Room temperature structure of Pb(ZrxTi1-xO3) around the morphotropic phase boundary region: A Rietveld study

JOURNAL OF APPLIED PHYSICS VOLUME 92, NUMBER 6 15 SEPTEMBER 2002

Room temperature structure of Pb „ZrxTi1Àx…O3 aroundthe morphotropic phase boundary region: A Rietveld study

Ragini, Rajeev Ranjan, S. K. Mishra, and Dhananjai Pandeya)

School of Materials Science and Technology, Institute of Technology, Banaras Hindu University,Varanasi-221005, India

~Received 5 July 2001; accepted for publication 16 April 2002!

We have carried out a detailed Rietveld analysis of x-ray powder diffraction data of Pb~ZrxTi12x!O3

~PZT! compositions across the morphotropic phase boundary~MPB! region ~x50.515, 0.520,0.525, 0.530!. It is shown that the structure of PZT is pure tetragonal forx<0.515 with space groupP4mm. In the MPB region, 0.515,x,0.530, the tetragonal and monoclinic~space group:Cm!phases are found to coexist as a result of a first order phase transition between the low temperaturemonoclinic and high temperature tetragonal phases. Further, arguments are advanced to show thatthe hitherto believed rhombohedral structure~FR

HT! of PZT for 0.530<x<0.62 is more likely to bemonoclinic. © 2002 American Institute of Physics.@DOI: 10.1063/1.1483921#

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I. INTRODUCTION

Pb~ZrxTi12x!O3 ~PZT! ceramics are used in a variety opiezoelectric, pyroelectric and ferroelectric memodevices.1–5 In carefully prepared PZT ceramics, Mishet al.6 have shown that the structure of the room temperaferroelectric phase is tetragonal~FT! for x,0.520 and rhom-bohedral~FR! for x>0.530 while the two phases coexist fox50.525. Both theFT and FR phases transform to a cubparaelectric phase on heating.1,6,7 For 0.530<x,0.550, theFR phase transforms to cubic phase via an intermediateFT

phase while forx.0.550, theFR phase transforms directlinto the cubic phase.6–8 The FR–FT phase transition in PZTceramics has been shown by Mishraet al.6–8 to be accom-panied with a wide coexistence region spread over 200 °Cx50.525 indicating first order nature of theFR–FT phasetransition. Further, these workers have shown that theFT tocubic phase transition is also of first order type forx,0.550 as confirmed by the thermal hysteresis in dielecmeasurements. TheFR to cubic direct transition forx>0.550, without the intermediateFT phase, is, on the othehand, of second order type indicating a tricritical poaroundx50.545.7

Recently, Nohedaet al.9,10 have reported a tetragonal tmonoclinic ~FM! phase transition below room temperatufor x50.500 and 0.520. Using electron diffraction daRaginiet al.11 have shown that this monoclinic phase~whichwe shall hereafter refer to asFM

HT phase! for x50.515 and0.520 undergoes a cell doubling transition to another moclinic phase~FM

LT! at still lower temperatures. This cell doubling transition is reminiscent of a similar transition aboroom temperature in theFR phase on the Zr-rich side of thmorphotropic phase boundary~MPB!.12 The characteristicsuperlattice reflections for the cell-doubling transition adiscernible in the electron diffraction patterns but not in tpowder x-ray diffraction~XRD! patterns as a result of whicNohedaet al.9,10 missed the existence of the second ph

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transition observed by Raginiet al.11 Ragini et al. have fur-ther shown that this cell-doubling transition is accompanwith anomalies in the temperature dependence of piezoetric resonance frequency and dielectric constant. The discery of the cell-doubling transition11 has raised doubts abouthe correctness of monoclinic space groupCm, as assignedby Nohedaet al.10 for x50.520 atT520 K, which is wellbelow the second transition temperature for this compositsince the superlattice reflections observed by Raginiet al.11

cannot be accounted for in terms of this space group. Mrecently, Ranjanet al.13 have carried out a detailed powdeneutron diffraction study forx50.520 and confirmed the occurrence of an antiferrodistortive~AFD! phase transitionleading to cell doubling transition around 210 K. Further,has been shown that the correct space group of theFM

LT phaseof PZT with x50.520 below the AFD transition temperatuis Cc14 and notPc as originally proposed13 on the basis ofthe Rietveld analysis of the powder neutron diffraction dcollected at 10 K.

The boundary separating theFT andFR phase fields inthe PZT phase diagram is nearly temperature indepenand is commonly known as MPB.1 This phase boundary is ospecial interest since the piezoelectric and dielectric respoof PZT is maximum near the MPB composition. Seveworkers have reported coexistence of theFT andFR phasesover a range of compositions across the MPB.15–25However,depending on the method of preparation, different workhave reported different composition widths for the coexience region. The narrowest width of the coexistence regDx'0.01, has been reported by Singhet al.,19,20 and Mishraet al.6,8 in compositionally homogeneous samples prepaby a semiwet route.

Based on the concepts of thermodynamics of solutioit has been argued that the stable state of the system inMPB region should be a mixture ofFT andFR phases.15,16,26

Kakegawaet al.17,18,21attribute the coexistence ofFT andFR

phases in the MPB region to extrinsic factors like excePbO21 and poor compositional homogeneity, especiallysamples prepared by the solid state reaction method.17,18

6 © 2002 American Institute of Physics

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3267J. Appl. Phys., Vol. 92, No. 6, 15 September 2002 Ragini et al.

These workers have proposed that the MPB should beabrupt boundary between theFT andFR phases without anycoexistence region in compositionally homogeneosamples. Mishraet al.,6–8 on the other hand, have proposethat the phase coexistence in the MPB region is neitherto the considerations based on the concepts of the thermnamics of solutions nor due to extrinsic factors like compsitional fluctuations but is due to a first order phase transibetween theFT andFR phases. Using XRD and piezoelectrresonance frequency data as a function of temperature, tworkers have shown that even a pureFR phase near theMPB, i.e., 0.530<x,0.550, passes through a coexistenregion~FT1FR! before transforming into the pureFT phase.The phase coexistence observed by Mishraet al. has subse-quently been confirmed by Nohedaet al.27 in their high reso-lution XRD studies. The widest phase coexistence regionbeen reported6–8 for x50.525 where theFT andFR phasespersist from room temperature up to about 220 °C awhich it becomes pureFT .

The presence of triplet of peaks at the 200 pseudocuposition and doublet of peaks at the 111 pseudocubic ption in the room temperature powder XRD patterns of Pwith x50.525 has been taken by earlier workers15–18includ-ing Singhet al.19,20 and Mishraet al.6,8 as an evidence fothe coexistence ofFT and FR phases. We have recentfound that the 200 pseudocubic reflection sometimes dnot appear as well resolved triplet expected for the coexence ofFT andFR phases in powder XRD patterns of PZsamples of the same composition~x50.525! prepared by thesame method. At the same time, the 200 pseudocubic retion is not a singlet either. Further, the pseudocubic 111flection appears as a doublet. The XRD pattern of ssamples bears close resemblance with that of the monocphase ~FM

HT! reported recently by Nohedaet al.9,10 andRagini et al.11 at low temperatures forx50.520. In view ofthis, there is a need to reexamine the room temperature Xdata of PZT near the MPB compositions.

In the present work, we have attempted to settleroom temperature structure of PZT in and around the Mregion using Rietveld analysis of powder x-ray diffractiodata for four different compositions,x50.515, 0.520, 0.525and 0.530. Of these, the compositionsx50.515 and 0.530are representative of the pureFT andFR phases just outsidethe MPB region. It is shown that the structure of PZT forx50.520 and 0.525 consists of a mixture ofFM

HT and FT

phases. Further, we show that the hitherto believed rhomhedral phase~FR! of PZT for 0.530<x<0.620 may probablybe monoclinic. Probable factors responsible for the coexence of the monoclinic and tetragonal phases in the Mregion are also outlined.

II. EXPERIMENT

Samples used in this investigation were prepared bsemiwet route which gives excellent chemical homogenand narrowest MPB region~Dx'0.01!.19,20 In this method,one first prepares~ZrxTi12x)(OH)4 by chemical coprecipita-tion. This hydroxide is then decomposed into the correspoing oxide ~ZrxTi12x!O2 on heating at 900 °C for 3 h. Thi


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solid solution precursor oxide is ball milled for 6 h usinZrO2 balls with PbCO3 powder. The mixed powder is calcined at 700 °C for 6 h. Sintering was carried out at 1100for 6 h in PbOatmosphere using PbZrO3 as a spacer powdeto compensate for the PbO loss during sintering. The Xdata using CuKa radiation was recorded atD~2u!50.02°interval in the 2u range 20–110°~except forx50.515 forwhich the data was collected for 20°–120° range! at a count-ing rate of 1° per minute on a 12 kW rotating anode basRigaku powder diffractometer operating in the BraggBrentano geometry and fitted with a curved crystal graphmonochromator in the diffracted beam.

III. RIETVELD REFINEMENT DETAILS

Rietveld refinement was carried out using the XRD din the 2u range 20°–120° forx50.515 and 20°–110° forx50.520, 0.525, and 0.530 with the help of theDBWS-9411

program.28 It was verified that the refined parameters did nchange on increasing the 2u range beyond 110°. The background was fitted with sixth order polynomial, while thpeak shapes were described by pseudo-Voigt profiles. Inthe refinements, scale factor, zero correction, backgrouand half width parameters, lattice parameters~a,b,c,a,b,g!,positional coordinates~x,y,z! and thermal parameters wervaried. Occupancy parameters of all the ions were kept fiduring refinement. Use of anisotropic thermal paramet~Ui j ! for Pb21 ion invariably led to improvement in theRfactors, and were therefore considered in all the refinemeFor other ions, only the isotropic thermal parameters~U iso!were refined. No correlation between the positional and thmal parameters was observed during refinement and asit was possible to refine all the parameters together.

IV. RESULTS AND DISCUSSION

A. Refinement of the structure of Pb „Zr0.515Ti0.485…O3

The structure of the tetragonal phase of PZT has recebeen refined by Nohedaet al.10 for x50.520. In their refine-ment of the room temperature structure, they have assuthe coexistence of a cubic phase in order to account fordiffuse scattering between the tetragonal00l andh00 Braggpeaks. This led to considerable improvement in theirR fac-tors. The assumption of a coexisting cubic phase in thefinement of the tetragonal structure is, however, physicaunrealistic. TheFT to cubic phase transition for this composition occurs around 676 K.6–8 One may expect a coexistence ofFT and cubic phases around the transition tempeture because of the weakly first order nature of ttransition,6,7 but the coexistence region is highly unlikely tbe as wide as 376 K taking room temperature as 300 K.XRD pattern of our tetragonal PZT sample withx50.515dose not contain diffuse scattering of the type mentionedNohedaet al.10 as can be seen from Fig. 1 which depicts t111, 200, and 220 pseudocubic peaks for various PZT cpositions. We attribute it to the excellent compositional hmogeneity at the Zr41/Ti41site and strict Pb21 stoichiometryin our samples prepared by the semiwet route. We expectthe results of our refinement will be true representativepure tetragonal phase of PZT just outside the MPB regio


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3268 J. Appl. Phys., Vol. 92, No. 6, 15 September 2002 Ragini et al.

The space group of the tetragonal phase of PZT at rotemperature isP4mm.There are four ions in the asymmetrunit of this structure with Pb in 1~a! sites at~00z!; Zr/Ti andOI in 1~b! sites at~1/2, 1/2,z! and OII in 2~c! sites at~1/2, 0,z!. For the refinement, the initial values of the lattice paraeters were obtained from our XRD data by least squamethod, whereas the values of the structural parameterstaken from Nohedaet al.10 Following Nohedaet al.,10 wehave considered both isotropic as well as anisotropic therparameters for Pb21 which was fixed at~0,0,0! in our refine-ment. The use of anisotropic thermal parameters led to slimprovement in theR factors. Alternatively, following No-hedaet al.,10 we also considered the effect of off-center dplacement of Pb21 ions in the^110& directions along withisotropic thermal parameters of Pb21 in our refinement. It

FIG. 1. XRD profiles for the 111, 200, and 202 pseudocubic reflections~a! x50.515,~b! x50.520,~c! x50.525,~d! 0.530,~e! x50.600, and~f!x50.900.


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was found that a minimum value ofRWP was obtained forPb21 shift of 0.131 Å as can be seen from Fig. 2. Howevthe R factors, for the off-center Pb21 displacement modewith isotropic Pb21 thermal parameter are comparablethose obtained using anisotropic Pb21 thermal parameterswith no off-center displacement suggesting that the twoproaches are equivalent.

Figure 3 depicts the observed, calculated and differeprofiles for the refined structure. The fit is quite good. Trefined structural parameters are given in Table I. A compson of the positional coordinates of Ti41/Zr41, OI

22 and OII22

ions obtained by us and those reported by Nohedaet al.10 forx50.520 shows that theDz displacements of these ions anearly comparable even though the tetragonality~h5c/a21! for our composition~h50.0310! is slightly larger thanthat of Nohedaet al.10 ~h50.023 08!. Since our compositionis 0.5% richer in Ti41, a slightly higher value ofh isexpected.1 Our thermal parameter values for Zr41/Ti41andO22

I are slightly higher than those reported by Noheet al.10 However, not much physical significance may betached to thermal parameters obtained from powder diffrtion data. It is important to note that we could get better fitcompared to that obtained by Nohedaet al.10 even without

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FIG. 2. Variation of the agreement factorRWP as a function of Pb21 shiftsfor refinements with various fixed values of displacements along tetrag^110& direction.

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FIG. 3. Observed~dots!, calculated~continuous lines!, and difference~bot-tom of the figure! profiles in the 2urange 20–60 for Pb~Zr0.515Ti0.485!O3using tetragonal phase model. Insshows the patterns in the 2u range62°–110°. Bars represent the peak psitions for CuKa1 . The small peaksaround 2u528° and 35° are due to im-purity phases.



TABLE I. Refined structural parameters of Pb~Zr0.515Ti0.485!O3 using tetragonal~space group:P4mm! structure.

Anisotropic thermal parameters for Pb21 Local ^110& shift of Pb21

Ions x y z U ~Å! x y z U iso (Å 2)

Pb21 0.0 0.0 0.0 U115U2250.047(1)U3350.033(1)

0.026 0.026 0.0 0.0278~2!

Zr41/ Ti41 0.5 0.5 0.451~2! U iso50.021~1! 0.5 0.5 0.451~2! 0.021~3!OI

22 0.5 0.5 20.095~8! U iso50.04(1) 0.5 0.5 20.097~8! 0.05~3!OII

22 0.5 0.0 0.379~4! U iso50.022(6) 0.5 0.0 0.378~4! 0.022~6!

a5b54.0174(2) Å,c54.1420(2) ÅRB515.45,RW-P515.17,Rexp55.31,x258.16 RB515.58, RW-P515.18, Rexp55.30, x258.20

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postulating a coexisting cubic phase. One of the reasonsthis could be a possible coexistence of the monoclinic phin their samples~x50.520! at room temperature which wanot taken into account in their refinement. We shall returnthis point while presenting the results of refinement of Pwith x50.520 in the next section.

B. Refinement of the structure of Pb „Zr0.520Ti0.480…O3

The structure of PZT withx50.520 has been reported tbe tetragonal by earlier workers.6–11 Nohedaet al.10 havealso assumed the tetragonal structure~P4mmspace group!for this composition in their room temperature structurefinement. Figure 1 compares the powder XRD profiles111, 220, and 220 pseudocubic reflections forx50.520, withthose forx50.515 and other PZT compositions. It is evidefrom this figure that at room temperature the 202 peakbroader than the 220 peak forx50.520. This is not so for theneighboring tetragonal compositionx50.515. Nohedaet al.10 have attempted to account for such anisotropic pbroadening forx50.520 in terms of distribution of latticeparameters. However, Raginiet al.11 have shown that oncooling below 263 K, the 202 peak splits into two peaks dto a phase transition into the low temperature monocli~FM

HT! phase. This clearly suggests that the extra broadeat room temperature of the 202 peak is not due to distribuof lattice parameters, as assumed by Nohedaet al.,10 but dueto the coexistence of theFM

HT phase with theFT phase onaccount of the first order nature of theFT–FM

HT phase tran-sition. In view of this, we carried out Rietveld analysis of t


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XRD data assuming coexistence ofFT ~P4mmspace group!

andFMHT ~Cmspace group! phases. Nohedaet al.10 have also

used a coexistence model to account for the diffuse scaing between00l andh00 Bragg peaks for thex50.52 com-position but as mentioned in Sec. IV A, they have assumecoexisting cubic~Pm3mspace group! phase which is physi-cally unrealistic. Our structural model, based on the coexence ofFT and FM

HT phases, gives satisfactory fits withopostulating the coexisting cubic phase and/or distributionlattice parameters as can be seen from Fig. 4. Our fit is qsatisfactory compared to Nohedaet al. for the model basedon theFT structure with distribution of lattice parameters aa coexisting cubic phase.

The refined parameters obtained by us for theFT andFM

HT phases are given in Table II. For comparison, we carrout refinements assuming coexistence of cubic andFT

phases, as used by Nohedaet al.,10 and alsoFR andFT , andFR andFM

HT phases. Thex2 values for the four possibilitiesare given in Table III. Although the model based on tcoexistence ofFT and FM

HT phases gives the smallestx2

value,x2 ~3.42! for the model based on the coexistenceFT andFR phases is not significantly higher than that for tFT1FM

HT phase model. It is therefore not possible to makunique choice betweenFT1FM

HT and FT1FR coexistencemodels purely on the basis of Rietveld analysis. Howevthe fact that theFT to FM

HT first order transition11 occurs justbelow room temperature forx50.520 ~Tc5265 K! makesthe FT1FM

HT coexistence model more plausible.

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FIG. 4. Observed~dots!, calculated~continuous lines!, and difference~bot-tom of the figure! profiles for Pb~Zr0.520Ti0.480!O3obtained for theFT

1FMHT model in the 2u range 20–60.

Inset shows the patterns in the 2urange 62°–110°. The upper bars reprsent tetragonal peak positions anlower bars represent the monoclinipeak positions for Cu Ka1 .



TABLE II. Refined structural parameters of Pb~Zr0.520Ti0.480!O3for the tetragonal~FT! and monoclinic~FM! phase coexistence model.

Tetragonal phase with space groupP4mm,a5b54.0429(2) Å,c54.1318(3) Å

Monoclinic phase with space groupCm, a55.7520(1) Å,b55.7431(2) Å,c54.0912(4) Å andb590.48(1)°

Ions xT yT zT U ~Å 2! xM yM zM U ~Å 2!

Pb21 0.00 0.00 0.00 U115U2250.0310~3!U3350.027~3!

0.00 0.00 0.00 U1150.2208~2!U2250.0265~3!U3350.0744~3!U1350.0296~3!

Zr41/Ti41

0.50 0.50 0.447~2! U iso50.005~2! 0.578~3! 0.00 0.473~3! U iso50.0147~3!

OI22 0.50 0.50 20.109~6! U iso50.029~1! 0.50~1! 0.00 20.10~1! U iso50.00~1!

OII22 0.50 0.00 0.389~3! U iso50.029~1! 0.36~1! 0.219~8! 0.404~8! U iso50.04~1!

%Molar 41.47~2! ~Tetragonal! 58.53~2! ~Monoclinic!

R-factors RB56.18 ~Tetrag!, 4.05 ~Mono!; Rw-p512.84, Rexp56.97, x253.39

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C. Refinement of the structures of the morphotropicphase Pb „Zr0.525Ti0.475…O3 .

For the rhombohedral phase of PZT, the 111 pseudobic reflection appears as a doublet while 200 is a singlet.the tetragonal phase, the pseudocubic 200 and 111 reflecappear as doublet and singlet, respectively. In the powXRD pattern of PZT withx50.525, the 111 pseudocubreflection appears as a doublet while 200 is not a singlecan be inferred from the large asymmetric broadening onlower 2u angle side of the peak~see Fig. 1!. These featurescannot be accounted for in terms of a pure rhombohedratetragonal structure but can be accounted for in terms ofmonoclinic structure of PZT discovered by Nohedaet al.9,10

and Raginiet al.11 The monoclinic phases were observedthese workers at low temperatures as a result of a succeof phase transitions from the pure tetragonal phase fox50.500, 0.515, and 0.520. The data presented in Fig. 1the other hand, indicates that the monoclinic phase maystabilized even at room temperature on increasing the Z41

content fromx50.520 to 0.525.In view of the foregoing, the structure of the morphotr

pic phase was refined assuming monoclinic space groupCmusing Rietveld technique. There are four ions in the asymetric unit of theFM

HT phase withCm space group. In thiscase, Pb21, Zr41/Ti41, and OI

22 are in 2~a! sites at (x, 0,z)and OII

22 in 4~b! sites at (x, y, z). Following Nohedaet al.,10 Pb21 was fixed at~0,0,0!. Initial values of positional

TABLE III. x2, RB, RW-P values for six different models for the structurePb~Zr0.520Ti0.480!O3.

S No. Phases x2 RB RW-P

1 Tetragonal1monoclinic 3.39 6.18~T!4.05~M!

12.84

2 Tetragonal1rhombohedral 3.42 6.18~T!3.81~R!

12.86

3 Monoclinic1rhombohedral 3.84 5.19~M!3.07~R!

13.67

4 Tetragonal1cubic 3.88 6.20~T!4.04~C!

13.67

5 Monoclinic 4.62 9.78 20.666 Tetragonal 4.97 16.65 27.56


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coordinates, lattice constants and thermal parameters fofinement were taken from Nohedaet al.’s10 work. Refine-ment was carried out in the same sequence as that fortetragonal phase.

Table IV. lists the refined structural parameters for troom temperature monoclinic phase of PZT withx50.525.The observed, calculated and difference profiles are giveFig. 5 which indicates a satisfactory fit . The off-center dplacements of the Ti41/ Zr41 and OI

22 along the @110#pseudocubic direction obtained by us for the room tempeture FM

HT phase are less than those reported by Nohet al.10 for the FM

HT phase below room temperature forx50.520, whereas our values for OII

22 displacements areslightly higher than theirs. The isotropic thermal parametfor Ti41/ Zr41 and OII

22 are lower in our case as comparedthe values obtained by Nohedaet al.10

Although the refinement of the structure of PZT withx50.525 assuming it to be pureFM

HT phase gives acceptabl‘‘ R’’ factors, the fit between observed and calculated profifor pseudocubic reflection like 220 is not very good. In tlight of the results of refinement of the structure of PZT wx50.520, where we found coexistence ofFT1FM

HT phases,we decided to examine the possibility ofFT1FM

HT and FT

1FR phases coexisting in sample withx50.525 also. Ourresults show a considerable improvement in thex2 value,

TABLE IV. Refined structural parameters of Pb~Zr0.525Ti0.475!O3 usingmonoclinic ~FM

HT! phase~space group:Cm! model.

Ions x y z U ~Å 2!

Pb21 0.0 0.0 0.0 U1150.044~3!U2250.002~3!U3350.042~3!U1350.023~3!

Zr41/Ti41

0.515~6! 0.0 0.452~3! U iso50.006~2!

OI22 0.53~2! 0.0 20.10~1! U iso50.089~2!

OII22 0.30~1! 0.24~1! 0.409~7! U iso50.000~1!

a55.745(1) Å,b55.7347(9) Å,c54.0972(7) Å,b590.367(9)°

RB55.70, RW-P514.04, Rexp57.91, x253.15


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FIG. 5. Observed~dots!, calculated~continuous lines!, and difference~bot-tom of the figure! profiles in the 2urange 20–60 for Pb~Zr0.525Ti0.475!O3

using monoclinic~FMHT! phase model.

Inset shows the patterns in the 2urange 62°–110°. Bars represent thpeak positions for CuKa1 .

FIG. 6. Observed~dots!, calculated~continuous lines!, and difference~bot-tom of the figure! profiles for Pb~Zr0.525Ti0.475! O3 in the 2u range20–60 with FT1FM

HT model. Insetshows the patterns in the 2u range62°–110°. The upper bars represent ttragonal peak positions and lower barepresent the monoclinic peak postions for CuKa1 .

FIG. 7. Observed~dots!, calculated~continuous lines!, and difference~bot-tom of the figure! profiles for Pb~Zr0.525Ti0.475!O3in the 2u range 20–60refined with FT1FR model. Insetshows the pattern in the 2u range 62°–110°. The upper bars represent tetraonal peak positions and lower barrepresent rhombohedral peak positionfor Cu Ka1 .

TABLE V. Refined structural parameters of Pb~Zr0.525Ti0.475!O3 for tetragonal~FT! and monoclinic~FMHT! phase coexistence model.


Monoclinic phase with space groupCm, a55.7532(8) Åb55.738(1) Å,c54.0900(4) Å andb590.49(8)°

Ions xT yT zT U ~Å 2! xM yM zM U ~Å 2!

Pb21 0.00 0.00 0.00 U115U225 0.029~5!U3350.012~5!

0.00 0.00 0.00 U1150.008~3!U2250.049~5!U3350.030~4!U1350.001~2!

Zr41/Ti41

0.50 0.50 0.46~1! U iso50.019~8! 0.517~5! 0.00 0.443~4! U iso50.000~3!

OI22 0.50 0.50 20.09~2! U iso50.02~5! 0.56~2! 0.00 20.11~2! U iso50.00~3!

OII22 0.50 0.00 0.38~1! U iso50.00~2! 0.31~1! 0.23~1! 0.46~2! U iso50.05~2!

%Molar 23.64~1! ~tetragonal! 76.36~4! ~monoclinic!

R-factorsRB56.69 ~tetragonal!, 3.91 ~monoclinic! Rw-p512.87,Rexp57.88,x252.67

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TABLE VI. Refined structural parameters of Pb~Zr0.525Ti0.475!O3 for tetragonal~FT! and rhombohedral~FR! phase coexistence model.


Rhombohedral phase with space groupR3m,a5b55.7493(6) Å,c57.093(2) Å

Ions xT yT zT U~Å 2! xR yR zR U~Å 2!

Pb21 0.00 0.00 0.00 U115U22

0.031~4!U3350.018~3!

0.00 0.00 0.56~1! U115

U2250.012~3!U3350.071~7!

Zr41/Ti41

0.50 0.50 0.446~3! U iso50.004~5! 0.00 0.00 0.01~1! U iso50.00(3)

OI22 0.50 0.50 20.129~9! U iso50.03(5) 0.261~9! 0.131~9! 0.1667 U iso50.05(1)

OII22 0.50 0.00 0.371~6! U iso50.01(1)

%Molar 46.32~2! ~tetragonal! 53.68~1! ~rhombohedral!

R-factorsRB54.47 ~tetragonal!, 2.94 ~rhombohedral! RW-P513.10, Rexp57.9, x252.75

thr-om

he

orfosss-

m

m

te-boo

era-ncethe

refulon0 Kithga-om-

forasy

ll to

yf

re-

r-

r

which decreased from 3.15 for pureFMHT phase model to 2.67

for FT1FMHT phase model and 2.75 forFT1FR phase model.

The fits between the observed and calculated profiles forFT1FM

HT and FT1FR phase models, along with the diffeence profiles, are shown in Figs. 6 and 7. It is evident frthe difference profiles that theFT1FM

HT phase model gives abetter fit . We have therefore acceptedFT1FM

HT phase modelas the correct model for the MPB region. Table V lists trefined parameters for this model. Since thex2 value for theFT1FR phase model is only marginally higher than that ftheFT1FM

HT phase model, we list the refined parametersthe former model in Table VI for the sake of completene

The equivalent elementary perovskite cell parametertheFM

HT phase coexisting with theFT phase at room temperature ~300 K! in the MPB region forx50.520 and 0.525~ap54.0673 Å,bp54.0610 Å,cp54.0918 Å for x50.520and ap54.0681 Å, bp54.0574 Å, cp54.0900 Å for x50.525! are closer to the pseudorhombohedral cell paraeter ~aR54.0681 Å forx50.530! just outside the MPB re-gion than the cell parameters of theFT phase given in TablesII and V. The equivalent elementary perovskite cell paraeters of theFM

HT phase discovered by Nohedaet al.9 for x50.520, on the other hand, are closer to the cell parameof the FT phase. Nohedaet al. have determined the cell parameters assuming the structure to be pure tetragonal a263 K and pure monoclinic below this temperature. F

TABLE VII. Refined structural parameters of Pb~Zr0.530Ti0.470!O3usingmonoclinic ~FM

HT! phase~space group:Cm! model.

Ions x y z U ~Å 2!

Pb21 0.0 0.0 0.0 U1150.014(2)U2250.042(3)U3350.052(4)U1350.001(1)

Zr41/Ti41

0.511~2! 0.0 0.431~2! U iso50.0011(8)

OI22 0.581~7! 0.0 20.059~9! U iso50.006(8)

OII22 0.310~7! 0.232~6! 0.4230~6! U iso50.0304(6)

a55.7760(4) Å,b55.7508(5) Å,c54.0900(3) Å,b590.471(5)°

RF511.76, RW-P512.25, Rexp55.33, x255.28


e

r.of

-

-

rs

ver

higher temperatures, and especially near the room tempture, the pure structural model may lead to ambiguities sithe tetragonal and monoclinic phases coexist. We, onother hand, have determined the cell parameters by a caRietveld profile fitting procedure for the coexistence regiand therefore the cell parameters obtained by us at 30should be more reliable. Comparison of our results wthose of Nohedaet al.10 clearly suggests that on increasinthe temperature from 20 to 300 K, the monoclinic cell prameters change from pseudotetragonal type to pseudorhbohedral type.

D. Refinement of the structure of PZT with xÐ0.530

The structure of PZT prepared by the semiwet routecompositions withx>0.530 has all along been regardedrhombohedral.6–8,19,20 As per the phase diagram given bJaffe et al.1 and more recent work of Corkeret al.,29 thestructure of PZT changes from a simple rhombohedral cea doubled rhombohedral cell forx'0.62. This doubled cellrhombohedral phase~FR

LT! transforms into the elementarcell rhombhohedral phase~FR

HT! on heating. In the course othe present work, we observed that the 200 pseudocubicflection, which must be a singlet for theFR

HT phase, is con-siderably broader than the neighboring 111 or 111¯reflection.The 200 reflection of theFR

HT phase is broader than the co

FIG. 8. Variation of ratio of FWHM of 200 and 111 Bragg profiles fodifferent compositions of PZT.


e


FIG. 9. Observed~dots!, calculated~continuous lines!, and difference~bot-tom of the figure! profiles in the 2urange 20–60 for Pb~Zr0.530Ti0.470!O3

using monoclinic~FMHT! phase model.

Inset shows the patterns in the 2urange 62°–110°. Bars represent thpeak positions for CuKa1 .

ul-is

thur-od

ng

is-ldc-

c

ciza

de

n-ibleolu-

but

theeup.

om-ttice

ula

o--sedOnbe

del

he

responding 200 reflection of the pureFT phase~x50.515!also. Figure 8 depicts the variation of the ratio of the fwidth at half maximum~FWHM! of the 200 and 111 reflections for six different compositions. It is evident from thfigure, that this ratio is close to 1 for theFT phase~x50.515) and also for theFR

LT phase withx50.80 and 0.90.For theFR

HT phase, this ratio is as high as 1.6 forx50.530and gradually decreases with increasingx. All these observa-tions suggest that the 200 reflection of the so-calledFR

HT

phase may not be a singlet but a superposition of moreone reflection. This clearly implies that the room temperatstructure of PZT for 0.530<x,0.70 may not be rhombohedral. A perusal of the high resolution XRD data for the scalled rhombohedral structure of PZT given by Noheet al.27 and Guoet al.30 for x50.580~in their description, itcorresponds tox50.420! also shows anomalous broadeniof the 200 pseudocubic peak.

A similar situation has recently been observed31,32 inPbFe0.50Nb0.50O3 and has been attributed to monoclinic dtortion of the pseudorhombohedral unit cell. In fact, Rietverefinement for PZT compositions with rhombohedral struture by Corkeret al.29 did not yield satisfactory results unless local displacements along^110& directions of the el-ementary perovskite cells were postulated. These lodisplacements, in the light of the discovery of theCm phase~FM

HT! by Noheda et al.,10 correspond to the monoclinistructure. Apparently, the coherently scattering domain sof the monoclinic phase for these compositions is too smto give rise to characteristic peak splittings on the pow


l

ane

-a

-

al

ellr

XRD patterns in Fig. 1. However, on application of an itense dc field, the monoclinic distortion becomes discerndue to merger and alignment of the domains on high restion powder diffraction patterns.30 In view of the foregoing,it is more appropriate to call the hitherto believedFR

HT asFM

HT , as the true structure is definitely not rhombohedral,is most likely to be monoclinic.

Accordingly, refinement for PZT withx50.530 was car-ried out assuming a monoclinic~Cm! structure. For the sakeof completeness, refinement was also carried out forrhombohedral structure usingR3m space group. There arthree atoms in the asymmetric unit of the latter space groIn this refinement, hexagonal axes were used for the rhbohedral structure. The rhombohedral and hexagonal laparameters are related asaH5bH5A2aR and cH5A3aR .The hexagonal unit cell contains three molecular formunits of PZT. In the asymmetric unit of the structure, Pb21

and Zr41/Ti41occupy 3~a! site at ~0,0,z!. O2- occupies the9~b! site symmetry at (2x,x,1/6).

We find that thex2 value for the monoclinic phasemodel ~5.28! is appreciably lower than that for the rhombhedral phase model~5.76!. Figures 9 and 10 show the observed, calculated, and difference plots for refinements baon monoclinic and rhombhohedral phases, respectively.comparing the difference plots for the two models, it caninferred that the fit is better for the monoclinic phase moespecially for thehh0 ~e.g., the 110 peak around 2u531o!andh00 ~e.g., the 200 peak around 2u545o! type pseudocu-bic reflections. Table VII lists the refined parameters for t

ee

FIG. 10. Observed~dots!, calculated~continuous lines!, and difference~bot-tom of the figure! profiles in the 2urange 20–60 for Pb~Zr0.530Ti0.470!O3using rhombohedral~FR! phasemodel. Inset shows the patterns in th2u range 62°–110°. Bars represent thpeak positions for CuKa1 .


wiT

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teth.th-

it

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ra

true

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th

tos

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.-E.

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Rev.

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aki,

am.

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. A.

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, J.

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monoclinic phase model. Thus, our results suggest thatincreasing Zr41 content, the tetragonal structure of PZtransforms to monoclinic~FM

HT! through a two-phase regioshowing coexistence of these two phases. The monocdistortion of the pseudorhombohedral phase of PZT fox50.530 is very small and is similar to the low temperatumonoclinic phase of Pb~Fe0.50Nb0.50!O3. 31,32 First principlecalculations by Bellaicheet al.33 predict the existence of astable monoclinicFM

HT phase field over a narrow intermediarange of composition which may act as a bridge betweenFR

HT andFT phases. The FWHM analysis presented in Figshows that theFM

HT phase is stable at room temperature inentire composition range 0.530<x<0.62. The exact composition at which theFM

HT phase field disappears and theFRLT

phase appears is currently being investigated by us butclear that theFM

HT phase acts as a bridge between theFT andFR

LT phases and not between theFT and theFRHT phases lead-

ing to significant modifications to the existing phase diagrof PZT, the details of which will be reported elsewhere.34

V. CONCLUSIONS

We have carried out a detailed Rietveld analysis of x-powder diffraction data for PZT samples withx50.515,0.520, 0.525, and 0.530 to settle the room temperature sture of PZT in and around the MPB region. Results obtainfrom Rietveld analysis confirm that PZT withx50.515 has atetragonal structure. The structure of PZT withx50.520, onthe other hand, is not pure tetragonal, as was believedearlier workers,6–11 but it has a coexisting monoclinic~FM

HT!phase. This coexistence of monoclinic~FM

HT! phase with thetetragonal~FT! phase is due to the first order nature oftragonal ~FT!-monoclinic ~FM

HT! phase transition which occurs around 265 K forx50.520.11 For x50.525 also, theFM

HT andFT phases are found to coexist at room temperatuAs shown elsewhere,34 theFM

HT to FT phase transition for thiscomposition occurs around 483 K and is accompanied wiwide coexistence region of about 200 K.34 The structure ofPZT changes abruptly atx50.530. Our XRD results andtheir analysis reveal that the structure of theFR

HT phase ofPZT for 0.530<x<0.620 is not rhombohedral, as hitherbelieved all along, but is most likely to be monoclinic. Thuthe MPB region in PZT is quite narrow~0.515,x,0.530!and separates theFT ~x<0.515! andFM

HT ~0.530<x<0.620!phase fields.

ACKNOWLEDGMENTS

The authors acknowledge the partial support by InUniversity Consortium for Department of Atomic Energy Fcilities, Mumbai Center, India. One of the authors~D. P.! isgrateful to Professor T. V. Ramakrishnan for drawing thattention towards the recent PZT papers. S. K. M. is grat


th

ic

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is

y

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rul

to the Council of Scientific and Industrial Research~CSIR!of India for the award of a Research Associateship.

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Documents

Room temperature structure of Pb(ZrxTi1-xO3) around the morphotropic phase boundary region: A Rietveld study