SolidStateCommunications, Vol. 13,pp. 423—426,1973. PergamonPress. Printedin GreatBritain

INDEX OFREFRACTIONIN ‘DIRTY’ DISPLACNE FERROELECTRICS*

GeraldBums andB.A. Scott

IBM ThomasJ.WatsonResearchCenter,Yorktown Heights,NewYork 10598,U.S.A.

(Received9 April 1973by E. Burstein)

We reportmeasurementsof theoptic indexof reflectionas a function oftemperature,n (T), for severalhighly disorderedferroelectrics:PLZTceramic [Pb1_~La~(Zro.65Tio.35)1_~,4O3wherex = 0.08] andsinglecrystalsof Pb3(MNb2 )09 whereM = Zn andMg. Theresultsare qualitativelydifferentfrom the usualdisplaciveferroelectricbehaviorand thedifferenceis clearlydueto local disorder.

IN THIS paperwe reportmeasurementson the index In ordinaryperovskiteferroelectricsn(T) hasanof refractionvstemperaturen(T) for several extracontributionbelowT~thatvariesas thesquareperovskiteferroelectricsof thetype we havecalled of the spontaneouspolarization.This resultis showndirty displaciveferroelectrics.

1As will be seen,the schematicallyin Fig. 1 wheren (T) hasan abruptferroelectricsdiscussedare all highly disordered breakin slopefor T < T~.This canbe understoodbymaterialsdueto vacanciesor randomsiteoccupancy. treatingn(T) in the low temperatureferroelectricTheresultantn(T) datais qualitativelydifferentfrom phaseasresultingfrom a biasedquadraticelectroopticacceptedferroelectricbehavior, effectwithin thehigh temperaturecentrosymmetric

phase.Thebias canresulteitherfrom alargeexternalTheindexof refractionmeasurementsweremade biasor by thecrystalbiasingitself with its own

as a functionof temperatureon prismsby the minimum spontaneouspolarization.In contractedtensordeviationtechnique.2As will bediscussed,the notation3~(1 In2 )~= g~

11’12, whereggj is the quadratic

materialsstudiedare optically isotropicbelowthe electro.opticconstant,whichisexpectedto betem-transitiontemperature,T~,soa singleaveragedindex peratureindependent.Fornormalferroelectricsis measured. whereP

3 is thereversiblespontaneouspolarization,

—— i~n1= flrfl? = g,3n1P, (I)

n? is the referencestate,or in this case,the index forP, = 0. This would bethe linearextrapolationfrom

‘~3 hightemperaturesasindicatedin Fig. 1. The 3-directionis takenasparallelto thespontaneouspolarizationand

_______ the 1-directionisperpendiculartoP8.As longas the‘rEIERATuRE ferroelectricis axial only two indicesarerequired.

SinceP~entersequation(1) and theg’s are usuallyFIG. 1. Schematicdiagramof theindexof refraction all positive,~n isusuallya negativenumberasshownvs temperatureshowingtheeffect of a spontaneous in Fig. I. Experimentalresultssimilar to Fig. I havepolarization, beenreportedin a largenumberof ferroelectric

* Partiallysupportedby the Army ResearchOffice, materials.4

Durham,N.C., U.S.A.

423

424 INDEX OF REFRACTION IN ‘DIRTY’ DISPLACIVE FERROELECTRICS Vol. 13,No.3

I I I2.54 - #~46APb3ZnM~2O92.53~~T

‘C

~2.52

25

,,, z

a5c~ ~2.51 - ITEMPERATURE (‘C)

FIG. 2. The temperaturedependenceof the indexof 2.5!refractionfor P~T(12/65/35)measuredat 6328A. ~

Figure 2 showsa newtype of experimentalresult. x

zmaterialPLZT

5 (8/65/35)in which T~= 145°C.T~ —

is heredefmedas thetemperaturebelowwhich theThemeasurementsare of n (T) of the ferroelectric 7 #~46Ecrystallographicphaseis differentfrom thecubicphaseaboveT,.At T~the dielectricconstante(0)peaksand a5~.blow T~areversiblespontaneouspolarization,F

5, canbe measured.Actually, for dirty displaciveferroelectrics ~ soo 6ootheretendsto be arangebetweeenT~and~ T~,+ 10° TEMPERATIJ�(‘C)wherevariousexperimentersclaim P5 canbe observed. FIG. 3. The temperaturedependenceof the index ofAs canbe seenin Fig.2, n(T)deviatesfrom a straight refractionfor Pb3ZnNb209 (uppercurve)andline at ~ 300°C.This isnotwhatis normallyobserved Pb3MgNb2O9(lower curve)measuredat 6328A. Thefor ordinarydisplaciveferroelectrics.Normally linear pointsare theexperimentalmeasurements.Theinsertbehavioris observedfor T> T~as in Fig. i. is the temperaturedependenceof the low frequency

dielectric constantof Pb3ZnNb209.To determineif theresultsin Fig. 2 aregeneral

for otherhighly disorderedperovskiteferroelectrics, Theresultsfor n (T) of Pb3ZnNb209 appearinwe measuredtwo materialswhich fall into the same the upperpartof Fig. 3. Again, it is noticedthat therecategoryasPLZT. ThesearePb3(ZnNb2)O9,[Which is no sharpbreakat T~,(= +150°C)butratherwhatcouldbewritten asPb(Zn113Nb213)O3], for which might beinterpretedasa deviation from thehightern-

= +150°C,andPb3(MgNb2)O9with Tc = 50°C. peraturelinear behavior 300°CaboveT~.In fact,TheRussianliteratureoften refersto thesetypesof the deviationis sofar aboveT~that it is notveryclearmaterialsasferroelectricswith a diffusephasetransition.

6 that a linearregionexists.To checkthis questiontheThesematerialscontainZn~(or Mg) andNb~ionson indexof refractionof Pb

3MgNb2 09 wasmeasured.theB-site. In principle, it is possiblethat thesematerials l’his crystalis verysimilar to the Zn compoundexceptcouldbeorderedasin Ba3(ZnNb2)O9in which tWO = —50°C.Thusalinear behaviorof n(T) shouldadjacent(111)planescontainNb ionsfollowedby one benoticeableatlower temperatures.The resultscan(ill) planecontainingZn ions

7 (i.e. . . . Nb, Nb, Zn, be seenat the bottom partof Fig. 3. Besidesa smallNb, Nb, Zn . . . stackingin the (Ill) planes).However, differencein themagnitudeof the index (averticalthePb-saltsare notorderedandthe immediateenviron- displacement)thetwo curvesappearto bedisplacedmentof anyparticularB-site will in generalbe different by 200°C.As canbe seen,linearbehavioris observed.from theenvironmentof neighboringB-sites.Thus, The magnitudeof the deviation from theextrapolatedfrom the disorderstandpointthesematerialsare similar high temperaturelinear behaviorfor Pb

3ZnNb209 isto PLZT(8/65/35). n—n°~ 0.04. ForPLZT (8/65/35)it is 0.02.These

Vol. 13, No. 3 INDEX OF REFRACTION IN ‘DIRTY’ DISPLACIVE FERROELECTRICS 425

values are similar to the values observed in ordinary displacive ferroelectrics several hundred degrees below Te and described by equation (1). It should be remem- bered that the index of refraction results shown in Figs. 2 and 3 are averaged results because the materials are optically isotropic because PLZT is in ceramic form” and Pbs(ZnNbs)Os has domains in all (111) directions. Thus, for axial materials, with n, the index along the unique axial direction and n, the index perpendicular to that direction, the measured n(T) = (rz, + 2n,)/3. For deviations from the extrapolated high temperature index data the observed An(T) = (An, + 2AnJ3. For BaTiOs a n - no = 0.03, which is close to the values shown in Figs. 2 and 3.

From the n(T) data in Figs. 2 and 3 several points seem clear. First, the magnitude and sign of the shift An(T) from the extrapolated value for zero polarization is approximately what is expected for most displacive perovskite ferroelectrics. Second, the n(T) curve starts to deviate from the zero polarization, high temperature value more than 150°C above the respective T, values for the different materials. Third, very little happens to the n(T) curve at T,., in sharp contrast to the usual behavior as shown in Fig. 1. These results can be explained by the appearance, far above T,, of small regions of crystal having a polarization. This polarization would exist on the scale of several unit cells rather than macroscopic dimensions - 1 I.C. The local fields in this small volume due to the particular arrangement of atoms and defects cause the local distortion of the atoms and determine the volume of distortion and the direction of polarization. This polarization is not reversible since no reversible polarization is observed far above T,. For example, in a PLZT crystal the atoms surrounding a vacancy would shift to give an ionic polarization, and distort to give an electronic polariz- ation. The polarization would not be reversible but in the local area there would be a contribution to the index of refraction since the square of the polarization enters equation (1). As the temperature is lowered other regions of the crystal will have local field large enough for a local polarization to exist. This apparently happens in a quasi-continuous manner. Near T, most of the crystal is already polarized. However, in this region the longer range cooperative coupling becomes large enough so that the polarization of many of these regions can be reversed. Again we emphasize that in this region near T,., various authors report various extensions of a reversible (60 Hz) spontaneous polar- ization.6 This effect may actually be sample dependent

in that some samples could have more order than others. Below T, the polarization would grow as is normally observed in ferroelectrics and more of the small regions of polarization become reversible.

FIG. 4. Raman results for PbsMgNba O9 and Pbs ZnNbs 0s. In the polarized spectra the laser and Raman scattered light are polarized parallel to each other (VV). Depolarized indicates the two are ortho- gonal to each other (VI-I).

It is interesting to note that variation of internal fields, which destroys the translational symmetry of the crystal, is clearly manifest in the Raman measure- ments. Figure 4 shows single crystal data of the Raman spectra for the ferroelectrics shown in Fig. 3. The Raman emission shown in Fig. 4 is intense, and is first order Raman emission as evidenced by a temperature dependence in agreement with a Bose-Einstein factor. Except for the Bose-Einstein factor the data are independent of temperature above and below T,. In fact, at room temperature Pbs MgNbz 0s is above T, and, statistically, cubic with point group Oh. For a cubic perovskite AEOs crystal no first order Raman

426 INDEX OF REFRACTIONIN ‘DIRTY’ DISPLACIVE FERROELECTRICS Vol. 13,No.3

emissionis allowedby symmetry.We interpretthe Thus,we seethatdirty displaciveferroelectricsresultsin Fig.4, in a mannersimilar to amorphous behavein a mannerqualitatively differentfrommaterials,10as dueto a breakdown in the k-selection ordinary displaciveferroelectricswith respectto n(T).rules(phononmomentum)within the Brillouin zone. It appearsthat thebehavioris intimatelyconnectedThis leadsto Ramanemissionthat is aweightedaverage with the lack of local translationalsymmetrydue toof thedensityof phononstatesin the Brillouin zone,10 vacanciesor disorder.whichwould be fairly independentof temperature.Any soft k = 0 phononswould be extremelydifficult Acknowledgements— it is a pleasureto acknowledgeto detectsincethedensityof statesfor k ~ 0 is very discussionswith E. Burstein,J.Feder,A. Lurio,

E. Pytte,N. Shirenand B.D. Silverman.G. HaertlingandC.E. Landkindly suppliedtheoptical qualityPLZTceramic.F.H.DacolandK.H. Nicholsprovidedtechnicalassistance.

REFERENCES

1. BURNS G. andSCOTTB.A., precedingpaper.

2. SeeBOND W.L., J. App!.Phys.36, 1674(1965).Themeasurementsweremadein a furnacedescribedin,BURNSG. andSCOTTB.A.,Phys.Rev.,B7, 3088(1973).

3. SeeNYE J.F.,PhysicalPropertiesofQystals,OxfordUniversityPress,Oxford(1957).

4. For exampleseeSMITH A.W., BURNSG. and O’KANE D.F.,Jr.,Appl.Phys.42, 250 (1971)andreferenceslisted there.

5. HAERTLING G.H. and LAND C.E.,J. Am.Ceram.Soc.54, 1(1971);HAERTLING G.H.,ibid. 34,303(1971).Somestudiesasto wherethevacanciesactually residearepresentedin: HARDTL K.H. andHENNINSD.,ibid. 55, 230(1972).The notation8/65/35refersto the solid solutionPb

1_0.08La,,~.08(Zr0.65Ti0.35)1_0.~,403asdiscussedin the referencesquotedhere.

6. SMOLENSKYG.A.,J. Phys.Soc.Japan,SuppL28,26(1970).

7. GALASSO F.S.,Structure,PropertiesandPreparationofPerovskiteTypeCompounds,PergamonPress,Oxford(1969).

8. SeeJONAF. andSHIRANE G.,FerroelectricCrystals,p. 121,MacMullen, NewYork (1962)for BaTiO3 results.

9. LOUDON R.,Adv.Phys.13,423(1964).

10. SeeSHAKER R. andGAMMON R.W.,Phys.Rev.Lett. 25, 222 (1970),andSMiTH J.E., BRODSKY M.H.,

CROWDERB.L., NATHAN Mi. andPINCZUK A.,Phys.Rev.Lett. 26,642(1971).

Wir berichtendie MessungenderoptischenAnzeigungder Strahlenbrechung,als Funktion derTemperaturfür einigesehrungeordnetenFerroelektrika.PLZT Kermik [Pb1_~La~(Zro.65Tio.35)1_~,4O3,wox = 0.08ist] und Em-Kristallevon Pb3(MNb2 )O9 mit M = Zn und Mg. DasErgebnis1stvon demgewOnhlichenverschiebungsFerroelektrikaqualitatlichverschieden,undderGrunddesUnterschiedsin diesemFall mussörtlicheUnordnungsein.