CERAMICSINTERNATIONAL

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http://dx.doi.org/0272-8842/& 20

Ceramics International 40 (2014) 16081–16084www.elsevier.com/locate/ceramint

10.1016/j.ceram14 Elsevier Ltd

Rebuttal to “density functional theory investigation of siteprediction of Fe substitution in barium titanate”

Abstract

Through this letter to the editor (Rebuttal), we had given our explanation for the queries raised by Professor Juan J. Meléndez commenting onthe high substitution energies, the small simulation supercells, and the inconsistence of experimental data and simulation results. We agree withthe comment that applying a “chemical potential diagram” is a general way to study defect system. However, there are some experimentalconcerns on “what the initial materials should be used”, whereas many degrees of freedom become feasible. Therefore, the formation energyequation (with foreign atoms substitution) cannot be trivially answered by the formation energy within a chemical potential diagram framework,unlike substitution energy calculated directly from our suggested chemical equation. We explain in the details on our approach and confirm thevalidity of our main equation; FeOþBa8Ti8O23-Ba8Ti7FeO23þTiO2 for the substitution energy with 2� 2� 2 supercell size which the resultsstill show some suggestive trends.& 2014 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Keywords: B. Impurities; D. BaTiO3; D. Perovskites

1. Comments on the paper entitled “Density functionaltheory investigation of site prediction of Fe substitution inbarium titanate” [Ceramics International 39 (2013),293–296] by Juan J. Meléndez.

Several physical inconsistencies in this paper were found.First, the authors report unrealistically high (and thereforeincorrect) substitution energies. These values arise because thechemical potentials of the species involved are not takeninto account in their definition of substitution energy; smallcontributions may also arise from the use of too smallsimulation supercells. Secondly, the trends shown by theresults does contradict the evidence that iron incorporates tobarium titanate mostly as Fe(III). Finally, the authors find iron-doped barium titanate to exhibit a metallic character, which isclearly inconsistent with experimental data and simulationresults. Some suggestions to get much more realistic resultswere given.

In their interesting paper [1], Nimmanpipug and co-workersuse the DFT formalism within the LDA approximation toelucidate the most favorable mechanism for incorporation ofiron to the lattice of tetragonal barium titanate. For the valencecharges þ2 and þ3, the authors place the dopant at the hostbarium and titanium sites [for Fe(II)]or the titanium one [for Fe(III)], create the proper charge-compensating defects (oxygen

int.2014.07.078and Techna Group S.r.l. All rights reserved.

vacancies) and study the variation of the substitution energywith the relative positions of the dopants and the oxygenvacancies. Their results are listed in Tables 1 and 2 of Ref. [1].In addition, the authors investigate the effect of the incorpora-tion configuration on the band structure and density of states ofthe system. In my opinion, DFT is indeed one of the possibleright frameworks to deal with this problem, since electroniceffects are greatly involved in the defect structure of solids [2].However, the authors' results do not seem tobe correct for anumber of reasons:The authors do not use the right definition of the substitution

energies. Let us consider, for instance, the incorporation of Fe(II) to the titanium site with compensation by an oxygenvacancy, which may be described by the Kröger–Vinkequation:

FeOþTiTiþOo-Fe00Tiþνo∙∙ þTiO2 (1)

The authors calculate the substitution energy as

Esub¼E(FeTi)þE(νo)þE(TiO2)–E(FeO) (2)

Where E(a) seems to hold for the energy per atom ofconfiguration a. This expression yields unrealistic values ofabout 119 eV (in absolute value) as listed in Table 2 of Ref.[1]. It is relatively easy to realize that Eq. (2) is actually wrong.Indeed, the effect of the last term in the right-side member is to

P. Nimmanpipug et al. / Ceramics International 40 (2014) 16081–1608416082

counter balance the appearing of a “strange” iron atom in alattice which otherwise will contain only titanium, barium andoxygen in their respective positions. But the iron atomincluded in the defective barium titanate lattice has a chemicalenvironment which is different than that in FeO and, therefore,such a correction does not suffice. Please note that Eq. (2)would be applicable, however, within a semi-classical formal-ism (i.e., molecular dynamics), where electronic effects are notexplicitly taken into account.

The defect substitution energy, assuming the defect to beneutral, is instead calculated according to

Esub ¼ EðdefectÞ–EðpureÞ–Σiniμi ð3Þwhere E(defect) and E(pure) are, respectively, the energies ofthe defective and defect free supercells, is the number of atomsof defective species which have been added to (ni40) orremoved from (nio0) the supercell when the defect has beencreated, and is the chemical potential of the species i, whichaccounts for the particular chemical environment within thelattice [3].

The authors use a very small simulation supercell. In asupercell framework, which assumes periodic boundary con-ditions to hold in all directions, it is well known that dopantsinteract with their periodic images, much more markedly ifthey are charged, and such spurious interactions may well alterthe results of substitution energies. Since thecomputationalresources available may be limited, one should use simulationsupercells of increasing size until the energies are calculatedwithin a prefixed tolerance. 2� 2� 2 Supercells, like thoseused by the authors, have been found to be small in bariumtitanate and similar systems [4]; 3� 3� 3 ones, instead, arereasonably accurate. One could also rescale the results with thesize of the simulation supercell. Indeed, the images of neutraldefects interact mainly elastically, and the corrections to theenergy scale as V�1 (being V the volume of the supercell); forcharged defects, the corrections vary as V�1/3 instead [5,6].The authors could run simulations using 3� 3� 3 cells or,alternatively, using cells of different volumes and fit theirresults to the appropriate scaling law.

Apart from the previous, and assuming that the results showthe right trend (although not the right values), the authors'results are inconsistent with the almost unanimous evidencethat iron incorporates as Fe(III) to barium titanate [7–10];valence changes seem to occur only after thermal treatments[10,11]. In any case, the differences of energy between valencecharges are not large, which explains why the incorporationmechanism may be so sensitive to the thermodynamic (i.e.,oxygen partial pressure) or stoichiometric (i.e., Ba/Ti molarratio) conditions under some circumstances. I do not think thatenergy differences of the order of 30 eV or more may bephysically justifiable.

The authors build the band structure of two defectivesystems [Fe(II) and Fe(III) in their most probable configura-tions] as well as the corresponding densities of states (cf. Fig. 2of Ref. [1]). In both cases, the Fermi level lies within an energyband instead of within thegap. In other words, the authorspredict Fe-doped barium titanate to be a metal, contrarilyto the

wide evidence of its insulating character [see, for instance, [12]and references therein]. This is obviously not related to thewrong definition of substitution energy, but to a limitation ofDFT itself. Indeed, when atoms with partially filled d shells arepresent,standard DFT is known to delocalize the inner elec-trons much more than they actually are,which makes a fakemetallic character to appear. This may be solved by using theexact exchange(EXX) approximation, although its applicationto solids is extremely costly from the computational point ofview. Alternatively, one may adopt the so-called DFTþUformalism [13,14], in which an extra term penalizing theoccupations of the d shells to benon-integer is added to theenergy functional; this is much more less computationallyexpensive and, under some circumstances, may be derivedfrom first-principles [15]. Iron atoms have unfilled inner dshells and, therefore, the DFTþU formalism should be useful.The forced localization of the inner electrons is likely to giverise to the energy gap which is experimentally observed. Anadditional issue is that, because of the existence of theincomplete d shells, the spin-polarized LDA should be used;please note that the authors do not provide any information onthis respect.Iron-doped cubic barium titanate has been the subject of a

recent paper [16] which uses the DFT formalism within theGGAþU approximation. Using 3� 3� 3 simulation super-cells,the authors use Eq. (3) and report that Fe(II) incorporationwithin barium titanate yields energies of the order of 3 eV for anumber of mechanisms, except for a few quite unlikely caseswhich involve the creation of the very energetic titaniumvacancies. Energies of this order are much more realistic thanthe abnormally high negative values reported by Nimmanpi-pug and co-workers. The most stable mode is found to beacceptor incorporation of Fe(III) at two titanium sites with thecreation of an oxygen vacancy, but the most important, whichagrees well with the experimental evidence. In addition, thedensity of states of both pure and iron-doped barium titanateexhibit a gap, within which the Fermi level lies, consistentlywith the insulating behavior of these systems.

2. Rebuttal

Through this rebuttal, we would like to give our explanationin the section accordingly for the queries/comments raised byProf. Juan J. Meléndez on our published paper “Densityfunctional theory investigation of site prediction of Fe sub-stitution in barium titanate [Ceramics International 39 (2013),293–296]”.The substitution energy depends upon the chemical potential

of relevant species in the reservoir. All possibility of dopantscomposing of Fe(II) and Fe(III) substituting in bariumtitanatebased on typical synthesis process were carried out. Since thepurpose of this work is to provide additional information forthe general view of how the impurity in the form of Fe(II) andFe(III) incorporates into the tetragonal BaTiO3, we thereforeinitially define where each applicable oxidation state of Feshould technically come from. Specifically, we have carriedthis out by employing FeO and Fe2O3 as the source for Fe(II)

P. Nimmanpipug et al. / Ceramics International 40 (2014) 16081–16084 16083

and Fe(III), respectively, whereby this technique follows theexperimental preparation of Fe-doped BaTiO3 which usedFe2O3 as a substrate [17]. Note that, the substituted atoms(i.e. Ba and Ti) may form their oxide compounds as supportingphases, so the particles are conserved.

We agree with the comment that applying a “chemicalpotential diagram” is a general way to study the defect system.However, there are some experimental concerns on “what theinitial materials should be used”, whereas many degrees offreedom become feasible. Therefore, the formation energyequation (with foreign atoms substitution) cannot be triviallyanswered by the formation energy within a chemical potentialdiagram framework, unlike substitution energy calculateddirectly from our suggested chemical equation.

On the other hand, it is possible to see that the substitutionenergy in (4) is equivalent to the defect formation energy in (5)by using a set of the atomic chemical potential available in theaccepted domain corresponding to the equilibrium growthcondition of BaTiO3 and denying the formation of anundesirable phase, e.g. FeO. For example, in the case of Fe(II) substitution at the titanium site with oxygen vacancycharge compensation, we suggested:

FeOþBa8Ti8O23-Ba8Ti7FeO23þTiO2

as a reasonable reaction (where 8 is from multiplicity due to2� 2� 2 supercell size). The substitution energy (ourapproach) would be calculated from

Esub¼E(Ba8Ti7FeO23)þE(TiO2)�8E(BaTiO3)�E(FeO), (4)

where Esub is substitution energy and 8E(BaTiO3) is the totalenergy of pure BaTiO3 with 2� 2� 2 supercell size. Then, weconsidered the condition on TiO2 edge (mTiþ2mO¼mTiO2) ofBa–Ti chemical potential diagram as well as iron chemicalpotential defined as mFe¼mFeO�mO (FeO upper bound). Withappropriate energy reference, the chemical potential of acompound can be conveniently defined as its specific energy.Therefore it leads to mTiO2

¼E(TiO2) and mFeO¼E(FeO) aswell as the condition for equilibrium growth of the hostBaTiO3, i.e. mBaþmTiþ3mO¼mBaTiO3

¼E(BaTiO3). Thus, itcould be simply shown that (4) can be rewritten to

Esub¼E(Ba8Ti7FeO23)–8E(BaTiO3)þ (mTiþ2mO)� (mFeþmO)

which simplifies to

Esub¼E(Ba8Ti7FeO23)–8E(BaTiO3)þmTiþmO�mFe. (5)

As can be seen, this confirms the validity of our main equation.However, the defined value of oxygen chemical potential (mO)should sustain for both conditions, mTiþ2mO¼mTiO2

andmFe¼mFeO–mO. Also, from an unpublished work of our co-workers (where LDAþU was used), the FeO upper bound(mFe¼mFeO–mO) and TiO2 edge (mTiþ2mO¼mTiO2

) conditions arevalid for the value of mO covering the range (�439.75, �437.75)and (�439.99, �435.85) eV, respectively (where mO was notused to define the energy reference, with respect to its elementaryphase). The intersection of these two sets of mO suggest that there

are many possible sets of (mTi, mBa, mO, mFe) allowing for theconsistency between (4) and (5).We also agree with the fact that “Fe in BaTiO3 may have

different oxidation states due to different physical and chemi-cal environments”, so this has to be checked by “Borneffective charge” calculation. However, as reported in thiswork, we considered the cases where the ion maintains itsoxidation state in the doping process, which can be preparedusing other specific techniques rather than the solid statereaction. However, the variation in the oxidation will becarried out in future deeper investigation.Concerning computational protocol, there are various mod-

els and methods proposed to elucidate such complicatedphenomena. An optimum super cell 2� 2� 2 within LDAfunctional has been used to investigate the effect of impurityzirconium on BariumTitanate and the result of position ofzirconium in structure is good agreement with experimentaldata [18]. Some other cases studied the effect of impurity, thenumber of atoms used in system at rather limited number of 40atoms [18–23]. We agree with the comment that we used smallsupercell, but this was because computational resource limita-tion. However, the results still show some suggestive trends.Although there is deviation of trend of band structure and

density of state, the value of band gap which is an importantvalue in the semiconductor is in good agreement with experi-mental data [24]. Despite an underestimation of the 3d orbital ofthe Ti atom in calculation using LDA-PWC, LDA-VWN, LDA-PWC, GGA-BLYP, GGA-PW91, GGA-BP, GGA-HTCH andGGA-PBE give similar band gap energy in a range of 2–2.3 eVwhich will be reported in our ongoing work.

References

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Piyarat Nimmanpipugn, Laongnaun SrisombatComputational Simulation and Modeling Laboratory (CSML),

Department of Chemistry, Faculty of Science,Chiang Mai University, 239 HuayKaew Road,

Chiang Mai 50200, ThailandThailand Center of Excellence in Physics, Commission on

Higher Education, 328 Sri Ayuthaya Road,Bangkok 10400, Thailand

E-mail address: piyaratn@gmail.com (P. Nimmanpipug)

nCorresponding author. Tel.: þ66 53943341; fax: þ66 53892277.

Aroon SaelorComputational Simulation and Modeling Laboratory (CSML),

Department of Chemistry, Faculty of Science,Chiang Mai University, 239 HuayKaew Road,

Chiang Mai 50200, Thailand

Vannajan Sanghiran LeeComputational Simulation and Modeling Laboratory (CSML),

Department of Chemistry, Faculty of Science,Chiang Mai University, 239 HuayKaew Road,

Chiang Mai 50200, ThailandThailand Center of Excellence in Physics, Commission on

Higher Education, 328 Sri Ayuthaya Road,Bangkok 10400, Thailand

Department of Chemistry, Faculty of Science,University of Malaya, 50603 Kuala Lumpur, Malaysia

Sittichain Pramchu, Yongyut LaosiritawornThailand Center of Excellence in Physics, Commission on

Higher Education, 328 Sri Ayuthaya Road,Bangkok 10400, Thailand

Department of Physics and Materials Science, Faculty ofScience, Chiang Mai University, 239 HuayKaew Road,

Chiang Mai 50200, Thailand

14 July 2014; accepted 15 July 2014