energy, the m(111)surfacesarepredictedto have somewhat higher energies. Thus, we sug-gestedthat thesuppressionof thetetragonalto monoclinicphasetransitionin smallparticlesmaybedueto thethermodynamicallyunfavorablenatureof m(111)surfacesthatwould beforcedto form. This ideapromptedustoconsiderwaysto keepZrO� in the tetragonalphaseover a very wide tem-peraturerange.Onepossiblesolutionis to embedthesmallZrO� particlesin an aluminamatrix, for example,asin the ideabehindthenanolaminatefilms comprisedof ZrO� andAl � O� multilayers.

We thenundertooka DFT-GGA study(within theProjectorAugmentedWave formalism)198 of the ZrO� -Al � O� interface, in order to understandhow aluminamight serve thispurposeof confining/stabilizingsmallt-ZrO�particlesandto shedlight on thenatureof theinteractionbetweenthebondcoatandtheTBC thatoccurswhenthebondcoatis oxidizedto Al � O� .199

Our main conclusionsare that the alumina/zirconiainterfaceis weaklyinteracting: we find negligible charge transfer, no evidenceof covalentbonding,anda very low adhesionenergy of 1.065J/m� . Thelow adhesionenergy is probablydue to the fact that thesesurfacesof ZrO� andAl � O�reconstructto obtainapproximatecoordinative saturation,andthereforethelackof danglingbondsonthesesurfacesminimizestheinteractionthey havebetweenthem.Thissuggeststhattheroleof theAl � O� in thenanolaminatecoatingsis simplyto actasaphysicalbarrierto growth of theZrO� layerand


that thereis no true chemicalbondin

atomic-level properties of thermal barrier coatings ...atomic-level properties of thermal barrier...

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