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Publicly Available Published by De Gruyter May 18, 2019

Double perovskites REBaCo2−xMxO6−δ (RE=La, Pr, Nd, Eu, Gd, Y; M=Fe, Mn) as energy-related materials: an overview

Dmitry S. Tsvetkov , Ivan L. Ivanov , Dmitry A. Malyshkin , Anton L. Sednev , Vladimir V. Sereda and Andrey Yu. Zuev EMAIL logo

Abstract

This work, based on the experimental and theoretical research carried out by the authors during the last decade, presents an overview of formation, stability and defect thermodynamics, crystal structure, oxygen nonstoichiometry, chemical strain and transport properties of the double perovskites REBaCo2−xMxO6−δ (RE = La, Pr, Nd, Eu, Gd, Y; M = Fe, Mn). These mixed-conducting oxides are widely regarded as promising materials for various energy conversion and storage devices. Attention is focused on (i) thermodynamics of formation and disordering, oxygen nonstoichiometry, crystal and defect structure of the double perovskites REBaCo2−xMxO6−δ, as well as their thermodynamic stability and the homogeneity ranges of solid solutions, (ii) their overall conductivity and Seebeck coefficient as functions of temperature and oxygen partial pressure and (iii) the anisotropic chemical strain of their crystal lattice. The relationships between the peculiarities of the defect structure and related properties of the double perovskites are analysed.

Introduction

The complex oxides with double perovskite structure REBaCo2O6−δ, where RE – rare-earth metal, have attracted great attention in the past decade due to their unique properties such as high oxide ion and electronic conductivity as well as promising activity as cathodes in the intermediate-temperature solid oxide fuel cells (IT SOFCs) [1], [2], [3], [4]. The double perovskite GdBaCo2O6−δ was also found to possess giant magnetoresistance [5], [6] at low temperatures.

Despite scattered reports in which we have addressed different challenges related to this important class of the double perovskites, their “thermodynamics–composition–crystal and defect structure–properties at elevated temperature” relationships have not been consolidated into a systematic, comprehensive review.

For this reason the first priority goal of the present paper was to give an overview of our recent results on formation, stability and defect thermodynamics, defect and crystal structure, oxygen nonstoichiometry, chemical strain and transport properties of the double perovskites REBaCo2−xFexO6−δ at elevated temperatures. Secondly, the question of how the oxygen nonstoichiometry affects the formation thermodynamics and crystal structure of these oxide materials was addressed. Thirdly, it was of key importance to find the relationship between the oxygen content and the defect structure of the double perovskites studied, on the one hand, and related properties, such as chemical strain and charge transfer by both ionic and electronic carriers, on the other.

In order to answer these questions, a joint analysis of the defect structure along with the combined data on the oxygen nonstoichiometry, chemical strain, oxide ion and electronic conductivity, and the Seebeck coefficient as functions of temperature (T) and oxygen partial pressure (pO2) was carried out for the double perovskites REBaCo2−xMxO6−δ, where RE=La, Pr, Nd, Eu, Gd, Y and M=Fe, Mn.

Preparation and homogeneity range

Powder samples of nominal composition REBaCo2−xFexO6−δ, where RE=Pr and Gd (x=0–1.0 and 0–0.6 for Gd and Pr, respectively), GdBaCo1.8Mn0.2O6−δ, and REBaCo2O6−δ (RE=Nd, Eu, Sm, Y) were prepared by means of glycerol-nitrate method using RE2O3 (Pr6O11), BaCO3, Co, FeC2O4·2H2O and MnO2 as starting materials [7], [8], [9], [10], [11]. All materials used had a purity of 99.99%.

The stoichiometric mixture of precursors was dissolved in the concentrated nitric acid (99.99% purity) and required volume of glycerol (99% purity) was added as a complexing agent and a fuel. Glycerol quantity was calculated according to the full reduction of corresponding nitrates to the molecular nitrogen N2. The as-prepared solutions were heated continuously at 100°C until complete water evaporation and pyrolysis of the dried precursor had occurred. The resulting ash was subsequently calcined at 1100°C for 10 h to get the desired double perovskite powder [7], [8], [9].

Powder samples of GdBaCo1−xFexO6−δ (x=0, 0.2) were also synthesized by means of standard ceramic technique using Gd2O3, BaCO3, Co3O4 and Fe2O3 as starting materials [10], [11]. All materials used had a purity of 99.99%. The stoichiometric mixture of the starting materials was calcined at temperatures between 800 and 1100°C in air with 100°C step for 10 h at each stage followed by mixture regrinding [10], [11].

The phase composition of the powder samples prepared accordingly was studied at room temperature by means of X-ray diffraction (XRD) with Equinox 3000 diffractometer (Inel, France) using Cu Kα radiation. XRD showed no indication for the presence of a second phase in all as-prepared oxides except GdBaCo1−xFexO6−δ with x≥0.7, where the XRD patterns contained peaks related to impurities such as Ba1−yGdyCoO3 and GdFe1−zCozO3 phases. Therefore, the solubility limit in GdBaCo1−xFexO6−δ, xmax, lies somewhere in the composition range between 0.6 and 0.7.

Since the LaBaCo2O6−δ phase cannot be obtained like the other double perovskites, the powder of the cubic perovskite La0.5Ba0.5CoO3−δ was first prepared by means of the glycerol-nitrate method as described above [12]. The double perovskite LaBaCo2O6−δ was obtained by calcination of the as-prepared perovskite La0.5Ba0.5CoO3−δ at 1100°C in a flow of dry (log(pH2O/atm)=−4.0) nitrogen with log(pO2/atm)=−4.3 and 108 h dwell time. The sample was then slowly cooled (100°C/h) to room temperature in the same atmosphere and subsequently oxygenated in pure dry O2 at 500°C for 7 h with 100°C/h as a heating/cooling rate [10]. The XRD spectra recorded using Shimadzu XRD 7000S diffractometer (Shimadzu, Japan) with Cu Kα radiation showed no indication for the presence of a second phase in the as-prepared samples of LaBaCo2O6−δ [12].

Thermodynamics and structure

Thermodynamics of formation

The samples of REBaCo2O6−δ (RE=Gd, Pr) and GdBaCo1.8M0.2O6−δ (M=Fe, Mn) with different oxygen content, 6−δ, were prepared by annealing the corresponding double perovskite powders at different temperatures and pO2 in ambient gas atmosphere followed by quenching to 25°C [13], [14]. Standard enthalpies of dissolution of the as-prepared double perovskites in the hydrochloric acid were determined with an isothermal solution calorimeter, and the standard enthalpies of formation from elements (ΔfHREBaCo2O6δ) were calculated using the thermochemical cycle. The calorimetric setup and technique, as well as the thermochemical cycle employed, are described in detail elsewhere [13], [14].

Standard enthalpy of GdBaCo1.8M0.2O5.5 (M=Fe, Mn) formation was found to decrease upon doping, indicating the corresponding growth of relative thermodynamic stability of the double perovskites [13]. This growth is most likely due to increasing 3d-metal – oxygen binding energy, caused by the substitution of Fe or Mn for Co. At the same time, it follows from Fig. 1 that both ΔfHGdBaCo2O6δ and ΔfHPrBaCo2O6δ become more negative with oxygen content, 6−δ, increase, showing increasing relative thermodynamic stability of the corresponding double perovskites upon decreasing oxygen nonstoichiometry.

Fig. 1: Standard formation enthalpy of GdBaCo2O6−δ and PrBaCo2O6−δ at 25°C as a function of the oxygen content [14].
Fig. 1:

Standard formation enthalpy of GdBaCo2O6δ and PrBaCo2O6δ at 25°C as a function of the oxygen content [14].

Crystal structure

The crystal structure of the double perovskites REBaCo2−xFexO6−δ, where RE=Pr, Gd and x=0–0.6, was studied in the temperature range between 25 and 1100°C in air by means of in situ XRD with Cu Kα radiation using Equinox 3000 diffractometer (Inel, France) equipped with the high temperature camera HTK 16N (Anton Paar GmbH, Austria) [7], [8], [11].

The PmmmP4/mmm phase transition upon temperature increase was found [7], [11] to occur in GdBaCo2−xFexO6−δ (0≤x≤0.4). This transition is observed at the same temperature of around 475°C for the compositions with 0≤x≤0.1, while the transition temperature reaches maximum (515°C) for the compound with x=0.2 and then decreases gradually with increasing iron content [7], [11]. Unlike GdBaCo2−xFexO6−δ (x=0–0.4), the heavily doped GdBaCo1.4Fe0.6O6−δ was shown to have the tetragonal P4/mmm structure at room temperature. However, its structure undergoes P4/mmmPmmm transition at 170°C, while the inverse one is already observed at 290°C in air, and the structure remains the same upon further temperature increase [7].

In contrast with GdBaCo2−xFexO6−δ, the double perovskites PrBaCo2−xFexO6−δ (x=0–0.6) were shown to have the tetragonal P4/mmm structure in air over the complete temperature range investigated (up to 1100°C). However, the P4/mmmPmmm structural transformation was found [8] to occur in PrBaCo2O6−δ under reducing conditions with phase transition temperature decreasing from 500°C at pO2=10−3 atm down to 350°C at pO2=10−4 atm.

In addition to the temperature dependences of the unit cell parameters, it is of a great interest to consider how they change with the oxygen content, because the structure of the double perovskites REBaCo2O6−δ was believed [2], [4] to depend on the oxygen content only. In other words, it was presumed that the orthorhombic structure, which is due to the oxygen vacancies ordering along b axis, can be retained only at the oxygen content around 5.5, at which such ordering occurs.

The unit cell parameters vs. the oxygen content for GdBaCo2−xFexO6−δ, as an example, are given in Fig. 2. Such dependences were obtained using the data on the oxygen nonstoichiometry (see Section “Defect chemistry”). As seen, the PmmmP4/mmm structural transition is observed at the same value of the oxygen content, which is equal to 5.47 for the compounds with x=0 and 0.2. Meanwhile, the said transition takes place at 6−δ=5.54 for GdBaCo1.6Fe0.4O6−δ. In this regard, it is surprising that in GdBaCo1.4Fe0.6O6−δ the P4/mmmPmmm transition and the inverse one occur not only at the same oxygen content, but also at temperatures below 300°C where no oxygen exchange between the sample and the atmosphere takes place [7].

Fig. 2: Lattice parameters of double perovskites GdBaCo2−xFexO6−δ with x=0, 0.2 (a) and x=0.4, 0.6 (b) vs. the oxygen content [7]. Lines are a guide to the eye only.
Fig. 2:

Lattice parameters of double perovskites GdBaCo2−xFexO6−δ with x=0, 0.2 (a) and x=0.4, 0.6 (b) vs. the oxygen content [7]. Lines are a guide to the eye only.

In this respect, it is also worth mentioning that the threshold oxygen content of 5.5 in PrBaCo2−xFexO6−δ (x=0–0.6) oxides is reached in air at temperatures between 850 and 1080°C depending on the iron content [8]. However, the structural transition is not observed in these compounds under these conditions. Since the lack of the transition is caused, most likely, by the thermal disordering of oxygen vacancies at high temperatures, it is quite expected that the corresponding transition could occur in, at least, the undoped PrBaCo2O6−δ at temperatures significantly lower than 850°C under reducing atmosphere, if the threshold value of 5.5 is reached under such conditions. This assumption was supported completely by the results of in situ XRD analysis of PrBaCo2O6−δ in gas atmospheres with reduced pO2 given in Fig. 3.

Fig. 3: In situ temperature-dependent XRD pattern of PrBaCo2O6−δ, recorded in 2Θ range 45–48° at pO2=10−3 atm [7].
Fig. 3:

In situ temperature-dependent XRD pattern of PrBaCo2O6−δ, recorded in 2Θ range 45–48° at pO2=10−3 atm [7].

As seen, the transition from the tetragonal P4/mmm to the orthorhombic Pmmm structure occurs at around 500°C at pO2=10−3 atm when the oxygen content in PrBaCo2O6−δ reaches 5.5 (see Section “Oxygen nonstoichiometry and thermodynamic stability”). At pO2=10−4 atm the oxygen content attains 5.5 at temperature as low as 350°C, and, accordingly, the phase transition shifts to this temperature. Therefore, the lowering of the temperature corresponding to the oxygen content of 5.5 in REBaCo2O6−δ enables the possibility for the oxygen vacancy ordering and, as a consequence, induces the structural phase transition.

Aforementioned observations give rise to a conclusion that the P4/mmmPmmm structural transition in the double perovskites REBaCo2−xMxO6−δ, where M is dopant, is affected not only by the oxygen content, as was believed previously, but also by the temperature and the nature of a dopant.

Oxygen nonstoichiometry and thermodynamic stability

The relative change of the oxygen nonstoichiometry (Δδ) in the double perovskites REBaCo2−xFexO6−δ, where RE=La, Pr, Nd, Eu, Gd, Y, was measured in the wide ranges of T and pO2 by both thermogravimetry (TG) and coulometric titration techniques described in detail elsewhere [15]. The relative change was then recalculated to the absolute scale (δ) using the absolute oxygen content, determined by means of either direct sample reduction by H2 in a thermobalance (TG/H2) or sample redox titration [15]. The oxygen nonstoichiometry (δ) of different double perovskites REBaCo2O6−δ, measured as a function of pO2 and temperature, is given in Figs. 4 and 5.

Fig. 4: Oxygen nonstoichiometry of EuBaCo2O6−δ (a) and LaBaCo2O6−δ (b) [12] as a function of pO2 at different temperatures. Points are experimental data and lines are given as a guide to the eye (a) and corresponding fitted model (b).
Fig. 4:

Oxygen nonstoichiometry of EuBaCo2O6−δ (a) and LaBaCo2O6δ (b) [12] as a function of pO2 at different temperatures. Points are experimental data and lines are given as a guide to the eye (a) and corresponding fitted model (b).

Fig. 5: Oxygen nonstoichiometry of YBaCo2O6−δ (a) [9] and PrBaCo2O6−δ (b) [16] as a function of pO2 at different temperatures. Points are experimental data and lines are given as a guide to the eye.
Fig. 5:

Oxygen nonstoichiometry of YBaCo2O6δ (a) [9] and PrBaCo2O6δ (b) [16] as a function of pO2 at different temperatures. Points are experimental data and lines are given as a guide to the eye.

The data on the oxygen content in PrBaCo2O6−δ, shown in Fig. 5, were corrected for the cobalt oxide exsolution from the A-site understoichiometric Pr1−xBa1−xCo2O6−γ as a result of its reduction. Such exsolution of B-site-element-containing phases seems to be typical of the perovskite-type oxide materials that can accommodate vacancies in oxygen- and A-sublattices simultaneously [16]. As follows from the comparison of Figs. 4, 5 and 7, the oxygen content in REBaCo2O6−δ changes within their stability region in the wide span – from 5.78 for RE=La in air at 400°C down to 4.85 for RE=Gd at 1000°C and log(pO2/atm)=−6.2.

It is worth noting that the pO2 dependences of the oxygen content measured at a given temperature for different REBaCo2O6−δ exhibit inflections when the oxygen content reaches the value of 5. This particularity is closely related to the defect chemistry and will be explained in the Section “Defect chemistry”.

The vertical segments of the titration curve, like those presented in Fig. 5 for YBaCo2O6−δ, correspond to the oxide decomposition and clearly indicate its thermodynamic stability limits with respect to reduction (at low pO2) and oxidation (at high pO2). Remarkably, among the double perovskites studied, the only one that is unstable in air at certain temperatures is YBaCo2O6−δ. Thus, the curve plot enclosed between the vertical segments corresponds to the oxygen content change in YBaCo2O6−δ within the thermodynamic stability region.

In order to determine the possible decomposition products for YBaCo2O6−δ at high pO2, the coulometric measurements, carried out at a given temperature, were interrupted after reaching the highest pO2 value corresponding to the vertical segment, and the coulometric cell was cooled quickly down to room temperature. XRD of the YBaCo2O6−δ sample cooled accordingly showed the presence of YCoO3, BaCoO3 and BaCoO2.63 as products of YBaCo2O6−δ decomposition. Thus, the decomposition of YBaCo2O6−δ in oxidizing conditions undergoes as

(1)YBaCo2O6δ+δz2O2=YCoO3+BaCoO3z

where the value of the oxygen content, 6−δ, depends on temperature and varies from 5.012 at 800°C up to 5.035 at 900°C (see Fig. 5).

In order to find out the products of REBaCo2O6−δ (RE=Gd, Y) decomposition at low pO2 stability limit, their single-phase samples were annealed at 1000°C in gas atmospheres with log(pO2/atm)=−4 and −6.2 for RE=Y and Gd, respectively, for 12 h and then quenched to ice at –18°C. The XRD pattern of the GdBaCo2O6−δ sample prepared accordingly showed the presence of Gd2BaCoO5 as well as complex mixture of barium cobaltites with overall stoichiometry “BaCoO2”, and CoO. Thus, taking into account the appropriate value of the oxygen content, the decomposition of GdBaCo2O6−δ at 1000°C can be written as

(2)GdBaCo2O4.85=0.5Gd2BaCoO5+0.5BaCoO2+CoO+0.175O2

One can assume that the other REBaCo2O6−δ except YBaCo2O6−δ decompose in an analogous way.

The XRD pattern of the YBaCo2O6−δ sample, prepared as mentioned in the previous paragraph, showed the presence of YBaCo4O7, BaCo1−xYxO3−z and Y2O3. Therefore, the decomposition of YBaCo2O6−δ at low pO2 stability limit proceeds according to the following reaction

(3)YBaCo2O6δ=pY2O3+nYBaCo4O7+mBaCo1xYxO3γ+qO2

where m=23+x,n=1+x3+x,p=3x+12(3+x) and p=2xδ13+6δ4γ7x4(3+x). The oxygen content in the hexagonal YBaCo4O7 can be neglected here because in this oxide it is very close to 7 in the vicinity of its low pO2 stability limit: for example, it comes to 6.99 at 900°C and log(pO2/atm)=−3.5 [17].

Thermodynamic stability limits of REBaCo2O6−δ (RE=Gd, Y), determined accordingly, are summarized in the stability diagrams shown in Fig. 6 as log(pO2)=f(1/T). For the sake of comparison, the data on stability of cubic oxides GdCoO3 and LaCoO3 [18] are given ibidem.

Fig. 6: Thermodynamic stability limits of YBaCo2O6−δ (a) [9] – points are experimental data and lines are given to guide the eye, and GdBaCo2O6−δ (b) –points are the experimental data and line is a guide to the eye, the upper two lines are the reference data for GdCoO3 and LaCoO3 [18].
Fig. 6:

Thermodynamic stability limits of YBaCo2O6δ (a) [9] – points are experimental data and lines are given to guide the eye, and GdBaCo2O6δ (b) –points are the experimental data and line is a guide to the eye, the upper two lines are the reference data for GdCoO3 and LaCoO3 [18].

As follows, the stability of the double perovskite GdBaCo2O6−δ exceeds that of the “simple” perovskite GdCoO3 by about six orders of pO2 magnitude.

The values of pO2 at which the conductivity drop was observed for YBaCo2O6−δ [9] upon decreasing oxygen partial pressure are also given in Fig. 6 depending on reciprocal temperature. As seen, the data on the stability limits obtained by means of different methods are in agreement with each other.

Defect chemistry

Choice of a suitable reference (perfect) crystal, which defines the background, i.e. the regular constituents and defect species in the crystal lattice studied, is of a cornerstone importance for the defect structure analysis. Cubic RE2Co2O6, or, in other words, RECoO3 (RE=rare-earth element) with doubled unit cell, can be chosen as a reference crystal for the double perovskites REBaCo2O6−δ. In this case, the regular constituents are RERE×,CoCo× and OO×, whereas the point defects can be defined as BaRE,V0,CoCo (Co+2 or electron localized on cobalt site) and CoCo (Co+4 or hole localized on cobalt site). Within the framework of the model proposed [8], [10], [11], [12], 19] the following defect reactions were taken into account:

  1. Formation/annihilation of oxygen vacancy during oxygen release/uptake from the cobaltite lattice under reducing/oxidizing conditions

    (4)OO×+2CoCo=1/2O2+V0+2CoCo×

    and

    (5)OO×+2CoCo×=1/2O2+VO+2CoCo
  2. Charge disproportionation involving the transfer of an electron between adjacent CoCo× sites

    (6)2CoCo×=CoCo+CoCo
  3. Oxygen vacancies ordering by the formation of pseudo-clusters (VORERE×)

    (7)RERE×+VO=(VORERE×)

    The latter reaction represents the preferred location of the oxygen vacancies in the RE-O planes of the double perovskite structure, as has been proven recently by scanning transmission electron microscopy (STEM) coupled with electron energy loss spectroscopy (EELS) [20] and first-principles DFT with Monte Carlo simulations [21].

Equilibrium constants of reactions (4)–(7) (note that among the reactions (4) and (5) only one is independent) along with the mass conservation and the electroneutrality condition allow defining the following set of equations

(8){K5=PO20.5[VO][CoCo]2[OO×][CoCo×]2=K50exp(ΔH50RT)K6=[CoCo][CoCo][CoCo×]2=K60exp(ΔH60RT)K7=[(VORERE×)][RERE×][VO]=K70exp(ΔH70RT)[CoCo]+2δ=[CoCo]+[BaRE][CoCo]+[CoCo]+[CoCo×]=2[VO]+[(VORERE×)]=δ[RERE×]+[(VORERE×)]=1[BaRE]=1[OO×]=6δ

The analytical solution of the set (8) yields the model function of the REBaCo2O6−δ defect structure model

(9) log(pO2/atm)=4log(22K5K76δ(A2)(2δ(4K61)+4K6+1A)K7(δ1)+B1)

where

(10)A=12K64δ2(4K61)+4δ(4K61)+1

and

(11)B=K72(δ1)2+2K7(δ+1)+1

Let us note that the complex model represented by the set Eq. (8) can be applied to REBaCo2O6−δ (for instance, RE=Gd [10], [16]) oxygen content of which reaches values less than 5.0 and, therefore, oxygen vacancies can be formed randomly in oxygen octahedra in addition to those located in RE-O planes. For the other double perovskites where the oxygen content is more than 5.0 the reactions (5) and (7) can be combined, eliminating the free oxygen vacancies from the model. This leads to the simplified defect structure model, which has been successfully verified for LaBaCo2O6−δ [12].

Since the oxygen nonstoichiometry of REBaCo2O6−δ was measured in relatively narrow temperature range, the defect formation enthalpies can be treated as constants. This assumption enables the substitution of the equilibrium constants in the fitting function Eq. (9) by their thermodynamic temperature dependences [see Eq. (8)] and, as a consequence, allows verifying the defect structure model using the whole pO2-T-δ data set at once. As an example, the results of the least square fitting for REBaCo2O6−δ, where RE=La, Pr and Gd, are shown in Figs. 4 and 7, respectively. As seen, the model proposed perfectly fits the experimental data on the oxygen nonstoichiometry of the double perovskites. In addition, the determination coefficient, R2, close to unity indicates unambiguously the suitability of the model proposed for the REBaCo2O6−δ defect structure [8], [10], [12], [19].

Fig. 7: Results of the defect structure modeling for GdBaCo2O6−δ (a) [19] and PrBaCo2O6−δ (b) [16]: points – experimental data, surfaces – fitted model.
Fig. 7:

Results of the defect structure modeling for GdBaCo2O6δ (a) [19] and PrBaCo2O6δ (b) [16]: points – experimental data, surfaces – fitted model.

Charge transfer

Oxide ion conductivity of GdBaCo2O6−δ, σVO, measured as a function of pO2 at different temperatures using a polarization technique with YSZ microelectrode [22], is shown in Fig. 8. As seen, σVO increases with decreasing pO2 since the oxygen vacancy concentration, [VO], grows at the same time. Oxygen vacancy self-diffusion coefficient, DVO, also given in Fig. 8, was calculated from σVO using the pO2-T-δ diagram (see Fig. 7) and the well-known relations

(12)UVO=σVO2FδVcNAa
(13)DVO=RT2FUVO
Fig. 8: Oxide ion conductivity vs. pO2 (a) and oxygen vacancies self-diffusion coefficient vs. δ (b) for GdBaCo2O6−δ at different temperatures [19], [22].
Fig. 8:

Oxide ion conductivity vs. pO2 (a) and oxygen vacancies self-diffusion coefficient vs. δ (b) for GdBaCo2O6δ at different temperatures [19], [22].

where UVO,σVO, 2, F, δ, VC, NA, and a are the oxygen vacancy mobility, the oxide ion conductivity, the oxygen vacancy charge, the Faraday constant, the oxygen nonstoichiometry, the unit cell volume, the Avogadro constant and the number of formula units of GdBaCo2O6−δ per unit cell, respectively.

The growth in σVO with decreasing pO2, observed even at 850°C, becomes more pronounced at higher temperatures. This behavior coincides with the observed increase in the oxygen diffusion coefficient with temperature, shown in Fig. 8, because σVO is directly proportional to the diffusion coefficient DVO as follows from the comparison of Eqs. (12) and (13). The activation energy of self-diffusion of oxygen vacancies in GdBaCo2O6−δ, calculated using the obtained values of DVO, varies from 0.56 eV at δ=0.8 up to 0.80 eV at δ=1. This tendency appears to support the defect structure model suggested for GdBaCo2O6−δ (see Section “Defect chemistry”), according to which all the oxygen vacancies are formed in Gd-layers up to δ<1, whilst the rest of the oxygen vacancies are randomly distributed over the oxygen octahedra at δ>1 where the rare-earth layers do not contain oxide ions at all. Thus, the oxygen transfer in REBaCo2O6−δ at δ<1 proceeds through the oxygen vacancies in RE-layers, which form transport channels in the structure of the double perovskites. Such a “channel transport” requires lower activation energy, as compared to that of the oxygen transport proceeding through the statistically distributed vacancies [2] like it is in the cubic non-layered perovskites RECoO3−δ.

Oxygen tracer diffusion coefficient in GdBaCo2O6−δ was determined by means of 18O-isotope exchange with gas-phase analysis [19] using ceramic samples prepared from the same single-phase powder of GdBaCo2O6−δ used for the polarizations measurements [19], [22]. As seen in Fig. 9, the oxygen self-diffusion coefficient is in very good agreement with the oxygen tracer diffusion one.

Fig. 9: Oxygen self-diffusion coefficient vs. pO2 for GdBaCo2O6−δ [19] (a) and oxygen vacancy mobility for REBaCo2O6−δ (RE=Pr, Sm, Gd) in atmosphere with pO2=10−2 atm [23] (b) at different temperatures: open and closed symbols (a) correspond to results of isotope exchange and dc-polarization, respectively.
Fig. 9:

Oxygen self-diffusion coefficient vs. pO2 for GdBaCo2O6δ [19] (a) and oxygen vacancy mobility for REBaCo2O6δ (RE=Pr, Sm, Gd) in atmosphere with pO2=102 atm [23] (b) at different temperatures: open and closed symbols (a) correspond to results of isotope exchange and dc-polarization, respectively.

Oxygen tracer diffusion coefficient in REBaCo2O6−δ (RE=Pr, Sm) was determined likewise [23]. The oxygen vacancy mobility for different double perovskites, evaluated on the basis of such measurements, is given in Fig. 9 depending on temperature. It can be observed in Fig. 9 that this mobility decreases gradually in the series PrBaCo2O6−δ–SmBaCo2O6−δ–GdBaCo2O6−δ.

Overall conductivity of polycrystalline ceramic GdBaCo2−xFexO6−δ and single crystal EuBaCo1.9O6−δ measured in the directions parallel ([120]) and perpendicular ([001]) to the growth direction are shown in Fig. 10 as functions of temperature in air [24], [25].

Fig. 10: Overall conductivity as a function of temperature in air for ceramic GdBaCo2−xFexO6−δ (a) and single crystal EuBaCo1.9O6−δ (b) measured parallel ([120]) (closed spheres) and perpendicular ([001]) (open squares) to the growth direction. Insertion (b) shows the ratio σ(I||[120])/σ(I||[001]) [24], [25].
Fig. 10:

Overall conductivity as a function of temperature in air for ceramic GdBaCo2xFexO6−δ (a) and single crystal EuBaCo1.9O6δ (b) measured parallel ([120]) (closed spheres) and perpendicular ([001]) (open squares) to the growth direction. Insertion (b) shows the ratio σ(I||[120])/σ(I||[001]) [24], [25].

All the oxides studied possess rather low electrical conductivity near room temperature. Upon heating, the conductivity of GdBaCo2O6−δ and EuBaCo1.98O6−δ grows abruptly (up to around 500 S/cm for GdBaCo2O6−δ) and then gradually decreases. The conductivity of the iron-doped GdBaCo1.8Fe0.2O6−δ exhibits similar behavior, albeit the low-temperature conductivity increase is much less steep. The abrupt change in the conductivity around 80°C, observed on the temperature dependences given in Fig. 10 for GdBaCo2O6−δ and EuBaCo1.98O6−δ, is most likely caused by the metal-insulator transition. Besides, the evidence for the structural PmmmP4/mmm transition is clearly seen at around 450°C on the σ(T) dependence measured for the single crystal EuBaCo1.9O6−δ (see Fig. 10). It is noteworthy that total conductivity is strongly anisotropic in EuBaCo2O6−δ, as shown in Fig. 10, and, most likely, in the other double perovskites. This can be attributed to the localization of oxygen vacancies in RE-O planes in REBaCo2−xO6−δ with δ<1.0. Such localization disrupts the conducting Co–O–Co chains along c-axis and hampers the electron and hole movement in this direction, as compared to the charge transfer in the ab-plane where Co–O–Co chains are retained.

Overall conductivity and the Seebeck coefficient of polycrystalline REBaCo2O6−δ (RE=Gd, Eu) measured as a function of pO2 using a standard 4-probe technique [22], [25] are given in Figs. 11 and 12, respectively, at different temperatures. The decrease in the conductivity with simultaneous increase in the Seebeck coefficient upon reducing pO2 in surrounding gas atmosphere was observed. Such behavior is in favor of holes as predominant charge carriers in REBaCo2O6−δ.

Fig. 11: Overall conductivity of polycrystalline EuBaCo2O6−δ (a) and GdBaCo2O6−δ (b) vs. pO2 at different temperatures: lines for eye guide only.
Fig. 11:

Overall conductivity of polycrystalline EuBaCo2O6δ (a) and GdBaCo2O6δ (b) vs. pO2 at different temperatures: lines for eye guide only.

Fig. 12: Seebeck coefficient of EuBaCo2O6−δ (a) and GdBaCo2O6−δ (b) vs. pO2 at different temperatures: lines are given to guide the eye.
Fig. 12:

Seebeck coefficient of EuBaCo2O6δ (a) and GdBaCo2O6δ (b) vs. pO2 at different temperatures: lines are given to guide the eye.

Dependences σ=f(pO2) and Q=f(pO2) were recalculated to σ=f(δ)T and Q=f(δ)T using pO2-T-δ diagram presented above in Sections “Oxygen nonstoichiometry and thermodynamic stability” and “Defect chemistry”. Figure 13 shows the results of such calculations for Seebeck coefficient of GdBaCo2O6−δ and EuBaCo2O6−δ.

Fig. 13: Seebeck coefficient of EuBaCo2O6−δ (a) and GdBaCo2O6−δ (b) vs. oxygen nonstoichiometry at different temperatures: points – observed, lines – calculated according to the model proposed.
Fig. 13:

Seebeck coefficient of EuBaCo2O6δ (a) and GdBaCo2O6δ (b) vs. oxygen nonstoichiometry at different temperatures: points – observed, lines – calculated according to the model proposed.

As follows from comparison of Figs. 8 and 11, the oxide ion conductivity of REBaCo2O6−δ is less than the overall one by a few orders of magnitude. This allows neglecting the transference number of oxygen vacancies and, as a consequence, expressing the total conductivity of REBaCo2O6−δ by the following equation

(14)σ=a|e|Vc(Ue[CoCo]+Uh[CoCo])

where a, |e|, VC, Ue, Uh, CoCo and CoCo are the number of formula units of REBaCo2O6−δ per unit cell, the charge of an electron, the unit cell volume, the mobilities of electrons and holes, and the concentration of electrons and holes localized on cobalt ions, respectively.

Seebeck coefficient of REBaCo2O6−δ as a function of concentration of the charge carriers can be given as

(15)Q=[CoCo]Qe+[CoCo]Qh[CoCo]+L[CoCo]

where Qe and Qh are the partial thermoelectric coefficients of electrons and holes, respectively, and L=Uh/Ue is a ratio of their mobilities. According to Heikes [22], Qe and Qh can be expressed as

(16)Qh=k|e|[ln([CoCo×][CoCo])+Shk]
(17)Qe=k|e|[ln([CoCo×][CoCo])+Sek]

where k is the Boltzmann constant, Sh/e=Hh/e/T and Hh/e are the entropy and the enthalpy, respectively, of the hole/electron transfer.

Substituting Eqs. (16) and (17) into Eq. (15) using the defect species concentrations [CoCo]=f1(δT) and [CoCo]=f2(δT) calculated on the basis of the verified defect structure model (see Section “Defect chemistry”) yields the model function Q(δ,L,Se,Sh)T, which can be fitted to the experimental data on Q depending on δ at different temperatures. Fitted lines are shown in Fig. 13 along with the experimental data, where a good agreement between the experimental data and those calculated is demonstrated. Mobilities of electrons and holes in REBaCo2O6−δ (RE=Eu, Gd), calculated using Eq. (14) and the fitted values of L, are plotted vs. δ at different temperatures in Fig. 14.

Fig. 14: Mobilities of holes and electrons vs. oxygen nonstoichiometry at different temperatures in EuBaCo2O6−δ (a) and GdBaCo2O6−δ (b) vs. oxygen nonstoichiometry at different temperatures.
Fig. 14:

Mobilities of holes and electrons vs. oxygen nonstoichiometry at different temperatures in EuBaCo2O6−δ (a) and GdBaCo2O6−δ (b) vs. oxygen nonstoichiometry at different temperatures.

The Fig. 14 shows that the mobility of holes exceeds that of the electrons by around 4 and 8 times in case of EuBaCo2O6−δ and GdBaCo2O6−δ, respectively. What is more, these ratios practically do not change over the complete oxygen nonstoichiometry range studied. These findings explain why the Seebeck coefficient remains positive even at low oxygen content of REBaCo2O6−δ when the concentration of holes becomes very small, according to the defect structure modeling results (see Section “Defect chemistry”).

One can note, in addition, that activation energy, Ea, of mobility of electrons and holes decreases with δ: for instance, for GdBaCo2O6−δ from 0.25 eV at δ=0.8 down to 0.08 eV at δ=1.1. The magnitude of these values is typical of the transfer of localized charges.

Thermal expansion and chemical strain

As was mentioned in Section “Crystal structure”, the crystal structure of the double perovskites REBaCo2−xFexO6−δ, where RE=Pr, Gd and x=0–0.6, was studied in the temperature range between 25 and 1100°C in air by means of in situ XRD [7], [8], [11]. Temperature dependences of the normalized change of cell parameters or, in other words, the thermal strain in air is shown in Fig. 15 for tetragonal (P4/mmm) PrBaCo1.6Fe0.4O6−δ as an example. As seen, these dependences obey linear trend up to around 500°C and then those for a and c parameters exhibit positive and negative, respectively, deviation from this trend. Meanwhile, the thermal strain is expected to be a linear function of temperature over the complete temperature range investigated because the origin of thermal strain lies in the anharmonic vibrations of atoms in a crystal lattice. The deviations from linearity are caused by the oxygen exchange between surrounding gas atmosphere and the oxide crystal lattice since their onset coincides completely with that of the oxygen release or uptake upon heating. As the oxygen exchange is accompanied by the oxygen vacancy formation or consumption in the lattice, i.e. by the point defect interactions, the related expansion phenomena are called chemical or defect-induced strain (or expansion) [8], [13].

Fig. 15: Lattice parameters (a) and chemical strain (b) of PrBaCo1.6Fe0.4O6−δ as a function of temperature in air.
Fig. 15:

Lattice parameters (a) and chemical strain (b) of PrBaCo1.6Fe0.4O6δ as a function of temperature in air.

The chemical strain of PrBaCo1.6Fe0.4O6−δ, calculated as

(18)εa=ameasuredaexpecteda0

and

(19)εc=cmeasuredcexpectedc0

where a0, c0 and ameasured, cmeasured are the lattice constants measured at room and a given temperature, respectively, and aexpected and cexpected – those given by the linear trends, is also shown in Fig. 15.

As seen, the positive chemical strain along a axis nearly compensates the negative one along c axis, by that means providing negligible volumetric chemical expansion. For this reason, the cell volume of tetragonal (P4/mmm) PrBaCo1.6Fe0.4O6−δ increases linearly with temperature, as if only the thermal expansion occurs.

These findings are completely supported by the results of in situ XRD [26] obtained for tetragonal (P4/mmm) phases of the double perovskites PrBaCo2O6−δ and GdBaCo2O6−δ and given in Fig. 16.

Fig. 16: Lattice parameters and cell volume of PrBaCo2O6−δ (a) and GdBaCo2O6−δ (b) vs. pO2 measured in situ at different temperatures.
Fig. 16:

Lattice parameters and cell volume of PrBaCo2O6δ (a) and GdBaCo2O6δ (b) vs. pO2 measured in situ at different temperatures.

As seen, PrBaCo2O6−δ and GdBaCo2O6−δ crystal lattices expand along a-axis and simultaneously contract along c-axis with decreasing pO2 in ambient atmosphere, i.e. when the oxygen content in the oxides decreases (see Fig. 7 in Section “Defect chemistry”). As a result, the unit cell is almost independent of the oxygen partial pressure over the complete pO2 range studied.

The chemical strain of pseudo-cubic oxides with perovskite structure can be explained quantitatively using the dimensional model based on a relative change of the weighted average ionic radius [15], [26], [27]. Within the framework of this approach, which was first developed for the isotropic expansion of pseudocubic perovskite-type oxides, it is assumed that the main reason for the chemical expansion is the change in the radii of metal cations, caused by their reduction/oxidation due to, in turn, the oxygen release/uptake by the oxide lattice. Using this assumption, the uniaxial chemical strain εa of a closely packed crystal lattice, formed by ions regarded as rigid spheres, can be calculated as follows

(20)εa=Δaa0=i(cirici0ri)ici0ri

where ci and ri are the concentration and ionic radius, respectively, of an ion i, and the subscript 0 in ci0 and a0 denotes that these properties belong to the oxide in an arbitrarily chosen reference state with certain oxygen nonstoichiometry δ0 at a given temperature. The sum is taken over all atoms belonging to the oxide formula, and ci refers to the molar concentration per unit formula in this compound.

The corresponding concentrations were calculated for REBaCo2O6−δ (RE=Gd, Pr) using the defect structure model proposed and verified (see Section “Defect chemistry”). Crystal ionic radii given by Shannon [28] can be used as ri, taking into account the corresponding coordination numbers (CN): for instance, for GdBaCo2O6−δ, rO2−=1.26 Å (CN=6), rBa2+=1.75 Å (CN=12), rGd2+=1.247 Å (CN=9), rCo2+=0.79 Å (LS, CN=6), rCo2+=0.885 Å (HS, CN=6), rCo3+=0.685 Å (LS, CN=6), rCo3+=0.75 Å (HS, CN=6), rCo4+=0.67 Å (HS, CN=6).

The chemical expansion calculated accordingly is given as solid lines in Fig. 17 for GdBaCo2O6−δ as an example. Perfect coincidence between the calculated and measured chemical expansion along a-axis of the tetragonal (P4/mmm) GdBaCo2O6−δ at different temperatures is clearly seen in this figure. Such coincidence appears to support the defect structure model proposed for the double perovskite GdBaCo2O6−δ. In addition, it leads to an assumption that the increase in the cation radii contributes the most to the chemical expansion of this oxide, as well as the other, in the ab-plane. In other words, the origin of the chemical expansion in the ab-plane of tetragonal A-site-ordered double perovskites REBaCo2O6−δ appears to be similar to that of the isotropic chemical expansion of pseudo-cubic “simple” perovskites [15], [26].

Fig. 17: Chemical strain of GdBaCo2O6−δ lattice vs. oxygen nonstoichiometry at different temperatures: points – the experimental data [26], lines – model calculation as described in the text.
Fig. 17:

Chemical strain of GdBaCo2O6δ lattice vs. oxygen nonstoichiometry at different temperatures: points – the experimental data [26], lines – model calculation as described in the text.

From the phenomenological point of view, the value of the chemical contraction of REBaCo2O6−δ along c-axis can be calculated, as a first approximation, using the coefficient similar to Poisson’s ratio, which characterizes anisotropy of elastic properties of materials. This coefficient, βAR, was introduced as the anisotropic ratio of chemical expansion [29]. This coefficient is dimensionless and equal to the ratio of the chemical strain along two perpendicular directions, and is defined as

(21)βAR=Δc/c0Δa/a0

where Δc/c0 and Δa/a0 are the normalized change in the c and a parameters, respectively. The subscript, 0, in c0 and a0 denotes in Eq. (21) that these properties belong to the oxide in the chosen reference state. This anisotropic ratio coefficient should depend significantly on the particularities of the oxide crystal structure and, to some extent, on its chemical composition. For cubic (space groups Pmm, Fmm) perovskite-type oxides βAR by definition equals unity, as their expansion is isotropic. For tetragonal (P4/mmm) REBaCo2O6−δ (RE=Gd, Pr), it was determined experimentally that βAR=−1 [29].

The total volumetric chemical strain of an oxide with tetragonal crystal structure can be expressed using βAR as follows:

(22)εV=1V(Vδ)T=2a(aδ)T+1c(cδ)T=2εa+εc=2εa+βARεa=εa(2+βAR)

where εa and εc are the linear chemical strain along a- and c-axis, respectively.

It should be emphasized that in the framework of the chemical strain model employed in our works the chemical strain, εa, of the tetragonal REBaCo2O6−δ along the a-axis (in the ab-plane) can be calculated on the basis of its defect structure model only using the Eq. (20), with no prior knowledge of the actual experimental values of the chemical expansion. Then, εc can also be estimated on condition that the anisotropic ratio coefficient is known. As an example, the chemical contraction along c-axis of the tetragonal lattice of GdBaCo2O6−δ was calculated as εc=βARεa, where εa is calculated as described above and βAR=−1. The result of such estimation is given by the dashed line in Fig. 16 for GdBaCo2O6−δ. Perfect agreement between the calculated contraction values and those observed experimentally is clearly seen in this figure.

Conclusions

Standard enthalpy of GdBaCo1.8M0.2O5.5 (M=Fe, Mn) formation was found [13] to decrease upon doping, indicating increasing relative thermodynamic stability of the double perovskites upon doping caused by simultaneous increasing 3d-metal – oxygen binding energy. However, such functions become more negative with increasing oxygen content of REBaCo2O6−δ (RE=Pr, Gd) showing that relative thermodynamic stability of the double perovskites grows upon decreasing oxygen nonstoichiometry.

P4/mmmPmmm structural transition in the double perovskites REBaCo2−xMxO6−δ, where M is dopant, was found to be affected by different factors such as the nature of a dopant, oxygen content and temperature. The double perovskites GdBaCo2−xFexO6−δ slightly doped with iron undergo this transition at the oxygen content close to 5.5 whereas the transition in the heavily doped oxide does not depend on the oxygen content at all. The double perovskites PrBaCo2−xFexO6−δ (x=0–0.6) do not exhibit P4/mmmPmmm transition upon heating in air up to 1050°C despite their oxygen content reaching 5.5 at temperatures between 850 and 1080°C depending on the iron content. At the same time, lowering oxygen partial pressure enables such transition, at least for undoped PrBaCoO6−δ.

The oxygen content in REBaCo2O6−δ was found to decrease depending on RE atomic number, temperature and oxygen partial pressure within wide range – from 5.78 for RE=La in air at 400°C down to 4.85 for RE=Gd at 1000°C and log(pO2/atm)=−6.2. All the double perovskites studied except YBaCo2O6−δ are stable in air and decompose at low oxygen partial pressure with formation of RE2BaCoO5, mixture of barium cobaltites, and CoO. YBaCo2O6−δ exhibits completely different behavior since the products of its decomposition at low pO2 were found to be YBaCo4O7, BaCo1−xYxO3−z and Y2O3 whereas YCoO3, BaCoO3 and BaCoO2.63 are the products of YBaCo2O6−δ decomposition in air.

The defect structure of the oxides studied was successfully described using the model based on three reactions: oxygen vacancies formation during oxygen release by the oxide lattice, charge disproportionation in cobalt sublattice, and oxygen vacancies ordering in the RE-O planes of the double perovskite structure. Defect species concentrations calculated as a result were then employed for explanation of the double perovskite properties such as Seebeck coefficient and chemical expansion. The former was evaluated within the framework of Heikes approach for hopping mechanism of electronic conductivity. Mobility of holes in REBaCo2O6−δ was shown to exceed that of electrons by 4–8 times depending on the nature of RE and, consequently, the Seebeck coefficient remains positive for all oxides studied even at very low hole concentrations.

The oxygen transfer in REBaCo2O6−δ was found to proceed via different pathways depending on the oxygen content. At δ<1 oxide ions move through the oxygen vacancies in RE-layers with lower activation energy, as compared to that of the oxygen transport through the statistically distributed vacancies at δ>1.

The chemical strain of REBaCo2O6−δ was shown to be anisotropic as crystal lattices expand along a-axis and simultaneously contract along c-axis with decreasing pO2 in ambient atmosphere (or the oxygen content in the oxide). As a result, the unit cell volume is almost independent of pO2/oxygen content. The chemical expansion of the tetragonal REBaCo2O6−δ (RE=Gd) along the a-axis (in the ab-plane) upon growing oxygen nonstoichiometry was successfully calculated on the basis of its defect structure model. The chemical contraction along c-axis was also estimated using the as-calculated expansion in the ab-plane and the phenomenological anisotropic ratio of chemical strain, introduced by analogy with the Poisson’s ratio in mechanics. A perfect agreement was shown between the contraction calculated accordingly and the one measured experimentally.


Article note

A collection of invited papers based on presentations at the 16th International IUPAC Conference on High Temperature Chemistry (HTMC-XVI), held in Ekaterinburg, Russia, 2–6 July 2018.


Award Identifier / Grant number: 18-33-20243\18

Funding statement: This work was supported by Russian Foundation for Basic Research, Funder Id: http://dx.doi.org/10.13039/501100002261 (Grant No. 18-33-20243\18).

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Published Online: 2019-05-18
Published in Print: 2019-06-26

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