Journal of Alloys and Compounds 604 (2014) 117–129

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Journal of Alloys and Compounds

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Strong smearing and disappearance of phase transitions into polarphases due to inhomogeneous lattice strains induced by A-site dopingin Bi1�xAxFeO3 (A: La, Sm, Gd)

http://dx.doi.org/10.1016/j.jallcom.2014.03.1030925-8388/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author.E-mail address: burc@sabanciuniv.edu (I.B. Misirlioglu).

M. Khodabakhsh, C. Sen, H. Khassaf, M.A. Gulgun, I.B. Misirlioglu ⇑Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla/Orhanli, 34956 Istanbul, Turkey

a r t i c l e i n f o

Article history:Received 27 September 2013Received in revised form 4 March 2014Accepted 19 March 2014Available online 29 March 2014

Keywords:Ferroic powdersBiFeO3

Phase transitions and structureDefects

a b s t r a c t

Doping of ferroics is often intended to generate new functionalities or enhance the already existing prop-erties, but it comes at the expense of local structural distortions around dopants in the lattice. We reporton the effect of A-site doping and their effect on the phase transition temperatures of sol–gel synthesizedBi1�xAxFeO3 (A: Gd, Sm, La) powders as a function of dopant type and concentration. A clear direct cor-relation between structural parameters and transition temperatures was noted as a function of ionic radiiof dopants for any given concentration, implying the effect of inhomogeneous lattice strains arounddopants. There is a dramatic reduction in the phase transition temperatures of BiFeO3 upon doping deter-mined with differential thermal analysis. This is accompanied by a partial volume of the grains graduallyshifting from the bulk rhombohedral towards a higher symmetry structure particularly in Sm and Gddoped powders while this change is minimal in La doped powders as evidenced by X-ray diffractionand Raman spectroscopy. We find that a phase mixture forms in powders whose fraction is a strong func-tion of dopant radius for a given concentration. Moreover, there is a direct correlation between the ionicradius and the extent of reduction in the transition temperature of the polar phase in the mixture for agiven dopant concentration. We suggest a mechanism to explain the inhomogeneous nature of the tran-sition of the sol–gel synthesized powders where the dramatic reduction in the transition temperatures ofSm and Gd doped BiFeO3 is due to local lattice strains around unitcells containing dopant ions that creategradients in polarization leading to internal depolarizing fields, possibly stabilizing non-polar phases. Weconclude that local disappearance of stereochemical activity of Bi3+ due to lone pairs is not sufficient toexplain the dramatic changes in phase transition temperatures because of strong dependence on ionicradii of dopants.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Multiferroic materials have been on the agenda of manyresearch groups owing to the coexistence of spontaneous electricand magnetic dipoles, namely ferroelectric and magnetic ordering.Many of these compounds actually exhibit improper ferroelectric-ity as the occurrence of permanent dipoles in these materials is aresult of spiral or helical spin structure favoring angled oxygen-cation bonds at low temperatures giving rise to local chargeseparation that forms the basis of weak but finite amplitude elec-tric dipoles. Such a mechanism of ferroelectricity occurs mostly attemperatures much lower than room temperature (RT) for thesematerials [1]. BiFeO3 (BFO) as a proper ferroelectric displaying a

first order structural transition, has probably been the mostinteresting compound in this regard because of its very high para-electric–ferroelectric transition temperature (around 820 �C) thatleads to the appearance of the electric polarization as the initial or-der parameter followed by a Neel point during cooling (around380 �C) giving rise to a helical-type magnetic ordering. Suchcharacteristics have allowed proposal of device designs with newfunctionalities [2–11], in particular following the studies claimingthat the magnetic ordering and the ferroelectric state are inti-mately coupled and that domain manipulation both via electricand magnetic fields is possible in thin films [5,6,12–16]. Moreover,reports exist claiming about 10 times increase in the remnantpolarization in epitaxial BFO films at RT compared to their bulkcounterparts [3,17–19]. Despite the continued interest in growthand characterization of BFO thin films, structural and electricalproperties of BFO in bulk form have been systematically studied

118 M. Khodabakhsh et al. / Journal of Alloys and Compounds 604 (2014) 117–129

by a few groups. Recent works have mostly focused on the effect ofsynthesis on morphology and RT phase stability in the presence ofdopants in addition to effects of these dopants on polarization andmagnetic structures [20–36] and, very importantly, leakage cur-rents. Many of the hysteresis loops in the works cited above havetendencies to fatten, a major sign of leakage. Leakage has been aforemost problem in BFO films and powders [18,30,37–39]. Whiledomain walls have been held responsible for leakage [30,40] manyof the above citations attribute leakage to the volatility of the Bi3+

ions that, when these sites are vacant, they act as p-type centers,accepting electrons from the valence band and causing p-type con-duction both in films and bulk form. Bi3+ ion vacancies have alsobeen held responsible for oxygen vacancy formation to sustain lo-cal electrostatic neutrality, which can again result in increasedconductivity.

Owing to the fact that a few A-site compatible ions such as La,Sm, Gd, Pr and Nd have significantly higher bond enthalpies withoxygen than the Bi–O bond, they are often added to BFO in orderto minimize carrier donating/trapping vacant sites via stabilizingthe oxygen in the lattice in addition to rendering a more ‘‘useful’’magnetic structure for potential applications especially in the caseof Gd and Sm. From the point of view of leakage, compensation ofvacancy generated carriers via doping can lead to a more ‘‘intrin-sic’’ BFO with relatively less free carrier densities. Rare earth ele-ments compatible with Bi3+ ions in radius that can substitute theA-sites stabilize Bi and oxygen along with reduction of the concen-tration of p-type centers accompanied by a shift of the Fermi leveltowards the middle of the band gap, which is one way to reduceand control the leakage currents as shown in our recent work[39]. Apparent polarization enhancement has also been attributedto the reduced leakage via La substitution to Bi sites, reducing theavailable Fe 3d states [41] that would otherwise drive a hopping-type conduction mechanism. A-site doping has also shown thatthe formation of secondary conducting phases can be prevented,likely upon stabilization of oxygen via higher bond enthalpy of do-pants [42–44] helping to sustain the equilibrium stoichiometry.

On the other hand, it is well understood that doping the BFOwith A-site substitutes should be expected to change the transitiontemperatures and impact the ferroelectric properties at room tem-perature (RT) as with any other polar oxide. However, we cameacross only a few articles that analyze the effect of various dopantson phase transition temperatures and characteristics [45–53].There have been numerous reports on the ferroelectric and mag-netic properties of BFO mostly at RT as a function of dopant typeand concentration only some of which we can cite here[20,21,23,24,26,28,29,31–34]. A significant number of these stud-ies are dedicated to thin films [2,3,6,17,25,49,54–59] where misfitstrains induced by the substrate are expected to screen structuralimpact of dopants and make the study of their effect alone ratherdifficult. Besides, that the film structure tries to cope with the mis-fit strains via several elastic variants of ‘‘strain stabilized’’ crystal-line structures carry the discussion on dopant effects to an entirelydifferent setting.

Generally speaking, that the ferroelectric properties can dimin-ish with dopants is often discussed envisioning unitcells shifting tohigher symmetry upon doping. Dopant effects in BFO have almostalways considered from the point of view of the local stereochem-istry of bonding of bismuth with oxygen however this mechanismsolely on its own cannot explain the significant reduction in thephase transition temperatures that strongly depend on ionic radiusmismatch with Bi3+ and additional mechanisms at a more globalscale need to be considered. Dopants also create extended inhomo-geneous strain fields in the lattice. Strain effects in BFO are quitewell understood in thin film studies where the stabilized phasescan be identified for a given misfit with the substrate and a similarapproach can be employed to evaluate dopant effects in powders.

With this in mind, we carried out a structural study to probe theeffect of rare earth (RE) A-site dopant radius on the structure ofBiFeO3 combined with a differential thermal analysis (DTA) analy-sis to determine the Curie point of this material and propose amechanism to qualitatively but consistently explain the the dopantradius sensitivity of BFO.

Here, we report on the structural changes of sol–gel preparedhigh quality BFO powders upon doping with La, Sm and Gd respec-tively. These dopants have a range of ionic radius misfit with Biwith La being the closest to Bi and Gd having the largest misfit.X-ray Diffraction (XRD) studies along with Rietveld refinement iscarried out followed by DTA and MicroRaman spectroscopy. Scan-ning Electron Microscopy was carried out to characterize the grainssize and morphologies of our powders with the intention of under-standing whether we might be encountering size effects in dopedpowders, i.e. disappearance of the ferroelectric state due to smallgrain size. One way to check this is to carry out hystereses mea-surements on compacted powder samples. Noting that bulk BFOin powder form, despite its very high Curie temperature, has asmall remnant polarization (around 3 lC/cm2) compared to mate-rials like BaTiO3 or PZT, moderate amounts of leakage in the pres-ence of dopants can easily overwhelm the displacement currentsemanating from dipole switching during hysteresis measurements,rendering detection of ferroelectricity nearly impossible. To probethe existence of the polar phase in our powders, we chose to con-duct Raman spectroscopy as we failed to obtain any reasonablehysteresis or butterfly-type capacitance–voltage curves due tounacceptable amounts of leakage in our samples. We found a directcorrelation between the changes in structural characteristics ofBFO upon doping with the reduction in Curie temperatures as astrong function of dopant radius. Although the phase transitionin our powders are expected to be first order owing to the fact thatthere are no external constraints or clamping as in the case of films,powders with relatively high doping display a smeared signal inDTA, pointing out the effect of inhomogeneous strain fields of do-pants. Finally, we propose a mechanism to qualitatively but consis-tently address the complicated and dopant radius dependentbehavior of the phase transitions we observe in DTA experimentsbased on the magnitude of the lattice strain the dopants induce.

2. Experimental

In this study, sol–gel technique was chosen as the method to obtain the pureand doped powders as it is fast, can be carried out at relatively low temperatures(it can help eliminate secondary phases compared to solid state calcination forexample, please see Ref. [60]), allows precise stoichiometry control and solutionsobtained are often used to grow thin films via techniques like spin coating or dipcoating. That one starts from a homogeneous solution in this technique is anotheradvantage to shed light on segregation effects of dopants in later processing steps.The Flowchart given in Fig. 1 is an outline of the sol–gel method we used for thesynthesis process. Bismuth nitrate pentahydrate [Bi(NO3)3.5H2O] (99.99% Sigma–Aldrich) and iron nitrate nonahydrate [Fe(NO3)3.9H2O] (99.99% Sigma–Aldrich)were used as Bi and Fe ingredients respectively. By dissolving Bi and Fe nitratesin ethylene glycol and acetic acid separately followed by mixing at room tempera-ture, we obtained a transparent precursor solution. This precursor solution wasdried at 80 �C for about two days to obtain a residue-gel ready for calcination stageafter grinding in agate. In order to compensate the evaporation loss of Bi (causingdue to the volatility of bismuth) during post-annealing process, excess Bi was uti-lized. For doping with Gd, Sm and La, 1%, 5%, 10% and 15% of these to Bi sites, gad-olinium nitrate octahydrate [Gd(NO3)3.8H2O], lanthanum nitrate hexahydrate[La(NO3)3.6H2O] and samarium nitrate hexahydrate [Sm(NO3)3.6H2O] (99.99%GFS chemicals) were substituted for the same percentage of bismuth nitrate penta-hydrate in the first stage. After pyrolysis, a two-stage thermal path was used for cal-cination where the dried gels were kept in 550 �C and 700 �C each for 1 h and theheating rate was 10 �C/min. Then powders were all free-cooled down to room tem-perature. The structure of the powders with various doping concentrations werecharacterized by an X-ray diffractometer (BRUKER Axs) using Cu Ka radiation. TO-PAS 4.2 software was used for Rietveld refinement of XRD data. We found out thatour method was optimal to get high quality powders with no evident concentra-tions of impurity phases until the solubility limit of dopants were exceeded.

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powders. (b) The heating and cooling regimes during crystallization followed to getpure and doped powders.

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M. Khodabakhsh et al. / Journal of Alloys and Compounds 604 (2014) 117–129 119

Differential thermal analyses were performed with a Netzsch, STA 449 in N2atmosphere from RT to 900 �C at a heating rate of 10 �C/min to determine the tran-sition temperature of pure and doped powders. Raman spectra was obtained with aRenishaw in via Reflex Raman Microscope and Spectrometer working in back-scat-tering mode using random polarized laser beam of 532 nm wavelength having aspot radius of 100 lm, 1 cm�1 spectral resolution at reduced beam intensity (5%)to avoid local overheating of the samples. A Leo Supra Scanning Electron Micro-scope (SEM) was used to identify the morphology of the powders and possiblechanges in their grain size upon doping. We chose to work with Gd, Sm and La asthe dopants as these atoms, when in ionized form, can substitute the Bi3+ sitesand have solubility in the BFO lattice in addition to reports about their effect onelectrical and magnetic properties. Additionally, the varying ionic radii of dopantswas expected to reveal the dopant size dependence of the structure, phase stabilityand transition temperatures.

3. Results and discussion

3.1. X-ray diffraction and Rietveld refinement

We first provide the h–2h XRD patterns of our powder sampleswith pure BFO as the reference in Fig. 2. There are no impurityphases and a Rietveld refinement using the R3c space group yieldsa perfect fit with the data.

Upon doping with La, Sm or Gd, changes in peaks shapes andpositions are observed especially once 5% is exceeded. Thesechanges are more significant for Sm and Gd doped powders asthese two have lower ionic radii than La. For both pure BFO anddoped powders, our comparative results of the Rietveld refinementof our data are given in Table 1. We start our discussion first with

the La doped samples as the effect of La doping is relatively weakbelow 10% contrary to Sm and Gd doped samples. Please note that,where needed, we had to refer to the DTA results of our powdersfor a reasonable discussion of the XRD and Rietveld resultsalthough we try to give the data in a sequence for a better and con-sistent comprehension.

A reduction in the unitcell volume of the doped BFO scalingwith the dopant radius and concentration is clearly visible. Thisis consistent with the fact that La, Sm and Gd have smaller ionic ra-dii than Bi. The unitcell volume reduction is more dramatic in Smand Gd doped BFO as these dopants have larger ionic radius misfitwith Bi compared to La where the latter one has only 1% ionic ra-dius misfit in 8 coordination within the pseudocubic structureapproximation.

3.1.1. La doped powdersLa doping until around 5% does not have a considerable impact

on the XRD peaks where the original BFO peaks and their h posi-tions are almost conserved (see Fig. 3a) after which a gradual shiftto higher angles start that is visible only in high resolution asshown for the peaks around 32� in Fig. 3b. The space group ofthe La-doped BFO structure appears to be preserved as R3c withthe possibility of few percent of Pbnm after around 10% La dopingdeduced from the Rietveld refinement where an A-site occupancyratio as the powder stochiometries we work with was used. Pbnmis a non-polar orthorhombic phase. Polar and anti-polar ortho-rhombic phases did not reveal better fits than Pbnm in theR3c + Pbnm phase mixtures and therefore we give only the resultsfor the R3c + Pbnm fits in La doped powders in Table 1 for brevity.

Stability of the R3c phase for La 6 10% was also confirmed byour Raman spectroscopy results given in the next section. Similarresults have also been reported for the relatively low La doping re-gime [61–66]. At La concentrations exceeding 10%, we start observ-ing a clear broadening of peaks in the 20–60� scale accompanied bya slight peak shift towards higher angles, implying an averagegradual shrinkage in the unitcells. The peak shift and broadeningfor the 104–110 planes in high resolution is given in Fig. 3b. Whilethe peak broadening should be expected due to increased amountof local strain fields around unitcells containing La3+ as this ion hasaround a 1% ionic radius mismatch with Bi3+ in 8 coordinationwithin the pseudocubic approximation [67], the gradual mergingof peaks for La > 10% is consistent with what is reported in Refs.[64–66] where an apparent shift toward a higher symmetry struc-ture happens for at least some of the grains and R3c still persists asthe dominant phase. For La > 10%, our Rietveld refinement fits indi-cate that Pbnm or Pnma phases, both of which yield a good fit,

Table 1Results of the Rietveld refinement carried out for our doped powders for various phase possibilities. a, b and c are unitcell parameters (GOF: Goodness of the fit), R0p: backgroundcorrected R-pattern (residual of least squares refinement) R0p ¼

PjYO;m � YC;mj=

PjYO;m � Bkgmj where YO,m is observed data, YC,m is calculated data and Bkgm is the background

data at point m of the intensity-2h data. The lattice parameters are given for the dominant phase in phase mixtures.

R0p GOF Phase fraction a (Å) b (Å) c (Å) Unitcell volume (Å3)

Gadolunium doped BiFeO3

R3c 0% Gd 5.58 1.00 100% 5.57841 5.57841 13.87210 373.8475% Gd 6.38 1.04 100% 5.57325 5.57325 13.8551 372.7010% Gd 6.21 1.03 100% 5.56334 5.56334 13.8003 369.9015% Gd 8.85 1.34 100% 5.5636 5.5636 13.772 369.19

R3c + Pbnm R3c% Pbnm%0% Gd 5.58 1.00 100 0 5.57825 5.57825 13.87076 373.8475% Gd 6.54 1.03 89.00 11.00 5.5746 5.5746 13.8608 373.0310% Gd 6.30 1.02 82.6 17.4 5.5624 5.5624 13.8041 369.8815% Gd 7.04 1.11 23.8 76.2 5.554 5.554 13.583 362.815% Gd* 7.04 1.11 23.8 76.2 5.6092 5.4290 7.8229 238.23

R3c + Pn2(1)a R3c% Pn2(1)a%0% Gd 5.58 1.00 100 0 5.57825 5.57825 13.87076 373.8475% Gd 6.52 1.03 95.8 4.2 5.57356 5.57356 13.8544 372.7210% Gd 6.48 1.03 97.3 2.7 5.5636 5.5636 13.8027 370.0115% Gd 6.86 1.08 36.5 63.5 5.5473 5.5473 13.7715 367.0015% Gd* 6.86 1.08 36.5 63.5 5.6173 7.8210 5.4360 238.82

Samarium doped BiFeO3

R3c 0% Sm 5.58 1.00 100 5.57841 5.57841 13.87210 373.8475% Sm 6.43 1.05 100 5.57212 5.57212 13.8377 372.07910% Sm 6.20 1.03 100 5.56523 5.56523 13.7936 369.9815% Sm 7.85 1.22 100 5.5569 5.5569 13.661 365.32

R3c + Pbnm R3c% Pbnm%0% Sm 5.58 1.00 100 0 5.57841 5.57841 13.87210 373.8475% Sm 6.76 1.05 95.6 4.4 5.57267 5.57267 13.8382 372.1710% Sm 6.00 1.02 86.94 13.06 5.5652 5.5652 13.7970 370.0515% Sm 7.23 1.14 46.3 53.7 5.5605 5.5605 13.7805 366.8115% Sm* 7.23 1.14 46.3 53.7 5.4462 5.5935 7.9015 240.70

Lanthanum doped BiFeO3

R3c 0% La 5.58 1.00 100 5.57825 5.57825 13.87076 373.8475% La 6.24 1.04 100 5.57760 5.57760 13.83963 372.86410% La 6.33 1.04 100 5.57708 5.57708 13.80836 371.95215% La 5.74 1.00 100 5.57777 5.57777 13.7796 371.720

R3c + Pbnm R3c% Pbnm%0% La 5.58 1.00 100 0 5.57825 5.57825 13.87076 373.8475% La 6.34 1.04 97.5 2.5 5.57764 5.57764 13.83967 372.87010% La 6.34 1.04 98.16 1.84 5.57731 5.57731 13.80923 372.00515% La 5.67 1.00 85.2 14.8 5.57732 5.57732 13.7818 371.269

* The lattice parameters and unitcell volume of orthorhombic BiFeO3 phase.

120 M. Khodabakhsh et al. / Journal of Alloys and Compounds 604 (2014) 117–129

could be getting stable along with the polar R3c where the latter isstill the dominant structure. Pnma is the LaFeO3 space group. Inaddition, a shrinkage in unitcell volume could be expected to re-duce polarization stability due to the restriction of the displaciveshift of B-site cation along [111] in the R3c phase along with theloss of the 6s2 lone pairs at La3+ sites, weakening the shift of theFe3+ along [111]. We found out that La is fully soluble in the BFOlattice even at 20 at.%, higher values were reported[20,31,65,68,69] in powders synthesized using various methodsand such a high value is possibly emanating from the identical io-nic radii of Bi3+ and La3+ for 8 coordination.

3.1.2. Sm and Gd doped powdersIn the case of Sm and Gd doping, the XRD data of powders con-

taining the two dopants are nearly identical despite the fact thatSm3+ in 8 coordination has around 8.5% ionic radius mismatch withBi3+ and this value for Gd3+ is around 11% obtained from Ref. [67].In contrast to the case of La, such a difference in the ionic radii ofSm and Gd has an immediate impact on the XRD patterns where, atpercentages of Sm and Gd doping 5% and higher, a significant peakbroadening together with merging of the double peaks are visible(see Fig. 4c and d for the high resolution graph for the 32� range).In our experiments, we find that Sm has a solubility limit of around

15% in BFO while this is nearly 12% for Gd after which non-perov-skite impurity phases form. Due to the large ionic radius mismatchof Sm3+ and Gd3+ with Bi3+ for 8 coordination, the grains should beexpected to contain a large fraction of inhomogeneous strainsaround unitcells containing the dopants, causing the highly visiblepeak broadening along with the possibility of a dopant drivenstructural shift away from R3c. The Sm and Gd doped powdershave also a lowered transition temperature with respect to La3+

for a given concentration evidenced by our DTA data that is dis-cussed in the next section.

Before going onto the discussion of the XRD Rietveld analysisfor Sm and Gd doped powders, we noted that these samples haveconsiderably smaller grains than pure BFO and La doped BFO up toaround 10%, a conclusion we reach after SEM observations (seeFig. 5). Inhibited diffusion in BFO due to Sm and Gd has been re-ported previously [28,35,43,70,71], possibly due to reducedamount of vacancies owing to the high enthalpy of Sm–O andGd–O bonds and the shrinkage of the unitcell. A more than 200%reduction in grain size with respect to pure BFO with higher Smand Gd dopant concentrations is another possibility to explainpeak broadening but cannot directly be held responsible for peakshifts. While this conclusion might appear obvious or even trivialat first, it forms the basis of the discussion for the relation between

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M. Khodabakhsh et al. / Journal of Alloys and Compounds 604 (2014) 117–129 121

the observed Curie temperature behavior (discussed in the nextsection) and the grain sizes making us pose the following question:Are the changes in Curie temperatures due to a size effect in ourdoped powders or is there another mechanism taking effect upondoping? Size effects are usually observed in such systems but onlyat or even below 20–30 nm grain sizes [72–74] while we havegrains of about 300–500 nm in size for heavily doped samples. Infact, Jiaswal et al. has reported that the BFO powders with 50–60 nm particle sizes have only a slightly reduced transition tem-perature compared to bulk BFO [75]. Therefore, it is likely thatour powders are well above the grain size where a size effect couldbe claimed. Moreover, we see that the change in powder size for Gdand Sm doped samples even after a few percent is negligible, how-ever the reduction of the Curie temperatures depends directly onthe dopant radius and concentration.

Ruling out a possible size effect, we conclude that the changesin XRD patterns upon doping, in the light of our Rietveld refine-ment, is a result of significant distortion of the BFO structure upondoping, resulting in stabilization of a phase with higher symmetrythan R3c along with the R3c itself even at 5% Sm and Gd dopantconcentrations. We concluded so because we obtained the bestRietveld refinement fits to our Sm and Gd doped powders if weconsider a orthorhombic (Pbnm) + rhombohedral (R3c) phase mix-ture following trial runs with P1, C2, Pnma for Sm doped powdersand Pn21a as other possible structures reported previously indoped powders: particularly for Sm and Gd doping concentrationsgreater than 5%, we can argue that the orthorhombic Pbnm phasecomprises around 5–15% (please see the Rietveld refinement re-sults in Table 1) of the total powder volume, possibly by the chem-ical pressure induced by dopants along with internal electric fieldsemanating from inhomogeneous strain fields of these dopants (dis-cussed in the forthcoming section). From here onwards we insertthe � to indicate that the R3c discussed at RT is a distorted R3cstructure and call it R3c� with a weakened polarity, hence areduced transition temperature. Regarding Sm doped powders,we get the best fit for Pbnm whereas in Ref. [76], the authors havegiven a very clear analysis of the La, Sm and Nd doped BFO and

report the Pnma phase for Sm as the stable structure at RT. Pnmais an antipolar orthoferrite similar to PbZrO3 however the appear-ance of such an antipolar phase upon cooling from high tempera-ture should yield a signal in the DTA in our 10% and 15% Smdoped powders, similar to what one can expect in PbZrO3 around231 �C, which we do not see in our experiments. The signal wesee in 10% Sm doped powders is most likely coming from the para-electric (PE) ? R3c� transition of the dopant depleted regions as weget the best fits for a R3c� + Pbnm phase mixture and that the R3c�

must have formed above RT (see the detailed discussion in the nextsection). The authors of Ref. [76] see a DTA peak around 309 �C thatthey attribute to the formation of Pnma, the phase they report at

Fig. 5. SEM image of the synthesized (a) BiFeO3, (b) Bi0.9La0.1FeO3, (c) Bi0.9Gd0.1FeO3 and (d) Bi0.9Sm0.1FeO3 showing the impact of doping on grain size. The magnification is40 K in all images. Similar images were obtained in 5% doped powders. hh.

122 M. Khodabakhsh et al. / Journal of Alloys and Compounds 604 (2014) 117–129

RT, and this could point out the effect of sample preparationtechnique because in their work they have chosen the solid statecalcination method. Similarly, we also found out that Pn21a, thepolar orthorhombic phase, yields a fit to our Sm and Gd dopedpowders just as good as or even slightly better than Pbnm for Gddoped samples, a point mentioned in Ref. [24] however lack ofany relevant transition peaks in DTA analyses between 900 �Cand RT (please see next section) for high concentrations of Sm(P10%) and Gd (>10%) in our samples led us to choose the non-polar Pbnm. Pbnm structure could also be stable at high tempera-tures in contrast to the unlikely existence of polar stability suchas the Pn21a which also does not exist at high temperatures evenin pure BFO according to neutron diffraction experiments [77,78].We revisit this argument for Sm and Gd doped powders in thecoming section.

The Pbnm phase constitutes a significant volumetric fraction ofthe grains when the Sm and Gd levels exceed 10% of Bi sites. If wecarry out the Rietveld refinement for 15% Gd doped powders,despite the impurity phases appearing in this regime, we find thatthe samples have more than 79% of their volume in non-polarPbnm phase, confirming our argument in the light of our DTA datagiven in the next section. At 15% of Sm doping, we find a phasemixture that enables the best fit between the experiment andRietveld refinement but with around 54% Pbnm orthorhombicphase compared to 79% in Gd doped samples with the sameconcentration.

Nature of the chemical bonding between dopants and theneighboring oxygen ions have been discussed to effect theferroelectric distortions for reasons other than the chemical pres-sure induced by mismatch in ionic radii. The lack of the 6s2 lonepairs in RE elements upon bonding is discussed to be unfavorablefor the structural distortions leading to the spontaneous dipole for-mation in BFO driven by the ionic polarizability degree of freedomof Bi3+. Therefore, that La3+, having an ionic mismatch of onlyaround 1% with Bi3+ under 8-fold coordination, causes a small de-crease in the Curie temperature can be elaborated from the point ofthe lack of the stereochemistry that is actually present in Bi3+.However, this reduction in transition temperature directly scaleswith the ionic radius mismatch of the A-site dopants with Bi asshown in our work as well as others [76] implies that ionic radiusmismatch becomes a stronger contributor to the noticeable

changes in phase transition temperatures and accompanyingstructural distortions. For Sm3+ and Gd3+, the effect is indeed mostlikely due to chemical pressure rather than changes in the localchemistry combined with natural formation of internal electricfields owing to the electrostrictive nature of the polar regions ofthe matrix material keeping in mind that strong internal fieldscan stabilize non-polar centrosymmetric phases with higher sym-metry than the polar phase. There is direct correlation between thedopant type and percent and the amount of reduction in transitiontemperatures as will be shown. We tried try to link the systemat-ically acquired DTA data to the XRD results and define a sequenceof phase transitions in our doped powders in the next section andshow that the dominant high temperature phase could even bePbnm in case of Sm and Gd at or more than 15%.

3.2. Differential thermal analysis and Raman spectroscopy

After determining the crystalline phases via XRD at RT, we car-ried out DTA experiments to see the effect of dopants on transitiontemperatures as a function of their ionic radii. The measurementswere done between RT and 900 �C. We do not see any degradationor irreversible dissociation in any of our samples: XRD results at RTbefore and after DTA remain exactly the same (not shown here).Irreversible dissociation of BFO was reported to occur around930 �C [7] and we stayed under this limit in our experiments. InFig. 6, we give the DTA plots of the pure and doped powder sam-ples and Fig. 7 provides the transition temperature (strongestpeak) as a function of dopant concentration for the three dopantelements. For 1% doping of La, Sm and Gd, no significant changein high temperature transition is observed and we have a sharpDTA peak in all cases. Therefore, a common result is that 1% dopingfor all elements has a little impact on the transition temperature ofBFO, which is around 820 �C and the samples all appear to bemainly in the R3c phase as confirmed by the Rietveld analysis. 5%and higher concentrations of dopants in the powders studied herestart to make a difference that is a function of the dopant type:increasing La occupancy at A-sites induces a gradual reduction inthe transition temperature while this reduction is much more ra-pid for increasing Sm and Gd content. For 5% Sm and Gd doping,the major visible dip indicating a phase transition shifts to muchlower temperatures compared to that of 5% La. For 10% Sm and

0 200 400 600 800 1000-0.25-0.20-0.15-0.10-0.050.000.050.100.150.200.25

Pow

er I

nput

(μv/

mg )

Temperature (°C)

Pure BFOBLFO 1%

BLFO 5%BLFO 10%

BLFO 15%

0 200 400 600 800 1000-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Pow

er I

nput

(μv/

mg)

Temperature (°C)

Pure BFOBSFO 1%BSFO 5%BSFO 10%

0 200 400 600 800 1000-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

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er I

nput

(μv/

mg)

Temperature (°C)

Pure BFOBGFO 1%BGFO 5%BGFO 10%

0 200 400 600 800 1000-0.30-0.25-0.20-0.15-0.10-0.050.000.050.100.150.200.25

Pow

er I

nput

(μv/

mg)

Temperature (°C)

BGFO 15%BSFO 15%

(a)

(b)

(c)

(d)

Fig. 6. DTA curves for pure BFO and various doping levels of Bi1�xAxFeO3 (A: La, Sm,Gd) samples.

0 2 4 6 8 10 12 14 16300350400450500550600650700750800850

Tra

nsiti

on T

empe

ratu

re (

o C)

Dopant Percentage (%)

La Sm Gd

Fig. 7. Temperature for the possible PE ? R3c* transition for doped powders as afunction of dopant concentration.

M. Khodabakhsh et al. / Journal of Alloys and Compounds 604 (2014) 117–129 123

Gd doping, the dips in the DTA curves are at around 400 �C and300 �C respectively. Near and beyond the solubility limit of Smand Gd (15% for Sm and 12% for Gd), we found that doping with15% Sm and 12% Gd apparently suppresses the transition to belowRT in majority of the grains as we observed no indication, i.e.signal, of a transition. On the other hand, 15% La doped powdersexhibit the dip at around 530 �C, still a significantly high

temperature with respect to 10% Sm and Gd containing powdersamples. The major visible dip at the transition for doped samplesshifting to lower temperatures is accompanied by a strong smear-ing along with intensity loss with increased dopant content. Thissmearing and intensity loss is much more profound in Sm andespecially Gd doped samples at 10%. An outcome of this type isoften expected in a phase mixture where the dominant phaseundergoes no transition while the other might have a transitionyielding a reduced signal in DTA. Remembering that La doped pow-ders appear to be mostly in the R3c phase and that a Pbnm + R3c�

mixture forms in Sm and Gd doped powders at or above 5%, theweakening of the DTA signal for the case of powders with Smand Gd > 5% might imply that a considerable volume of the grainsare in Pbnm phase for the entire temperature range, noticing alsothat the kink appearing around 800 �C also weakens with doping.We discuss the possible origin of this kink in the forthcomingparagraphs.

The DTA data can be interpreted in the light of what is observedin the XRD analysis: increasing the dopant concentration with ionshaving radii less than Bi3+ reduces the Curie point to lower temper-atures concurrent with ionic radius mismatch with Bi3+. Powderswith low doping (1%) are in R3c phase and have a transitiontemperature close to bulk BFO. This trend is still valid for 5% Ladoped powders. For phase mixtures that appear to be the casefor powders with Sm and Gd > 5% and La > 10%, the portion ofgrains having a lower transition temperature is in the R3c� at RT.The loss of signal intensity in the case of large dopant concentra-tions indicates that there is a ‘‘background’’ or ‘‘parent’’ phase thatdoes not undergo any transition. This structure is probably thePbnm phase as any transition from a high temperature PE phaseinto Pbnm would give a strong peak in DTA, which is not observedin the temperature range considered here. Referring to the previ-ous section, this also helps us to identify the Rietveld refinementfit of the phase mixture as the Pbnm + R3c at RT because we wouldexpect to see a peak in DTA had there been any transition from theparaelectric non-polar Pbnm state to polar P21na phase above RT. Inlight of this argument, larger volumetric fraction of Pbnm phasewould mean a greater loss in signal intensity in DTA and thisexpectation is totally consistent with the case of our doped sam-ples. Moreover, the increase in Pbnm volume fraction appears tobe imposing a further reduction of the temperature at which R3c�

occurs (because it is present at low amounts in the phase mixtureat RT). In the rest of the discussion, we call the non-polar high tem-perature phase ‘‘paraelectric (PE) phase’’ for sake of generality asthere is still some on-going discussion on the structure of thisphase in the literature and we do not have any precise tools fordetermining the structure of this phase, which is also outside thescope of our work. The high temperature PE phase has beenclaimed to have the non-polar P21/m space group symmetry in

124 M. Khodabakhsh et al. / Journal of Alloys and Compounds 604 (2014) 117–129

[46,79] which is probably true for our pure BFO. However, weremind here again that our DTA data combined with the RT XRDresults hints at the strong possibility that we might have thenon-polar Pbnm phase in heavily doped (>10%) Sm and Gd powdersin the entire temperature range of our DTA experiments owing toabsence of any peaks above RT but with a small fraction of grainspossibly depleted of dopants displaying the regular PE ? R3c tran-sition. This transition makes itself visible with the small smearedkink just below 800 �C and is independent of dopant type and con-centration range considered in this work.

The general reduction of the temperature for the PE ? R3c�

transition eventually becoming prominent for dopants with smal-ler ionic radii occurs in grains that are likely to be not in Pbnmphase of the phase mixture when present. This dependency ondopant radius can directly be correlated to inhomogeneous latticestrains induced by these dopants in grains which can undergo aPE ? R3c� transition. The greater the ionic radius misfit of the dop-ant with Bi3+ the stronger the reduction of this temperature alongwith the smearing as observed in our DTA data, keeping in mindagain that the presence of the Pbnm phase volume only amplifiesthis behavior. At 15% doping of both Sm and Gd, we observe nopeaks in DTA and this is an expected outcome if one refers to theRietveld results where the non-polar orthorhombic structure isthe dominant volumetric phase at RT. This could indicate thatthe remaining small R3c volume is also saturated with dopantsand has very weak ferroelectricity, hence we call it R3c�, along witha very strong smearing of its transition and such a mechanism isvery well documented in earlier text books on defect effects inphase transition anomalies [80].

We now discuss the all-time presence of the kink in DTA dataaround 800 �C visible in our samples regardless of dopant typeand concentration. Such a dip in the DTA curves in the vicinity ofthe pure BFO Curie point (�820 �C) would normally be associatedwith the PE ? R3c transition. For low doping concentrations, nosuch observation can be claimed as the entire volume appears tobe transforming from the paraelectric state to ferroelectric rela-tively close to bulk BFO. At increasing dopant concentrations, thispeak or ‘‘kink’’ is relatively easier to distinguish in all our powdersdespite the fact that it becomes weaker with increased dopant con-centration. Such a result points out to a rather inhomogeneousphase transition of the R3c phase in our powders where one canenvision the situation of some grains depleted of dopants trans-forming at higher temperatures than others, having inhomoge-neous strains due to dopants, for instance during cooling. Theremaining fraction is either PE + Pbnm phase mixture that trans-forms to R3c� + Pbnm upon further cooling or another possibilityis PE transforming into R3c� + Pbnm particularly when dopant con-centration exceeds 5% (>10% in case of La) as we always find aphase mixture at RT XRD in these cases. We can, however, elimi-nate PE transforming into R3c� + Pbnm as this would yield eithera very strong peak, or at least two peaks at different temperaturesin DTA owing to the fact that the appearance of the non-polar Pbnmand polar R3c� phase at the same temperature is very unlikely andneither of it is present in our doped powders.

The decrease of the amplitudes of the ‘high temperature’ dips inpowders with dopant concentrations P5% for Sm and Gd, >10% forLa, indicate that majority of the grains undergo a transition at low-er temperatures as can be justified by the relatively stronger,although smeared, intensity of the low temperature peak (occur-ring around 300–400 �C). We think that this is a consequence ofstrain fields around dopants in grains that can still transform intoR3c� from the parent non-polar PE phase. With the amount of suchgrains decreasing in volume in our powders with increasingdopant concentrations, the peak associated with the above transi-tion is expected to weaken and get smeared. In the light of our DTAand XRD data discussed above, the following sequence of transi-

tions can be proposed upon cooling from 900 �C to RT in dopedsamples:

PE phaseþ Pbnm #! R3c^ þ Pbnm #! R3c� þ Pbnm #for Sm and Gd 6 10% ð1Þ

PE phaseþ Pbnm "! R3c^ þ Pbnm "! R3c� þ Pbnm "for Sm and Gd P 15% ð2Þ

where we used ^ to indicate the R3c capable of forming in grainswith low dopant concentration having a transition temperatureclose to bulk BFO, ; indicates either ‘‘non existing’’ or ‘‘low-to-moderate in volume fraction’’ and similarly " ‘‘high in volume frac-tion’’. Sequence given in (2) exhibits no apparent peaks in DTA below780–800 �C (except that the temperature at which the smeared lowintensity ‘‘kink’’ exists as with all other powders, likely due to a verylow fraction of grains exhibiting the PE phase ? R3c^ transition) andis probably dominated by the non-polar Pbnm phase, concurrent withthe Rietveld refinement. Note that this also signals the possibility thatP15% Sm and Gd doped powders could be predominantly in Pbnmstate at high temperatures and only a small amount of ‘‘dopant de-pleted’’ grains transform to R3c^ slightly below bulk BFO transitiontemperature, yielding the relevant weak and smeared but all-timeexisting kink in DTA. The transitions proposed in (1) is a function ofdopant type and concentration for Sm and Gd doped powders whilesingle R3c phase appears to be stable and dominant in La doped pow-ders until around 15%. The visible peaks in DTA associated with tran-sitions in (1) are stronger for low amounts of Pbnm phase if the dopantconcentration is not larger than 5%, in particular for Sm and Gd dopedsamples. Therefore, the strong signal upon the likely transition fromthe PE phase to R3c� comes from majority of the grains that have al-most no Pbnm or low dopant concentration. As described previously,this signal is reduced at high dopant concentrations most likely be-cause of the increased stability and volume fraction of Pbnm andthe low amount of R3c� formation in a range of temperatures alsoleading to smearing of the signal. Note that the peaks we see in therange 300–700 �C in 5% or 10% doped samples (see transitions givenin (1)) cannot be originating from a PE ? Pbnm transition becausethen we would expect to see another peak or kink associated withthe Pbnm ? R3c� before reaching RT as we find that the RT phase ispredominantly R3c� even in 5% Sm and Gd doped BFO following thebest Rietveld fits.

The structures with high dopant concentration and lowertransition temperatures can then be expected to exhibit reducedintensities of Raman scattering according to the given interpreta-tion until now. This a way to probe ferroelectricity especially inleaky samples like ours where electrical measurements areinconclusive. That the paraelectric–ferroelectric transition of BFOtakes place is evident at the expected temperature consistent withprevious reports and we now give in Figs. 8 and 9 the comparativeRaman spectroscopy results of our powders to reveal the effect ofdopants on intensity of allowed vibrations of the R3c particularlyin the small wave vector regime.

Looking at Fig. 8, the pure BFO exhibits 11 modes of all 4A1 + 9Ephonon modes that are allowed in the non-centrosymmetrical R3cin part of the spectra until 800 cm�1. A comparison of Raman peakpositions for pure BFO obtained from this study and other works isprovided in Table 2 for reassurance of the presence of the R3cphase in BFO. Moreover, we noted that the peak positions of nearlyall 1–5% doped samples coincide with the R3c phase consistentwith our XRD results with some visible weakening of intensitiesin Sm and Gd doped samples.

In powders containing high concentrations of Sm and Gd (>10%)the R3c modes are very weak or nearly absent as can be seen inFig. 9. There is a gradual disappearance of the low frequency modes(large wavelength phonons) upon increased doping concentrations

100 200 300 400 500 600 700

5000

10000

15000

20000

25000

E7

E6

A-4E

5E4

E3

E2

A-3

A-2

A-1

E1

Inte

nsity

(a.

u)

Raman Shift (cm-1)

BFO Measured Raman spectraBFO simulated Raman spectraBFO Decomposed active Modes

Fig. 8. Measured spectra, simulated spectra of the deconvoluted (decomposed)Raman active modes for pure BFO.

(a)

(b)

(c)

Fig. 9. Effect of doping on Raman peaks of (a) La doped, (b) Sm doped and (c) Gddoped powders for increasing dopant concentrations. Pure BFO is given in all plotsfor reference.

Table 2Raman modes for R3c BFO in our work and their comparison with other studies.

BFO Ramanmodes

Yuan et al.(2007) [81]

Fukumura et al.(2007) [82]

Singh et al.(2006) [83]

Presentstudy

A�11

126 147 136 129.96

A�21

165 176 168 166.47

A�31

213 227 211 212.69

A�41

425 490 425 419.5

E1 111.7 – 77 111.44E2 259.5 265 275 257.10E3 – 279 335 293.5E4 339.6 351 365 338.67E5 366.9 375 – 365.59E6 473.3 437 456 458.75E7 599.6 525 597 519.53

M. Khodabakhsh et al. / Journal of Alloys and Compounds 604 (2014) 117–129 125

and this is prominent in 5% and 10% Sm and Gd doped powdersthat exhibit much lower transition temperatures in the DTAmeasurements. Thus, the Raman spectra implies a dopant induced

‘‘weakening’’ of the ferroelectric state upon doping of the largemismatch A-site cations. At this point we also sought trace of thePbnm modes that appear to be the case in Sm and Gd doped pow-ders giving the best Rietveld refinement results consistent with thepicture revealed by DTA. In search of the experimental Ramanspectra of the orthorhombic phase, we came across the systemat-ical work of Yang et al. [84] where the orthorhombic phase ofBFO was obtained and analyzed in situ by Raman spectroscopy un-der high hydrostatic pressure. They observed that intensity of twopeaks in the 300–400 cm�1 region was enhanced with increasinghydrostatic pressure that was attributed to FeO6 octahedra tilts.At first sight, it seems reasonable to compare our Raman data tothe pressure-induced orthorhombic phase again owing to the factthat the Rietveld results yield the best fit to orthorhombic phasefor >5% Sm and Gd doped powders. We do observe a relative in-crease in intensity of the modes around 300–400 cm�1 regionalong with a near-disappearance of low frequency modes of theR3c but because of the inhomogeneous nature of our powders,we can clearly confirm here the disappearance of the R3c modesrather than appearance of the possible Pbnm modes. The inhomo-geneous nature of the dopant distribution in our powders isexpected to reduce the intensities of the Raman peaks. Althoughwe did not carry out Raman spectroscopy for 15% Sm and Gd dopedBFO after observing the almost-total disappearance of R3c peaks in10% Sm and Gd powders, it is useful to remind here that the Riet-veld analysis on this composition has the uncomparably best fit forPbnm. In another systematic work carried out by Bielecki et al. [66].Tb doped powders (Tb has a very close ionic radius to Gd in 8 coor-dination) showed a similar trend with the R3c modes rapidly losingintensity after around 10% doping but not a clear signal of the sec-ondary phase was detected despite that they mention a gradualtransition upon doping citing precise neutron diffraction studies.The Pnma space group modes in that work, which is claimed tobe the phase that the R3c transforms into, started to exhibit them-selves only after 17.5% Tb concentrations in the Raman spectra butthey also started to see impurity phases such as Bi2Fe4O9 (only intheir XRD analysis) which we tried to avoid in our work to reducecomplications in data interpretation. It turns out that dopants in-duce a higher symmetry phase than R3c and the fraction of thisphase is a strong function of dopant radius. Despite the use ofthe sol–gel method where homogeneous solutions are prepared,there is strong evidence for ‘‘dopant depleted’’ grains upon crystal-lization which do undergo a PE ? R3c transition but with atendency of smearing and reduced temperatures depending ondopant radius for a given concentration. It is important to add herethat we systematically sought evidence for the inhomogeneousdistribution of dopants during SEM sessions as signaled by theDTA results but our efforts were inconclusive mostly because ofsubmicron grain size. However, with the available structuraland thermal analysis data we gathered, we can suggest an apt

126 M. Khodabakhsh et al. / Journal of Alloys and Compounds 604 (2014) 117–129

mechanism using well known phenomena in ferroelectric crystalsto explain these interesting results in the next section.

3.2.1. Transition into polar R3c phase from non-polar PE phase indopant depleted grains

In this section we discuss the reason for the shift of the transitionpeak in DTA to lower temperatures accompanied by a smearingwith dopant concentration. Our DTA data implies that, in powdershaving A-site doping of 5% or more, a small fraction of possibly dop-ant depleted grains still exhibit the PE ? R3c^ transition slightlybelow 820 �C with another small fraction of grains exhibiting a re-duced transition temperature similarly for the PE ? R3c� especiallyfor Sm and Gd doped samples when the doping level less than 15%.We thought so as the peak associated with any transition getsweaker and smeared with higher dopant concentrations. We al-ready elaborated on the possible structures stabilized followingthese transitions, but it remains important to understand the originof the reduction in the temperature for the PE ? R3c� transition as afunction of dopant radius in some volume of doped powders keep-ing in mind that our XRD results strongly suggest phase mixtures.

As mentioned previously, transition from the polar symmetry toa non-polar one or disappearance or weakening of ferroelectriccharacter in BFO (which is mostly due to reduction of the paraelec-tric–ferroelectric transition) has been often attributed to localbonding changes due to hybridization states between valence elec-trons and the presence of 6s2 lone pairs, strongly screened from thenucleus of Bi3+ that are absent in rare earth elements such as La, Gdand Sm. Such an effect is also expected to reduce the polarizabilityof these ions, a driving force often required for distortions leadingto ferroelectricity. Despite this often-discussed mechanism, how afew percent of A-site dopants can make a significant reduction inthe phase transition temperature of the entire sample remains asa non-trivial question. One must bear in mind that the numberof unitcells and therefore the bonds have the same percentage asthe dopant concentration. For instance, in the pseudocubic perov-skite structure with 5% dopant concentration, there will be onaverage about 5 unitcells housing a dopant atom out of 100unitcells and yet for Sm and Gd doping we observe that there isa considerable reduction in the phase transition temperatureaccompanied by a clear DTA signal, implying that majority of thestructure behaves the same. 5% doped powders that we have yieldR3c� as the dominant phase particularly in Sm and Gd doped sam-ples and the shift of the peak position in DTA to lower tempera-tures is associated with this phase. No such strong reduction isobserved in 5% La doped samples. This reduction in transition tem-peratures cannot simply be explained by local bonding chemistryor absence of lone pairs because it is a strong function of dopantradius for a given concentration, keeping in mind the similar va-lence arrangements and close atomic masses of La, Sm and Gd.With the above picture in sight, we refer to the sensitivity of ferro-electric crystals to inhomogeneous lattice strains to explain thereduction in transition temperature that appears to be dramati-cally dependent on dopant radius. It is well-understood that anystructural inhomogeneity in a ferroelectric crystal is a source ofelectric field as the Maxwell relation divD = q (q is space chargedue to defects and carrier depletion, D is dielectric displacement)universally holds in these materials as with any other dielectric.This equation, when expanded and expressed in terms of electricalpotential, takes the following form, namely the Poisson equation,considering x, y, z are coordinates in space, the ferroelectric polar-ization components Px, Py and Pz giving rise to the ferroelectricpolarization in BFO along [111] direction:

d2/F

dx2 þd2/F

dy2 þd2/F

dz2 ¼1

ebe0

dPx

dxþ dPy

dyþ dPz

dz� q

� �ð3Þ

with /F being the electrostatic potential in the ferroelectric med-ium, q is space charge (often called the depletion charge in widebandgap materials such as BFO) that could correspond to both freecarriers and ionized defects or dopants depending on how they aredistributed, e0 is permittivity of vacuum (8.85 � 10�12 F m�1), eb isthe background dielectric constant (non-ferroelectric, linear re-sponse of the crystal), a value on the order of 5–10. Note that evenin the absence of q Eq. (3) will lead to generation of fields aroundthe dopant sites due to polarization gradient terms. The solutionof this equation in a random shaped crystallite neighboring othersis nearly an impossible task due to the high ambiguity in definingproper boundary conditions both for electrostatic potential and fer-roelectric polarization but we can still deduce common sense impli-cations: one can immediately see from (3) that spatial potentialdistribution will be a function of the polarization gradients inducedby the position dependent strain around the dopant sites that will

generate electric fields coupling to the [111] polarization of bulk

BFO equal to P2x þ P2

y þ P2z

� �1=2in magnitude. Even if these gradient

variations are less than 1% several unitcells far from the strainsource, for instance, it is striking to see that such small variationsscale with 1/ebe0, a very large number that is close to a value of1011 m/F for a background dielectric constant of 8. This means thata variation of 0.1% in any polarization component due to inhomoge-neous strains would lead to local electric fields at the order of 109 V/m, a very large value compared to coercive field of such systems.Moreover, due to the large Debye screening lengths (at the orderof 10–20 nm, see Ref. [85] which was shown for a formal thin filmgeometry) even in leaky perovskites, such electric fields will not bescreened by free charges and penetrate into a significant volume.Therefore, a random distribution of dopants in the grains, whichis the most conservative and natural case to consider, can createrandom internal electric fields at the order of or higher than coer-cive field of BFO via their position-wise varying strain fields owingto the electrostrictive nature of the crystal where strain inducedpolarization is Pi = (ujk/Qijk)1/2 where ujk Qijk are the strain and elec-trostrictive tensors with i, j and k denoting the indices for the ele-ments of the tensors respectively. Such electric fields emanatingfrom gradual change of polarization, called depolarizing fields, areoften present in thin films with imperfect charge screening atfilm-electrode interfaces [86,87] but the regular and high-symme-try orientation of the entire crystal there helps to naturally developregular up-down domain patterns to confine the field to the inter-face, stabilizing ferroelectricity although not in single domain state.In the case of random source distribution of these fields due to dis-tortions around dopants in A-sites within randomly shaped grains,such a mechanism is not possible and one should expect stronginternal fields with random direction that can only weaken ferro-electric distortions bearing in mind that random internal fields can-not ‘‘enhance’’ ferroelectricity but only reduce it [80]. The extent ofstrain field penetration of a point defect such as a dopant is welldocumented in perovskites and strain fields of such defects extendas much as 4–5 unitcells [88], corresponding to a ‘‘volume underinfluence’’ consisting of about 125 unitcells. That a large portionof unitcells neighboring a dopant-site will be under the influenceof such ‘‘inhomogeneous train driven’’ internal fields can be con-cluded even for compositions less than 1 dopant/125 unitcells.BFO grains can then certainly be expected to experience these inter-nal electric fields around dopant sites especially if the ionic radiusmisfit of the dopant with Bi3+ is significant, in qualitative agreementwith our experimental findings. Large internal depolarizing fieldscan be capable of suppressing ferroelectricity and therefore stabilizecentrosymmetric phases. It is therefore feasible to expect that a fewpercent dopant concentrations might stabilize 15–20% Pbnm if thedopant radius misfit with Bi3+ is large. Higher dopant concentra-tions with ‘‘smaller ionic radius’’ will introduce a larger ‘‘distorted

M. Khodabakhsh et al. / Journal of Alloys and Compounds 604 (2014) 117–129 127

volume’’ distribution and amplify the above mechanism furtherwhile low-to-moderate dopant concentrations with radius close toBi3+ (the case of La) will have a lesser impact as observed in ourexperiments. Note that dopant induced strains in the case of dopantradius <Bi3+ will not neutralize or cancel each other as sign of straininduced by local displacements will be negative, i.e., pointing to-wards the strain source that is the dopant itself. A similar effect isdocumented in ferroelectric crystals with dislocations where thedislocation produces local strain fields that decay away from thecore and is a function of Burgers vector magnitude, analogous tothe ionic radii mismatch between the dopant and native A-siteatom, leading to a degradation [89,90] and smearing [80,91] inferroelectric properties. It is also well understood that increase indefect density will only degrade polar properties.

Therefore, we have solid evidence to argue that the reduction ofthe Curie temperature in powders with dopants having smallerionic radius for a given concentration is mainly due to the inhomo-geneous strain fields introduced and this effect dominates over themechanism that takes into account the local chemistry of bondswith dopants in the BFO lattice. The effect of RE dopants in BFOis two fold: (i) dopants with large ionic radii misfit stabilize non-polar phases such as the Pbnm structure, leading to a phase mix-ture and (ii) the polar phase portion of the phase mixture willexperience strong inhomogeneous strains that, via electrostrictivecoupling, generate internal electric fields capable of dramaticallyaltering the PE ? R3c� temperature, a well understood phenomenain ferroelectric crystals. The sensitivity of the structure and subse-quent Curie temperatures being a function of dopant radii canactually be used as a design parameter especially when consider-ing film growth on misfitting substrates. The magnetic substruc-ture of BFO has not been considered as a parameter in discussingchanges of the structure as the changes in magnetic ordering attemperatures near RT will be negligible due to the very weak mag-netostriction. We also did not see a visible signal to judge the effectof doping on the paramagnetic–antiferromagnetic transitionaround the reported Neel temperature for pure BFO as powdersdo not exhibit an identifiable signal except a very gradual slopechange in the DTA analysis. Additionally, had extensive dopingwith Gd and Sm been capable of inducing a detectable magnetictransition above RT in DTA, we would have seen it in P5% Sm orGd doped powders, which does not reveal itself. Thus, the detect-able peaks in our DTA can be concluded to arise from the structuraldistortions leading to transitions between various space groups.

4. Conclusions

We studied the effect of A-site dopant radius on the phase tran-sition temperatures and structure of BiFeO3, a magnetoelectricmaterial attracting intense attention. While several works existin the literature on dopant effects, our main point in revisiting dop-ant effects in BFO was to bring an explanation of the serious impactof dopant radius on phase transition temperatures and latticestructure in the light of experimental data. RT XRD h–2h results re-veal that the peaks tend to broaden, merge and shift to higher an-gles faster for dopants with larger ionic radius misfit with Bi3+,implying a shrinkage of the unitcell and a tendency towards a ‘‘lessdistorted rhombohedral’’ which we named as R3c�. In fact, Rietveldanalysis indicated the presence of a R3c� + Pbnm phase mixture forSm and Gd doped films above 5% and La above 10%, with the Smand Gd doped powders experiencing the strongest decrease inthe transition temperatures. Our DTA data interpreted togetherwith the RT XRD and Raman spectroscopy results point out tothe presence of dopant depletion in some grains because of theall-time present signal in the vicinity of 800 �C followed by anothersignal that shifts faster to lower temperatures accompanied byintensity loss and smearing upon increase in dopant concentration.

This shift along with intensity loss and smearing is much strongerin Sm and Gd doped powders. We proposed a sequence of phasetransitions that can consistently explain the experimental dataand that the Pbnm phase might be the dominant ‘‘background’’phase in the phase mixtures for high concentration of dopants.As a result, doping with elements having a smaller ionic radiusthan Bi3+ can stabilize the Pbnm phase even down to RT with someremnant R3c with a reduced transition temperature. The fraction of‘‘non-Pbnm’’ grains in doped powders have a reduced PE ? R3ctransition mostly because of the inhomogeneous strains associatedwith dopant sites that are still expected to be present. Smaller ionicradius of a dopant creates steeper strain gradients that are capableof creating stronger internal electric fields that is expected to re-duce the PE ? R3c transition more rapidly along with a strongsmearing as also observed in our doped powders. A possible sizeeffect due to inhibited grain growth in doped powders was consis-tently eliminated as a possible mechanism behind the reduction inthe transition temperatures or even disappearance of structuraltransitions in highly doped powders. Doping with rare earth ele-ments to enhance dielectric and magnetic properties has been acommon practice in BFO but our work draws attention to the pos-sible strong impact of structural inhomogeneities and sensitivity ofBFO to such formations and that local bonding environmentscannot be the sole cause of degradation in ferroelectric behavior.Despite the care shown in preparation of homogeneous precursorsolutions, one may end up with inhomogeneous structures with lo-cally varying properties. Comparing our results with that of othergroups who have carried out similar experiments with RE dopantsbut on samples synthesized through a different route, we findrather different phases and phase transition characteristics, point-ing out the significance of the synthesis method on properties. Wealso hope that our results can motivate detailed atomistic compu-tational analysis of dopant effects with particular emphasis on theinhomogeneous strain effects on electronic structure of BFO.

Acknowledgements

This work was supported by TÜB_ITAK 1001 Grant 109M686 andpartially by funds of TÜBA GEB_IP. The authors acknowledge the useof Sabanci University SUNUM facilities for Raman spectroscopy.

Appendix A. Supplementary material

Supplementary material associated with this article can befound, in the online version, at http://dx.doi.org/10.1016/j.jallcom.2014.03.103.

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