review combinatorial search of structural transitions ...€¦ · ternary thin-ﬁlm composition...

INVITED FEATURE PAPERS

Review

Combinatorial search of structural transitions: Systematicinvestigation of morphotropic phase boundaries in chemicallysubstituted BiFeO3

Daisuke Kana)

Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742;and Institute for Chemical Research, Kyoto University, Kyoto 611-0011, Japan

Christian J. LongDepartment of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742

Christian Steinmetz and Samuel E. LoflandDepartment of Physics and Astronomy, Rowan University, Glassboro, New Jersey 08028

Ichiro TakeuchiDepartment of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742

(Received 23 July 2012; accepted 30 August 2012)

We review our work on combinatorial search and investigation of morphotropic phase boundaries(MPBs) in chemically substituted BiFeO3 (BFO). Utilizing the thin-film composition spreadtechnique, we discovered that rare-earth (RE 5 Sm, Gd, and Dy) substitution into the A-site of theBFO lattice results in a structural phase transition from the rhombohedral to the orthorhombic phase.At the structural boundary, both the piezoelectric coefficient and the dielectric constant aresubstantially enhanced. It is also found that the observed MPB behavior can be universally describedby the average A-site ionic radius as a critical parameter, indicating that chemical pressure effect dueto substitution is the primary cause for the MPB behavior in RE-substituted BFO. Our combinatorialinvestigations were further extended to the A- and B-site cosubstituted BFO in the pseudoternarycomposition spread of (Bi1�xSmx)(Fe1�yScy)O3. Clustering analysis of structural and ferroelectricproperty data of the fabricated pseudoternary composition spread reveals close correlations betweenthe structural and ferroelectric properties. We show that the evolution in structural and ferroelectricproperties is controlled solely by the A-site Sm substitution and not the B-site Sc substitution.

I. INTRODUCTION

The combinatorial approach in materials science,1,2 inwhich a large compositional landscape is rapidly mappedand screened for desired physical properties, is an effectiveway to accelerate the traditional time-consuming andserendipitous trial-and-error processes that we rely onfor discovering and developing novel high-performancematerials. Owing to recent developments in atomic-scalethin-film fabrication and characterization techniques forinorganic materials, various types of sophisticated com-binatorial library designs such as the continuous com-position gradients are available not only for identifyingmaterials with desired properties but also for systemati-cally tracking the details of the structure–property relation-ships of targeted materials.3�6

It has been widely accepted that materials at bound-aries where different structural phases with very similarenergy levels coexist can display a colossal susceptibilityresponse in reaction to weak external stimuli such astemperature, electric field, or magnetic field. Indeed, giantpiezoelectric responses are achieved in some ferroelec-trics at their morphotropic phase boundaries (MPBs).7–11

While such boundaries are often identified by composi-tional tuning of the materials, experimental processes forthe identification of structural boundaries can require syn-thesis and characterizations of an enormously large numberof individual samples. To overcome this challenge, we haveimplemented the combinatorial approach, which allowsrapid identification of structural boundaries.5,12,13

BiFeO3 (BFO)14–16 with the rhombohedrally distorted

perovskite structure has drawn considerable attention andhas been considered as a candidate for Pb-free ferro-electrics due to its multiferroic nature (i.e., coexistence offerroelectricity and antiferromagnetism) as well as robustferroelectric properties at room temperature. However,

a)Address all correspondence to this author.e-mail: [email protected]

This paper has been selected as an Invited Feature Paper.DOI: 10.1557/jmr.2012.314

J. Mater. Res., Vol. 27, No. 21, Nov 14, 2012 �Materials Research Society 2012 2691

this oxide suffers from high leakage current, large coercivefields, and its electromechanical coefficient is much smallerthan those of traditional Pb-based piezo/ferroelectrics. Toimprove these shortcomings, chemical substitution intoeither A- or B-site (of the BFO perovskite cell) has beenattempted.17�27 An important consequence of the chemicalsubstitution is a structural phase transition from the rhom-bohedral ferroelectric phase of the parent compound (pureBFO) into another structural phase. This indicates thatthe chemically substituted BFO may emulate the perfor-mance of Pb-based piezoelectrics at MPBs.

In this paper, we present our combinatorial studies ofthe structural and ferroelectric properties of chemicallysubstituted BFO. We discovered the substitution-inducedMPB behavior with the enhanced piezoelectric coeffi-cient and dielectric constant. At the MPB, a structuraltransition from the rhombohedral phase for pure BFO toan orthorhombic phase occurs, which is accompanied bya double hysteresis behavior in polarization–electric field(P-E) hysteresis loops. We find that the behavior can beuniversally described as a function of the average A-sitecation radius. We also investigated the B-site substitutioneffect on the structural and ferroelectric properties of BFOwith a pseudoternary composition spread of the A- andB-site cosubstituted BFO. We found that the structuraland ferroelectric properties are less influenced by theB-site substitution. This behavior was further verified byan extensive clustering analysis of experimental datafrom different characterization techniques for the ternarylibrary. The results demonstrate the significance of theA-site substitution on the structural and ferroelectricproperties of BFO. We show that such a comprehensivemapping approach is effective not only in quickly de-lineating the structural boundaries but also for identifyingsubtle (yet important) correlations between physical andstructural properties in compositional phase spaces ofmultifunctional materials in general.

II. EXPERIMENTAL DETAILS

To systematically investigate the A- and B-site sub-stitution effect on structural and ferroelectric properties ofBFO, we fabricated combinatorial pseudobinary andternary thin-film composition spread libraries based onpulsed laser deposition (PLD) technique. The PLD sys-tem was equipped with an automated shadow mask anda multitarget system (Pascal Inc., Japan). For fabricatingcomposition spread libraries, gradient wedge layers ofend compositions of the library, where the thick end ofthe wedge is less than the pseudocubic perovskite unitcell (0.4 nm), were deposited in an alternating manner inopposing directions by moving the shadow mask backand forth at the epitaxial deposition condition.1 Thethickness of the wedge layer was controlled by the numberof shots of the laser pulses, which is determined based on

the deposition rate calibrated for each composition. Thefabrication of the unit cell height wedge layers is criticalfor obtaining atomic-scale mixing of the deposited con-stituent compositions. The wedge layer depositions wererepeated until the film thickness reaches the desired value.In our study, the total thickness was set to be 200 nm. Thedetails for our library fabrications were given in Refs. 28,29, and 30. Our library was deposited on a (001) SrTiO3

substrate buffered with a 50-nm-thick SrRuO3 film, whichserves as the bottom electrode. We note that no interfacialreaction between the library layer and the bottom electrodewas observed in transmittance electron microscopy (TEM)observations.31 The composition across the library wasdetermined by an electron probe (JEOL JXA-8900,Tokyo, Japan) with an uncertainty of 61.5% at eachmeasurement point. To track structural evolution due tothe A- and B-site substitutions, we mainly used scanningx-ray microdiffraction [Fig. 1(a)]. For x-ray diffraction(XRD) measurements, the x-ray incident beam spot wasfocused into 0.5 mm fwith an aperture, and the diffractedsignals were collected with a two-dimensional (2D) de-tector (Bruker D8, Karlsruhe, Germany) as shown inFig. 1(a). The Raman scattering spectra were obtainedfrom a confocal Raman spectrometer (U1000, HoribaJobin-Yvon, France) operating in the backscattering con-figuration. The source was a 532-nm diode laser withabout 10 mW of power incident on the sample. The signalfrom the substrate was subtracted from the spectra. Forelectrical characterizations [Fig. 1(b)], a 100-nm-thick Pdtop electrodes layer with 50 � 50 lm2 squares was sput-tered and patterned through a conventional liftoff process[Fig. 1(b)]. The P-E hysteresis loops were acquired at5–20 kHz with a ferroelectric test system (Premier II,Radiant Technologies Inc., San Diego, CA). Dielectricconstants were evaluated with an LCR meter (4275A,Hewlett Packard/Agilent, SantaClara, CA)with anAC signalof 80 mV at a frequency of 100 kHz. The out-of-plane piezo-electric coefficient d33 versus electric field curves wasobtained by piezoelectric force microscopy (PFM) with aPt-/Ir-coated cantilever.

FIG. 1. Schematics describing the central concept of the combinatorialsearch of the structural boundary in RE-substituted BFO with the thin-film composition spread technique. In the schematics, the color gradientrepresents the composition gradient, which is typically created over a6-mm length along one direction of the sample. By performing (a) XRDand (b) polarization hysteresis (P-E loop) measurements along the directionof the composition gradient, we obtain the RE substitution-induced changesin structural and ferroelectric properties in BFO.

D. Kan et al.: Combinatorial search of structural transitions: Systematic investigation of MPBs in chemically substituted BFO

J. Mater. Res., Vol. 27, No. 21, Nov 14, 20122692

III. COMBINATORIAL DISCOVERY OF A MPB INRARE-EARTH-SUBSTITUTED BFO

To discover the MPB in chemically substituted BFO,we explored the substituting composition regions wherethe lattice parameters display large concomitant changes,using the thin-film composition spread technique. Weselected rare-earth elements (RE31 5 Sm31, Gd31, andDy31), for which the ionic radii are smaller than Bi31, assubstituting dopants and fabricated pseudobinary compo-sition spreads of (Bi1�xREx)FeO3 (RE-BFO).

Figure 2(a) displays a series of 2h–h scans of Sm-substituted BFO around the (002) STO Bragg reflectionas a function of Sm composition. Only (002)pc reflectionsfrom the film and the substrate are seen, confirmingepitaxial growth of the film over the substitution compo-sition range studied here, where the subscript pc denotesthe pseudocubic perovskite notation. It is seen that withincreasing Sm substitution [Fig. 2(a)], the (002)pc re-flection from the Sm–BFO layer shifts toward the higher2h side, indicating that the Sm substitution results inshrinkage of the out-of-plane lattice parameter d001_pc.This shift can also be seen in Fig. 2(b), where the d001_pcdetermined from the (002)pc reflection is plotted againstthe Sm composition. The lattice constant shift is consistentwith the fact that Sm31 has a smaller ionic radius than Bi31.We note that d001_pc undergoes a large drop of;0.09 Å inthe substitution composition region from 10% to 15%,suggesting that the rhombohedral phase for pure BFOundergoes a structural phase transition. Indeed, detailedstructural characterizations based on x-ray and electrondiffraction techniques28,29,31,32 (see Sec. IV for details)have revealed that the observed drop in d001_pc corre-sponds to the structural phase transition from the rhom-bohedral phase to an orthorhombic phase at Sm 14%.

We also found that at the structural boundary, bothout-of-plane dielectric constant e33 and piezoelectric co-efficient d33 are enhanced.

28,33 Figure 3(a) shows the Sm

composition dependence of e33 and loss tangent (tand)measured at 10 kHz. The e33 reaches a maximum at Sm14%, while tand at this composition is relatively low at;0.01. In Fig. 3(b), we plotted the high field piezoelectriccoefficient d33 evaluated by quantitative PFM as a functionof the Sm composition. Around Sm 11–13%, the effectived33 displays a rapid increase, peaking at 110 pm/V for Sm14%, which is where the structural transition occurs.Beyond this composition, it rapidly decreases to ;55 pm/Vfor Sm 17%.We note that the measured remanent and highfield d33 here are comparable to values previously reportedfor epitaxial thin films of Pb-based compounds such asPb(Zr,Ti)O3 (PZT) at MPB.34 In addition, the polarizationhysteresis (P-E) loop exhibits the concomitant changesacross the structural transition as shown in Fig. 3(c). As theSm substitution increases, the square-shaped ferroelectrichysteresis loops begin to be distorted, and at the transitionboundary, the loops exhibit a transition from single todouble hysteresis loops. It is worthwhile to note that simi-lar behavior was seen for the cases where RE5 Gd31 andDy31,33,35 both of which have ionic radii smaller than thatof the Sm31 ion.

In comparing nominally similar thin-film samples ofthe same thickness,34 the MPB behaviors discovered hereexhibit intrinsic piezoelectric properties, which are amongthe best. The added advantage of the present system is thatit is a much simpler system in terms of the solid-statecrystal chemistry compared to some of the other reportedPb-free compounds,36 and it has a relatively easy methodfor processing.

IV. UNIVERSAL BEHAVIOR INRE-SUBSTITUTED BFO

In Sec. III, we showed that RE-substituted BFO hasa MPB with enhancement of e33 and d33. The next stepis to consider the mechanism behind the enhanced prop-erties at MPB. To this end, we expanded our study andsystematically compared structure–property relationshipsin RE-substituted BFO (RE 5 Sm, Gd, and Dy) with thethin-film composition spread technique. We selected tri-valent Sm, Gd, and Dy as substituting dopants whose ionicradii with 12-fold coordination are Bi31 (1.36 Å). Sm31

(1.28 Å) . Gd31 (1.27 Å) . Dy31 (1.24 Å).37 For eachcomposition spread with a different RE31 dopant, the dop-ant concentration was continuously varied from x 5 0(pure BFO) to a fixed value (typically, x 5 0.3) along thedirection of the spread sample, as shown in Fig. 1.

Figures 4(a)–4(c) show typical 2D XRD images takenfor (Bi1�xDyx)FeO3 with xDy 5 0, 0.07, and 0.1, re-spectively. The images capture essential and commoncharacteristics of the substitution-induced structural evo-lution for all RE (5Dy, Gd, and Sm) cases. For pure BFO[xDy 5 0, Fig. 4(a)], only (001) and (002) reflections fromthe film and the substrate are observed. With increasing

FIG. 2. (a) X-ray 2h–h profiles across the structural phase transition forSm-substituted BFO thin films. All scans were performed at roomtemperature. The colored solid arrows denote the (002)PC reflectionsfrom Sm-substituted BFO layer. (b) Substitution-induced evolution ofthe out-of-plane lattice parameter d001_pc for Sm-substituted BFO. Thelattice parameter is determined from the (002)pc reflection. The dottedline is drawn as a guide to eyes.


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xDy, extra diffraction spots [denoted by red arrows inFig. 4(b)] begin to appear in addition to the fundamentalspots. Corroborated by TEM images and zone axis selected-area electron diffraction patterns,31,38 the extra spots areassigned as 1/4{011} spot and arise from the antiparallelcation displacements along the [011] direction in the localregion. Although this structure closely resembles that of thewell-established antiferroelectric (AFE) structure in PbZrO3

(PZO),23,39�41 macroscopic properties of the films in thecomposition range, where the 1/4 spots are observed, arethose characteristics of a ferroelectric phase not an AFEphase, which is consistent with the fact that the structureassociated with the 1/4 spots is a minority phase.

With further increase in xDy [Fig. 4(c)], the 1/4{011}superstructure spots disappear and new superstructurespots (marked with yellow arrows) begin to emerge. Thesenew spots correspond to the 1/2{010} reflection spotsresulting from the unit cell doubling along the in-planedirection as compared to the rhombohedral BFO lattice.From detailed x-ray reciprocal space mappings,29,32 a filmwith the 1/2{010} spots is in an (pseudo-) orthorhombicstructural phase with the unit cell having the dimensions ofO2apc � O2apc � 2apc, where apc is the pseudocubicperovskite lattice parameter.

In the upper panel of Fig. 4(d), we plot the normalizedintensities of the (0, 1/4, 7/4) spot (a 1/4{011} spot) arisingfrom the PZO-type minority phase and the (0, 1/2, 2) spot(a 1/2{010} spot) due to the occurrence of the celldoubling in the majority phase for Dy–BFO. The intensityof the 1/4{011} spot reaches a maximum at 6% sub-stitution. Beyond this substituting composition, the1/4{011} spot intensity decreases, while the 1/2{010}spot becomes dominant due to the phase transition fromthe rhombohedral phase to the orthorhombic one. In theupper panel of Fig. 4(d), we also plot the zero bias e33,which reaches a maximum of ;250 at the structuralboundary. The observed structural evolution and theenhanced properties are common to all three RE dopants[Fig. 4(d)]. A key observation is that the composition of

the structural transition shifts toward the larger composi-tion values as the ionic radius of the RE dopant becomeslarger. For RE 5 Dy, which has the smallest ionic radiusof the three elements, 8% substitution is sufficient to inducethe transition. On the other hand, for RE 5 Sm, which hasthe largest radius, 14% substitution is necessary. Thisobservation is attributed to a hydrostatic pressure effect

FIG. 3. (a) Dielectric constant e33 and tand of (Bi1�xSmx)FeO3 as a function of Sm composition. The data were measured at 1 MHz (zero bias).(b) High field d33 determined by PFM as a function of Sm composition. (c) P-E hysteresis loops with 25 kHz at compositions of xSm 5 0.1, 0.14,and 0.16. In (a) and (b), the curve is a guide to the eye.

FIG. 4. (a–c) 2D XRD images for the Dy–BFO composition spreadfilm on (001) SrTiO3 substrate. (a) xDy5 0. (b) xDy5 0.07. (c) xDy5 0.1.The 2D XRD images are recorded in the 2h-v plane with the incidentx-ray beam parallel to the [100]STO direction. For (b) and (c), the spotsmarked with arrows belong to 1/4{011} and 1/2{010}, respectively. Allspots are indexed by the pseudocubic unit cell notation. (d) NormalizedXRD intensities of (0, 1/4, 7/4) (filled square, denoted as 1/4, or 1/4 spot)and (0, 1/2, 2) (open square, denoted as 1/2, or 1/2 spot) XRDsuperstructure spots and e33 at zero bias (black dot) as a function of REdopant composition. (e) All data in (d) are plotted against rave. The ionicradii in 12-fold coordination are 1.36 Å for Bi31, 1.28 for Sm31, 1.27 forGd31, and 1.24 for Dy31 ions.37 This change in rave corresponds to thechange in the Goldschmidt tolerance factor from 0.954 (rave 5 1.36 Å)to 0.947 (rave 5 1.34 Å) with 0.645 and 0.14 Å for the ionic radii ofFe31 and O2-, respectively.



caused by the smaller radii of the isovalent RE ions,namely a chemical pressure effect. Figure 4(e), where thesame data shown in Fig. 4(d) are plotted together againstthe average A-site ionic radius rave, captures the behavioruniversal to all the RE dopants. The curves collapsetogether, revealing an underlying common behavior as afunction of rave. We also note that the observed structuralevolution is independent on the thickness (in the thicknessregion larger than 200 nm) and the type of substrate.29

This observation rules out the possibility that the observeduniversal structural evolution results from some thickness-or substrate-induced effects.

It is interesting to note that the change in rave alsoresults in the change in the average A-site ionic polariz-ability. This is due to the fact that for RE elements(lanthanides), the ionic polarizability is directly propor-tional to the ionic radius.42 Thus, one can look at theobserved universal trend as a function not only of rave, andthus chemical pressure, but also as a function of the A-siteionic polarizability. In fact, a similar looking universalbehavior as seen in Fig. 4(e) can be obtained when theproperties are plotted against the average ionic polariz-ability (not shown).

We also note that there have been a number of the-oretical and experimental investigations on pressure-induced structural transitions in BFO.43�45 It is knownthat BFO itself undergoes a pressure-induced structuraltransition into the Pnma (GdFeO3-type) orthorhombicphase that has the same structure as the one for RE-orthoferrites. It is reasonable that the chemical pressureeffect due to A-site substitution results in a similartransition.

To further investigate the phase stability and the role ofthe superstructures in determining the functional behav-ior, we also tracked the structural evolution across thecomposition spreads as a function of temperature using2D XRD images. In Fig. 5(a), we show contour plots ofthe (0, 1/4, 7/4) and the (0, 1/2, 2) XRD spot intensities asfunctions of temperature and the average ionic radius ravefor the case of Sm-substituted BFO thin films, to closelymonitor the occurrence of the PZO-type structure and theorthorhombic structure, respectively. Near the structuralboundary composition region, as the temperature is raisedfrom room temperature, the 1/4 spot gradually decreasesin intensity, while the 1/2 spot intensity gets enhanced.This indicates that on the higher temperature side, theorthorhombic phase is the stable phase. More importantly,the same rhombohedral to orthorhombic structural phasetransition induced by RE substitution occurs with in-creasing temperature.A similar temperature-induced struc-tural phase transition from the rhombohedral phase to theorthorhombic one was also observed from the synchrotronXRD study.46 It is worthwhile to note that Dy-substitutedBFO exhibits essentially the same contour plots of the 1/4and 1/2 spot intensities.29 This indicates again that the

average ionic radius rave is the critical parameter thatgoverns the structural properties of RE-substituted BFO.Based on the results, we arrive at a universal phase dia-gram for RE-substituted BFO, as illustrated in Fig. 5(b).On the lower temperature side, the composition region inlight blue where the minority phase gives rise to the 1/4spot is seen to “bridge” the ferroelectric rhombohedralphase regions (marked in blue) and the orthorhombicphase (marked in green). This bridging phase has beenpreviously shown to result in lattice incommensurationat the rhombohedral–orthorhombic phase boundary.31 Asthe temperature is elevated, the composition region withthe 1/4 spot phase disappears, and the orthorhombic phaselies directly adjacent to the ferroelectric region.

The ferroelectric properties also display concomitantevolution in response to the substitution-induced struc-tural changes, and thus, the universal behavior also existsin the ferroelectric properties in RE-substituted BFO.This is shown in Fig. 6, where room temperature polari-zation hysteresis loops for the films with various REsubstituting compositions are displayed such that rave isthe same for each group of curves. For each rave, thehysteresis loops collapse together, and the general shapeand ferroelectric character of the hysteresis loop areconstant. This indicates that rave is the universal parameterto describe not only the structural but also the ferroelectricproperties. Therefore, we can conclude that the chemicalpressure effect provided by the RE substitution is theprimary cause for the MPB behavior in RE-substitutedBFO.

As we cross the structural boundary (corresponding torave ; 1.35 Å at room temperature), the polarizationhysteresis loop consequently exhibits a transition from

FIG. 5. (a) Contour plots of intensities (counts per second) of (0, 1/2, 2)(1/2 spot, upper panel) and (0, 1/4, 7/4) spots (1/4 spot, bottom panel) asfunctions of temperature and the average A-site ionic radius for theSm-substituted BFO composition spread thin films. (b) Proposed phasediagram for (Bi1�xREx)FeO3. The black line represents the structuralphase boundary between the rhombohedral (in blue) and the ortho-rhombic (in green) structural phases. At lower temperature side, the1/4 spot is observed in the region in light blue. The double hysteresisloop behavior [see main text and Fig. 6 for details] emerges in the regionin dark green.



single to double hysteresis loops with decreasing rave,as shown in Fig. 6. The corresponding Goldschmidttolerance factor for this rave is 0.9509. (For pure BFO,the tolerance factor is 0.954.) For the ferroelectric com-position region immediately adjacent to the transition(rave . 1.35 Å), the ferroelectric square-shaped hysteresisloops with saturated polarizations of 70 lC/cm2 are ob-served. As one approaches the transition (rave ; 1.35 Å),the hysteresis loop first becomes distorted, and then, ittransitions to a fully developed double hysteresis loopbeyond the transition (rave , 1.35 Å). Based on a first-principles calculations study,29 an electric field-inducedtransformation from a paraelectric orthorhombic phase toa polar rhombohedral phase was proposed as the origin ofthe double hysteresis behavior as well as the associatedenhancement in the piezoelectric coefficient. The proposedelectric field-induced phase transformation events can alsoexplain the enhancement of d33 at the boundary. Similarelectric field-induced transformation and the resultingenhancement of piezoelectric response have been observedin Pb-based ferroelectric materials at MPBs7�11 such asPb(Zr,Nb)O3–PbTiO3, PZT, and Pb(Mg,Nb)O3–PbTiO3.We believe that the enhancement in the electromechanicalproperties we see in the present RE-substituted BFO thinfilms28,29,33 is of similar nature.

V. COMBINATORIAL INVESTIGATIONS OFSTRUCTURAL AND FERROELECTRICPROPERTIES OF A- AND B-SITECOSUBSTITUTED BFO

According to the universal behavior in RE-substitutedBFO,29 the structural transition boundary emerges whenthe average A-site ionic radius rave is 1.35 Å. This ionicradius corresponds to a tolerance factor of 0.9509. Thesame tolerance factor can, in fact, also be obtained bymaking B-site substitution into the BFO lattice. This raisesan important question about whether B-site substitutioncan also introduce a MPB in BFO. Given that the ferro-electric polarization mainly results from the 6s lone pair47

of the Bi ion in the A-site, one might expect that B-sitechemical substitution would improve the ferroelectric anddielectric properties at the structural boundary of BFO.

However, to date, little has been known about the B-sitesubstitution effect in BFO.

To address the question, we investigated the structuraland ferroelectric properties in the A- and B-site cosub-stituted BFO in the form of a pseudoternary compositionspread library.30 Figures 7(a) and 7(b) show an opticalimage and a design schematic of the fabricated library,respectively. In this design, the substituting compositionof each dopant (A- or B-site dopant) varies along one ofthe sides of the triangle, which allows us to easily separatethe A- and B-site substitution effect. We selected Sm28,31

and Sc48 as the substitutional dopants for the A- and B-site,respectively. As both dopants have a robust 31 valencestate, the substitution is unlikely to result in an increase inleakage current. Besides, in terms of the ionic radius,Sm31 has a smaller ionic radius (1.28 Å in 12-foldcoordination) than Bi does (1.36 Å), and Sc31 has a largerionic radius (0.745 Å in 6-fold coordination) thanFe31 does (0.645 Å). Thus, according to the tolerancefactor picture, we expect that the substitution inducesdistortions or tilting of the oxygen octahedral in the BFOlattice. In fact, the end materials SmFeO3 and BiScO3 have(distorted) orthorhombic structures with dimension ofO2apc � O2apc � 2apc

49,50 and 2O2apc � O2apc � 4apc,51

respectively.The scanning 2D XRD revealed that the fabricated

library undergoes a structural evolution similar to theones observed for RE-substituted BFO pseudobinarycomposition spreads, which is characterized by 1/4{011}and 1/2{010} superstructure spots. In Figs. 7(c) and 7(d),we plot normalized intensity of the 1/4{011} and 1/2{010}spots against the measurement position in the ternary,respectively. We note that these extra spots have highintensities at the right bottom region in the library, and thatboth 1/4 and 1/2 spot intensities vary along the right edgeof the library, where Sm composition is varied continu-ously. Along this edge, we see that the 1/4 and 1/2 spotintensities switch over at the same composition as weobserved for the above-discussed RE-substituted BFObinary spreads (Fig. 4), again indicating the occurrenceof a structural transition boundary from the rhombohedralphase to the orthorhombic one. Importantly, the compo-sition measurements found that the structural boundaryoccurs at 14% Sm substitution, irrespective of Sc compo-sition (see Fig. 10 for details). The observed behaviorindicates that Sm substitution into the A-site of the BFOlattice plays a dominant role in the rhombohedral-to-orthorhombic structural transition, and that the B-sitesubstitution has smaller influence on the structural transi-tion in BFO in the composition region studied here.

We also performed Raman scattering measurements onthis ternary library. Figure 8 presents a series of Ramanspectra taken along the side of the library where Sm31 orSc31 substitution was varied continuously. For the lowsubstitution region, we see the three prominent peaks for

FIG. 6. Universal behavior in polarization hysteresis loops across thestructural transition for RE-substituted BFO thin films (RE 5 Sm, Gd,and Dy). Room temperature P-E hysteresis loops for 200-nm-thick filmsare plotted for rave. For each rave, the hysteresis loops collapse intoa single curve. This clearly demonstrates universal behavior in ferro-electric properties of RE-substituted BFO.



the A1 phonon modes at 147, 179, and 230 cm�1. Thepositions of the A1 phonon modes are in a good agreementwith the reported values of the A1 phonon mode for theBFO single composition thin films.52,53 We found thatthe Raman spectra display a distinct evolution dependingon the substitution site. As the A-site Sm substitution in-creases up to 8% [Fig. 8(a)], the A1 phonon peaks begin toshow a decrease in intensity along with a slight increasein Raman shift. With further Sm substitution, the scatter-ing intensities eventually disappear except a weak featurenear 170 cm�1 and a new broad peak at 310 cm�1. Aroundthe Sm 13% substitution, the signal all but disappears witha weak feature near 170 cm�1 and a new broad peak at;310 cm�1. At Sm 14.9%, the only observed feature isthe peak at 310 cm�1, which can be attributed to theorthorhombic phase of SmFeO3.

54 In the case of the B-siteSc substitution [Fig. 8(b)], the three A1 phonon modes areclearly seen in the all spectra, with only some decrease inintensity, which is in sharp contrast to the Sm substitutioncase. This is consistent with the fact that the A-sitesubstitution controls the structural properties of BFO[Figs. 7(c) and 7(d)].

We also see concomitant changes in ferroelectric prop-erties in response to the substitution-induced structural

evolution. In Fig. 9, we present all room temperature P-Ehysteresis loops taken across the library. Each loop is dis-played at the position of the corresponding top electrodewhere the measurement was made. In the low substitutionregion, unclosed loops resulting from high leakage cur-rent are observed. As the Sm and Sc substitutions are

FIG. 7. (a) Real image of the fabricated ternary library of (Bi,Sm)(Fe,Sc)O3. (b) Design schematic of the ternary library. The equilateral triangle-shaped library with the 8-mm-long side was made on the substrate with 10 by 10 mm in size. The compositions in the schematic were determinedby the electron probe. (c, d) The normalized intensities of (c) (0, 1/4, 7/4) (1/4{011}) and (d) (0, 1/2, 2) (1/2{010}) spots are respectively displayedagainst the position in the library.

FIG. 8. Representative Raman spectra taken for the fabricated ternarylibrary. In (a) and (b), the spectra are collected along (a) Sc 5 0% and(b) Sm 5 0% sides of the library where Sm and Sc substitutions arevaried, respectively.



increased, square-shaped P-E hysteresis loops with a sat-uration polarization of about 70 lC/cm2 begin to appear.This indicates that the substitution results in a reduction ofthe leakage current. The fact that the composition regionwhere only Sc is substituted corresponds to hysteresisloops that are characteristic of leaky ferroelectrics suggeststhat Sm substitution is more effective in reducing theleakage current than Sc substitution. It is interesting topoint out that in the composition region where the square-shaped ferroelectric hysteresis loops begin to appear, wesee appearance of the 1/4 spot due to the local antiparallelcation displacements (Fig. 7). This suggests that thereduced leakage current is perhaps not caused by the Smsubstitution into the rhombohedral BFO lattice alone, butinstead, it is due to the substitution-induced phase co-existence between the rhombohedral phase and the 1/4spot structural phase.

In Fig. 9(b), we display the P-E hysteresis loops indi-cated by the red box in Fig. 9(a). As one approaches theMPB at Sm 14%, the ferroelectric hysteresis loops becomedistorted, and the double hysteresis behavior begins toappear. Beyond Sm 14%, fully developed double hyster-esis loops are observed. This behavior is in good agree-ment with that observed for RE-substituted BFO thin films(Fig. 6). It is seen that the evolution in the ferroelectric

properties occurs along the Sm substitution compositionaxis, as in the case for the structural properties (Fig. 7).Thus, this leads to the conclusion again that the A-sitesubstitution, which provides the chemical pressure effect,plays the crucial role in both structural and ferroelectricproperties across the structural boundary in BFO.

To further delineate the composition dependence ofthe structural and ferroelectric properties in BFO, we plotthe normalized intensities of the (0, 1/4, 7/4) (referred toas 1/4) and (0, 1/2, 2) (referred to as 1/2) XRD spots, aswell as the remanent polarization (Pr) of the P-E loopsagainst the Sm and Sc substitution compositions inFigs. 10(a)–10(c), respectively. We note that in theseplots, the data points, which were triangularly distributedon the original library layout, have been displaced in sucha way that the Sm and Sc compositions vary along thevertical and horizontal axes, respectively. All three pa-rameters [Figs. 10(a)–10(c)] are muchmore strongly depen-dent on A-site Sm substitution than on Sc substitution.Above 14% Sm, the 1/4 and 1/2 spot intensities switchover, confirming the occurrence of the rhombohedral toorthorhombic structural transition. As a consequence ofthe structural transition, Pr also becomes zero at Sm� 14%,which corresponds to the transition from square ferroelec-tric hysteresis loops to double hysteresis loops, as seen in

FIG. 9. (a) All polarization hysteresis loops taken for the fabricated ternary library. The loops are displayed at the position of the top electrodes,which are located 200 lm apart horizontally and 150 lm apart vertically on the ternary library. All loops are obtained at 5 kHz at room temperature.For each loop, the horizontal axis ranges from�500 to 500 kV/cm for electric field, and the vertical axis is from�120 to 120 lC/cm2 for polarization.(b) “Zoom up” of the hysteresis loops in the red box in (a).



Fig. 9. In Figs. 10(d)–10(f), we compare the observedtrends in the structural and ferroelectric properties withthe changes in rave in the A-site, rave in the B-site, and thetolerance factor, respectively. To calculate the parametersin Figs. 10(d)–10(f), we used 1.36 Å as an ionic radius forthe Bi31 ion in 12-fold coordination and 1.28 Å for theSm31 ion.37 For the Fe31 and Sc31 ions with 6-foldcoordination, 0.645 and 0.745 Å are used, respectively.The substitution-induced variations in the 1/4 spot in-tensity, the 1/2 spot intensity, and Pr in Figs. 10(a)–10(c)essentially agrees with changes in the average A-site ionicradius [Fig. 10(d)]. This reinforces the picture that theaverage A-site radius is the controlling parameter and thatthe chemical pressure provided by A-site substitutiongoverns the structural and the ferroelectric propertiesin BFO.

VI. CLUSTERING ANALYSIS OF THECOSUBSTITUTED BFO TERNARY LIBRARY

To further delineate the relationships among theobserved substitution-induced evolution of structuraland ferroelectric properties, we performed agglomerativehierarchical clustering analysis of the Raman spectraand P-E hysteresis loops. Hierarchical cluster analysis55

has previously been applied to combinatorial materials ex-periments, where example applications include the analysisof XRD spectra,56,57 Raman spectra,58 and gas sensor“fingerprints.”59 The analysis here was performed usingCombiView, which is written in MATLAB. The ideabehind performing clustering analysis is to map out theregions of composition space that have similar properties

(in this case, similar Raman spectra or P-E loops) byforming discrete groups of similar samples. Once thegroups of samples have been determined, the composi-tions for each group are plotted on the ternary compositiondiagram, providing a map of compositions with similarproperties. This mapping allows us to identify criticalcompositions where there is a systematic change in thematerials properties. In particular, these critical composi-tions are often found at the interface between two groupsof similar samples. The specific change in the materialsproperties is then identified by looking at the physicalproperty data for samples near the interface betweengroups. The cluster analysis therefore serves as a guidefor rapidly identifying such material’s composition atthe interface between groups with similar physicalproperties.

The details of the agglomerative hierarchical clusteranalysis performed here include the choice of a distancemetric, a linkage method, and a threshold distance. Thedistance metric determines the definition of the “similar-ity” between two spectra. The distance metric used herewas the correlation distance. The correlation distance isdefined as one minus the Pearson correlation coefficientbetween two spectra. Therefore, a distance of zero be-tween two spectra corresponds to identical spectra, whilea distance of two would correspond to the maximumdissimilarity. In addition to defining the distance betweena pair of spectra, hierarchical clustering also requires away to define the distance between two groups of spectra.This is called the linkage method. In our case, we used thegroup average linkage method. In the group averagelinkage method, the distance between two groups of

FIG. 10. Plots of (a) (0, 1/4, 7/4) (1/4{011}) spot intensity, (b) (0, 1/2, 2) (1/2{010}) spot intensity, (c) remanent polarization Pr, (d) average A-siteionic radius, (e) average B-site ionic radius, and (f) tolerance factor as function of Sm and Sc substitution composition. In (a), (b), and (c), themaximum (red hue) and minimum (purple hue) of the color bar are 1.0 and 0.0, respectively. In (d), the maximum is 1.36 Å and the minimum is1.344 Å. In (e), the maximum is 0.664 Å and the minimum is 0.645 Å. In (f), the maximum is 0.953 and the minimum is 0.945.



spectra is taken to be the mean distance for all possiblepairs of spectra, where each pair entails one spectrum fromeach group. The final parameter in the cluster analysis isthe threshold distance. This level determines how fine-grained the final groups are. A high distance thresholdallows a larger average distance between groups, pro-ducing larger groups. The interfaces between these largergroups tend to correspond to more significant variationsin the physical properties. On the other hand, we wouldlike to exploit the power of the combinatorial approachin identifying subtle trends in the data acquired fromthe library, so it is desirable to set the threshold low toproduce small groups. In practice, the lower limit forthe threshold is often set by measurement artifacts ornoise present in the data, which create artificial divisionsbetween groups.

Before performing cluster analysis for the Ramanspectra, some preprocessing of the spectra was per-formed. In particular, the spectra were renormalized suchthat the total counts in the region from 530 to 730 cm�1

were constant. This region was chosen because there wasno Raman signal from the fabricated library layer. Second,the Raman spectra were cropped down to the region from100 to 550 cm�1, which is the region containing all thefilm peaks.

In Fig. 11, we present the results of the clusteringanalysis for the Raman spectra. Figure 11(a) presentsa dendrogram containing the hierarchy of sample group-ings as a function of the correlation distance betweengroups, along with the threshold correlation distance(which is ;0.03) used to produce the final groupings ofRaman spectra. As one moves from small thresholddistance to large threshold distance, the small groups arejoined together (agglomerated), as denoted by horizontalconnecting lines. Figure 11(b) shows the regions of thecomposition space covered by each group of similarRaman spectra. To identify the difference in the Ramanspectra from one group to another, we select a subset ofsamples that crosses the boundary between adjacentgroups. We plot the Raman spectra for these selectedsamples as a heat map, with the Raman shift along theabscissa and the spectrum number along the ordinate axis.The arrows in Fig. 11(b) indicate the ordering of theRaman spectra displayed in Fig. 11(c). As we move alongthe arrow (1), from the cyan to the red group, we findthe gradual decrease in the intensities of the A1 phonons.As we move along the arrow (2), from the red to the purplegroup, we see that the intensities of the A1 phonons arehighly attenuated except the weak feature near 170 cm�1.Finally, as we move along the arrow (3), we find that at

FIG. 11. Cluster analysis of the Raman data. (a) A dendrogram showing the threshold correlation distance (;0.03) used to create the groups ofRaman spectra. Each Raman spectrum is represented by a vertical line at the base of the dendrogram. The agglomeration of Raman spectra into groupsis indicated by horizontal tie bars at the correlation distance between the groups. (b) The groups of similar Raman spectra marked on the ternarydiagram. The three arrows in the figure indicate the compositions and ordering of Raman spectra displayed in the (c). (c) A selection of Raman spectrathat traverse the groups produced in the cluster analysis. The transition between groups of similar spectra occurs roughly in the middle of each verticalarrow.



the boundary between the purple and green groups, abroad peak appears at 310 cm�1. The groupings pre-sented here therefore map out the major features of theRaman data in the composition space (Fig. 8).

To perform cluster analysis on the P-E loops, the loopswere “unrolled” into two spectra. That is, for any givenP-E loop, we consider two spectra, one for the electric fieldat each data point, hereafter called the E-spectrum, andone for the polarization at each data point, hereafter calledthe P-spectrum. To make a valid comparison betweenP-spectra constructed in this way, it is necessary that theelectric field at each data point in each loop is the same.That is, the E-spectra for all the data set must be the same.However, it turned out that the large leakage current ina shorted test capacitor causes some variation in theE-spectra. We therefore removed the leaky loops for thecompletely shorted capacitors from the set of the P-Eloops before performing cluster analysis on the P-spectra.

The results of the cluster analysis for the P-spectra aredisplayed in Fig. 12. Comparing the cluster results to theP-E loops in Fig. 7, it can be seen that the cluster analysishas formed groups that depend on the features of the P-Eloops. In the cyan group, the loops are unclosed due to theleakage in the films. The red group corresponds to thecomposition region where the square-shaped P-E loopsare seen, indicating that the films are ferroelectric in thisregion. In the purple group region, we see well-developeddouble hysteresis loops. In the green group region, theloops are characteristic of paraelectric behavior (less-pronounced double hysteresis behavior32 here).

Combined with the structural evolution determined byXRD [Figs. 7(c) and 7(d)], the cluster analysis revealsclose ties between the structural and ferroelectric proper-ties in cosubstituted BFO. The substitution-inducedbehaviors are summarized in Fig. 13. It is obvious thatthe behaviors are less dependent on the B-site Sc sub-stitution. For the rhombohedral phase with no or lowerSm substitution (composition regions in cyan), the Raman

A1 phonon peaks are pronounced, and the P-E loops areunclosed due to the leakage. With increasing the Smsubstitutions (composition regions in red), the 1/4 XRDspot due to the PZO minority phase is seen, and the P-Eloops become closed and square shaped indicating that theleakage currents are reduced in the presence of the 1/4phase. In this composition region, the Raman A1 phononpeaks are largely decreased in their intensity with a weakfeature around 170 cm�1. When the Sm substitutionreaches at 14%, MPB emerges where the rhombohedralphase undergoes to the structural transition to the ortho-rhombic phase, which is characterized by the 1/2 XRDspots. Beyond the boundary, the double hysteresis behav-ior in the P-E loops is well developed due to the electric-field-induced structural transformation from a paraelectricorthorhombic phase to the polar rhombohedral phase.29

Since the electric field required for the occurrence of thefield structural transformation event increases with in-creasing the Sm substitution,29 the double hysteresisbehavior is less pronounced, and the loops become thecharacteristic of paraelectric behavior for the orthorhom-bic phase in the composition region away from the MPB.

VII. CONCLUDING REMARKS AND FUTUREPERSPECTIVES

In conclusion, we reviewed our combinatorial searchand investigations of the MPBs in chemically substit-uted BFO thin films by using the pseudobinary thin-film composition spread technique. We discovered thatRE-substituted BFO has a MPB behavior with substan-tially enhanced properties. It was also found that at theboundary, the rhombohedral phase undergoes a structuraltransition to the orthorhombic phase, which exhibits thedouble hysteresis behavior. The discovered MPB behav-ior can be described as a function of the average A-siteionic radius as a universal parameter. We also extendedour combinatorial investigations into A-site and B-site

FIG. 12. Cluster analysis of the P-E loops. (a) A dendrogram showing the threshold correlation distance (;0.13) used to create the groupspictured in (b). (b) Groups of similar P-E loops based on cluster analysis. The groups identified correspond to the different types of P-E loopsvisible in Fig. 9.



cosubstituted BFO by fabricating pseudoternary libraries.The cluster analysis of the ternary library finds theintimate links between the structural and ferroelectricproperties of cosubstituted BFO and confirms that theseproperties have a strong dependence on the A-site sub-stitution, while the B-site substitution has less influenceon the properties. We have shown that an integratedapproach, which combines synthesis of combinatoriallibraries, rapid characterization of various properties, andcluster analysis of all the data pooled together, can beused to quickly obtain a comprehensive picture of thecomposition–structure–property relationship near struc-tural boundaries.

It is desirable to fabricate and investigate the thin-filmcompositions studied here in ceramic forms to see howthe structural evolution and the concomitant propertychange manifest themselves in bulk materials. To reap thefull benefit of the enhanced properties at MPB in thesubstituted BFO, bulk samples need to be synthesized.Recent investigations of RE-substituted BFO ceramics23,26

have revealed a similar overall trend in substitution-inducedstructural phase evolution: with increasing substitution,the rhombohedral BFO first undergoes a structural transi-tion into an antipolar structural phase, followed by anothertransition to an orthorhombic phase. One significant dif-ference between the ceramics and thin-film cases is theway in which the antipolar structural phase appears: for theceramics case, it appears as a single or majority phase,while for the thin-film specimens, the AFE 1/4 structuralphase is seen as a minority phase embedded in the R3crhombohedral matrix. Although the origin of the differ-ence remains unclear at this point, our experimental results(see Sec. V) imply that this difference may explain why the

thin-film samples studied here have good enough insu-lation to allow full characterization of their functionalproperties as compared to the ceramic samples, wherepoor insulation has been an issue to be overcome. Pre-liminary leakage reduction behavior seen with Ti doping24

is promising, and perhaps, further substitutional investi-gation will reveal additional pathways toward eliminatingthe leakage issue of bulk BFO altogether. These are someof the key points of future investigation of chemicallymodified BFO.

ACKNOWLEDGMENTS

We would like to acknowledge the work of S. Fujinoand R. Suchoski (University of Maryland) for film fabri-cations and P-E loop measurements; V. Anbusathaiah,C.J. Cheng, and V. Nagarajan (University of SouthWales) for PFM and TEM studies; A.Y. Borisevich(Oak Ridge National Labs) for TEM observations;S.B. Emery, B.O. Wells, and S.P. Alpay (University ofConnecticut) for synchrotron XRD measurements; andL. Palova and K.M. Rabe (Rutgers University) for first-principles calculations. This work was supported byNSF-MRSEC at the University of Maryland, DMR05-20471. This work was also supported by ARO MURIW911NF-07-1-0410 and the W.M. Keck Foundation.

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