Solid StateCommunications, Vol. 9, pp. 813—817, 1971. PergamonPress. Printed in GreatBritain

RAMAN SCATTERING IN THE FERROELECTRICSYSTEM Pb1~Ba~TiO

GeraldBurns and Bruce A. Scott

IBM WatsonResearchCenter, Yorktown Heights, New York

(Received4 January 1971 by E. Burstein)

Most of the vibrational modeshavebeenmeasuredin the tetragonalferroelectric phaseof Pb1_~Ba~TiO3for 03~x~ 1 using the powderRamantechnique. For x = 1 (BaT1O3)the resultsare in excellentagreementwith recentpolariton resultsfor the A1 modesand infraredmeasurementsof the E modes.

THE LATTICE vibrational spectrumof tetragonal The A1 modeshavenot beenmeasuredby infra-ferroelectricBaTiO3 consistsof threepairs of red techniques. Still more recently, forward

A1 + E modes,with polarizationsrespectively in scatteringRaman(polariton) measurements11give

the z(A,) andx or y(E) directions,and a pair A1 modesin agreementwith the early 1.2

having B1 + E character. The former modesderie and thus in disagreementwith the recentstudies.’°

from thethree infraredactive T1~modesin the The reasonfor the disagreementand generalcubic phase(T > 120°C),while the latter pair difficulty of interpretingdata obtainedby straight-arise from the cubic silent T2~mode. Considerable forward Ramanscattering(not polariton measure-disagreementhasarisenin assigningthesemodes ments) is fairly clear. The lines arevery broad,from the Rarnanspectraof BaTiO3. The first two do not always appearto obey the appropriateinvestigations

12 using single domaincrystals selectionrules (althoughthis may arisefrom

with well defined scatteringgeometrywere scatteringfrom other surfaces,particularly ininterpretedto give results in basicagreement small samples)andappearin the cubic phase

with eachother,although betterdefined geometry in apparentcontradiction of symmetry rules.wasrequiredto define the longitudinal modes.2 Also, the A

1 modeRamandatacan not be directly

However, thesepapersdid not agreewith each comparedto infrared results.~other or with the infrared work

35 on the lowestfrequencyE mode.45 Earlier Ramanstudies on In this paperwe presentdata obtainedby amultidomain sampleswith undefinedscattering different approach,12 namely,powder Ramangeometrieswere lessuseful.68 Observationsof spectroscopyof the Pb

1_~Ba~TiO3systemfora very overdampedE mode, in agreementwith the x = 0—1.0. Analysis of the Ramanspectraof

infrared results, was subsequentlyreported.9 A polycrystalline ceramicsnot only reveals

more recentRamaninvestigation10 at room information aboutthe solid solution systembut,temperatureyielded E modefrequenciesin more importantly, allows interpretationof thesubstantialagreementwith earlier Raman12,9 Raman spectrumof BaTiO

3, the end memberand infrared

35 work, but transverse,4~modes componentat x = 1. The spectracan be interpretedin disagreementwith the earlier Ramanwork. 1.2 becausePbTiO

3 exhibits underdampedmodes____________ that obey the appropriateselectionrules in both* Partially supportedby the Army Research the tetragonalandcubic phases,and is well

Office, Durham,N.C., GovernmentContract understood.13 Thus, the effect of Ba2~substitutions

DA—31—124—ARO....D—205 for Pb2~can be observedin the Ramanspectra

813

814 RAMAN SCATTERINGIN THE FERROELECTRIC SYSTEM Pb1..~,BaTiO3 Vol. 9, No. 11

asx variesfrom 0 to 1.0. The sampleswere _______________________

preparedby solid statereactionof BaTiO3—PbTiO3

mixtures in aPbO atmosphere.Our measurementsof the cubic paraelectricto tetragonalferroelectrictransition temperaturesarein good agreement

J~i~with the literature,’4 showingthem to vary from ~0490°Cat x = 0 to 120°Cfor x = 1.0. The 0IexperimentalRamanpowderprocedureis given

in reference12. 03

Figure 1 showsthe spectraobtainedat

23°Cfor samplesof Pb1_~Ba~TiO3with several

different values of x. The uppermostcurve isthat of ceramicPbTiO3 (x = 0) and the arrows

Note that as x increasesthe resultsapply tocorrespondto previoussingle crystal results.~datatakenrespectivelycloserto the transitiontemperature.Datatakenat —170°Care very

similar to resultsat 23°C,except at lowertemperaturesthe lines aresharperandthusbetter resolved. 09

As x increasesthe data in Fig. 1 immediately 0

showhow the lattice vibrational modesvary with coo ~o �oo ~oo ~oo 0D�9GY~T (~)

composition. For example,the transverseopticA~(TO) and E(TO),which for x = 0 appear FIG. 1. The23°Cpowder Ramanexperimentalrespectivelyat 651 cm’ and 508 cm~, coalesce results for various x in thePb1_~Ba~TiO3

system. The curvesarebrokenat approximatelyas x increases. A1(TO) decreasesin energyto 350 cm_I and sometimesat 100 cm

1 becausea muchlargerextentthan E(TO). Figure 2 of gain changes. The arrows on the top arethe

illustrates thesevariationswith greaterclarity, results for the various modesas indicatedforand permits us to extract the (roomtemperature) single crystal PbTiO

3 (reference13).BaTiO3 modefrequenciesin the limit x -+ 1. Inthe following discussionlessattentionwill be Table1. The valuesof the A1(TO) andA,(LO)directedtowardBaTiO3 E moderesultsbecause

the various infrared works35 are in good agree- modefrequenciesobtainedby the powderRamantechniquecomparedto thosereported in

ment with one anotherand the findings of the reverences10 and 11. The E modefrequenciespresentstudy. Also E modeRamanmeasure- obtainedhereare in agreementwith infrared35ments’~’0at roomtemperaturewere found to and Raman12’°resultsand the valuesare listedagreewith the infrared data, with the exception

in the text.of the “soft” (lowest energy) E(TO) modeas _________________________________________previouslynoted, the situation with respectto Present Polariton1’ Right anglethe A modesis quite different. Infraredresults work results scattering10havenot beenreportedand previousRamandataarenot in good agreement.For example, A

1(TO) — 170 =180considerabledisagreementexists for two of A 1 (LO) — 185 178thethreeA~(TO) modeson comparingprevious A1 (TO) 270 270 180polariton’

1 and single crystal polarization A1 LO 470 475 470

results.’° A1TO 515 520 470A1(LO) 725 725 727

Vol. 9, No. 11 RAMAN SCATTERING IN THE FERROELECTRIC SYSTEM Pb,..~Ba~TiO3 815

(c) The x = 0 E(TO) modeat 508 cm’ alsoI I I I I I varies smoothlyacrossthe solid solution system

700LA,(LQ) to a value 500 cm~at x = 1. This is in1 *1(10)

j excellent agreementwith BaTiO3 singlecrystal£110) —°--~. results.’

5 It should benotedthat theroom

LO)___________ temperaturevalues in Fig. 1 for x = 0.8 and 0.9.ç~4ooL~~~*~1101 do not showthis E modequite resolvedfrom the

~~~~~0~~~~~~~

higherA1(TO) mode. At temperaturesbelow 0°C~ £110) 4 lines widths decreaseenoughin thesesamplesto~ ~ resolvethesemodeswith no shift (within experi-

~T £110) mentalerror) in position of either mode. It is

eo thereforecompletelyclear that no modecrossing

60 occurs.(d) The x = 0 modeat 445 cm’ is an

40 ~C unresolvedA,(LO) and E(LO) mode.’3”6 A!though

20 I0 02 04 06 0.8 .o weak, it hasbeenfollowed to x = 0.6 at 462 cm~.X(inPbix$axTlOs) In severalother systems,’7 (Pb, Ca)Ti0

3,

FIG. 2. The vibrational modeenergiesvs x for (Pb, Sr)Ti03, andalso Pb(Ti, Zr)03,’2 this mode

Pb1.~Ba~TiO3.The labelson left referto the is observableover a larger rangeof composition.

results on single crystals of PbTiO3 (reference13). As here, it is found to vary by relatively small

amounts(= 20 cm1), so an extrapolationto

Beginningwith the largestenergyshift, we 465 cm’ for x = 1 is reasonable.The modediscussthe separatemoderesults shown in frequencywould then agreewith infrared results5Fig. 2, andcollected in Table 1. for an E(LO) and single crystal Ramanresults2’10’1’

for an A1(LO), but would not agreewith reference

(a) For x = 0 and A1(LO) modeoccursat 10 for an A1(TO).778 cm

1. There is an E(LO) slightly lower inin energybut it can not be observedeven in (e) The A

1(TO) modeat 357 cm1 for x = 0

single crystals. its position hasbeendetermined’3 is particularly interesting, since it decreasesby measuringthe quasimodespectrum. As x with increasingx and crossesthe silent modeincreasesthe datavaries smoothly to 725 cm~ [at x = 0.7 (seef)J. Thereare no symmetry

at x = 1 (BaTiO3), which is in excellentagree- restrictionsto forbid crossing,which occurs in

1710,11 a numberof other systems. Its limiting valuement with single crystal BaTiO3 results for

the highest A1 mode. However, for powder Raman of 270 cm’ at x = 1 is in good agreementwithmeasurements,polarizationcan not easily be used previousresults.~to discriminatebetweenA1 andE modesso it can (f) The “silent” modein the cubic perovskitenot be statedwith certainty whethersomeE phaseis T2~which is not infrared or Raman

characteris appearingunresolvedin this mode active. In the ferroelectric C4~.phaseit exhibitsasx increases.From the agreementwith the B~and E character,both of which areRamanBaTiO3 results it would appearthat no E active, but only E is infrared active. Thus bycharactermodeis observedas x increases. symmetry, the E modemusthavea LO and TO

(b) The A1(TO)at 640 cm_I for x = 0 varies part. In practice, the mode is not observedin

smoothly to x = 1. The frequencyobtainedat infrared measurementsso the separationmustbex = 1 is 520 cm

1. This value is in closeagree- small. Indeed,measurements13in single crystalment with the findings of reference11, but in PbTiO

3 asa function of phonon propagationdisagreementwith reference10. Sincethis directionhave shown that the separationis lessmodecrossesno other modeit would be fortuitous than 2 cm’ . The datahereshow the mode toif its characterwere to changebetween vary from 290 cm

1 to 307 cm~1asx increasesx = 0—1. from 0 to 1. This result is in excellentagreement

with previoussingle crystal Ramanwork. 10

816 RAMAN SCATTERING IN THE FERROELECTRIC SYSTEM Pb~~Ba~TiO3Vol. 9, No. 11

(g) The PbTiO3 E(TO) mode at 220 cm1 overlappingof other modesas Caor Sr is added.

decreaseswith increasingx. However, this Also, the structureat 150 cm_I goessmoothlyregion of the spectrumis difficult to interpret to lower energyandthe A

1(TO) is not observed.

becausea modeapparentlyof secondorderA1 Thus in Pb1_~Ba~TiO3it would appearthat thecharacter’

3occursin PbTiO3 at 1.50 cm

t. To E(TO) goes from 220 cmt to 174 cm’ at x = 1

further complicate matters,the first order lowest in good agreementwith other work andthat theenergyA

1(TO) should appearat 127 cm~for powderRamanmeasurementsprobablydont’tx = 0, but is too weak to be observedeven in showthe weak A1(TO) mode.single crystals, except in quasimodespectra.~For BaTiO3, all workers”

2”°” report at least (h) The soft modeE(TO) at 89 cm’ forx = 0 decreasesin energyto 42 cm~’ for x = 0.7.oneweak A

1(TO)mode in the 170—180cm’ region,This modecan also be seen,for x 0.8 (Fig. 1),

aswell as an E(TO) modeat 185 cm~’. Thus,but it appearstoo highly dampedto determineawithout aid of polarization measurementsit isharmonicfrequency. This is very interestingnot possibleto directly clarify thesemodesinsince the soft E(TO) mode in BaTiO3 hasbeenthe powder Ramanspectra,although it is alsoreportedto havea harmonic frequencyof

difficult to do so from singlecrystal BaTiO3 34 cm1 and is highly overdamped.~ From

measurements.However, it is possible in thex = 0 to 0.8 the soft mode is underdamped.

powder Ramantechniqueto get very considerablehelp from otherclosely related systems.’217 In Hencethe dampingin BaTiO

3 probablycan notbe attributedto point impurities.

the systemsPb1_~Ca~TiO3and Pb1_~Sr~TiO3the resultsareclear. 17 The E(TO) mode in

Acknowledgements— The technicalassistancePbTiO3 at 220 cm

1 variessmoothlywith of F. Dacol and K.H. Nichols is very gratefullyincreasingx to 170 cm~1at x = 1, with no acknowledged.

REFERENCES

1. PARSONSJ.L. and RIMAI L., Solid StateCommun.5, 423 (1967) andRIMAI L., PARSONSJ.L.,HICKMOTT J.T. andNAKAMURA T., Phys.Rev. 168, 623 (1968).

2. PINCZUK A., TAYLOR W.T., BURSTEIN E. and LEFKOWITZ I., Solid State Commun.5, 429 (1967).

3. SPITZER W.G., MILLER R.C., KLEINMAN D.A. and HOWARTH L.E., Phys. Rev. 126, 1710 (1962).

4. BALLANTYNE J.M., Phys.Rev. 136, A429 (1964).

5. BARKER A.S. Jr., Phys.Rev. 145, 931 (1966).

6. BOBOVICH Y.S. and BURSIAN E.V., Opt. i Spetroskopiya11, 131 (1961)[English transl.:

Opt. Spectry.(USSR)11, 69 (1961)].7. IKEGAMI S., J. Phys.Soc.Japan 19, 46 (1964).

8. PERRY C.H. and HALL D.B., Phys.Rev.Lett. 15, 700 (1965).

9. DIDOMENICO M Jr., PORTO S.P.S.andWEMPLE S.H., Phys.Rev.Lett. 19, 855 (1967).

10. DIDOMENICO M. Jr., WEMPLE S.H., PORTO S.P.S.and BAUMAN R.P., Phys. Rev. 174, 522 (1968).

11. PINCZUK A., BURSTEIN E. and USHIODA S., Solid State Commun.7, 139 (1969).

12. BURNS G. and SCOTT B.A., Phys.Rev.Lett., 25, 1191 (1970).

13. BURNS G. and SCOTT B.A., Phys.Rev.Lett. 25, 167 (1970).

14. SHIRANE G. andTAKEDA A., J. Phys.Soc.Japan6, 329 (1951); NORMURA S. and SWADA S.,J. Phys.Soc.Japan6, 36 (1951).

Vol. 9, No. 11 RAMAN SCATTERING IN THE FERROELECTRIC SYSTEM Pb1~Ba~TiO3 817

15. Reference10 reportsthat the highest E(TO) modehasdifferent energiesdependingon whetherit ispropagatingin the xy plane(486 cm

1 ) or in the z direction (518 cm~1).In PbTiO3,where the spectrum

is much clearer,this hasnot beenobserved(reference13) and it would appearthat at long wavelength (k = 0) it should not be observed.

16. BURNS G. andSCOTT B.A.; a detailed paperon single crystal PbTiO3 andrelatedcrystals is inpreparation.

17. BURNS G. andSCOTT BA., work in progress.

Mit der Pulver—RamanMethodewerdendie meistenSchwingungsmodender tetragonalenferroelektrischenPhasedesPb 1_~,Ba12,TiO3für0 ~ x ~ 1 gemessen.Für x = 1 (BaTiO3) stimmendie Ergebnissesehrgut mit kürzlich veroffentlichten Polariton-Messungender A1Modenund Infrarot-Messungender E Moden iTherein.