Analysis and application of the theories that rationalize the crystalline structures of fluorite-related rare earth oxides
Abstract
The main current theories dealing with the crystalline structures of the fluorite related rare earth oxides, including those corresponding to reduced oxides, one based on the distribution of the coordination defect inside the fluorite structure, and the other which proposes the establishment of modular sequences constituted by modules with fluorite structure, are presented and comparatively explored in detail. Our in-depth analysis of both approximations indicates that they in fact provide smart and efficient rationalizations of the currently known intermediate rare earth oxides structures. We prove however that the strict application of the principles and rules proposed by each theory does not yield unique and unambiguous results for most of the members of the homologous series, as it has been claimed up to now. Moreover, the controversy about the reliability of these two, apparently different and competing, theories is definitely clarified and the exact equivalence of their structural predictions is demonstrated. Finally, we propose new extra systematization rules, not considered up to now in neither of these theoretical approaches, to overcome the observed limitations to properly rationalize the structure of this so technologically important family of oxides.
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1 Post‐printof:CatalysisTodayvolume180,Issue1,17January2012,pages161–166 Analysisandapplicationofthetheoriesthatrationalizethecrystallinestructuresoffluoriterelatedrareearthoxides C.López‐Cartes(a),J.A.Pérez‐Omil(b),J.M.Rodríguez‐Izquierdo(b),J.J.Calvino(b) aDepartamentodeQuímicaInorgánica,InstitutodeCienciadeMaterialesdeSevilla,Centro MixtoUniversidaddeSevilla‐CSIC,AvdaAméricoVespucio49,41092Seville,Spain bDepartamentodeCienciadeLosMaterialeseIngenieríaMetalúrgicayQuímicaInorgánica, FacultaddeCiencias,UniversidaddeCádiz,11510PuertoReal,Cádiz,Spain Abstract Themaincurrenttheoriesdealingwiththecrystallinestructuresofthefluoriterelatedrare earthoxides,includingthosecorrespondingtoreducedoxides,onebasedonthedistribution ofthecoordinationdefectinsidethefluoritestructure,andtheotherwhichproposesthe establishmentofmodularsequencesconstitutedbymoduleswithfluoritestructure,are presentedandcomparativelyexploredindetail.Ourin‐depthanalysisofbothapproximations indicatesthattheyinfactprovidesmartandefficientrationalizationsofthecurrentlyknown intermediaterareearthoxidesstructures.Weprovehoweverthatthestrictapplicationofthe principlesandrulesproposedbyeachtheorydoesnotyielduniqueandunambiguousresults formostofthemembersofthehomologousseries,asithasbeenclaimeduptonow. Moreover,thecontroversyaboutthereliabilityofthesetwo,apparentlydifferentand competing,theoriesisdefinitelyclarifiedandtheexactequivalenceoftheirstructural predictionsisdemonstrated.Finally,weproposenewextrasystematizationrules,not considereduptonowinneitherofthesetheoreticalapproaches,toovercometheobserved limitationstoproperlyrationalizethestructureofthissotechnologicallyimportantfamilyof oxides. Keywords Oxideswithfluoritestructure;Lanthanideoxides;Coordinationdefect;Modularsequence 1.Introduction Theoxidesoftherareearthsingeneral,andmorespecificallyceriumoxides,eitherpureor mixedwithatransitionelementorasecond4felement,havebeenusedinawidevarietyof applicationsinthefieldsofheterogeneouscatalysis[1]and[2],fast‐ionoxygenconductors[3] orchemicalsensors[4].Theinterestingfunctionsofthesematerialsstemfromthefactthat someoftheseelements(Ce,TbandPr)havetheabilitytostabilizeboth+4and+3oxidation stateintheiroxides. Thelanthanideelement‐oxygenbinarysystems,andthediagramphasescorrespondingto oxygen–cerium,praseodymiumorterbiumhavebeenwellestablishedforcompositions
2 rangingfromthesesquioxides(Ln2O3)tothedioxides(LnO2)[5].Forthesesystems,withinthe hightemperatureregion,twodisorderedareasarefound,onecalledσforoxygen/lanthanide ratiosfrom1.5to1.7,andasecondonenamedasαinthecompositionratiosfrom1.7to2.0. Atlowertemperatures,αregionyieldsavarietyofapparentlynon‐stoichiometricphases.The wholesetofthesephases,withgeneralformulasLnnO2n−2m,isknownasthehomologous seriesofrareearthoxides.Thefirstmemberofthisseriesofreducedlanthanideoxidesisiota phase(ι)whoseformulaisLn7O12,anditisfollowedbycompoundswithformulaeLn9O16 andLn11O20,zeta(ζ)anddelta(δ)phasesrespectively. EarlyX‐raystudiesofsomeofthemembersoftheseries[6]clearlyshowedtheclose relationshipofthesephasestotheparentfluoritestructureofthefullyoxidizedphases(LnO2), butnoreasonableresultswereachievedtodeterminetheirstructuresfromsinglecrystalX‐ray diffractiondata.Fortunately,theapplicationofHighResolutionElectronMicroscopyand ElectronDiffractiontechniqueshasbeenverysuitabletoconfirmtherelationshipwiththe fluoritestructureofthedioxides,andtoobtaintheunitcellparametersofthestablephases thatcouldbeprepared[7],[8]and[9].Morerecently,thestructuresofsomeofthemembers ofthehomologousserieswerefurtherrefinedbyhigh‐resolutionneutronpowderdiffraction [10],[11],[12],[13]and[14]. Giventherelevanceofredoxprocessesinthecatalyticactionoftheseoxides,rationalizingthe structureofthemembersofthehomologousseries,i.e.improvingourknowledgeaboutthe basicprincipleswhichgoverntheaccommodationofoxygendeficiencyintheseoxides,seems ofutmostimportancetounderstandtheirmacroscopicperformance. Afirstattempttorationalizethestructuralprinciplesoftheseseriesofoxidesarguedthat oxygenvacanciescouldnotbepresentaloneinthecrystalbut,instead,thattheyshould interactanddistributeinspaceintheformofvacancypairsalongthe〈111〉directionof thehostfluoritestructure[6].Accordingtothisidea,alltheobservedstructureswouldthenbe basedontheso‐calledBevancluster.Athightemperaturetheseclusterswouldberandomly distributedinthestructure,butatlowertemperaturetheywouldorderincrystallographic planesparalleltothe〈135〉reciprocaldirectionofthefluoritestructure,togeneratethe membersofthehomologousseries[7].Therefinementofthestructuresbyneutrondiffraction studiesclearlyshowedthatoxygenvacanciescanbeaccommodatedbypairsforthehighly reducedphases,butthattheywerepresentassinglevacanciesintheoxygen‐richmembersof theseries.Aftertheseresults,thedifferentmodelsproposedtorationalizethestructuresof thereducedphaseshadtoberevisited. Inthispaper,tworelevanttheoreticalmodels–thecoordinationdefectmodelbyMartinand co‐workers[15],[16],[17],[18]and[19],andthemodularsequenceoffluoritestructure modulesmodelbyEyringandco‐workers[20],[21],[22]and[23]thattrytoestablishsome basiccriteriatounifythewholesetofknownstructuresinthefluoriterelatedoxidesare comparativelyanalyzedandtheirsimilaritiesandlimitationstopredictthestructureofthese oxidesdiscussed. Themotivationofthisworkwas,ontheonehand,todefinitelyclarifytheon‐going controversysetoutbytheauthorsoftheabovementionedtheoriesaboutthesuitabilityof theirmodelsinsolvingandpredictingthecrystallinestructuresoftheintermediateoxides.
3 Thus,themajormistakesinthewaytheCoordinationDefect(CDT)andtheModularSequence (MST)theorieshavebeenappliedwillbediscussedindetail.Giventhatouranalysisrevealed limitationsinthepotentialofbothmodelstounivocallydeterminetheexactarrangementof oxygenvacanciesinthestructureofbothknownandunknownmembersofthehomologous seriesofreducedoxides,wealsoaimedatfindingoutadditionalcriteriatocomplete satisfactorilythistask. 2.Discussion 2.1.Coordinationdefecttheory(CDT) AccordingtothetheoryproposedbyMartinandco‐workers[15],[16],[17],[18]and[19],the vacantpositionhasnotindependentexistenceinthefluoritestructure.Onthecontrary,itis stronglycoordinatedbysixnearneighboringO2−anionswhichformanoctahedralstructural entity□O6.Thisentywhichhasasignificantthermodynamicstabilitywascalledcoordinaon defect(CD).ArepresentationofthisstructuralunitisshowninFig.1.Takingintoaccountthat eachsmallcubethatconstitutestheCDisanoctantofthetotalfluoriteunitcellofLnO2,its compositionisgivenbyLn3.5O6.TheCDbasicunitisconsideredinthistheoryasthebuilding blocktoobtainthestructuresofthemembersincludedinthehomologousseriesofrareearth elementoxides.Asdepictedinthefigure,theoctantscanpresenttwodifferentorientations withrespecttothelanthanidecationsublattice,andthereforethecoordinationdefectcould haveeitherλorδorientation.Anotherimportantaspectofthetheoryisthetopological restrictionsthatlimitthewayinwhichthecoordinationdefectscanbedistributedinsidethe fluoritestructuretooriginatetheorderedreducedphase.Theshortestdistancebetweenthe centersoftwoadjacentCDslocatedatdifferent{001}Foctantlayersis1/2〈111〉F,Fig.2d. Aclosepackingofcoordinationdefectsinthisarrangementyieldsthestructureofiotaphase (Ln7O12)whosecompositionisequaltothatofthebasicunit.Inthesameoctantlayerthe closestdistributionoftwoCDscorrespondsto1/2〈120〉Fdistance,Fig.2a. Onthebasisofthistheory,theauthorsproposedthewayinwhichbothknownandunknown structurescouldbeobtained[19].Thestartingpointinvolvesrepresentingaunitcellintwo dimensionsandusingasinglelayerofoctantswhichisinagreementwiththecrystallographic dataoftheknownphaseandwithitschemicalcomposition.Thevacanciesrequiredtomatch thestoichiometryofthephasearethenaddedintheformofcoordinationdefectsfollowinga seriesofrules.Theresultingstructuresforiotaandzetaphases,themembersofthe homologousserieswithnequalto7and9respectively,asdescribedintheoriginalpaper,are showninFig.3.Inthisrepresentation,thestructuresareobtainedviewedalongthe〈001〉 Forientation.Thelabels(+,−,2+)indicatetheheightofthedifferentCDswithrespecttothose locatedatthecornersoftheparallelograminthebaseoctant{001}Flayer.Byapplyingthe rulescitedabove,onlyonestructureispredictedfortheiotaphase,whichisingood agreementwiththerefinedstructure[13].However,thisisnotthecaseforzetaphase.For thislaststoichiometrytwomodelsemergefromtheapplicationofCDT:aso‐calledmodel4,in whichthevacantsitesareorderedasstringsalong〈111〉Fdirection,andamodel8/17 whichpresentsdiscretepairsofvacantpositions. 2.2.Modularsequencetheory(MST)
4 ThesecondtheorythatisdiscussedinthisworkwasproposedbyEyringandco‐workers[20], [21],[22]and[23].Theseauthorsassumethatallthestructuresofthehomologousseriescan beobtainedbyorderingso‐calledmoduleswithfluoritestructure.Eachofthesemodules, exceptthatnamedasFmodule,isdeficientinoxygen,theyallcontaininginsidenotmorethan twovacancies(seeFig.4).AccordingtotheprinciplesofMST,thegenerationofoxygen vacanciesinvolvesthecreationofbothchargecentersanddipolarmomentswhoseintensities andspatialorientationsdependonthenatureofthemoduleconsidered.Theordered distributionofthedifferenttypesofmodules,whichinthistheoryisreferredastomodular sequence,willtrytocompensatetheselocaldipolarmoments.Thus,toestablishthemodular sequenceforaparticularphasetherearesomeforbiddendistributionsofadjacentfluorite modules.ExamplesofallowedandforbiddensituationsareshowninFig.5. Inthistheorytheauthorsusethe〈112〉Fprojectiontorepresentthedifferentstructures becausethisdirectioniscommonfortheprincipalc‐axesofallthemembersofthe homologousserieseitherwithknownstructuresor,atleast,phaseswhosecellparameters havebeenestimatedbyelectronmicroscopystudies.Usingthecellparametersofaspecific phase,andtakingintoaccounttheequalprobabilityoftheeightoxygenpositionsinsidethe fluoriteunitcelltogeneratetherequiredvacancies,themodularsequenceofastructurewith formulaLnnO2n−2mcanbeobtainedbyorderinganumberofnmodulesalongthemain fluoritedirections.Themodularsequencesforiotaandzetaphases,andtheirrepresentations alongthe〈112〉Forientation,arerepresentedinFig.6.Thesestructureswerereportedby theauthorsasthoseresultingfromtheonlypossiblemodularsequencethatcanbeobtained foreachofthesephases.Theseproposedstructuresareinperfectagreementwiththerefined crystallographicdataobtainedbyneutronpowderdiffraction[10]and[13]. 2.3.AnalysisofCDandMStheories Inthissectionadetailedanalysisofthewayinwhichtheauthorsofthetheoriesapplythe rulestheyproposetoobtainthestructuresofbothknownandnotrefinedstructuresiscarried out.Ascommentedbefore,tryingtosolvethecontroversyaboutthereliabilityoftheexposed theoriesisthemainmotivationofthisanalysis. Thefirstaspectworthmentioningisthefactthat,duringthestructurebuildup,theauthorsof thetheorybasedontheCDdidnotpayattentiontotherelativeorientationofthisvacant entitywithrespecttothecationsublattice.ThisideaisillustratedinFig.7.TheschemeinFig. 7arepresentsthedistributionofvacanciesfortheiotaphase,consideringδorientationforthe coordinationdefectlocatedatthecorneroftheunitcell.Ontheotherhand,inFig.7b,aλ typeorientationhasbeenusedforthevacantsitesattheoriginoftheunitcell.Thedetailed analysisofbothschemesrevealsthattheycorrespondtothesamemodel,thatcorresponding totherefinedcrystallinestructureforiotaphase,inwhichtheoxygenvacantpositionsare interconnectedbyintermediatemetalcationsitesinthefluoritestructure,leadingtopairsof vacancies. Thisisnotthecaseforthemodelsproposedforthezetaphase.Twomodels,labeledas4and 8/17respectively,werefoundfortheLn9O16stoichiometrybyapplyingtherulesproposedin theframeworkoftheCDT.Thus,Fig.8showstheresultofchangingtherelativeorientationof thecoordinationdefectattheoriginoftheunitcell.AsrepresentedinFig.8aandb,the
5 applicationoftheCDTtomodel4,asitalsooccursinthecaseofiotaphase,resultsonlyinone structure,withindependenceoftheorientationofCDswithrespecttothecationsublattice. Theoxygenvacantpositionsarealsointhiscaseconnectedbyanintermediatemetalatomof thecationsublatticeinbothschemes.However,forthemodel8/17,themodificationofthe orientationfromλtoδinthecoordinationdefectattheoriginofthecell,yieldstwodifferent structures,Fig.8candd.Thedifferencebetweenthemistherelativepositionofthepairsof vacancieswithrespecttothemetalcationsublattice.Consequently,notonlytwomodels(4 and8/17)canbeproposedforzetaphase,butalsothreedifferentstructurescouldbe predictedbycorrectlyapplyingtheprinciplesandrulesofthetheory. Similarresultsareobtainediftheanalysisiscarriedoutfordeltaphase,Ln11O20.Forthisless reducedstoichiometry,insteadofthethreemodelsproposedbytheauthors,labeled4,9/16 and6/19respectively[19],fivedifferentstructuralmodelscanbepredictediftherulesare correctlyapplied. Afterthisanalysis,itseemsclearthatthestructuralpredictionforthemembersofthe homologousseriesbythecoordinationdefecttheoryisuniqueonlyforthemostreducedone, iotaphase.Theapplicationoftherulestoanyotherofthephasesproducesmorethanone possiblestructurethatfullyfollowstherequirementsofthetheory. AnalogousresultsareobtainedwhentheprinciplesoftheMSTarestrictlyappliedtothe predictionoftheintermediateoxidestructures.Apartoftheiotaphase,thatgivesasingle modularsequencematchingquitewelltherealstructureobtainedbyneutrondiffraction technique,theapplicationofthissecondtheorytoanyothermemberoftheseriesdoesnot originateasingleandunambiguouspredictedstructure.Thisfactisclearlycontradictorywith theideapostulatedbytheauthorsintermsofitsvaliditytodirectlyelucidate,withoutany otherconsideration,therealstructureofanyknownorunresolvedcrystallinephase.To illustratethisidea,inFig.9twomodularsequencesdifferenttothatoriginallyproposedinthe literatureforzetaphaseareshownwhichalsofullycomplywiththesetofrulesestablishedby MST.ThesetwonewpossiblestructuresforLn9O16phaseareconsistentwiththeunitcell parameterscharacteristicofthisphaseandcoherentwiththephenomenologicalprinciplesof thetheory.Thedistributionsofthevacantoxygenpositionsinsidethefluoritelatticeareinthis casedifferenttothatobservedintheoriginalmodularsequencedeterminedforzetaphaseby theauthorsofthetheory.Similarconclusionscanbeobtainedfromtheanalysisofthedelta phase,inthiscasebeingpossibletodistributethefluoritestructuremodulesnecessaryto accountforitsstoichiometryinfivevalidanddifferentmodularsequences. 2.4.Comparisonofthetheories Intheprevioussectionithasbeenprovedthat,withtheexceptionoftheiotaphase,the applicationofthesetofrulesofeithertheCDortheMStheoriesdoesnotresultformostof thestoichiometriesofthereducedintermediatephasesinasinglestructuralpredictionbut, instead,inasetofpossibilitieswhichagreewiththelatticeparametersdeterminedfrom diffractiondatabutthatdifferinthedetailsofthedistributionofoxygenvacancies.Moreover, thenumberofpossiblestructuralmodelsincreasesasthereductiondegreeofthe intermediateoxidedecreases,being,forexample,threepossiblestructuresforzetaphaseand fivefordelta.
6 Takingintoaccountthatboththeoriesgeneratethesamenumberofpredictedstructures,an interestingquestiontobesolvediswhetherornottheyareequivalent.Toclarifythiscrucial point,inFig.10themodelscomingfromtheCDTforiotaandzetaphases,alreadypresentedin Fig.3andFig.8,havebeentranslatedintothemoduleswithfluoritestructureusedinthe MST.Followingthecolumnsandrowsofthisfigure,whichcorrespondtothe[100]and[010] directionsinthefluoritematrix,itiseasytorealizethattherearestraightcorrespondences betweenthestructuralmodelspredictedbybothmodels.Model4forzetaphase(Fig.7a), whichistranslatedintermsofamodularsequenceinFig.10b,isexactlyequivalenttothe structureshowninFig.9a.Followingthesameargument,models8/17consideringλorδ orientationfordecoordinationdefectlocatedattheoriginoftheunitcell,areequivalentto themodularsequencesshowninFigs.10aand6b,respectively. Consequentlyitisdemonstratedthatboththeoriesoriginatethesamenumberofpossible modelsforaspecificphaseandthereisaonetoonecorrespondencebetweenthemodels predictedbythetwotheories.Therefore,boththeories,thoughstartingfromdifferentbasic structuralconceptsdrivetoexactlythesamestructuralpredictions.Moreover,inneithercase auniqueandunambiguouspredictioncanbeproposedformostoftheintermediatephases. Thekeyunsolvedquestionthatlimitstheapplicabilityofanyofthesetheoriesis:whatarethe additionalfactorsthatdriveaparticularstoichiometrytochoosebetweenoneofthedifferent possibilitiespredictedbythesetheories?Theanalysisofthepredictedstructuresandthe comparisonofthedistributionofoxygenvacancieswiththatobservedintheRietveldrefined crystallinestructureshelptoputforwardreasonableproposalstoanswerthisquestion. Forthatpurpose,thedistancesbetweentheoxygenvacanciesfordifferentmodelshavebeen calculated.Table1gatherstheresultsofthecalculationcarriedoutonthethreepredicted modelsforzetaphase.ThemodelshavebeenlabeledinthisTablefollowingthenomenclature proposedintheCDapproximation.Allthedatainthistableareexpressedasvectorsinthe fluoritecubicstructure,sothedistancesbetweenvacanciesareequaltohalfthemodulusof eachvectorinthetable.Theanalysisofthedatacontainedinthetableleadstotheideathat inmodel8/17theoxygenvacanciesaremorespreadthatinmodel4.Inthelatter,every vacancyhastwoothersdefectsatadistanceequalto1/2〈111〉F.For8/17modelsonlyone vacancyislocatedatsuchdistance. Theseresultsthereforesuggestthatanoverallmaximizationofdistancesbetweenvacanciesis akeyfactorwhichinfluencesthefinalstructuralchoice.Thisconceptneedshoweverbe refinedsincethereisnotanydifferenceintherelativedistributionofthecoordinationdefects oroxygenvacanciesbetweenthe8/17(λ)and8/17(δ)models.Thedifferencebetweenboth modelsisjusttherelativepositionoftheoxygenvacancieswithrespecttothemetalcation sublattice.Inthe8/17(λ)modelthepairofvacancieslocatedat1/2〈111〉Fdistancearenot connectedbyametalatom.Howeverinthe8/17(δ)modelbothvacanciesareseparatedbya cationofthestructure. Whenthepredictedmodelsarecomparedwiththerefinedatomicpositionsforzetaphase [10],itisobservedthatthe8/17(δ)modelistheonethatreproducestherealstructureandit consequentlymustbeconsideredtheonedescribingthemostprobableorderingofoxygen
7 defectsinzetaphase.Similarresultsareobservedwhenananalogousanalysisiscarriedout fordeltaphase. Atthispointitispossibletoestablishthensomeadditionalrulestocompletetheequivalent CDandMStheoriesthatallowusdeterminingthemostprobablestructureforanymemberof thehomologousseries,irrespectivethatsuchstructurehasbeenrefinedbydiffraction methodsornot. Amongthesetofpredictedmodelsforaspecificstoichiometryandcrystallographiccell parameters,themostprobablestructurewouldcorrespondtotheonethatmaximizesthe distancesbetweenadjacentoxygenvacancies.Therefore,forthosememberswhose stoichiometrycorrespondstoalowreductiondegree,theoxygenvacancieswilltendto distributeinthestructureassinglevacanciesinsteadofgroupingintopairs. Whendistancesbetweenvacanciesaretheshortestpossible,1/2〈111〉F,andare consequentlydistributedbypairsinsidethestructure,themostlikelystructurewillbethatin whichthesevacanciesareinterconnectedbyametalatom. 3.Conclusions Thetwotheoriescurrentlyavailabletorationalizethestructuresofthereducedintermediate phasesofRareEarthOxideswithfluoriterelatedstructureshavebeenanalyzedindepth.We haveprovedthatthestrictapplicationofthebasicrulesofboththeories,somethingwhich surprisinglyhasbeenmissedinpreviouslyreportedworks,drivestoidenticalstructural predictionswithindependenceoftheparticulartheory,CDTorMST,used.Thereforeboth approachesarefullyequivalentanditdoesnotmakeanysenseatalltomaintainthe controversyaboutwhichofthemismorepreciseasstructuralpredictivetool.Moreover,with theonlyuseofthesetofrulesestablishedbyanyofthesetheories,inmostcasesitisnot possibletoarrive,startingfromaparticularstoichiometry,toauniquemodelwhich unambiguouslypicturesthedistributionofoxygenvacancieswithinthefluoritematrixbut, instead,tosetsofpossiblestructures.Thenumberofcandidatestructureswithinthesesets increasesasthetotalnumberofvacanciesintheunitcelldecreases,i.e.asreductiondegree decreases. Twoadditionalcriteriahavebeenaddedinthisworkwhichfinallyallowsusselectingoneof thepossiblestructureswithinthesesetsasthatexperimentallyexpected.Withthisultimate addition,anyofthetheories,MSTorCDT,becomeintosuccessfulpredictivetools. Inrelationtotheseextrarules,ouranalysissuggeststhatboth,theexactdistributionof distancesbetweenoxygenvacanciesandtherelativepositionofthesevacancieswithrespect tothemetalcationsublatticearekeyfactorstodecideonthemostadequatespatialpattern toaccommodateoxygendeficiencyinthisfamilyofoxides. Thestructureofallthemembersofthehomologousserieswhichhavebeenrefinedby diffractionmethodscanbesatisfactorilyexplained,rationalized,onthebasisofthisexpanded versionofanyoftheavailabletheories.Moreover,withthistoolwecannownotonlypropose
8 modelsforthosememberswhosestructureiscurrentlyundeterminedbutalsotousethese modelsasinitialguesses,inputdata,forDFTcalculations. Acknowledgements WeacknowledgefinancialsupportfromMICINN‐FEDER(Proj.Ref:MAT2008‐00889‐NANand CSD2009‐00013)andJuntadeAndalucia(TEP217andFQM334).
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