Solid StateCommunications,Vol. 37,pp.901—906. 0038—1098/81/110901—06$02.00/0PergamonPressLtd. 1981.Printedin GreatBritain.

TEMPERATUREAND COMPOSITIONDEPENDENCEOFVIBRATIONAL MODES IN Sm1.~La~A1O3

P. Alain

U.E.R.SciencesFondamentaleset Appliquees,Universitéd’Orléans,andCentrede Recherchesur la PhysiquedesHautesTemperatures,CentreNationalde la RechercheScientifique,45045OrleansCedex,France

and

B. Piriou

LaboratoiredesElementsde Transitiondansles Solides,E. R. 60210,CentreNationalde la RechercheScientifique,1 PlaceA. Briand,92140Meudon-Bellevue,France

(Received14January1980;in revisedform 3 October1980 by M. Balkanski)

At room temperatureandfor x0 ‘~ 0.43, thesystemSm1_~La~A1O3undergoesa first orderphasetransitionin which anorthorhombicstruc-ture transformsinto a rhomboedralstructureasx increases.This phasetransitionwasinvestigatedby Ramanscatteringexperimentson poly-crystallinecompoundsin the range0 ~ x ~ 1. The dependenceof lowfrequencymodesonx is reportedandcomparedwith their well knowntemperaturedependence.Soft modeshavebeenobservedin the orthor-hombic (D~)andrhomboedral(D~)phases.It wasfound that thefirstorderphasetransitionis probablydrivenby a doubledegeneratemodewhosetwo componentsin the low symmetryphasedisplaya linearcompositiondependenceof their squaredfrequencies.The sourceofanomalousbehaviourof Ramanbandsnear the phasetransitionisdiscussed.

1. INTRODUCTION increases,or asthe temperatureis raised.Furthermore,

ONE OF THE MOST interestingaspectsof lattice the transitiontemperaturesdecreaseasthelattice dis-dynamicsof rare earthaluminatecompoundsis the tortion diminishes.Since thestructuralfeaturesareoccurrenceof severalstructuraldistortionswith respect dependenton the meanionic rare earthradiusonemayto the idealcubicperovskitestructureof which the expectto observethe first orderphasetransitionin thestability is dependenton the temperatureandthe ionic solid solution Sm1_~La~AlO3at room temperature.Inradiusof therare earthelement.For compoundscon- otherwordswe supposethat Sm

3~andj~3+arestatistic-cernedherethe lowesttemperaturephaseis orthor- ally distributedin thelattice,the overall effectbeinghombic(D~),which may transformto the trigonal that of anaveragecation,with a meanradiusequaltophase(D~d)by a first order transitionat temperature xrLa + (1 — x)rsm.X-raymeasurementsshowthat the

T0. At higher temperaturethis latterphasetransforms solid solution Sm1_~La~AlO3exhibits thetwo phases

to the cubic structure(O,) by a secondordertransition foundin theseriesof purerare earthaluminatesatat temperatureT~.Thus at roomtemperatureSmA1O3 roomtemperature.Thesolid solutionis continuoushasanorthorhombicstructureandundergoesa first overthe wholecompositionrangeand theexpectedordertransitionat aboutT0 = 1050K, whereasLaA1O3 first orderphasetransitionoccursfor T = 300 K atof trigonal structureat room temperaturetransforms x = -~ 0.43.MoreoverX-ray analysisshowsthatain cubicstructureat T~ 800 K. Thechangein struc- singlephaseis present,with orthorhombicstructurefortureandassociatedsoft modebehaviourhavebeen x ~ 0.40, and rhombohedralfor x ~ 0.45.No group—extensivelystudiedby hightemperatureRamanscatter- subgrouprelationscanexist betweenD3d andD2hing on singlecrystals [1—3]. Unfortunatelyit wasnot symmetries,sothephasetransitionis necessarilyofpossiblein most casesto obtain accurateRamanspectra first order.This changeof structureis similar to thaton thehightemperaturephase,henceabovethe tran- observedin SmA1O3 with increasingtemperature[3].sition temperaturethe latticevibrationsare poorly It suggeststhat the studyof the systemSm1_~La~AlO3characterized. may leadto a betterunderstandingof this phasetran-

Thecommonfeatureobservedfor all thecompounds sition in orthorhombicrareearthaluminates.is that distortiondecreasesasthe ionic rare earthradius

901

902 VIBRATIONAL MODES IN Srn1~La~A1O3 Vol. 37,No. 11

x~.15 /V i’

x=.2 I

~J/J~)I

TH~TT~±~~I I

250 200 ISO 100 50FREQUENCY (cm

1

Fig. 1. Low frequencyRarnanspectraof Srn1_~La~AlO3for differentcompositionsx.Thearrowsindicatethe

positionof theA~soft mode,denotedby C’ in rhombohedralphase(xo <x <1), andof thecorrelatedAg modedenotedby Cm orthorhombicphase(x <xo). The spectraarevertically shifted by different amounts.

Therefore,it is of considerableinterestto determine In this paperwe reportsomelattice dynamicalwhetherthe structuraltransitionsof the mixed corn- aspectsof thesystemSrn1_~La~AlO3.We studiedthepoundareassociatedwith the softeningof opticalmodes, concentrationdependenceof the opticalmodesin bothRecenthightemperatureRarnanexperimentson phasesby Ramanspectroscopy.The behaviourof the

- Sm08La02A1O3 [5] haveshownthat belowandabove Ramanspectraindicatesthat we simulatedthephasethefirst ordertransitiontemperatureT0, the Raman transitionin rare earthaluminatecompoundswith van-spectraare similar to thoseobservedat roomtempera- ablecompositionsin the seriesSm1_~La~AlO3.ture for SmA1O3or LaA1O3 singlecrystalsrespectively.In addition,theexistenceof a soft modeof Aig sym- 2. EXPERIMENTALAND DISCUSSIONmetryin therhombohedralphasesuggeststhat thefurthersecondorderphasetransitionwould exist at TheRamanexperimentswere carriedout with ahighertemperature.Suchan inferenceis reinforcedby CodergPhOspectrometerusingcontinuousdetection.the evolutionof the latticeparameters[4, 5] on the The Ramanspectrawere excitedby thepolarized514.5seriesof rareearthaluminates. nm line of an Ar~laser.The detailsof the experimental

Vol. 37,No. 11 VIBRATIONAL MODES IN Sm1~La~AlO3 903

arrangementhavebeendescribedelsewhere[5]. I I I I I I I I I

Measurementswere carriedout on polycrystallinecorn-pounds,exceptthe endmembercompositions,for which - —

singlecrystalswere available.Most of the polycrystal- 500 - — — —--- — — —

line sampleswere synthesizedby meltingat the solarfurnacefacility in Sendai~ The pureoxides(Al2 03:99.999,Sm~O3:99.9and La203: 99.99)were ground -

togetherin the desiredproportions,pressedinto rodsofsquaresection,andsinteredfor 15h at 1450°C. In orderto avoid anycontamination,only thetop partof these —

rodswas slowly meltedat the focusof a horizontal E 300

axis solar 100 Kw furnace.Additionalsampleswere ~preparedby J. P. Couturesat Odeillot by solarmelting,following a slightly differenttechnicaspreviouslydes- 200 .- ..~. —~&~ -

cribed [5]. For agiven composition,no differencewere -

observedby X-ray characterizationor in the Rarnan .:~--— —- — ‘ —

spectra. — -•~-... I

Typicalcompositiondependenceof low frequency 100

Ramanspectaof Smj_~La~A1O3are shownin Fig. 1 ~ E9

for arbitraryintensitynormalizations.The remarkablefeaturein thesespectraconcernsthe changeof the I I I I 1X I I I

spectralprofile withvarying composition.With increas- 0 .1 ~ .5 .6 .7 .8 .9

ing x Ramanspectrabehaveexactlylike unpolarized ‘ ~ x 3

Ramanspectraof thepurerare earthalunilnateSmA1O3 Fig. 2. Compositiondependenceof all theRamanmodeswhenthe temperatureis increased.If allowanceis made observedin bothphases.Vertical dashedline markstheforusualbroadeningdue to thermaleffects,thecorn- first orderphasetransition.Solid linesreferto softparisonof thesespectrato thoseobtainedin previous mo es.work [5] showsthat thereare nomeaningfuldifferencesin thethermalevolutionof SmA1O3spectrabelowT0 rhombohedralphaseasit is well knownin LaA1O3 [1],and theevolutionof roomtemperaturespectraof mixed andtheyare presentin all the spectraabovex0. A simi-compoundsforx <x0. The sameholdsfor high tempera- larbehaviourisfoundin hightemperatureRamanstudiesturespectraof SmAlO3 andthoseof the relevantsystem of rare earthaluminatemixed compounds[5]. It wouldfor x >x0. At aboutx0 = 0.43 a drasticchangein the benotedthat a one modebehaviouris found in eitherRamanspectraoccurs.The threefoldspectralstructure phaseof thesystemoverthewholerangeof compositions.with correspondinglinesat 109, 140, 170cm~for In the rhombohedralphasewe observethat thex = 0 disappearsat thetransition.The spectrabroaden strongestline A’ sharpensandshowslittle changeinwhenapproachingthe phasetransition,i.e. by increasing frequency,whereasthemodedenotedby C’ at aboutx up to x0. In the rhombohedralphase,i.e. for x >x0, 240 cm~shiftsrapidly to lower frequenciesasthecorn-the spectrasharpenagain.Carefulinspectionof the positionis increased.Figure 2 showsthecompositionRamanspectrarevealsan importantshift in frequency dependenceof modefrequencieswhichwere obtainedof the peaksat 80 and285 cm~,respectivelylabelled directly from the completespectra.Due to the con-A andCfor x <x0. Wealso observea moreobvious tinuousbehaviourof the Ramanlines in eitherphases,shift of the line B at 136 cm

1 whichemergesfrom the asx varies,thesymmetryassignmentsareunambiguouslythreefoldspectralstructure.Newlinesasanintense deducedfrom the Ramanspectraof theendmemberspeaknear35 cm~labelledA’ and a weakline about for which polarizedRamanmeasurementson single160cm~clearly appearin spectrawith composition crystalswere previouslymade[1 3] . Mode symmetryclosetox

0. Theselinesare characteristicof the speciesareindicatedin Fig. 2.Particularlywe note that the peakC’ andthe lowest

peakA’ are respectivelyascribedto the low frequencymodesof A lg andEg symmetrytype in LaAlO3. This

* ResearchInstitutefor ScientificMeasurements, modecorrelationinvolvesthe two componentsof theTOhOkuUniversity,Sendai,Japan. triply degeneratezoneboundarysoft modeassociated

t LaboratoiredesUltra-Réfractaires,CNRS,BP 6 with awell known rhombohedral-cubicphasetransitionOdeillo,66120Font Romeu,France. [6]. Thereforeit seemsreasonableto expectthat these

904 VIBRATIONAL MODES IN Sm1.~La~Al03 Vol. 37,No. 11

I I I

1000 T0(x)

~ ~ 500

-

~<s.1o4— T(.3) I -

500 1000 1500 2000 2500TEMPERATURE (K)

Fig. 3. Temperaturedependenceof the squareoftheAig soft modefrequenciesfor compositionsx= 0.1,0.2,0.3.Straightsolid lines representa plot of equation(1)for thebest fit to experimentalresults.Small verticaldashedlinesindicatetransitiontemperature.

A ig andEg symmetrymodesmay be also associated asshownby solid straight linesdrawnin Fig. 3. T~canwith the samestructuraltransformationin anymixed be consideredas a Curie temperaturethat may notbecompoundswith a given composition.On the basisof verydifferent fromT~.Deviationfrom theaboverelationthe experimentfeaturesobservedin Ramanspectrafor beginsto be only observedat about 150 K abovethex <x0 andtheDebye—Scherreranalysisat room tem- first orderphasetransitiontemperaturesTo(x),andthisperature,it is reasonableto believethat theSm1_~Lax is continuedin theorthorhombicphaseoccurringbelowA1O3 compoundsundergoa first orderphasetransition T0. Relation(1) clearly reproducesthe classicalbehav-at temperatureT0. This phasetransitiontemperatureis iour of a soft modeof Landau’stype andmustbe com-determinedjust by the spectralchangethatdisplaysa paredto theresult deducedfrom hightemperaturevery sensitiveandreadily observableindicaticn with the Ramandatain trigonal rare earthaluminates[1]suddendisappearanceof the threefoldspectralstructure Furthermore,In Fig. 2, we observethat theA ig softcenteredat about140cm~.At temperaturegreater modefrequencyexhibitsa strongnonlinearbehaviourthan T0, thephasesymmetryappearsto be rhombo- in the compositiondependenceforx >x0. A plot ofhedralas evidencedby Ramanstructuresobservedin the thesquaredfrequenciesvs compositionis presentedinhightemperatureregion. Ramanspectrain this range Fig. 4. Exceptfor a small regionin the neighbourhoodlook similar in manyrespectsto thoseobtainedin high of x0, experimentalresultsare well fitted by thefollow-temperatureinvestigationsof the seriesof rhombohedral ing linear relation:mixed compoundsup to LaAlO3 [1]. A plot of T0 vsx 2- . - . WA (x) = B(x~—x), (2)is shown in the msetof Fig. 3. ig

Let usfirst considerexperimentalresultsfor anyof whereB andx~,are determinedfrom theslopeandinter-thesecompositionsin the range0 <x <x0. Theyare ceptof the plot againstx. Due to theoccurrenceof apresentedin Fig. 3 in the form of a plot of the squared first orderphasetransitionthat causesa slight changeoffrequenciesversustemperature.Particularly,we are the eigenvectorbetweenthebothmodesA ig andAg,

interestedin thetemperaturedependenceof the freq- equation(2) is not expectedto hold for x <x0. Theuencyof theA ig soft modegenerallyassociatedwith weak discontinuityin frequencyat the transitionshowna secondorderphasetransition.Its behavioursuggests by this modeis certainlydue to a slight changein dis-therelation placementvectors.

W~tjg = A(T~—fl (1)

Vol. 37,No. 11 VIBRATIONAL MODES IN Sm~~La~AlO3 905

I I I I I I I I

\ O....o I-~ Ie

E I‘a I

‘ IB I

10~ 3g\\~ ~ s.io~

SOS ~O ____~ .. p.

I I I I I I I I I I0 .) .2 .3 .1. .5 .6 .1 .8 .9 1

X ifl A1(Smi_~La~)O3

Fig. 4. Compositiondependenceof the squareof the soft modefrequenciesin bothphasesat roomtemperature.Straightsolid linesare calculatedfrom equation(2).

Lastly,we considerthetwo modesofB3g andAg in the cubicphase,andB andCareparameterswhichsymmetrywhich exhibit the greatestinstability for mustsatisfythe conditionB<0 andC> 0 for firstx <x0 as shownin Fig. 2 andFig. 4. Theyare related ordertransformations.As it is well known, thesoftto the first orderphasetransitionandconnectedto the modefrequencyrepresentingfluctuationsin theordercompositionandthetemperaturedependencesof an parameterin the lowerphasesymmetryis then given,orderparameteri~.Suchorderparameterconnectsthe with the helpof equation(3), byatomicstaticdisplacementsof the lowerphaseto a ~ — ‘r / ~ T— T \1/2

2 i 2 M I McondensmgmodeofM3typeattheMpomt[~,4,0] of w (7) = -two ~ T —T + ~

14T —Tthe cubicBrillouin zonewhich representsthe rotational 0 M \ 0 M

vibrationof the A1O6 octahedraaroundthe cubicaxis W0 is the limiting valueof WM (7) asT0 is approached

[00 1] . Howevertheoccurenceof arhomboedralphase from above.at first modifiesthe normalmodewhich nowappearsat This form agreeswell with theB3g curvesvs T [2,theD point [~,~,0] of the trigonalBrillouin zoneand 3, 5] andalso with theAg that is consideredas anis accompaniedby the displacementsof the rareearth inducedsoft mode.ions.Nevertheless,onemay assumethat thecondensing Theoreticalstudieson the lattice dynamicsof perov-modeat theDpoint correlatedto theM3 typemode is skitecrystalswith substitutionalimpurities [8, 12, 13]by far the largestcomponentthatdrives thefirst order predict,to a first orderapproximation,alinearrelationphasetransition.Usinga Landau—Lifshitzapproach betweenc,.,2(x) andx suchasequation(2). This typeof[161 to describethis first ordertransition,the free compositiondependenceis obtainedif oneneglectsenergyis assumedto havethesimple familiar form anharmonicatomicforce constantsandassumesthat

F = ~ w2 7-~.,2+ ~B ~ + ~ (3~ themajor contributionto the frequencychangeis dueM( / 1 ‘ / to changesin short rangeharmonicforce constantswhen

wherec..)M(T)is thefrequencyof theM3 type mode impuritiesare present.As discussedby Dvorakand

that is assumedto dependlinearly on thetemperature Glogar [8] , the influenceof defectson the soft mode

906 VIBRATIONAL MODES IN Sm1~La~AlO3 Vol. 37,No. 11

frequencyleadsin the next approximationto alinear 3. CONCLUSIONshift of thetemperatureT~Soequation(1)will also

To conclude,this Ramanstudyshowsthe analogydescribethe datain rhombohedralphaseby assumingthat T0(x)= T°~+ (dT~/dx)(x— 1). Fromthe compo- of the dependenceof structuralparameterson tempera-tureandcompositionalvariables,with regardto thesition dependenceof T~we obtain

small structuralrearrangementsoccurringnearand

= —-21.5 x 102 K/x and T~= 800 K (4) during the phasetransitionsin rareearthaluminates.dx Thus,useof the compositionaldependenceallows usto

follow thesamestructuralchanges,i.e. thebehaviourofEquations(1) and(4) yield B = 70.6 x iU~(cm’ )2. thesofteningof modesinvolved in thefirst andsecondExperimentallywe find a slightly smallervalue in equa- order transitions,at roomtemperature,in betterexperi-tion (2),B = 67.5 x iO~(cm~)

2.CoefficientA in mentalconditionsthanfor temperaturestudies.Suchequation(1) is not expectedto dependon composition, analogyof temperatureandcompositionaldependencesincein the anharmoniclattice dynamicaldescription of structuralvariationhasrecentlybeenproposedin[10] of soft modes,it is determinedby the anharmonic frameworksilicates[14].termswhich areassumedto be independentof x. Con-versely,sucha constantvalue in equation(1) together Acknowledgements— We areindebtedto Prof. T.with linearvariationof T~asestablishedexperimentally Sakuraiandthe JapaneseSocietyfor thePromotionofconfirmthe ability of a linearapproximationto describe Sciencewho permittedDr B. Piniou to preparesamplessoft modefrequencychangeby composition.Neverthe- at theUniversityof TOhOku(Japan).We also thankDrsless,sucha simpletheoreticalmodel fails to account F. Gervaisand P. MacMillan for valuablediscussions.for critical effectswhich appearnearphasetransitions.In the presentanalysiswe confineourselvesto a brief REFERENCEScommenton theAg andA ig soft modebehaviourin 1. J. F. Scott,Phys.Rev.3, 823 (1969);J. F. Scott&thevicinity of the first orderdisplacivephasetransition. J. P. Remeika,Phys.Rev. BlO, 4182(1970).To explainanomalousfrequencybehaviouraswell as 2. P. Alain & B. Piriou,SolidStateCommun.10, 35linewidth divergenceof soft modes,variousmechanisms: (1975).

3. P. Main & B. Piriou,Rev.mt. HautesTemp.dynamicaldisorderphenomena[91andanharmonic Refract.12, 35 (1975).effectsstronglyenhancedby the approachof transitions. 4. S. Geller& P. M. Raccah,Phys.Rev. B2, 1167Oneexpectsthe latter to be essentiallyconcernedwith (1970).the soft modes,whereasthe formerwill affect the 5. P. Main, J. P. Coutures& B. Piriou,J.Ramanwhole of thespecta.It shouldbe notedthat theAig and Spect.8, 88(1979).

6. J. D. Axe, G. Shirane& K. A. Muller,BulL Am.Ag modesarenot really relatedto the first orderphase Phys.Soc.14, 61(1969).transition.Howevertheydisplayanomalousbehaviour 7. P. Main & B. Piriou,J.Phys~38, c7, 389 (1977)whichextendsfartherfrom thetransitionpoint with 8. V. Dvorak& P. Glogar,Phy&Rev. 143,344temperaturevariation(Fig. 3) thanby compositional (1966).change(Fig. 4). Similar resultshavebeenobservedfor 9. A. HUller, SolidStateC’ommun.7, 589 (1969).

10. R. A. Cowley,PhilMag 11,672(1965).linewidths.Two factsarethen worthy of note: (i)both 11. R. Migoni, H. Bilz & D. BaUerle,Phy&Rev. Lett.Ag andAig modesessentiallyinvolve oxygendynamical 37, 1155 (1976).displacements;(ii) oxygenatomsarestronglyconcerned 12. V. S.Vinogradov,F~oc.Conf on LatticeDynamics,by thephasetransitionwhich producesa changeof their Copenhagen,1963(Editedby R. F. Wallis),p. 421.meanpositions.Since it was claimedin recenttheory Pergamon,New York (1965).

13. A. A. Maradudin,Ferroelectricity(Editedby E. F.[11] thatoxygendeformabilityplays an importantrole Weller), p. 72.Elsevier,Amsterdam(1967).in phasetransition,onemay assumethat nonlinearpro- 14. R. Hazen,Phys.Chem.Minerals 1. 83 (1977.).pertiesof therelevantmodesare dominatedby anhar- 15. P. D. Dernier& R. G. Maines,Mat. Res.Bull. 6,monic effects,thoughthe existenceof anunderlying 433 (1971).dynamicaldisordercannotbe entirely discarded. 16. L. D. Landau& E. M. Lifshitz, StatisticalPhysics.

Addison-Wesley,Reading,Ma (1969).