The impact of oxygen nonstoichiometry upon partial molarthermodynamic quantities in PrBaCo2O5þδ

A.Yu. Suntsov a,n, I.A. Leonidov a,b, M.V. Patrakeev a, V.L. Kozhevnikov a

a Institute of Solid State Chemistry, Pervomaiskaya str.91, Yekaterinburg 620990, Russiab Ural Federal University, Mira str.19, Ekaterinburg 620002, Russia

a r t i c l e i n f o

Article history:Received 31 October 2013Received in revised form31 January 2014Accepted 1 February 2014Available online 11 February 2014

Keywords:Double cobaltitesPerovskite-type oxideOxygen non-stoichiometryPartial molar thermodynamic functions

a b s t r a c t

The coulometric titration data are utilized in order to calculate changes of oxygen partial entropy andenthalpy in PrBaCo2O5þδ with variations of oxygen content and temperature. The thermodynamicequilibrium of the cobaltite with the ambient gas phase is analyzed based on the interface of oxygenexchange and oxidation, and the intrinsic reaction of thermal excitation of Co3þ cations. The partialthermodynamic functions of the movable oxygen in PrBaCo2O5þδ are shown to be interrelated with thethermodynamic parameters of the defect formation reactions. The existence of a band gap of about0.4 eV in the electronic spectrum of the cobaltite follows from a favorable comparison of the calculatedand experimental dependencies of the partial thermodynamic functions of the movable oxygen.

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1. Introduction

Double perovskite-like cobaltites RBaCo2O5þδ, where R is arare-earth metal, exhibit a number of interesting properties suchas charge and orbital ordering, metal-to-insulator transition andlarge thermopower [1–3]. At elevated temperatures these materi-als reveal considerable conductivity [4], remarkably rapid oxygenion diffusion and surface exchange kinetics [5–7], thus suggestinga potential of their application as oxygen sensors, oxygen separat-ing membranes and SOFCs cathodes [8–10].

As well as other perovskite related compounds, RBaCo2O5þδcobaltites with δ¼1 are featured by the presence in their structureof corner linked metal-oxygen octahedra. However, R and Bacations are placed in alternating BaO and ROδ layers due to thesize difference so that a double elementary unit is observed alongc-axis [11]. The loss of oxygen on heating and oxygen pressuredecrease result in oxygen vacancies in ROδ layers and simulta-neous transformation of structural CoO6 octahedra to CoO5 pyr-amids [12]. The extreme δ¼0 is characterized by the presence inthe structure of CoO5 pyramids only linked via their vertices andcorners while rare-earth layers occur almost completely void ofoxygen ions. The electrical neutrality demand at δ¼0 suggestscoexistence of Co2þ and Co3þ cations in equal amount so that ahalf of the structural pyramids in the crystalline lattice contain

Co2þ and the other half is populated with Co3þ cations [13]. Theaverage oxidation state of cobalt cations is 3þ and a half of thepyramids become octahedra at δ¼0.5. Further increase in oxygencontent to δ¼1 is accompanied with oxidation of the half of Co3þ

to Co4þ cations and formation of octahedral oxygen environmentof cobalt species independently on their oxidation state. The inter-particle interactions in ROδ planes produce long-range ordering ofoxygen anions and vacancies below 500 1C [2,14,15]. At highertemperatures, when the thermal energy is large enough, theorthorhombic crystal lattice undergoes a phase transition totetragonal structure (space group P4/mmm) where oxygen anionsand vacancies occupy equivalent positions of O3 in ROδ planes.

Large variations in oxygen content may result not only inconsiderable redistribution of charge over cobalt species andstructural rearrangements in the crystalline lattice but also inprofound changes in properties of RBaCo2O5þδ cobaltites [16,17].It is important, therefore, to know how oxygen content may varywith temperature and partial pressure of oxygen in the environ-ment in order to be able to obtain equilibrated materials withdesirable oxygen non-stoichiometry. Moreover, the respective data(pO2–T–δ diagram) are of independent value because they mayhelp to gain a deeper understanding of defects and defect relatedproperties. However, equilibrium data on oxygen content andanalysis of defect equilibria in RBaCo2O5þδ remain few andcontroversial. For instance, authors [18] report on linear changesof the partial molar enthalpy of oxygen in GdBaCo2O5þδ at 5.05r(5þδ)r5.50 while the partial molar entropy is deduced to bepractically independent on oxygen composition. Quite differently,

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Journal of Solid State Chemistry

http://dx.doi.org/10.1016/j.jssc.2014.02.0040022-4596 & 2014 Elsevier Inc. All rights reserved.

n Corresponding author. Tel.: þ7 343 3623164; fax: þ7 343 3744495.E-mail address: suntsov@ihim.uran.ru (A.Yu. Suntsov).

Journal of Solid State Chemistry 213 (2014) 93–97

data [19] reveal concentration independent enthalpy and linearchanges in entropy of oxygen at 5.05r(5þδ)r5.15. Recently, weobtained equilibrium pO2–T–δ diagram [20] for PrBaCo2O5þδwithin the stability limits of tetragonal structure. It is shown thatthe experimental data can be explained based on the considera-tion of oxygen incorporation into structural oxygen vacancies andoxidation of cobalt species, and disproportionation reactions.Assuming localized charges these reactions can be presented withequilibria as follows:

2Co2þ þVOþ12O2 ¼ 2Co3þ þO2– ð1Þ

2Co3þ ¼ Co2þ þCo4þ ð2Þthe computer simulation of the data resulted in determinationof standard enthalpies ΔH 3

Ox and ΔH 3D and entropies ΔS 3

Ox andΔS 3

D for Reactions (1) and (2), respectively. Then the obtainedvalues were used in order to calculate variations in concentrationof cobalt species with temperature and oxygen pressure in favor-able comparison with the conductivity data. In extension of themodel [20] in this work we find interrelation of ΔH 3

Ox, ΔH 3D, ΔS 3

Oxand ΔS 3

D with thermodynamic parameters of defect speciesentering Reactions (1) and (2). It is shown that partial thermo-dynamic functions of oxygen in PrBaCo2O5þδ exhibit non-linearchanges even within the δ limits of existence of a single (tetra-gonal) phase. Moreover, we use our model in order to explain data[18] and to evaluate enthalpy for Reaction (2) in similar cobaltiteGdBaCo2O5þδ.

2. Experimental

The sample of PrBaCo2O5þδ was obtained via solid statesynthesis route [20]. The air synthesized cobaltite PrBaCo2O5þδwas confirmed to be a single phase having an orthorhombicstructure with the unit cell parameters a¼3.8981(1), b¼7.8069(2) and c¼7.6345(2) Å characteristic of a double perovskite. Thepowder sample was placed in a Setaram TG–92 thermoanalyzerand heated at 1000 1C in the atmosphere containing 90% He and10% H2. The oxygen non-stoichiometry parameter δ¼0.77 in as-synthesized samples was found to be in agreement with earlierresults [21]. Then, the change of the oxygen content in the as-prepared specimen at heating in air was determined with the helpof the thermoanalyzer. The oxygen content variations inPrBaCo2O5þδ at different values of temperature T and partialpressure of oxygen pO2 were obtained using a coulometric titra-tion technique [22] in the isothermal regime. The uncertainty inmeasuring δ values did not exceed Δδ¼70.001. The value of theoxygen content at 650 1C, which was obtained at TG heating of theas-prepared sample in air, was utilized as a reference point for thecoulometric titration isotherm at pO2¼0.21 atm and 650 1C.

3. Partial molar enthalpy and entropy of oxygen

For the sake of convenience the experimental results fornonstoichiometry variations with oxygen pressure and tempera-ture are shown for tetragonal PrBaCo2O5þδ in Fig. 1. These datacan be used in order to calculate the chemical potential μО (inPrBaCo2O5þδ) of oxygen in the cobaltite relative to the standardstate in the gas phase according to the known condition ofthermodynamic equilibrium.

ΔμОðδ;Т Þ � μОðin PrBaCo2O5þδÞ�1=2μO21¼ 1=2RT U lnðpO2Þ ð3Þ

The plots for ΔμО(δ,Т) at permanent δ's exhibit a linear depen-dence on temperature, Fig. 2. Therefore, partial enthalpy ΔHOðδÞ and

entropy ΔSOðδÞ of oxygen in tetragonal PrBaCo2O5þδ with differentoxygen content can immediately be obtained from

ΔμОðδ;Т Þ ¼ΔHOðδÞ�TΔSOðδÞ ð4Þ

The respective results in Fig. 2 reveal rather strong concentra-tion dependent changes of thermodynamic functions of oxygen inPrBaCo2O5þδ. In order to understand the underlying phenomenait may be helpful to consider intrinsic equilibration of chargedspecies that takes place in the crystalline lattice in response tooxygen intake/release and filling/depletion of oxygen vacancies inPrBaCo2O5þδ.

4. High-temperature equilibrium

Two possible reactions of the formation of charged cobaltspecies are shown by Eqs. (1) and (2) that respectively displaythe change in the composition due to interfacial solid–gas phaseexchange and intrinsic solid state redistribution of electric charge[23]. The formation of Co4þ species can also be envisioned due tothe reaction

2Co3þ þVOþ12O2 ¼ 2Co4þ þO2– ð5Þ

which, on the other hand, can be obtained by summing Reactions(1) and (2). Hence, it can be disregarded in further consideration.

Fig. 1. Isothermal plots of oxygen content in PrBaCo2O5þ δ vs. oxygen partialpressure. Solid lines show calculation results according to [20].

Fig. 2. Temperature variations of the chemical potential of oxygen in PrBaCo2O5þ δ

at different values of oxygen content (Δδ¼0.02).

A.Yu. Suntsov et al. / Journal of Solid State Chemistry 213 (2014) 93–9794

Before proceeding further it is necessary to note that we useordinary notations for the charge based on common consent thatit is a representation of effective electric charge of species in solids.The relation with quasi-chemical notations is Co3þ � Co�Co,Co2þ � Co0Co, Co

4þ � CodCo, O2� �O�

O , and VO � V�O . More important

is the understanding of the fact that the Kröger–Vink representa-tion may be rather inconvenient considering structural features inthe double perovskite cobaltites and large amount of defects,which is comparable with the amount of regular sites. Thus, inthe attempt to describe oxidation of the high-temperature tetra-gonal phase RBaCo2O5þδ one has to consider oxygen vacancies inO3 positions as interstitials. Correspondingly, oxygen ions in thesepositions must be treated as interstitial defects. The results of sucha picture may happen to be quite controversial. For instance,according to Ref. [19] positional exchange of quasi-neutral oxygenanions O�

O and vacancies V�O in structurally equivalent positions O3

yields charged oxygen vacancies VddO and interstitials O00

i thoughthe permutation is not accompanied with changes either instructure or free energy of the crystal. Moreover, barium cationsare suggested to be considered as charged defects Ba0R associatedwith oxygen vacancies ðVdd

O � Ba0RÞd. This occurs to be in apparentdisagreement with distinctive structural features in the doubleperovskite cobaltites where lanthanide and barium cations arequasi-neutral structural elements that reside in their individualpositions.

The coexistence of different charge states of cobalt at giventemperature and oxygen pressure can be expressed in the formulaPrBaCo2þ

n Co3þg Co4þ

p O5þδ of the cobaltite where subscripts n, g andp denote concentration of Co2þ , Co3þ and Co4þ cations, respec-tively. The Gibbs free energy G of the cobaltite can be expressed upto a constant as

G¼ G 3 þμ 3 ðPr3þ Þþμ 3 ðBa2þ Þþnμ 3 ðCo2þ Þþgμ 3 ðCo3þ Þþpμ 3 ðCo4þ Þ

þð5þδÞμ 3 ðO2� Þþð1�δÞμ 3 ðVOÞ�TSðconf Þ ð6Þwhere μ 3 and Sðconf Þ denote chemical potential of the involvedspecies and configuration entropy, respectively. Following [24] weassume that interaction energies between the species entering(1) and (2) are included in μ 3 's. Also, praseodymium and bariumcations reside in distinctively different structural positions in thedouble cobaltite. Therefore, the configuration entropy at randomdistribution of the defects can be calculated as

Sðconf Þ ¼ k lnð2NÞ!

ðNnÞ!ðNgÞ!ðNpÞ!þ lnð6NÞ!

ðNð5þδÞÞ!ðNð1�δÞÞ!

� �ð7Þ

where k is the Boltzmann constant and N is the Avogadro constant.The chemical potential of oxygen μO in PrBaCo2O5þδfollows from(6) and (7) as

μO ¼ ∂G∂ð5þδÞ ¼

∂G∂δ

¼ δn∂δμ 3 ðCo2þ Þþδg

∂δμ 3 ðCo3þ Þþδp

∂δμ 3 ðCo4þ Þ

þμ 3 ðO2� Þ�μ 3 ðVOÞ�TSOðconf Þ; ð8Þwhere

SOðconf Þ ¼∂Sðconf Þ

∂δ¼ R ln

1�δ5þδ

�Rδn∂δ

ln nþδg∂δ

ln gþδp∂δ

ln p� �

ð9Þand R¼N � k is the gas constant.

The concentration variations of cobalt species in PrBaCo2O5þδare limited by conditions of electrical neutrality (10) and structureconservation (11)

n¼ pþ2δ�1 ð10Þ

gþnþp¼ 2 ð11Þ

Additional constraint is imposed by the equilibrium constantfor Reaction (2)

KD ¼ nUpg2

ð12Þ

Therefore, the derivatives ∂p=∂δ and ∂g=∂δ can be expressed interms of ∂n=∂δ

∂n∂δ

¼ 2δ�1nþpþ4KDg

�1 ð13Þ

and used in (8) to obtain μO as

μO ¼ 2μ 3 ðCo4þ Þ�2μ 3 ðCo3þ Þþ∂n∂δ

½μ 3 ðCo2þ Þ�2μ 3 ðCo3þ Þþμ 3 ðCo4þ Þ�

þμ 3 ðO2� Þ�μ 3 ðVOÞ�TSOðconfÞ; ð14Þwhere

SOðconfÞ ¼ R lnð1�δÞg2ð5þδÞp2�

∂n∂δ

ln KD

� �ð15Þ

Then, the change of the free energy in Reactions (1) and (2)

ΔG 3Ox ¼ μ 3 ðO2� Þ�μ 3 ðVOÞþ2½μ 3 ðCo3þ Þ�μ 3 ðCo2þ Þ��1

2μ 3O2

ð16Þ

ΔG 3D ¼ μ 3 ðCo2þ Þþμ 3 ðCo4þ Þ�2μ 3 ðCo3þ Þ ð17Þ

in combination with the solid–gas phase equilibrium condition foroxygen

2μ 3O ¼ μ 3

O2ð18Þ

can be applied in order to simplify (14) and to find out how thechemical potential of oxygen in PrBaCo2O5þδ changes with oxygenstoichiometry δ

ΔμO ¼ μO�μ 3O ¼ΔG 3

Oxþ2ΔG 3Dþ

∂n∂δΔG 3

D�TSOðconfÞ ð19Þ

here, μ 3O is the standard chemical potential of oxygen in the

cobaltite. The enthalpy and entropy contributions to ΔμO followfrom (19) as

ΔHO ¼ΔH 3Oxþ2ΔH 3

Dþ∂n∂δΔH 3

D ð20Þ

ΔSO ¼ΔS 3Oxþ2ΔS 3

Dþ∂n∂δΔS 3

DþSOðconf Þ ð21Þ

These equations show how thermodynamic parameters ΔH 3Ox,

ΔH 3D, ΔS 3

Ox and ΔS 3D, Table 1, for reactions of oxygen exchange

(1) and charge disproportionation (2) influence thermodynamicfunctions of movable oxygen in PrBaCo2O5þδ. Respective calculationswith the help of (20) and (21) demonstrate a good coincidence withthe experimental data, Fig. 3. Note that the temperature decrease isaccompanied with the corresponding decrease of the disproportio-nation constant KD so that derivatives ∂n=∂δ, ∂p=∂δ, and ∂g=∂δexhibit more drastic changes near δ¼0.5 at lower temperatures.Still, their temperature variations do not seem particularly strong ascan be seen, e.g., from the plots of ∂n=∂δ in Fig. 4. Therefore, the

Table 1Thermodynamic parameters for equilibrium reactions in PrBaCo2O5þδ [20].

Reaction ΔH 3 (kJ �mol–1)

2Co3þ ¼ Co2þ þCo4þ 3574 –1272

2Co2þ þVOþ12O2 ¼ 2Co3þ þO2� –11579 –4372

2Co3þ þVOþ12O2 ¼ 2Co4þ þO2� –4574 –6775

A.Yu. Suntsov et al. / Journal of Solid State Chemistry 213 (2014) 93–97 95

overall shape of the plots for thermodynamic functions of oxygen inPrBaCo2O5þδ in the studied temperature range is mostly governedby oxygen content.

It can be shown from (13) that while changing in a step-likemanner around δ¼0.5 the derivative ∂n=∂δ approaches �2 and 0 atδ-0 and δ-1, respectively, Fig. 4. Hence, Relation (20) results in

ΔHOðδ¼ 1Þ�ΔHOðδ¼ 0Þ ¼ 2ΔH 3D ð22Þ

Therefore, considerable increase in the enthalpy ΔHO withoxygen content in the studied δ range reflects a contribution fromReaction (2), which is particularly expressed near δ¼0.5. More-over, the calculated enthalpy ΔHO¼�45.5 kJ/mol at δ¼1 must beequal to the oxidation enthalpy for Reaction (5). It is indeed so ifone takes in view the value �4574 kJ mol-1 obtained earlier fromthe pO2–T–δ diagram [20]. The concentration dependent behaviorof the enthalpy was also studied in structurally similar cobaltiteGdBaCo2O5þδ [18]. Based on a linear approximation of theobtained experimental data in Fig. 3a, the authors [18] supposedthat electronic contribution to the enthalpy is due to the Co3d–O2p band of itinerant charge carriers. On the other hand, theplacing of the data with Relation (20) enables one to obtain abetter description of the experimental results as can be seen inFig. 3a. Therefore, n- and p-type charge carriers in the double-perovskite like cobaltites rather seem to be separated with theband gap of about ΔH 3

D. One can note additionally that a smallerband gap value, which follows from comparison of the data inFig. 3 a, gives a natural explanation to the conductivity level higher

in GdBaCo2O5þδ than in PrBaCo2O5þδ [25]. As to the absolutevalue of the oxygen enthalpy, which is smaller in gadoliniumcobaltite than in praseodymium, it can be understood as reflectinga strong decrease of the parameter c and respective decrease ofthe distance between CoO2 and ROδ sheets in the crystalline lattice[26]. Consequently, the Coulomb repulsion for oxygen ions enter-ing the sheets increases, which is accompanied with the decreasein the energy of chemical bonding R–O, i.e., oxidation enthalpy inthe cobaltites with smaller R cations.

The entropy ΔSO generally tends to decrease with the increasein oxygen content in the entire range 0oδo1 due to thecontribution � ln(5þδ)/(1�δ) from oxygen ions and vacancies,Fig. 5. This trend is broken by electron–hole disordering so that akink takes place near δ¼0.5. As can be seen in Fig. 3b the obtainedexperimental data can be reasonably well described with the helpof Eq. (21).

5. Conclusion

The analysis of the high-temperature equilibrium pO2–T–δ dia-gram for tetragonal double-perovskite like cobaltite PrBaCo2O5þδwas carried out based on the consideration of oxygen exchangereaction and charge disproportionation of Co3þ cations. Thethermodynamic functions of the reactions are shown to beinterrelated with partial thermodynamic functions of movableoxygen in PrBaCo2O5þδ. The observed singular behavior of

Fig. 3. Concentration dependent changes of the partial enthalpy (a) and entropy (b) of oxygen in PrBaCo2O5þ δ . Solid lines show results of calculations with the help ofEqs. (20) and (21) at 650 1C. Data by Mogni et al. for GdBaCo2O5þ δ [18] are shown with filled circles.

Fig. 4. Oxygen content dependent changes of ∂n=∂δ in PrBaCo2O5þ δ according toEq. (13) at different temperatures.

Fig. 5. Oxygen content dependent changes of SOðconfÞ in PrBaCo2O5þ δ according toEq. (9) at different temperatures.

A.Yu. Suntsov et al. / Journal of Solid State Chemistry 213 (2014) 93–9796

thermodynamic functions of oxygen near δ¼0.5 can be explainedas manifestation of intrinsic reaction of electron redistributionover cobalt cations. The agreement of the experimentally obtainedresults and calculated plots for partial thermodynamic functions ofoxygen shows that the suggested description of the equilibrium ofcharged cobalt species in PrBaCo2O5þδ is quite correct. Thetemperature activated charge disproportionation of Co3þ cationsgives rise to the population of electron (Co2þ) and hole (Co4þ) likecobalt species on heating. Low mobility of n-type carriers can beinferred from the observation of the hole-type conductivity indouble-perovskite cobaltites [15] even in the domain of small δ'swhere only n-type conductivity is expected. Though being presentin a large concentration differently charged cobalt cations andmobile oxygen anions can be considered at high temperatures asdistributed rather randomly in the crystalline lattice.

Acknowledgments

Authors gratefully acknowledge partial support of this work bythe Russian Foundation for Basic Research (Grant no. 12-03-31570)and the Ministry of Education and Science of the Russian Federa-tion (Grant no. 8649)

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