Recent years have witnessed a revival of interest in pi-ezoelectric ceramics like PbZrO3–xPbTiO3 �PZT�,Pb�Mg1/3Nb2/3�O3–xPbTiO3�PMN–xPT�, Pb�Sc1/2Nb1/2�O3
–xPbTiO3�PSN–xPT�, and Pb�Zn1/3Nb2/3�O3
–xPbTiO3�PZN–xPT� following the discovery of newmonoclinic phases.1–10 A common characteristic of the phasediagrams of these technologically important ferroelectricsolid solutions is the existence of a nearly vertical phaseboundary, called morphotropic phase boundary �MPB�,which separates the stability fields of the tetragonal andpseudorhombohedral phases in their phase diagrams.7,11 Thepiezoelectric and dielectric properties of these ceramics aremaximized for the composition corresponding to the MPBwhich makes these compositions technologically important.The so-called rhombohedral phase on the lower Ti4+ contentside of the MPB has in recent years been shown to be mono-clinic in the Cm space group in the PZT and PMN–xPTceramics.6–8,12,13 More recently, high pressure phase diagramof even the pure PbTiO3 is reported to exhibit an MPB.14 Ithas been argued that the partial replacement of Ti4+ withZr4+, Mg2+ /Nb5+, and Zn2+ /Nb5+ in PZT, PMN–xPT, andPZN–xPT, respectively, stabilizes the MPB of pure PbTiO3
at ambient pressures.PbTiO3 forms continuous solid solutions with several
bismuth based transition metal perovskite oxides �likeBiFeO3, BiScO3, and BiMnO3�. These Bi-based solid solu-tions show very high value of ferroelectric transition tem-perature �TC�.15 They also exhibit16,17 MPB in their ambientpressure phase diagram similar to that in PZT and relatedmaterials. Of these solid solutions, the �1−x�BiFeO3–xPbTiO3 �BF–xPT� system is of special impor-
tance, as one of its end members, BiFeO3, is an attractiveroom temperature multiferroic with highest ferroelectric andmagnetic transition temperatures reported so far in the familyof multiferroic oxides.18,19 The BF–xPT solid solution showsseveral interesting features like unusually large tetragonalitywhich goes on increasing with increasing iron content until itattains the highest value for the tetragonal composition �x=0.31� closest to the MPB.20 The structure of BF–xPT on theother side of the MPB composition is reported to bemonoclinic21 similar to that in the other well known MPBsystems like PZT, PMN–xPT, and PSN–xPT7,10,11 but with asignificant difference. The space group of the monoclinicphase of BF–xPT is not Cm / Pm but rather Cc correspondingto a doubled perovskite cell with oxygen octahedra rotated inan antiphase manner in the neighboring unit cells corre-sponding to the a−a−c− tilt system in Glazer’s notation.22,23
According to our earlier investigations,20,21 the tetrago-nal and monoclinic phases in this MPB system are stable forcompositions with x�0.31 and x�0.27, respectively,whereas the two phases coexist in the MPB region corre-sponding to the composition range 0.27�x�0.31. However,in a recent report,24 it has been claimed that the so-calledphase coexistence region corresponds to the stability field ofan orthorhombic phase which separates the stability fields ofthe tetragonal and rhombohedral phases but they have notdetermined the space group of this orthorhombic phase. Theexistence of an intermediate phase with symmetry lower thanrhombohedral and tetragonal phase has also been predictedon the basis of electron diffraction studies,25 but the spacegroup of the possible low symmetry phase was not deter-mined in this work also. The width of the coexistence regionreported by Zhu et al.24 and Woodward et al.25 are unusuallylarge ��x�0.20 and �0.10, respectively� as compared tothat ��x�0.03� reported by Bhattacharjee et al.20 These
a�Author to whom correspondence should be addressed. Electronic mail:[email protected].
investigations24,25 raise three controversies: �i� is the struc-ture of BF–xPT on the BF rich side of the MPB rhombohe-dral or monoclinic proposed recently,21 �ii� does the MPBregion consist of a coexistence of the tetragonal and mono-clinic phases stable on the two sides of the MPB or it repre-sents the stability field of an orthorhombic phase, and �iii� isthe width of the MPB region �x�0.03 or much larger like0.10 or 0.20 reported in Refs. 24 and 25?
In the present work, we revisit the structure of BF–xPTin the entire composition range using Rietveld technique toresolve the existing controversies. Our Rietveld results ruleout the presence of any intermediate orthorhombic phase inthe MPB region of BF–xPT. Consideration of all possiblemode symmetry permitted subgroups of the cubic phase inthe rhombohedral, orthorhombic and monoclinic structuresin the Rietveld refinements reconfirms the correctness of theCc space group on the BF rich end of the MPB from x=0.27 to 0.10. We also present a structure-composition phasediagram at room temperature for the BF–xPT system.
After settling the controversies about the structure ofBF–xPT as a function of composition, we also address theissue of stability of various crystallographic phases of BF–xPT as a function of temperature. In the well-known PZTand PMN–xPT ceramics, the MPB is known to be tilted to-wards the monoclinic phase region, as a result of which themonoclinic compositions very close to the MPB transformon heating to the cubic paraelectric phase via an intermediatetetragonal phase.11 We show here that BF–xPT does not fol-low this sequence of transitions. Here the ferroelectric mono-clinic phase transforms directly to the paraelectric cubicphase whereas the ferroelectric tetragonal phase transformsto the paraelectric cubic phase via an intermediate mono-clinic phase. This reveals for the first time that the MPB inBF–xPT is tilted towards the tetragonal phase region in con-trast in the MPB in the well known PZT, PMN–xPT, andPZN–xPT systems where it is tilted towards the monoclinicphase region.
I. EXPERIMENTAL
A. Sample preparation
Different compositions of the solid solution system BF–xPT for x=0.1, 0.2, 0.25, 0.27, 0.28, 0.29, 0.3, 0, 31, 0.4, 0.5,0.6, 0.7, 0.8, and 0.9 were prepared by solid state thermo-chemical reaction route using analytical reagent grade Bi2O3
�99.5%�, Fe2O3 �99%�, PbO �99%�, and TiO2 �99%� re-agents. Calcination was carried out at 1033 K for 6 h in analumina crucible. Sintering was performed at 1173 K for 1 hin closed alumina crucible with calcined powder of the samecomposition kept inside the closed crucible as a spacer pow-der for preventing the loss of Bi3+ during sintering. It hasbeen found that inadequate control of loss of Bi3+ duringsintering leads to wider coexistence region across the MPB.For x-ray characterizations, sintered pellets were carefullycrushed into fine powders and then annealed at 973 K for 10hours to remove the mechanical strains introduced duringcrushing of the sintered pellets. Powder x-ray diffraction�XRD� study was carried out using an 18 kW Cu-rotatinganode based Rigaku �Tokyo, Japan� powder diffractometer
operating in the Bragg–Brentano geometry and fitted with acurved crystal graphite monochromator in the diffractionbeam and a high temperature attachment. The XRD patternsof BF–xPT at room temperature confirmed the absence ofany impurity phase except for x=0.1, for which a small im-purity peak ��3%� of Bi2Fe4O9 is observed.
B. Rietveld refinement
Rietveld refinements were carried out using FULLPROF
package.26 In the refinement process the background wasmodeled using linear interpolation method, while the peakshapes were described by pseudo-Voigt functions. Occu-pancy parameters of all the ions were kept fixed at the nomi-nal composition during refinement. Zero correction, scalefactor, background, half width parameters �u, v, and w�, lat-tice parameters, positional coordinates and thermal param-eters were varied during the refinement. For the tetragonalcompositions with 0.31�x�0.6, anisotropic thermal param-eters were used for A site cations �Pb/Bi� and oxygen as theisotropic thermal parameters were found to be too large,whereas for higher lead content compositions with 0.7�x�0.9, isotropic thermal parameters were found to be ad-equate for all atoms. For monoclinic compositions, isotropicthermal parameters were used for all the atoms present in theunit cell.
II. RESULTS
A. Structure of different crystallographic phases as afunction of composition
BiFeO3 shows rhombohedrally distorted perovskitestructure in the R3c space group symmetry. In this noncen-trosymmetric structure, the oxygen octahedra in the neigh-bouring unit cells are rotated in the antiphase manner aboutthe �111� pseudocubic direction which becomes the uniquethreefold axis of the rhombohedral phase. This structure withR3c space group can be visualized to result from the freezingof the zone centre �q=000� and zone boundary �q= �1 /2� �1 /2� �1 /2�� phonons of the paraelectric/paraelasticcubic phase in the Pm3m space group. As a result of thepresence of the antiphase rotated octahedra, the unit cell getsdoubled leading to the appearance of superlattice reflectionswhich are represented by three odd integered Miller indiceswith respect to the doubled pseudocubic perovskite cell.22,23
All the perovskite peaks on the other hand are represented bythree even integered Miller indices with respect to thedoubled pseudocubic perovskite cell.
Fig. 1 shows the XRD profiles in the two theta range 15°to 60° for x=0.1 to 0.9. On the BiFeO3 rich end of theBF–xPT solid solution, the structure is similar to the pureBiFeO3, as can be seen from Fig. 1�a� for x=0.10. The char-acteristic feature of the rhombohedral phase is the doubletcharacter of the pseudocubic 220 and 222 reflections, singletnature of 400 and the presence of the 311 superlattice reflec-tion �all indices are with respect to the doubled psuedocubiccell on account of antiphase octahedral tilts�. This BF typestructure persists upto x=0.27 as can be seen from Fig. 1�d�.With further increase in PT content by 1%, new peaks of asecond phase begin to appear �Fig. 1�e��. As for example, the
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vikash
Highlight
small peaks on both the sides of 220 psuedocubic reflectionat 2��30° and 33° have appeared for x=0.28. These peaksare marked with arrows in the inset of Fig. 1�e�. With stillhigher PT content �x=0.29 and 0.3�, this second phase be-comes the majority phase while the BF type phase is theminority phase. With further increase in PT content to x=0.31, the BF type reflections disappear �Fig. 1�h��. Further,the superlattice reflection of BF also disappears and the 222reflection of the BF type phase becomes a singlet whereas400 is now a doublet, as can be seen from Fig. 1�h�. These
are characteristics of the tetragonal phase which persists uptothe PT end. The pseudocubic 222 and 400 reflections of theBF type phase become 111 and 200 in the tetragonal phaseand the equivalent perovskite cell is no longer doublet due tothe absence of antiphase octahedral tilt.
Our results clearly show that the two phase region ex-tends from x=0.28 to 0.30, and the width ��x� of the MPBregion is �0.03. In a recent report, the width of the MPB isreported to be �x�0.15.24 However, a close examination ofthe XRD results of this paper �see Fig. 3, of Ref. 24� revealsthat the two phase region in their sample extends from x=0.2 to 0.4 giving an unusually large composition width of�x�0.2 of the MPB region in BF–xPT. Some of the com-positions interpreted as pure tetragonal phase compositionsin this work24 actually contain a small amount of the secondphase. The narrow width of the two phase region ��x�0.03� obtained by us is the result of good chemical homo-geneity of our samples. The large width of the MPB reportedby others is an artifact of compositional fluctuations and het-erogeneities. Thus the room temperature structure of BF–xPT is BF-like upto x=0.27 and PT-like for x�0.31 with anMPB region of 0.27�x�0.31 over which the two phasesseem to coexist in compositionally homogeneous samples.To provide quantitative confirmation to the above structuralmodels, we now proceed to present the results of Rietveldrefinements for the three representative composition ranges.
B. Rietveld refinements for x�0.27
As said earlier, the XRD profiles of BF–xPT for x=0.1,0.2, 0.25, and 0.27 show features similar to those expectedfor pure BiFeO3 including the presence of a characteristicsuperlattice reflection around 2��39°. Accordingly, therhobmohedral R3c space group of BiFeO3 was consideredfirst in the Rietveld refinements for all the BF–xPT compo-sitions with x�0.27.21 Megaw and Darlington27 have shownthat the rhombohedral perovskites with formula ABO3 in theR3c space group may be described in terms of nearly regularBO6 octahedra, tilted around the triad axis. The descriptionof atomic positions in such rhombohedral perovskites interms of the five structural parameters s, t, e, d, and � allowseasy recognition of physically important features.27 The sand t parameters describe the displacement of cations A andB from their ideal perovskite position giving rise to a dipolemoment and hence the spontaneous polarization in the ferro-electric phase. The parameter e is related to the tilt angle �of the oxygen octahedra by the expression tan �=43e andthe parameter d describes the distortion of the octahedra.�1+�� represents octahedral strain, i.e., compression or elon-gation along the triad axis and depends both on the latticeconstants and the tilt angle. The space group R3c has twoWyckoff sites: 6�a� occupied by Pb/Bi and Ti/Fe and 18�b�occupied by O with coordinates as: Pb /Bi= �0,0 , �1 /4�+s�,Ti /Fe= �0,0 , t�, and O= �1 /6−2e−2d,1 /3−4d,1 /12� withrespect to the hexagonal unit cell. Initial structural param-eters for the refinements were kept identical to those ofBiFeO3.
We depict in Figs. 2�a� and 3�a� the observed, calculated,and difference profiles for the 400, 440, and 444 psuedocubic
FIG. 1. �Color online� Room temperature XRD profile for BF–xPT solidsolution. Inset in the Fig. 1�a�–1�g� shows the 220 and 222 pseudocubicperovskite reflections and also the weak 311 superlattice peak.
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reflections for x=0.27 and 0.10 obtained after full patternRietveld refinement using the R3c space group. It is evidentfrom the figures that the fits are not satisfactory. This is alsoindicated by the high 2 values of 6.49 and 6.94 for x=0.27 and 0.10, respectively. The misfit is essentially due tothe anomalous peak broadening of the h00 type reflections,such as 400 in Fig. 2�a�. This reflection is a singlet for the
R3c space group and it should therefore have a peak widthsmaller than the higher angle reflections like the sharp 444peak. But it is the other way round in BF–xPT. The ratio ofthe full width at half maximum �FWHM� of the 400 peak tothat of the neighboring 222 peak should be close to 1 but itvaries from 1.625 to 1.93 for x=0.1 to 0.27, as shown in Fig.4.
In order to account for this anomalous peak broadening,we considered anisotropic strain broadening using Stephen’smodel. The consideration of the anisotropic strain broaden-ing leads to improvement in the fits for the 400 and 440reflections with a concomitant decrease in 2 to 3.08 and3.893 for x=0.27 and 0.10, respectively, but the fit for otherreflections like 444 �see Figs. 2�b� and 3�b�� worsens. Thusthe incorporation of anisotropic strain broadening functionsalso could not explain the observed diffraction profiles satis-factorily. We then considered split atom model for Bi/Pb siteto incorporate the effect of local disorder, which has beenreported for several Pb based compounds28 but this modelalso fails to fit the profiles satisfactorily, as can be seen fromFigs. 2�c� and 3�c�. All these refinements gave us sufficientindication that other lower symmetry space groups, similar tothat in PZT and PMN–xPT, have to be considered to explainthe observed XRD profiles.6,11,12
At this stage, software package ISOTROPY29 was used to
obtain probable space groups, that are subgroups of Pm3mfor a second order phase transition from the cubic paraelec-tric phase. This software package can be used to visualize thesequence of transitions in terms of irreducible displacementmodes. By freezing 4− and R4+ irreducible displacementmodes of the cubic Pm3m, which are responsible for theoff-centre displacements of cations and antiphase rotation ofoctahedra, respectively, the following space groups, whichare subgroups of Pm3m, were generated: �a� rhombohedralspace group: R3c, �b� orthorhombic space groups: Ima2 andImm2 and Fmm2 and �c�monoclinic space groups:Cm�2aP ,2bP , 2cP�, Cc�6aP , 2bP, 2cP�, andC2�2aP ,2bP , 2cP�, where aP, bP, and cP are elementary per-ovskite cell parameters.
All these space groups predict superlattice reflections ofthe type observed in pure BF and the mixed BF–xPT. We
FIG. 2. �Color online� Comparison of Rietveld refined profiles for 200, 220,and 222 psuedocubic reflections for three different structural models usingrhombohedral R3c space group for BF–0.27PT.
FIG. 3. �Color online� Comparison of Rietveld refined profiles for 200, 220,and 222 psuedocubic reflections for three different structural models usingrhombohedral R3c space group for BF–0.10PT.
FIG. 4. �Color online� Variation in the ratio of the FWHM of profiles of the200 and 111 Bragg reflections for monoclinic compositions of BF–xPT forx�0.27.
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carried out Rietveld refinement using powder XRD data inthe 2� range 15° to 120° for all the above mentioned spacegroups. The Rietveld fitted profiles are depicted for 400, 440,and 444 psuedocubic reflections in Fig. 5. It is clear from thefigure that the Rietveld fits for the Fmm2, Imm2, Ima2, andCm space groups are rather poor. R3c and C2 give better fitsfor the 400 and 440 psuedocubic peaks but cannot explainthe profile of the 444 reflection. Amongst the space groupsconsidered on the basis of symmetry arguments for a secondorder phase transition, the Cc space group gives the best fitas can be seen from Fig. 5. It also gives the lowest 2 valuewhich is statistically significant too. We thus conclude thatthe structure of BF–xPT for 0.1�x�0.27 is monoclinic inthe Cc space group and not rhombohedral as proposedrecently24 and in the earlier work30 as well.
For the Cc space group, there is only one Wyckoff sitesymmetry 4�a� with the asymmetric unit of the structure con-sisting of five atoms. Pb/Bi is fixed at 0.00, 0.25, and 0.00.The remaining atoms have coordinate as follows: Ti/Fe at0.25+�x, 0.25+�y, and 0.75+�z and three oxygen atoms O1at 0.00+�xI, 0.25+�yI, and 0.5+�zI, O2 at 0.25+�xII, 0.5
+�yII, and 0.00+�zII and O3 at 0.25+�xIII, 0.00+�yIII, and0.00+�zIII. Various �’s represent the refinable parameters.The refined parameters for the Cc space group for variouscompositions of BF–xPT with 0.1�x�0.27 are listed inTable I.
C. Rietveld refinements for x�0.31
The tetragonal phase of BF–xPT persists over a rela-tively large composition range starting from PT �x=1� endup to x=0.31. One of the most interesting features of thetetragonal phases of BF–xPT is that the tetragonality goes onincreasing with BF addition upto x=0.31, whereas for otherMPB solid solution system based on PbTiO3, including thefamous PZT ceramics, the tetragonality goes on decreasingwith decreasing PT content. Even for the other Bi basedMPB systems, like BiScO3–xPbTiO3 �Ref. 16� andBiMnO3–xPbTiO3,17 the tetragonality at the PT end de-creases with the substitution of Pb with Bi and Ti with Sc/Mn.
In order to get the structural insight into the tetragonalphase, Rietveld refinement for all the tetragonal composi-tions have been carried out. In the tetragonal phase withP4mm space group, the Bi+3 /Pb+2 ions occupy 1�a� site at �0,0, and �z�, Fe+3 /Ti+4 occupy 1�b� site at �1 /2,1 /2,1 /2+�z�. The three oxygens in the asymmetric unit of the per-ovskite cell occupy two different Wyckoff positions: 1�b� siteat �1/2, 1/2, and �z� and 2�c� site at �1 /2,0 ,1 /2+�z�. TakingPb/Bi at the origin, the atomic positions can be described interms of three parameters �zB, �zOI, and �zOII only. Thus thecoordinates of the asymmetric unit used in the refinementsare: Pb /Bi= �0,0 ,0� and Ti /Fe= �1 /2,1 /2,1 /2+�zB�; OI
= �1 /2,1 /2,�zOI� and OII= �1 /2,0 ,1 /2+�zOII�.31 The calcu-
lated, observed and difference patterns of BF–0.8PT and BF–0.4PT are shown in Fig. 6. The fit is quite good. We obtainedsimilar quality fits for other tetragonal compositions as well.The refined coordinates and lattice parameters for varioustetragonal compositions of BF–xPT are given in Table II.
D. Crystal structure for the two phase region
The two phase region is stable in the BF–xPT system forthe composition range 0.27�x�0.31. We have alreadyshown that the tetragonal and monoclinic phases in theP4mm and Cc space groups are stable for x�0.27 and 0.31,respectively. If the phase boundary between the P4mm andCc phases is a first order phase boundary, one expects acoexistence of tetragonal P4mm and monoclinic Cc phasesin the composition range 0.28�x�0.30. Zhu et al.,24 on theother hand, have proposed an orthorhombic phase in theMPB region. Such a possibility could arise if the MPB is asecond order boundary. If it is so, the structure in the MPBregion should be a super group of Cc and a subgroup ofP4mm space groups. Further, such an orthorhombic phaseshould result from freezing of the 4
− and R4+ irreducible
displacement modes of the cubic Pm3m paraelectric phase.The 4
− mode accounts for the ferroelectric nature while theR4
+ accounts for the observed superlattice peaks in the com-position range 0.28�x�0.30. As discussed earlier, there arethree possible orthorhombic space groups, as per the
84 85
x=0.27
χ2 = 2.21
400 440 444χ2 =3.1
Imm2
Ima2
Cm
C2
Cc
χ2=4.5
χ2 =5.2
χ2 =6.2Intensity(arb.unit)
2θ (degree)
χ2 =6.6
45 46
Fmm2
66 67
χ2 =16.1
R3c
FIG. 5. �Color online� Comparison of Rietveld refined profiles of 200, 220,and 222 psuedocubic reflections for BF–0.27PT using different space groupsymmetries permitted by group theoretical considerations �see text fordetails�.
124112-5 S. Bhattacharjee and D. Pandey J. Appl. Phys. 107, 124112 �2010�
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ISOTROPY29 package, namely Fmm2, Ima2, and Imm2, which
are also subgroups of the cubic phase. The XRD patternsshown in Figs. 1�e�–1�g� clearly reveal the presence of thetetragonal phase �P4mm space group� peaks. In addition,there are peaks corresponding to another coexisting phase�whose structure we wish to identify� for the compositionrange 0.28�x�0.30. Accordingly, we have considered thefollowing structural models in the Rietveld refinements: �i�P4mm+Cc, �ii� P4mm+Fmm2, �iii� P4mm+ Ima2, and �iv�P4mm+ Imm2. Since for the x=0.29 composition, the peaksof the two coexisting phases are nearly equally intense, wehave, therefore, selected this composition for deciding thestructure of the MPB phase by Rietveld refinement. The ob-served, calculated, and difference profiles obtained by Ri-
etveld refinement for these four models are compared in Fig.7. It is evident from this figure that the fit for P4mm+Ccmodel is the best and this model gives significantly lower 2
value as compared to those for the other three models. Ouranalysis thus rules out the possibility of any orthorhombicphase being present in the MPB region of BF–xPT, proposedin Ref. 24. As said earlier, the existence of an intermediatephase of BF–xPT in the two phase region with symmetrylower than rhombohedral �R3c, BiFeO3-type� and tetragonal�P4mm� has been predicted on the basis of electron diffrac-tion experiments.25 Our results show that the space group ofthe second phase coexisting with the tetragonal phase for x=0.29 is Cc which has a symmetry lower than rhombohedraland tetragonal in agreement with the predictions of a lowersymmetry phase in Ref. 25.
In the XRD profiles of two phase region, the monoclinic110 �psuedocubic 200� reflection lies to the left of 001 te-tragonal reflection and appears as a small hump of the 001tetragonal profile which has been erroneously interpreted asbeing due to an orthorhombic distortion in Ref. 24. Thismonoclinic peak gets clearly resolved from the tetragonalpeak for the second order reflections �i.e., psuedocubic 400or equivalently monoclinic 220 and tetragonal 002� of thesame family as shown in the inset to Fig. 7�a�. The Rietveldfit for the second order reflections shown in the inset con-firms that one of the peaks is due to the monoclinic phasewhereas the other one is due to the tetragonal phase and notdue to an orthorhombic phase. The refined coordinates andlattice parameters for various compositions in two phase re-gion of BF–xPT are given in Table III. The room temperaturephase diagram, i.e., variation in the cell parameters versuscomposition, of the BF–xPT system is shown in Fig. 8.
TABLE I. Rietveld refined position coordinates, thermal parameters, and lattice parameters for compositions with x=0.27, 0.25, 0.20, and 0.10 in themonoclinic phase.
FIG. 6. �Color online� Observed �dotted�, calculated �continuous line�, anddifference profiles �bottom line� obtained from Rietveld refinement of pow-der diffraction profile of BF–0.4PT and BF–0.8PT solid solutions usingtetragonal P4mm space group.
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E. High temperature stability of the tetragonal andmonoclinic phases on the two sides of theMPB
We have carried out high temperature XRD studies forsingle phase tetragonal and monoclinic compositions closestto the MPB, i.e. x=0.31 and 0.27. Figure 9 depicts the tem-perature variation in the diffraction profiles for the tetragonalphase. We note that the 100 and 110 psuedocubic peak issplit into 001, 100, and 110, 101 pair of reflections in thetetragonal phase. �see the XRD profiles for T�550 °C�. Onheating, new peaks begin to appear at �650 °C. For ex-ample, a pair of peaks has appeared in between 110 and 101reflections of the tetragonal phase at 650 °C. Further, anearly singlet peak appears from the tail of the 100 tetrago-nal peak. These peaks are marked with asterisk in the figurefor 650 °C. With further increase in temperature, the peakscorresponding to the new phase become stronger than thoseof the tetragonal phase, as can be seen in the diffractionpattern corresponding to 675 °C. All the new peaks could beeasily identified as being due to the monoclinic phase at thistemperature. With further increase in the temperature to700 °C, the splitting of all the peaks disappears. This disap-pearance of the splitting confirms the transformation to thehigh temperature paraelectric cubic phase. Our results thusshow that the tetragonal phase first transforms to the mono-clinic phase, with a small fraction of coexisting tetragonal
20 40 60 80 100 120
39.5 40.0
(b) χ2 =4.98P4mm +Ima2
(c) χ2 =7.74P4mm+Imm2
x=0.29
(a) χ2 =2.97P4mm + Cc
(d) χ2 =9.91P4mm+Fmm2
Intensity(arb.units)
2θ (degree)
T002M400
FIG. 7. �Color online� Observed �dotted�, calculated �continuous line�, anddifference profiles �bottom line� obtained from two phase Rietveld refine-ment of powder diffraction profile of BF–0.29PT using �a� tetragonal P4mmand monoclinic Cc, �b� tetragonal P4mm and orthorhombic Ima2, �c� tetrag-onal P4mm and orthorhombic Imm2, and �d� tetragonal P4mm and ortho-rhombic Fmm2 space groups. Inset in �a� shows the Rietveld fits for mono-clinic 400 �psuedocubic indices� and tetragonal 002 peaks.
TABLE II. Rietveld refined position coordinates, thermal parameters, and lattice parameters for compositions in the tetragonal phase.
124112-7 S. Bhattacharjee and D. Pandey J. Appl. Phys. 107, 124112 �2010�
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phase, both of which on further heating transform to thecubic phase. This clearly implies that the MPB region istilted towards the tetragonal phase region in the BF–xPTsystem in contrast to PZT, PMN–xPT, and other systems,7,11
where it is tilted towards the monoclinic phase region, as aresult of which the monoclinic compositions of PZT, etc.,transform to the cubic phase via the tetragonal phase. Thephase coexistence during the tetragonal to monoclinic phasetransition reveals first order character of this transition.
In contrast to the tetragonal composition x=0.31, themonoclinic phase in the BF–xPT transforms directly to the
cubic phase, as explained in what follows. The transforma-tion behaviour of BF–xPT for x=0.27 is shown in Fig. 10.The characteristic splitting of the 220 and 222 psuedocubicpeaks �indices with respect to the doubled psuedocubic cell�is clearly seen in the diffraction profiles upto 600 °C. Thesplitting of the 220 psuedocubic reflection, however, getsconsiderably reduced in the 600 °C pattern but the 222 psue-docubic peak is still well split. At 700 °C, the splitting ofboth the 220 and 222 peaks disappears. This clearly showsthat the monoclinic phase has transformed to the cubic phasearound this temperature. Thus in the BF–xPT system, themonoclinic phase transform directly to the cubic phase,whereas the transformation from the tetragonal to the cubicphase is via the intermediate monoclinic phase. Figure 11depicts a schematic x-T phase diagram prepared on the basisof the results of the present work and some of our unpub-lished work. The most notable point of this phase diagram isthat the MPB is tilted towards the tetragonal side of MPB.Further, all the phase boundaries shown in this diagram arefirst order with phase coexistence.
III. DISCUSSION
The room temperature phase diagram of the BF–xPTsystem is shown in Fig. 8. This phase diagram differs con-siderably from a recent phase diagram reported by Zhu etal.24 regarding the location and the structure of the MPBphases. It is, however, qualitatively similar to the phase dia-
TABLE III. Rietveld refined position coordinates, thermal parameters, and lattice parameters for compositions in the two phase region.
FIG. 8. �Color online� Variation in lattice parameters with composition forBF–xPT solid solution.
124112-8 S. Bhattacharjee and D. Pandey J. Appl. Phys. 107, 124112 �2010�
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gram reported earlier by Smith et al.30 with one importantdifference. The MPB separates the stability fields of the te-tragonal �P4mm� and monoclinic �Cc� phases in BF–xPT, asdiscussed in the previous sections and not the tetragonal andrhombohedral �R3c� phases reported by Smith et al.30 whodid not carry out any structural refinement study. Both thephases coexist in the MPB region which lies in the range0.27�x�0.31 giving an intrinsic width �x�0.03 to theMPB, whereas this width is reported to be �0.20 in Ref. 24.The large compositional width of the MPB region24 is due toextrinsic factors such as compositional fluctuations and het-erogeneities. From the variation in the cell parameters withcomposition in the tetragonal region of the phase diagram, itis evident that the “c” parameter increases continuously to-wards the MPB but the “a” parameter decreases, albeit
slowly, towards the MPB, with the result that the tetragonal-ity increases towards the MPB in agreement with the earlierreport.30 The tetragonality is much higher than that of the endmember PT. For BF–0.31PT, the ratio of the two cell param-eters, c/a, is around 1.187 �Ref. 20� which is probably thehighest c/a ratio in any ferroelectric MPB system.
The variation in the bond lengths formed by A site �Bi/Pb� and B site �Fe/Ti� cations with apical �O1� and planar�O2� oxygen anions as a function of composition is depictedin Fig. 11. With the decrease of PT content, the bond lengthscorresponding to Fe /Ti–O2 �B–O2 in the figure� andBi /Pb–O1 �A–O1� of the tetragonal phase split into fourunequal bonds, as the space group symmetry changes fromtetragonal to monoclinic. For Bi /Pb–O1 �A–O1� type of
FIG. 9. �Color online� Evolution of powder XRD profile in the 2� range of15° to 37.5° of BF–0.31PT with temperature from room temperature to700 °C.
FIG. 10. �Color online� Evolution of powder XRD profile in the 2� range of21° to 43° of BF–0.27PT with temperature from room temperature to700 °C.
124112-9 S. Bhattacharjee and D. Pandey J. Appl. Phys. 107, 124112 �2010�
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bonds in the monoclinic phase, two of these bonds havenearly equal value. The Bi /Pb–O2 �A–O2� bond lengthssplit into eight unequal bond lengths, as the structurechanges whereas only two different Fe /Ti–O2 �B–O1� typebond lengths exist in both tetragonal and monoclinic phases.We have also shown in Fig. 12 as continuous line the varia-tion of the ionic bond lengths expected on the basis ofShannon–Prewit ionic radii32 with composition. Very largedifference between the observed and ionic bond lengths isevident for the B–O1 bond lengths of the tetragonal phase,and somewhat less for the monoclinic phase. For the A–O1
bond in the tetragonal phase, this difference is even larger.Further one of the A–O2 bonds in the tetragonal phase, oneof the A–O1 and six of the A–O2 bonds in the monoclinicphase show a departure from the ionic value. On the otherhand, the B–O2 bonds in the tetragonal and monoclinicphase are close to the values expected for ionic bonding,except in the phase coexistence region. The bond length likeone of A–O1, one of the B–O1 in both tetragonal and mono-clinic phases, three of the A–O2 in the monoclinic phase andone AO2 in tetragonal phase are significantly shorter than theionic bond lengths suggesting strong covalency effects. Firstprinciples calculations predict strong hybridization of3d0 Ti4+ with 2p O2− and 6s2 Pb2+ /Bi3+ with 2p O2− inPbTiO3
33 and BiFeO3,34 respectively, and we believe that theshortening of these bond lengths is linked with these hybrid-izations. However, the composition dependency of the short-ening of the bond lengths with respect to the ionic bondlengths for B–O1, A–O1, and A–O2 are not similar. Thus,one of the B–O1 and A–O2 bond lengths decreases withdecreasing Pb content�x� in the tetragonal phase, whereas theA–O1 bond length slightly increases with increasing x. It canbe linked with the increasing c parameter and decreasing aparameter of the unit cell with decrease in Pb content�x�.
From the nature of variation in different bond lengths itis clear that the A–O2 and A–O3 �planar� type and B–O1
�apical� type bond lengths get shorter with decrease in PTcontent. Displacement of Ti/Fe cations is very large in thetetragonal phase and approaches a value of �0.312 Å forthe x=0.31 composition. This along with large c axis lengthleads to large Ti/Fe–O distance for one of the apical oxygens.For x=0.31, the B–O1 length is �2.85 Å as compared to2.0326 Å, expected on the basis of the ionic model.20 Thislarge distance eliminates the bonds between Ti/Fe with oneof the apical oxygens. As a result, the Ti /Fe–O6 cages trans-form into Ti /Fe–O5 complexes, similar to that reported byGrinberg et al.35 for Bi�Zn1/2Ti1/2�O3–xPbTiO3 �BZT–xPT�.
PT based solid solutions can be broadly classified intotwo categories. In the first category the c/a ratio decreaseswith decrease in PT content. Important examples of this cat-egory are PZT,11 PMN–xPT,5–7 PSN–xPT,10 and �1−x�Bi�Mg1/2Zr1/2�O3–xPbTiO3,15 etc. For the second cat-agory, c/a ratio increases with decrease in PT content. Solidsolution systems like BZT–xPT, Bi�Zn1/2Sn1/2�O3–xPbTiO3,and Bi�Zn1/3Nb2/3�O3–xPbTiO3,15,35–37 etc., are examples ofthis category. The increase in the c/a ratio of BZT–xPT withdecrease in PT content is because pure BZT shows very hightetragonality, with a c/a ratio �1.211.35 On forming solidsolution with PT, the c/a ratio decreases and appreaches thec/a ratio for PT which is 1.064. However, the important pointis that BZT–xPT does not show MPB in its phasediagram.35–37 It is interesting to note that the solid solutionsystem Bi�MgTi�O3–xPbTiO3 where Zn is replaced with Mgdoes show an MPB in its phase diagram but here the tetrago-nality does not increase with decrease in PT content. Thissystem, therefore, belongs to the first category. All the othersystems showing c/a ratio greater than that for BF–0.31PT donot exhibit any MPB effect. The BF–xPT system not only
FIG. 11. �Color online� Schematic x-T phase diagram of BF–xPT.
FIG. 12. �Color online� Variation in some selected Bi/Fe–O �A–O� andPb/Ti–O �B–O� type bond lengths with composition. The continuous lineshows bond lengths expected on the basis of ionic model.
124112-10 S. Bhattacharjee and D. Pandey J. Appl. Phys. 107, 124112 �2010�
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exhibits an MPB like the first category but also shows in-creasing c/a ratio with decreasing PT content like the secondcategory of PT based solid solutions.
All the experimental findings regarding enhanced tet-ragonality points towards important role played by some spe-cific B-site cations. It has been proposed that when B site isoccupied with ferroelectrical active cations, like, Zn and Ti, astrong coupling between A and B site distortion exists.36 Thisleads to very high ferroelectric distortion. However, in theBF–xPT system, Fe3+ is not in a “3d0” configuration andhence it is not supposed to be ferroelectric-active but stillincreasing the Fe3+ content at the Ti4+ site increases the c/aratio. The anomalously high tetragonality in BF–xPT system,therefore, cannot be understood in terms of the existing the-oretical models based on hybridization of 3d0 transitionmetal with 2p O−. Notwithstanding the limitations of theexisting theoretical models, even the BF–xPT system is sen-sitive to B-site cation. For example, in theBiFeO3–Pb�Ti1/2Zr1/2�O3 solid solution system, Ti ion sub-stitution with Zr, reduces the tetragonality and shows thenormal trend, i.e., tetragonality decreasing on approachingthe MPB, observed in the first category of PT based solidsolutions.30 The covalency effect is more pronounced in theFe-rich tetragonal compositions even though Fe3+ does notbelong to the 3d0 class of transition metal ion �like Ti4+,Nb5+, etc.�.
IV. SUMMARY
In this report, we have studied the effect of composi-tional variation and temperature on the stability of variouscrystallographic phases of BF–xPT solid solutions. Detailedstructural study has been carried out in the compositionrange 0.1�x�0.9 by Rietveld refinement technique of pow-der XRD. We have shown that in the tetragonal region withunusually large tetragonality, strong covalency effect are ob-served for the bonds between both B site and A site cationswith oxygen in agreement with the predictions of the firstprinciples calculations for PbTiO3 and BiFeO3 with one verysignificant difference. This strong covalency effect increaseswith increasing Fe3+ content, whereas first principles calcu-lations predict the absence of hybridization for 3dn transitionmetals like Fe3+ with 2p O orbitals. The structure of BF–xPT is reconfirmed to be pure monoclinic in the Cc spacegroup, and not rhombohedral proposed in Ref. 24, for 0.1�x�0.27, whereas it coexists with the tetragonal phase inthe MPB region of 0.27�x�0.31. There is no evidence forany orthorhombic phase in the MPB region proposed in arecent work.24 The recent proposition of an orthorhombicphase in the MPB region has been comprehensively ruledout. From the high temperature XRD studies for composi-tions closest to the MPB, it is shown that the MPB is actuallytilted towards the tetragonal side, an unusual feature notshown by other well known MPB systems like PZT, etc. Thehighest temperature phase for both the structure is shown tobe cubic.
1B. Noheda, D. E. Cox, G. Shirane, J. A. Gonzalo, L. E. Cross, and S-E.Park, Appl. Phys. Lett. 74, 2059 �1999�.
2B. Noheda, J. A. Gonzalo, L. E. Cross, R. Gao, S. E. Park, D. E. Cox, andG. Shirane, Phys. Rev. B 61, 8687 �2000�.
3Ragini, S. K. Mishra, D. Pandey, H. Lemmens, and G. V. Tendeloo, Phys.Rev. B 64, 054101 �2001�.
4D. M. Hatch, H. T. Stokes, R. Ranjan, Ragini, S. K. Mishra, D. Pandey,and B. J. Kennedy, Phys. Rev. B 65, 212101 �2002�.
5A. K. Singh and D. Pandey, J. Phys.: Condens. Matter 13, L931 �2001�.6A. K. Singh and D. Pandey, Phys. Rev. B 67, 064102 �2003�.7A. K. Singh, D. Pandey, and O. Zaharko, Phys. Rev. B 74, 024101 �2006�.8J. M. Kiat, Y. Uesu, B. Dkhil, M. Matsuda, C. Malibert, and G. Calvarin,Phys. Rev. B 65, 064106 �2002�.
9D. L. Orauttapong, B. Nohida, Y. G. Le, P. M. Gehring, J. Toulouse, D. E.Cox, and G. Shirane, Phys. Rev. B 65, 144101 �2002�.
10R. Haumont, A. Al-Barakaty, B. Dkhil, J. M. Kait, and L. Bellaiche, Phys.Rev. B 71, 104106 �2005�.
11D. Pandey and A. K. Singh, Acta Crystallogr., Sect. A: Found. Crystallogr.A64, 192 �2008�; B. Noheda and D. E. Cox, Phase Transitions 79, 5�2006�.
12Ragini, R. Ranjan, S. K. Mishra, and D. Pandey, J. Appl. Phys. 92, 3266�2002�.
13A. K. Singh, D. Pandey, S. Yoon, S. Baik, and N. Shin, Appl. Phys. Lett.91, 192904 �2007�.
14M. Ahart, M. Somayazulu, R. E. Cohen, P. Ganesh, P. Dera, H.-K. Mao, R.J. Hemley, Y. Ren, P. Liermann, and Z. Wu, Nature 451, 545 �2008�.
15I. Grinberg, M. R. Suchomel, P. K. Davies, and A. M. Rappe, J. Appl.Phys. 98, 094111 �2004�; M. R. Suchomel and P. T. Davies, ibid. 96, 4405�2004�.
16J. Chaigneau, J. M. Kait, C. Malibert, and C. Bogicevic, Phys. Rev. B 76,094111 �2007�.
17D. I. Woodward and I. M. Reaney, J. Phys.: Condens. Matter 16, 8823�2004�.
18Yu. E. Rogisnakaya, Yu. Ya. Tomashpol’skii, Yu. N. Venevtsev, V. M.Petrov, and G. S. Zhdanov, Sov. Phys. JETP 23, 47 �1966�.
19W. Kaczmarek, Solid State Commun. 17, 807 �1975�.20S. Bhattacharjee, S. Tripathi, and D. Pandey, Appl. Phys. Lett. 91, 042903
�2007�.21S. Bhattacharjee, V. Pandey, R. K. Kotnala, and D. Pandey, Appl. Phys.
Lett. 94, 012906 �2009�.22A. M. Glazer, Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem.
�1975�.24W. M. Zhu, H. Y. Guo, and Z. G. Ye, Phys. Rev. B 78, 014401 �2008�.25D. I. Woodward, I. M. Reaney, R. E. Eitel, and C. A. Randall, J. Appl.
Phys. 94, 3313 �2003�.26J. Rodriguez-Carvajal Laboratory, FULLPROF, a Rietveld and pattern match-
ing analysis program, Laboratoire Leon Brillouin-CEA-CNRS, France.27H. D. Megaw and C. N. W. Darlington, Acta Crystallogr., Sect. A: Found.
Crystallogr. A31, 161 �1975�.28D. L. Corker, A. M. Glazer, R. W. Whatmore, A. Stallard, and F. Fauth, J.
Phys.: Condens. Matter 10, 6251 �1998�.29H. T. Stohes, D. M. Hatch, and B. J. Campbell, ISOTROPY program.30R. T. Smith, G. D. Achenbach, R. Gerson, and W. J. James, J. Appl. Phys.
39, 70 �1968�.31G. Shirane, R. Pepinsky, and B. C. Frazer, Acta Crystallogr. 9, 131 �1956�.32R. D. Shannon and C. T. Prewitt, Acta Crystallogr., Sect. B: Struct. Crys-
tallogr. Cryst. Chem. B25, 925 �1969�.33R. E. Cohen, Nature �London� 358, 136 �1992�.34R. Ravindran, R. Vidya, A. Kjekshus, and H. Fjellvag, Phys. Rev. B 74,
224412 �2006�.35I. Grinberg, M. R. Suchomel, W. Dmowski, S. E. Mason, H. Wu, P. K.
Davis, and A. M. Rappe, Phys. Rev. Lett. 98, 107601 �2007�.36M. R. Suchomel and P. K. Davies, Appl. Phys. Lett. 86, 262905 �2005�.37T. Qi, I. Grinberg, and A. M. Rappe, Phys. Rev. B 79, 094114 �2009�.
124112-11 S. Bhattacharjee and D. Pandey J. Appl. Phys. 107, 124112 �2010�
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