10494 Phys. Chem. Chem. Phys., 2013, 15, 10494--10499 This journal is c the Owner Societies 2013

Cite this: Phys. Chem.Chem.Phys.,2013,15, 10494

Calculation of arrangement of oxygen ions andvacancies in double perovskite GdBaCo2O5+d byfirst-principles DFT with Monte Carlo simulations

Hiromasa Shiiba,a Masanobu Nakayama,*abe Toshihiro Kasuga,c Robin W. Grimesd

and John A. Kilnerd

The configurations of oxygen ions and vacancies at various oxygen stoichiometries and temperatures in

double perovskite oxides (GdBaCo2O5+d, 0 r d r 1) have been determined by density functional theory

(DFT) combined with Monte Carlo (MC) simulations. The MC simulations confirmed the existence of a

superstructure at d = 0.5, showing alternating linear ordering of oxygen ions and vacancies along the

b-axis in the GdO layer. This structure is identical to that reported experimentally. Increasing the

temperature up to 1200 K induces a phase transition manifested in the breaking of the oxygen/vacancy

arrangement at around d = 0.5. In the high-temperature phase, vacancies are distributed in the GdO

and CoO2 layers, whereas there are no vacancies in the BaO layer. In addition, the characteristic linear

arrangement is partly preserved even in the disordered high-temperature phase. Consequently, oxygen

ions can migrate between the GdO and CoO2 layers, as reported in previous classical molecular

dynamics simulation studies.

1. Introduction

Research on new oxides with fast oxygen transport is of greatimportance for the realisation of high-temperature electroche-mical devices. In particular, mixed ionic–electronic conductingdouble perovskite LnBaCo2O5+d (Ln = rare earth) oxides haverecently attracted considerable attention as cathode materials forsolid oxide fuel cells (SOFCs), since such materials are expectedto lower the presently required high operating temperatures to amore moderate temperature range (i.e. 500–700 1C).1 Therefore,various candidate materials have been investigated in terms oftheir crystal structure, oxygen diffusivity and electrochemicalproperties.2–18

GdBaCo2O5+d (GBCO), where 0 r d r 1, is an example of adouble perovskite oxide with relatively high mixed conductivity.19–25

The difference in size between the large Ba cation and the smallGd cation results in the formation of alternating GdO and BaOlayers (. . ., GdO, CoO2, BaO, CoO2, GdO,. . .) along the c axis(Fig. 1). One of the notable features of GBCO is its ability toaccommodate large deviations from ABO3 stoichiometry arisingfrom oxygen vacancy formation. Indeed, according to structuralstudies, the parent stable composition of GdBaCo2O5 contains1/6 of an oxygen vacancy per formula unit and forms an oxygen-ordered structure at low temperatures.23 Specifically, the oxygen

Fig. 1 Crystal structure of GdBaCo2O5.5. Black spheres, white spheres and whitepolyhedra indicate Ba, Gd and polyhedral Co, respectively.

a Department of Materials Science and Engineering, Nagoya Institute of Technology,

Gokiso, Showa, Nagoya, Aichi 466-8555, Japan. E-mail: masanobu@nitech.ac.jpb Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho Kawaguchi,

Saitama 332-0012, Japanc Department of Frontier Materials, Nagoya Institute of Technology, Gokiso, Showa,

Nagoya, Aichi 466-8555, Japand Department of Materials, Imperial College London, South Kensington Campus,

London, SW7 2AZ, UKe Unit of Elements Strategy Initiative for Catalysts & Batteries (ESICB),

Kyoto University, Katsura, Saikyo-ku, Kyoto, 615-8520, Japan

Received 23rd January 2013,Accepted 19th April 2013

DOI: 10.1039/c3cp50316j

www.rsc.org/pccp

PCCP

PAPER

Publ

ishe

d on

22

Apr

il 20

13. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 23

/08/

2013

18:

45:5

5.

View Article OnlineView Journal | View Issue

This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys., 2013, 15, 10494--10499 10495

stoichiometry of GBCO is close to d = 0.5 at room temperature,and its crystal symmetry is orthorhombic (space group: Pmmm),as depicted in Fig. 2, where oxygen ions and vacancies alternatealong with the b-axis in the GdO layer.

At do 0.45, GdBaCo2O5+d exhibits tetragonal symmetry, whereaswhen 0.45 r d r 0.60 the structure becomes orthorhombic.26

The change in symmetry from orthorhombic Pmmm to tetragonalP4/mmm takes place at around 450–500 1C.23,27 However, Taranconet al. reported that the phase transition exerts no appreciableeffect on the cathode performance23 and the oxygen transportproperties (diffusivity and/or surface exchange).16 The reason forthis lack of correlation between the phase transition and oxygentransport properties remains unclear.

Thus far, several studies have investigated the effect ofcation ordering on oxygen transport properties. For example,Parfitt et al. reported that oxygen self-diffusion in GdBaCo2O5+d

is strongly dependent upon the A-site cation order, and as such itis anisotropic.28 In addition, Burriel et al. confirmed anisotropyin the diffusion and exchange of oxygen for PrBaCo2O5+d byin-depth analysis of single grains with known orientation in apolycrystalline ceramic sample.29 Nevertheless, due to technicaldifficulties, such as the low X-ray scattering factor of oxygen, fewstudies have analysed the oxygen/vacancy arrangements ofGBCO in order to understand oxygen transport properties.

The aim of this paper is to clarify and demonstrate thedetailed oxygen/vacancy arrangement in GBCO as a function ofcomposition (d) and temperature. First-principles calculationsbased on density functional theory (DFT) have been carried outwith the aid of the cluster expansion approach and Monte Carlo(MC) simulations.

2. Method2.1 Density functional theory

The basic approach of the present investigation, which isidentical to that in ref. 30, is divided into three steps. Initially,first-principles calculations of GdBaCo2O5+d were performed to

obtain the total energy at various configurations of oxygen andvacancies. The Vienna ab initio simulation package (VASP)31,32

was utilised with the generalised gradient approximation(GGA-PBE)+U33,34 and projector-augmented wave (PAW) methods.35

For the GGA+U calculations, the U values for the f-orbitals of Gdand the d-orbitals of Co were set to 6.9 eV and 6.0 eV followingrelevant previous reports.36,37 Relaxation of the crystal structurewas allowed, and the final energies of the optimised structuralgeometries were recalculated to correct for changes in theplane-wave basis during relaxation. An energy cutoff of 500 eVand a k-point mesh were chosen such that the product of thenumber of k-points and the number of atoms in the unit cellwas greater than 500.

In the second step, a subset of the calculated B150 totalenergies corresponding to different oxygen/vacancy arrangementswithin the GBCO framework was converted into effective clusterinteractions (ECIs) to quickly obtain a precise estimate of the totalenergy E of the crystal for an arbitrary oxygen/vacancy arrange-ment. This can be achieved by using a generalised lattice modelbased on the cluster expansion formalism.30,38 In this, occupationvariables si are assigned to each oxygen/vacancy site i within thehost framework, where si is +1 if site i is occupied by oxygen and�1 if site i is occupied by a vacancy. The total energy E for anarbitrary oxygen/vacancy arrangement can be expressed as a sumof polynomials ja of the occupation variables:

E ¼X

a

Vaja (1)

ja ¼Y

i2asi (2)

This corresponds to the product of occupation variables asso-ciated with oxygen sites belonging to cluster a. In this study, acluster a consists of a pair of neighbours (nearest neighbour, nextnearest neighbour, etc.). As mentioned above, the coefficients Va

are ECIs and correspond to the constants determined by fitting tothe first-principles total energies. Note that the formalism isexactly the same as that of an Ising model if used within a paircluster.

The third step employs MC simulations using fitted ECIvalues, which enables us to determine the total energy for anyoxygen/vacancy configuration from eqn (1) and (2). The grandcanonical MC approach was used to evaluate the phase stabilityof GBCO as a function of the chemical potential of oxygen.The canonical MC approach was adopted for the structuralanalyses, such as the analysis of the site occupancy variationwith temperature. Note that the ECI values used in the MonteCarlo simulation are determined by referring to the DFT totalenergies with consideration of structural relaxation, such thatthe energies obtained in the Monte Carlo simulation reflectinformation about the local structure, such as changes infractional coordinates for Gd, Ba, Co and O owing to differencesin oxygen/vacancy configurations. However, the specific values ofthe fractional coordinates cannot be obtained by a Monte Carlosimulation in this case since the ECIs give only energy values for thesystem. A supercell constructed from a 24 � 24 � 24 expansion of

Fig. 2 Oxygen/vacancy arrangement in the GdO layer for GdBaCo2O5.5. Whitespheres, grey spheres and grey dotted squares indicate Gd, oxygen and oxygenvacancies, respectively.

Paper PCCP

Publ

ishe

d on

22

Apr

il 20

13. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 23

/08/

2013

18:

45:5

5.

View Article Online

10496 Phys. Chem. Chem. Phys., 2013, 15, 10494--10499 This journal is c the Owner Societies 2013

the cubic unit cell (ABO3) (with a total of 41 472 oxygen/vacancysites) was used in this study. The temperature was varied between300 and 2000 K, and the ATAT program package was used for thecluster expansion approach and the MC simulations.39,40

3. Results and discussion

Table 1 lists the calculated and reported lattice parameters forGdBaCo2O5.5 with the superstructure as shown in Fig. 2. Theresults are in close agreement with experimental data withinthe typical DFT-GGA error. Fig. 3(a) shows the partial density ofstates (PDOS) and (b) shows the total electron-spin difference(net spin) for cobalt ions in octahedral and pyramidal sites. Thenet spin was defined as the difference between up and downelectron spins as a function of the integration radius of thecorresponding ion core. The PDOS of Co exhibits a band gap,indicating insulating behaviour. Whereas, at a radius of 1.2 Å,the net spins of Co at octahedral and pyramidal sites are close

to 0 and +3/2 mB, respectively. In addition, the net spins arecalculated by integrating spin density inside a zero flux surfaceon which the spin density is a minimum perpendicular to thesurface, as in the method proposed by Bader.41 The calculatednet spins of Co at octahedral and pyramidal sites are +0.13 and+3.17, respectively, which agree with the calculated net spinthrough integration over volume. Assuming the oxidation stateof Co is +3 (for a total number of d-electrons of 6), the expectednet spins for low spin (LS), intermediate spin (IS) and high spin(HS) configurations are 0, 2/2 and 4/2 mB, respectively, atoctahedral and pyramidal sites (Fig. 3(c)). Thus, the presentcalculations confirmed that the spin configurations of Co atoctahedral and pyramidal sites are LS and HS, respectively.

According to the literature,14,42 GdBaCo2O5.5 acts as an insulatorbelow the temperature of its metal–insulator (MI) transition at 370 K.This agrees with the present DOS analysis, since the electronicstructure calculated by DFT should represent the structure at 0 K.In addition, the reported spin configurations for the lower tempera-ture phase are consistent with the present results. Therefore, we haveconfirmed the validity of the DFT calculations using the GGA-PBE+Umethod. Note that the MI transition at 370 K is ascribed to a switchfrom the LS to the HS state for octahedral Co3+ ions.42

Fig. 4(a) shows the formation energies for 150 types ofoxygen/vacancy configurations with various compositions (d)as calculated by using DFT (open circles) and the clusterexpansion formalism with the fitted ECI values (crosses). Notethat the formation energies DEf are defined as,

DEf (GdBaCo2O5+d) = E(GdBaCo2O5+d) � dE(GdBaCo2O6)

� (1 � d) E(GdBaCo2O5)

where E(X) is the total energy of configuration X. The configu-ration with the lowest energy, which corresponds to d = 0.5

Table 1 Calculated lattice parameters for the GdBaCo2O5.5 superstructure

Lattice constant Exp. [Å]39 This work [Å]

a 3.88 3.838b/2 3.915 3.926c/2 3.771 3.838

Fig. 3 (a) Partial density of states (PDOS) and (b) total difference of electron spinorientation (net spin) for cobalt ions in octahedral and pyramidal sites. The expectednet spin for low-spin (LS), intermediate-spin (IS) and high-spin (HS) configurations are0, 2 and 4, respectively, in octahedral and pyramidal CoO6(5) sites. (c) Crystal fielddiagram of a d orbital in octahedral and pyramidal sites for Co3+ in GdBaCo2O5.5.

Fig. 4 (a) The formation energies for 150 types of oxygen/vacancy configura-tions with various compositions (d) calculated by DFT (open circles) and by thecluster expansion formalism with fitted ECI values (crosses). (b) Relation betweenenergies calculated from ab initio DFT and energies calculated from CE fitting for150 different oxygen/vacancy configurations. The cross-validation score is 0.069.

PCCP Paper

Publ

ishe

d on

22

Apr

il 20

13. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 23

/08/

2013

18:

45:5

5.

View Article Online

This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys., 2013, 15, 10494--10499 10497

(GdBaCo2O5.5) is confirmed to be consistent with the reportedconfiguration shown in Fig. 1 and 2. The fitting accuracy of thecluster expansion is presented in Fig. 4(b), which shows therelationship between the energy calculated by ab initio DFTand that calculated by CE fitting. In light of the reasonableagreement between DFT and CE fitted energies and the relativelylow cross-validation score of 0.069, the CE formalism using fittedECI values was judged to reproduce the total energies of DFT forany arbitrary oxygen/vacancy configuration.

The variation of oxygen concentration (d) in GBCO asa function of the chemical potential of oxygen at varioustemperatures as obtained with the grand canonical MC methodis shown in Fig. 5. The chemical potential of oxygen in theoxygen molecule was set to 0 as a reference. At a temperatureof 500 K, two significant plateaus appear in the range of �1.2 om0 o �0.7 eV at d = 1 and d = 0.5. This implies that a stablesuperstructure forms at d = 0.5 and confirms the reportedoxygen/vacancy arrangement shown in Fig. 2. There are noother phases indicated in the present MC simulations,although a superstructure phase at d = 4/9 has beenreported.43–45 We infer that the energy difference between thereported superstructure phase at d = 4/9 and the solid solutionphase may be small due to the phase transition betweenordered and disordered structures occurring at a relativelylow temperature (798 K).23 Therefore, the present ECI valuescannot reproduce the superstructure (d = 4/9) due to the fittingerror (Fig. 4(b)). However, we focus mainly on the oxygen/vacancy arrangement at higher temperatures (>800 K), andthe effect of the fitting error should be negligible for thepurposes of the discussion below. By increasing the tempera-ture, the range of the oxygen chemical potential which forms asuperstructure phase (d = 0.5) is reduced, and the range of thesolid solution phase is expanded. Above 1200 K, the plateau ofthe superstructure phase (d = 0.5) disappears, indicating a

transition between ordered and disordered structures at atemperature between 1000 and 1200 K.

The temperature dependence of the oxygen/vacancy arrange-ment for the superstructure at d = 0.5 has been investigatedusing the canonical MC approach. Fig. 6 presents the evolutionof internal energy as a function of temperature, as calculatedusing canonical MC at d = 0.5. The specific heat at constantvolume, that is, the derivative of the internal energy, is alsoplotted in Fig. 6. The internal energy (total electron energy)profile during heating and cooling does not show hysteresis,and an exothermic (endothermic) peak is clearly visible at1230 K during heating (cooling) in the plot of the specific heat,suggesting a phase transition induced by changes in oxygen/vacancy arrangement. Although the absence of hysteresis andthe continuous function of the internal energy with respect totemperature indicate a second-order phase transition, wenevertheless ascribe to a first-order phase transition sincethe rearrangement of the oxygen/vacancy configuration for aphase transition between ordered and disordered states isaccompanied by migration of ions, which is not consideredin the MC algorithm. A large discrepancy in terms of phasetransition temperature is observed between the present com-putational results and an experimental report where Taranconet al.,23 found that the phase transition from orthorhombicPmmm to tetragonal P4/mmm takes place at 798 K. Thisdiscrepancy is due to a typical error caused by neglectingthermal vibration effects (i.e. the energetic contributions arisingfrom displacements of the atoms away from their ideal latticesites and entropic contributions arising from vibrational andelectronic excitations) in the MC simulations, which results in anoverestimation of the phase transition temperature, as reportedin ref. 46 and 47. Hence, we conclude that the calculated phasetransition at 1230 K corresponds to the reported phase transitionat 798 K.

Fig. 7 shows the occupancy of oxygen sites in the GdO, BaOand CoO2 layers as a function of temperature. At low temperatures(300 K) all oxygen vacancies are located in the GdO layer, and weconfirmed the aligned structure of oxygen/vacancy arrangementin the GdO layer (Fig. 8(a)). Starting from 900 K, oxygen occupancygradually increases and decreases with temperature in the GdOand CoO2 layers, respectively, and this tendency accelerates ataround 1200 K, where a phase transition occurs. On the otherhand, all oxygen sites are fully occupied in the BaO layer up to

Fig. 5 (Top) Oxygen content 5 + d as a function of the chemical potential ofoxygen for GdBaCo2O5+d at temperatures between 500 and 1500 K. (Bottom)Magnification of the top figure centred around an oxygen content of 5.5.

Fig. 6 Evolution of the internal energy as a function of temperature as calcu-lated by canonical MC at d = 0.5 (circles). The specific heat at constant volume isalso plotted (triangles).

Paper PCCP

Publ

ishe

d on

22

Apr

il 20

13. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 23

/08/

2013

18:

45:5

5.

View Article Online

10498 Phys. Chem. Chem. Phys., 2013, 15, 10494--10499 This journal is c the Owner Societies 2013

2000 K, indicating a strong attraction for oxygen in the BaOlayer. Therefore, disordering from the superstructure phase(Fig. 2(a)) could be induced by a vacancy exchange betweenthe GdO layer and CoO2 layer. As shown in Fig. 8, the one-dimensional oxygen/vacancy arrangement along the b-axis iswell preserved at 1000 K, whereas the one-dimensional arrange-ment is diminished at 1300 K. In contrast, the oxygen/vacancyarrangement in the CoO2 layer does not indicate superstructureformation. Considering the oxygen/vacancy arrangement, atwo-dimensional diffusion path is formed in the a–b plane(i.e. normal to the c-axis), in which oxygen hops between theGdO and CoO2 layers. In addition, this tendency is found inboth phases above and below the phase transition temperaturebecause of the random distribution of oxygen in the CoO2 layer.The present results are supported by the previous computa-tional and experimental studies by Parfitt et al. (conductedusing molecular dynamics simulations)28 and Burriel et al.(conducted using the oxygen isotope exchange depth profilingfor a single grain of the related material PrBaCo2O5+d).

29

It should be noted that the random arrangement of vacanciesin the GdO layer in the high-temperature phase at d = 0.5 stillshows a partial linear alignment directed along the a- and b-axes(Fig. 8(b)). In other words, the oxygen/vacancy ordering appearingin the low-temperature phase still exists within a short range even

in the high-temperature phase, even though long-range ordering,that is, crystal structure symmetry, is broken. Unchanged short-range oxygen/vacancy ordering remaining after the phase transi-tion may account for the fact that the phase transition does notaffect oxygen diffusivity, as reported in ref. 23.

4. Conclusions

The oxygen/vacancy configuration at various oxygen stoichio-metries and temperatures has been investigated in order to identifythe mechanism of oxygen migration in GBCO. A superstructureis observed only at d = 0.5 at temperatures below 1200 K. Thissuperstructure consists of a linear ordering of alternating oxygenions and vacancies along the b-axis in the GdO layer. The Gibbsenergy and the oxygen occupancy as a function of temperaturesuggest that a phase transition from orthorhombic to tetrahedralconfiguration takes place at 1230 K at d = 0.5. Above 600 K, asmall number of vacancies form randomly in the CoO2 layer dueto entropic effects, such that oxygen ions can migrate betweenthe GdO and CoO2 layers, as reported in the previous study usingmolecular dynamics simulations.28 Above the phase transitiontemperature, the long-range linear arrangement of oxygen ionsand vacancies is lost, but the short-range linear characteristicsremain intact. We conclude that the experimentally observedlack of appreciable change in oxygen diffusivity after the phasetransition23 could be related to remaining short-range lineararrangement of oxygen ions and vacancies.

Acknowledgements

Authors are greatly indebted to R. Jalem for many stimulatingdiscussions. H.S. was grateful for financial support from theInstitute of Ceramics Research and Education, NITECH. Thiswork was partially supported by JST, PRESTO and MEXTprogram ‘‘Elements Strategy Initiative to Form Core ResearchCenter’’ (since 2012), MEXT; Ministry of Education Culture,

Fig. 7 Changes in oxygen occupancy in the GdO layer (circles), the BaO layer(squares) and the CoO2 layer (triangles) with respect to temperature at d = 0.5.

Fig. 8 Oxygen/vacancy configuration of oxygen sites in the GdO layer at (a) 300 K and (b) 1500 K for d = 0.5. Light grey circles and dark grey circles indicate Gd and O,respectively.

PCCP Paper

Publ

ishe

d on

22

Apr

il 20

13. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 23

/08/

2013

18:

45:5

5.

View Article Online

This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys., 2013, 15, 10494--10499 10499

Sports, Science and Technology, Japan. Figures of the crystalstructure were drawn using VESTA.48

References

1 N. P. Brandon, S. J. Skinner and B. C. H. Steele, Annu. Rev.Mater. Res., 2003, 33, 183.

2 A. K. Azad, J. H. Kim and J. T. S. Irvine, J. Power Sources,2011, 196, 7333–7337.

3 C. Frontera, A. Caneiro, A. E. Carrillo, J. Oro-Sole andJ. L. Garcıa-Munoz, Chem. Mater., 2005, 17, 5439–5445.

4 D. Chen, R. Ran, K. Zhang, J. Wang and Z. Shao, J. PowerSources, 2009, 188, 96–105.

5 G. Kim, S. Wang, A. J. Jacobson, L. Reimus, P. Brodersenband C. A. Mims, J. Mater. Chem., 2007, 17, 2500–2505.

6 J. Xue, Y. Shen and T. He, J. Power Sources, 2011, 196, 3729–3735.7 Q. Zhou, T. He and Y. Ji, J. Power Sources, 2008, 185, 754–758.8 S. J. Lee, D. S. Kim, P. Muralidharan, S. H. Jo and D. K. Kim,

J. Power Sources, 2011, 196, 3095–3098.9 J. C. Burley, J. F. Mitchell, S. Short, D. Miller and Y. Tang,

J. Solid State Chem., 2003, 170, 339–350.10 T. V. Aksenova, L. Yu. Gavrilova, A. A. Yaremchenko,

V. A. Cherepanov and V. V. Kharton, Mater. Res. Bull.,2010, 45, 1288–1292.

11 Y. Lin, R. Ran, C. Zhang, R. Cai and Z. Shao, J. Phys. Chem. A,2010, 114, 3764–3772.

12 Y. N. Kim, J.-H. Kim and A. Manthiram, J. Power Sources,2010, 195, 6411–6419.

13 K. Zhang, L. Ge, R. Ran, Z. Shao and S. Liu, Acta Mater.,2008, 56, 4876–4889.

14 C. Frontera, M. Respaud, J. L. Garcia-Munoz, A. Llobet,A. E. Carrillo, A. Caneiro and J. M. Broto, Physica B, 2004,346–347, 246–249.

15 G. Kim, S. Wang, A. J. Jacobson, L. Reimus, P. Brodersenand C. A. Mims, J. Mater. Chem., 2007, 17, 2500–2505.

16 A. Tarancon, S. J. Skinner, R. J. Chater, F. Hernandez-Ramır-eza and J. A. Kilner, J. Mater. Chem., 2007, 17, 3175–3181.

17 G. Kim, S. Wang, A. J. Jacobson, Z. Yuan, W. Donner,C. L. Chen, L. Reimus, P. Brodersen and C. A. Mims, Appl.Phys. Lett., 2006, 88, 024103.

18 R. Frison, S. Portier, M. Martin and K. Conder, Nucl.Instrum. Methods Phys. Res., Sect. B, 2012, 273, 142–145.

19 A. Chang, S. J. Skinner and J. A. Kilner, Solid State Ionics,2006, 177, 2009–2011.

20 M. Burriel, M. Casas-Cabanas, J. Zapata, H. Tan, J. Verbeeck,C. Solıs, J. Roqueta, S. J. Skinner, J. A. Kilner, G. VanTendeloo and J. Santiso, Chem. Mater., 2010, 22, 5512–5520.

21 J.-H. Kim, F. Prado and A. Manthiram, J. Electrochem. Soc.,2008, 155, B1023–B1028.

22 A. A. Taskin, A. N. Lavrov and Y. Ando, Appl. Phys. Lett.,2005, 86, 091910.

23 A. Tarancon, D. Marrero-Lopez, J. Pena-Martınez, J. C. Ruiz-Morales and P. Nunez, Solid State Ionics, 2008, 179, 611–618.

24 M.-B. Choia, S.-Y. Jeona, J.-S. Leea, H.-J. Hwangb andS.-J. Song, J. Power Sources, 2010, 195, 1059–1064.

25 D. S. Tsvetkov, V. V. Sereda and A. Yu. Zuev, Solid StateIonics, 2011, 192, 215–219.

26 A. A. Taskin, A. N. Lavrov and Y. Ando, Phys. Rev. B: Condens.Matter Mater. Phys., 2005, 71, 134414.

27 E. Chavez, M. Mueller, L. Mogni and A. Caneiro, J. Phys.:Conf. Ser., 2009, 167, 012043.

28 D. Parfitt, A. Chroneos, A. Tarancon and J. A. Kilner,J. Mater. Chem., 2011, 21, 2183–2186.

29 M. Burriel, J. Pena-Martınez, R. J. Chater, S. Fearn,A. V. Berenov, S. J. Skinner and J. A. Kilner, Chem. Mater.,2012, 24, 613–621.

30 G. Ceder, A. van der Ven, C. Marianetti and D. Morgan,Model. Simul. Mater. Sci. Eng., 2000, 8, 311–321.

31 G. Kresse and J. Furthmuller, Phys. Rev. B: Condens. MatterMater. Phys., 1996, 54, 11169–11186.

32 G. Kresse and J. Furthmuller, Comput. Mater. Sci., 1996, 6, 15–50.33 J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson,

M. R. Pederson, D. J. Sing and C. Fiolhais, Phys. Rev. B:Condens. Matter Mater. Phys., 1992, 46, 6671.

34 J. P. Perdew and Y. Wang, Phys. Rev. B: Condens. MatterMater. Phys., 1992, 45, 13244.

35 P. E. Blochl, Phys. Rev. B: Condens. Matter Mater. Phys., 1994,50, 17953.

36 Y. B. Losovyj, D. Wooten, J. C. Santana, J. M. An,K. D. Belashchenko, N. Lozova, J. Petrosky, A. Sokolov,J. Tang, W. Wang, N. Arulsamy and P. A. Dowben, J. Phys.:Condens. Matter, 2009, 21, 045602.

37 F. Zhou, M. Cococcioni, C. A. Marianetti, D. Morgan andG. Ceder, Phys. Rev. B: Condens. Matter Mater. Phys., 2004,70, 235121.

38 D. De Fontaine, Solid State Phys., 1994, 47, 33–176.39 A. van de Walle, M. Asta and G. Ceder, CALPHAD: Comput.

Coupling Phase Diagrams Thermochem., 2002, 26, 539–553.40 A. van de Walle, CALPHAD: Comput. Coupling Phase Dia-

grams Thermochem., 2009, 33, 266–278.41 R. F. W. Bader, Atoms in Molecules-A Quantum Theory,

Clarendon Press, Oxford, UK, 1990.42 C. Frontera, J. L. Garcia Munoz, A. Llobet and M. A. G. Aranda,

Phys. Rev. B: Condens. Matter Mater. Phys., 2002, 65, 180405.43 D. D. Khalyavin, Phys. Rev. B: Condens. Matter Mater. Phys.,

2005, 72, 134408.44 D. D. Khalyavin, D. N. Argyriou, U. Amann, A. A. Yaremchenko

and V. V. Kharton, Phys. Rev. B: Condens. Matter Mater. Phys.,2007, 75, 134407.

45 W. Zhou, C. T. Lin and W. Y. Liritig, Adv. Mater., 1993, 5,735–738.

46 I. Ohnuma, Y. Fujita, H. Mitsui, K. Ishikawa, R. Kainumaand K. Ishida, Acta Mater., 2000, 48, 3113–3123.

47 A. van de Walle and M. Asta, Model. Simul. Mater. Sci. Eng.,2002, 10, 521–538.

48 K. Momma and F. Izumi, J. Appl. Crystallogr., 2008, 41, 653.

Paper PCCP

Publ

ishe

d on

22

Apr

il 20

13. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 23

/08/

2013

18:

45:5

5.

View Article Online