Experimental phase diagram determination and thermodynamic assessment of the Gd2O3–CoO system

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Acta Materialia 58 (2010) 4077–4087 www.elsevier.com/locate/actamat

Experimental phase diagram determination and thermodynamic assessment of the Gd2O3–CoO system T. Ivas a,*, A.N. Grundy b, E. Povoden a, S. Zeljkovic c, L.J. Gauckler a a

Nonmetallic Inorganic Materials, Department of Materials, ETH-Zurich, Wolfgang-Pauli-Strasse 10, HCI G 530, CH-8093 Zurich, Switzerland b Concast AG, To¨distrasse 9, CH-8002 Zurich, Switzerland c University of Banja Luka, Faculty of Science, Mladena Stojanovica 2, 78000 Banja Luka, Bosnia and Herzegovina Received 17 September 2009; received in revised form 8 March 2010; accepted 11 March 2010 Available online 4 May 2010

Abstract New phase diagram data and a thermodynamic assessment of the Gd2O3–CoO system using the CALPHAD approach are presented, giving liquidus data and mutual solid solubilities of Co in Gd2O3 and Gd in CoO. The thermodynamic model parameters for the ternary Gd–Co–perovskite phase and for the mutual solid solubilities of Co in Gd2O3 and Gd in CoO are optimized to reproduce these new experimental data, as well as phase diagram data from literature. The Gd2O3–CoO phase diagram is refined based on the results of experiments using combined differential thermal analysis and thermogravimetry, scanning electron microscopy and X-ray diffraction techniques. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: GdCoO3; Solid solubilities (Gd2O3, CoO); SOFC; CALPHAD

1. Introduction State-of-the-art solid oxide fuel cells (SOFC) with an Y2O3-doped ZrO2 (YSZ) electrolyte require high operation temperatures from 1173 to 1273 K. It was shown that a SOFC consisting of a mixed ionic–electronic conducting Gd2O3-doped CeO2 (CGO) electrolyte can be operated at lower temperatures, since CGO has an up to five times higher ionic conductivity than YSZ at intermediate temperatures (773–1073 K) [1,2]. Hence, a SOFC using a CGO electrolyte can be operated at a relatively low temperature, which reduces the overall costs of the fuel cell and potentially broadens its applicability. SOFC with a CGO electrolyte are operated in a temperature range where methane or higher alkenes can act as fuel, thereby showing significantly higher efficiency than a

*

Corresponding author. Tel.: +41 (0)44 6336994; fax: +41 (0)44 632 11

32. E-mail address: [email protected] (T. Ivas).

standard internal combustion engine operated with the same fuels. In SOFC with a Sr-doped lanthanum manganese (LSM) cathode, insulating La2Zr2O7 and SrZrO3 can form at the cathode–electrolyte interface owing to reactions of LSM with YSZ during the cell operation. This rapidly degrades the performance of the SOFC in a timescale of hours. Changing the cathode composition does not solve this problem [3]. However, coating the cathode with nano-sized particles of CGO inhibits undesirable reactions between the cathode and the electrolyte. The processing of pure CGO is complicated, since a high density requires a high temperature, making the production of the SOFC extremely expensive. Doping of CGO with small amounts of Co-oxide dramatically improves the sinterability of the material, while its excellent electrical properties are conserved [4]. The reason for this is the formation of a nano-sized intergranular film enriched with Co-oxide. The thermodynamic assessment of the Gd2O3–CoO system is an intermediate step in a project that aims at the full thermodynamic description of the Ce–Gd–Co–O system,

1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.03.019

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which can contribute to a better understanding of formation, thermodynamic stability and equilibrium thickness of intergranular films in CGO. The model descriptions of pure Gd2O3 and CoO are taken from previous assessments of the Gd–O [5,6] and Co–O systems [7]. Pure Gd2O3 exists in four different modifications: C-type Gd2O3 (cubic) up to 1425 K, B-type Gd2O3 (monoclinic) up to 2443 K, H-type Gd2O3 up to 2639 K, and X-type Gd2Co3 up to the melting temperature of 2683 K. Hitherto mutual solubilities of Co in Gd2O3 and Gd in CoO have not been investigated. The Gd2O3–CoO system is eutectic and contains one intermediate compound, oxygen–non-stoichiometric, perovskite–structured gadolinium cobaltite, GdCoO3d. 2. Literature survey Only a few experimental data on the Gd2O3–CoO phase diagram exist. Early experimental investigations of the phase diagram and the thermodynamic stability of gadolinium cobaltite were done by Kropanev and Petrov [8]. The decomposition temperature of gadolinium cobaltite of 1553 K determined by differential thermal analysis (DTA) was corrected to 1528 K by a high-temperature X-ray diffraction (XRD) analysis under isothermal conditions. Kropanev and Petrov [8] further measured the dissociation pressure of GdCoO3d to the oxides Gd2O3 and CoO from 1073 K to 1473 K using electromotive force (emf) measurements in a solid-state galvanic cell with a ZrO2-based electrolyte. Kitayama [9] studied phase equilibria in the system Gd2O3–CoO at 1473 K from pO2 ¼ 1 atm to pO2 ¼ 1012 atm. GdCoO3d was found to be the only ternary compound. Patil et al. [10] determined the Gibbs energy of the formation of GdCoO3 from the oxides in the temperature range 1000–1200 K using a solid-state galvanic cell with an YSZ electrolyte and a Ni–NiO reference electrode. Subasri et al. [11] measured the emf of the same reaction from 1100 to 1200 K using high-purity rare-earth oxides as the starting material for the perovskite synthesis. A two-component cell assembly with a Pt-reference electrode and a calcium-stabilized-zirconia tube was used for the measurements. The results of both studies [8,9] are in good agreement with the data from Kropanev and Petrov [8]. However, there is substantial disagreement between the thermodynamic data of GdCoO3 obtained by Patil et al. [10] and experimental results from Kropanev and Petrov [8] and Kropanev et al. [8,12]. GdCoO3d belongs to the group of perovskite-type rareearth cobaltites. Non-stoichiometries, charge disproportionation of Co, and other thermophysical properties are quite similar in this group of materials, as shown by several studies [13,14]. LaCoO3d perovskite serves as a wellresearched representative of rare-earth cobaltites: Raccah and Goodenough [14] proved the coexistence of low- and high-spin states in LaCoO3, and Bhide et al. [13] performed Mo¨ssbauer studies of cobalt ions in LnCoO3d (Ln = Gd,Co). These authors showed that cobalt ions are

in a low-spin state at low temperatures   and partially transform to a high-spin state Co3+ t42g e2g up to 200 K. Their

findings are, however, in conflict with the results from Abbate et al. [15]. Using soft-X-ray absorption spectroscopy (XAS), the latter authors conclude that LaCoO3d is in the low-spin state at low temperatures, and that from 550 K to 630 K there is a gradual transition to a mixed-spin state, in agreement with previous studies [13,14]. Unlike the former groups [13,14], they found no evidence for charge disproportionation from 80 K to 630 K. Casalot et al. [16] studied GdCoO3 in the temperature range 77–1200 K using combined DTA, XRD, magnetic susceptibility, electric conductivity and thermoelectric power investigations. They stated that the properties of GdCoO3 fit well to Goodenough’s [17] localized electron model. More recently, Korotinet al.[18] proposed the stability of an intermediate-spin t52g e1g

state based on elec-

tronic structure calculations of the perovskite LaCoO3 using a local-density approximation with orbital correction potential (LDA + U) approach. The main result of their calculations is the existence of an intermediate-spin solution which is lower in total energy than the high-spin solution in the temperature range 90–500 K. 3. Experimental GdCoO3 was synthesized from nitrate precursors using a wet-chemical co-precipitation technique: 25.830 g of ethylene diamine tetracetic acid (EDTA) were dissolved in 200 ml 25% ammonia under the release of hydrogen gas. An aqueous solution of 20.0 g Gd(NO3)36H2O (>99.9%, ABCR, CH) and 12.1740 g Co(NO3)36H2O (>99.9%, Fluka, CH) was added to the dissolved EDTA. An intermediate precipitate was formed, which was immediately dissolved after adding citric acid. This solution was heated in an oil bath up to 353 K and then to 413 K. After gelatinization of the solution the heating was stopped. The nitrate precursors obtained were calcined in air at 873 K and milled in an agate mortar. Pellets 10 mm in diameter were pressed at 2 kN axial pressure using a hydraulic press, and then at 800 kN in an isostatic press. The pellets were sintered using the temperature program proposed by Jud [19]. XRD of the powdered specimens using a Siemens D-5000 X-ray diffractometer confirmed that single-phase gadolinium cobaltite was obtained. After sintering in air for 3 days at 1373 K, the average grain size and composition were measured by scanning electron microscopy (SEM). The eutectic temperature was determined using differential scanning calorimetry (DSC; STA 449C Jupiter, NETZSCH GmbH, Germany) in samples with cobalt contents of CoO = 25, 50, and 75 mol.% at pO2 ¼ 0:05; 0:21 and 0.90 atm. All DSC experiments were carried out at a heating rate of 10 K min1 to 1673 K, with subsequent cooling to room temperature employing an equivalent cooling rate. The different oxygen atmospheres in the DSC experiments

T. Ivas et al. / Acta Materialia 58 (2010) 4077–4087

are obtained by a gas mixture of argon (Argon 4.8, PanGas AG, Switzerland), oxygen (Oxygen 5.0, PanGas AG, Switzerland) and 5% H2 in argon (Hydraargon 5, PanGas AG, Switzerland). The gas flow inside the DSC oven is controlled by electromagnetic valves (Bronkhorst AG, Switzerland) connected to a PC computer and operated using the in-house LabView program. The compositions of the eutectic phases were determined using energy dispersive X-ray (EDX) analysis in a scanning electron microscope (Leo Gemini 1530, Carl Zeiss AG, Germany). After preparation using EDTA co-precipitation and calcination, the samples were sintered as described by Jud [19]. The EDX measurements were performed for both fine- and coarsegrained eutectic structures. Three different compositions with cobalt contents of CoO = 60, 65 and 70 mol.% close to the assumed eutectic composition were chosen for exact experimental determination. The DTA samples in the Pt crucibles were heated in flowing air at 10 K min1, subsequently melted and finally cooled to room temperature with 10 K min1. The solubility of CoO in Pt–Co alloys can be large, depending on the oxygen partial pressure and temperature. Based on the experimental data of Schwerdtfeger and Muan [20], the maximum solid solubility of Co in Pt–Co alloy in equilibrium with CoO oxide at 1673 K under normal atmosphere conditions is 7 mol.%. In the present experiments, this value is certainly smaller owing to the short time high-temperature exposure of the specimen (140 min). Furthermore, all polished cross sections imaged by SEM were cut from the central part of the DTA sample, several hundred microns away from the wall of the Pt crucible. For an annealing period of 140 min, the mean penetration depth pffiffiffiffiffiffiffiffiffi ffi of cobalt of 18.5 lm is calculated using Dx ¼ 2D t as an approximation, whereby the chemical diffusion coefficient D  2  1010 cm2 s1 is adopted from Dieckmann [21]. The influence of the Pt crucible on the concentration of CoO in the DTA samples is thus neglected in the present study. The eutectic structures in the images were identified using the ImageJ program [22]. 4. Solid solubilities Gd2O3–CoO samples with CoO contents of 1.5, 3.0, 5.0, 7.5 and 10.0 mol.% were prepared. The samples were annealed at 1223 K and 1513 K for 168 h at ambient oxygen partial pressure. Subsequently, samples were put on a massive copper plate and quenched in a stream of compressed air. The estimated quenching-rate was 200 K s1. The solubility of CoO in Gd2O3 was determined by EDX analysis. The EDX measurements in Gd2O3–CoO samples can result in inaccurate CoO concentrations in Gd2O3: X-ray signals generated by the electron beam are created in a much larger concentric volume around the beam’s focal point; this gives additional signals of CoO due to the neighboring CoO-rich grains in the two-phase samples of Gd2O3–CoO. Thus, XRD was used in addition to verify

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whether the solid solubility of CoO in Gd2O3 obtained by EDX can be reproduced. In order to reduce the influence of grain boundaries and neighboring grains, the measurements of solid solubilities were carried out on grains of average size 20 lm, performing line scans across the grain interfaces. To determine the solubility of Gd2O3 in CoO, CoO-rich samples with Gd2O3 content of 1.5, 3.0 and 5.0 mol.% were investigated using the same routine as above. 5. Results of experiments and discussion The porous microstructure of CoO–Gd2O3 samples sintered for 3 days at 1373 K, as shown in Fig. 1, is caused by cobalt reduction at 1173 K and release of oxygen gas [23]. In the pre-fired powder produced by solid-state synthesis, reduction of Co3O4 to CoO occurred at 1202 ± 1 K. An endothermic peak during heating and an exothermic peak during cooling in syntactic air (21% oxygen–79% argon) are found at 1621 ± 1 K, indicating a eutectic reaction at 1621 ± 1 K in the Gd2O3–CoO system. The results of the DSC experiments at oxygen partial pressures pO2 ¼ 0:05, 0.21 and 0.9 atm are summarized in Table 1. In a reducing atmosphere, the eutectic temperature and the temperature of cobalt reduction are lower. In air at normal atmosphere condition, Gd2O3 contains < 1.5 mol.% CoO at 1173 K, and CoO contains less than 0.5 mol.% Gd2O3 at 1223 K. At 1513 K, the solubility of CoO in Gd2O3 is 2.4 mol.%. The solid solubility of Gd2O3 in the CoO at this temperature is 0.5 mol.%. The maximum Gd2O3 solubility in CoO is very small; it was estimated by EDX to be 0.5 mol.%, which is inside the error range of the machine used. The XRD analyses of the CoO sample with a Gd2O3 content of 1.5 mol.% clearly show the presence of the Gd2O3 phase, thus verifying the small solid solubility obtained by the EDX experiment. The determination of the solid solubility of CoO in Gd2O3 using the method developed by Vegard [24], which is based on the change in lattice parameters in a solid solution relative to the pure phase, did not lead to reliable results, since the change of the lattice parameters due to the solid solution is smaller than the error limit of the XRD device used. However, the extent of solid solution

Fig. 1. Microstructure of Gd2O3–CoO after sintering at 1513 K for 3 days with the overall composition 50 mol.% CoO–50 mol.% Gd2O3.

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Table 1 Summary of the results of DSC measurements at different oxygen partial pressures. CoO (mol.%)

25%

50%

75%

P1

P2

P3

P4

P1

P2

P3

P4

P1

P2

P3

P4

pO2 ¼ 0:05 pO2 ¼ 0:21 pO2 ¼ 0:9

869.1 931.9 968.7

1192.1* 1262.8 1272.7

1242.6 1306.9 1349.7

1386.6 1348.4 1366.7

865.6 930.6 968.6

1181.4 1281.4 1305.4

1263.1 1305.4 1349.7

1392 1348.4 1353.2

869.1 931.9 968.7

1192.1* 1262.8 1272.7

1242.6 1306.9 1349.7

1386.6 1348.4 1366.7

P1 – peak assigned to cobalt reduction, P2 – peak from perovskite decomposition, P3 – not identified, P4 – melting peak. All temperatures are given with precision ±1 °C determined from calibration runs with standard calibrations sets (DIN 570001) [46]. * Not well resolved.

of CoO in Gd2O3 can be estimated using the method of phase identification and peak intensity measurement [25]. The diffractrogram of the first appearing peak is shown in Fig. 2. From the first appearance of peaks belonging to GdCoO3 in a two-phase CoO–Gd2O3 specimen, the solubility of CoO in Gd2O3 was determined as <3 mol.%. More precise measurements by EDX resulted in a solubility of the same order of magnitude. The results of line scans across grain interfaces are shown in Figs. 3 and 4. The spread of data of 0.3 mol.% is relatively small, and the agreement with the EDX point measurements is satisfactory. The eutectic concentration was found by measuring the latent heat of the eutectic reaction for slightly varying CoO concentrations close to the expected eutectic composition. In order to avoid reactions of the specimens with the crucible under normal atmospheric conditions, Pt crucibles were used [7]. Three samples inside the eutectic range showed a fine mixture of a eutectic structure, as well as crystallites of CoO and Gd2O3. Fig. 5 shows the fine eutectic structure and the darker grains of the CoO-rich phase containing 0.21 ± 0.04 mol.% of Gd2O3, in contact with pure CoO. This result was not used in the optimization

Fig. 3. Results of EDX line scan measurements on a quenched solid pellet sintered at 1513 K for 168 h in air. The overall nominal composition of the pellet is 75 mol.% Gd2O3–25 mol.% CoO. The line scan is made across the phase (grain) boundary.

of the model parameters for the phase diagram, since it is believed that this sample was not completely equilibrated. As shown in Fig. 5, the specimen is dominated by a fine eutectic microstructure. This indicates that the eutectic composition is close to the bulk composition of the sample (65 mol.% CoO–35 mol.% Gd2O3). The existence of several large cobalt oxide particles suggests that the composition of the eutectic point is shifted to a composition that is slightly poorer in Co. In order to refine the determination of the eutectic composition, the area fraction of the eutectic was analyzed using the ImageJ program [22]. The large CoO grains are presumably the primary crystals and were thus excluded from the analysis. The image analysis is employed only for the fine eutectic microstructure using the built-in ImageJ function for the area-fraction analysis. The results are summarized in Table 2. Fig. 2. Diffractograms of samples containing CoO = 0.000, 0.015, 0.030, 0.050, 0.075 and 0.100 mol.% annealed at 1173 K for 60 h. The samples with CoO = 0.030, 0.050, 0.075 and 0.100 mol.% contain the phase assemblage GdCoO3 Gd2O3. N, peak positions of GdCoO3 (ICDD JCP2 No. 25-1057); j, peak positions of Gd2O3 (ICDD JCP2 No. 42-1465).

5.1. Thermodynamic modeling In recent work by Grundy et al. [26], the defect chemistry of oxides was treated in the framework of Calculation

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stoichiometry. This point is illustrated in detail in the following section. 5.2. Compound energy model of GdCoO3d In the rare-earth cobaltite ACoO3 (A = La, Pr, Sm, Nd, Eu, Gd) perovskites, only the existence of bivalent and trivalent Co-ions has been confirmed experimentally [27–30]. Thus the formula (Gd3+) (Co3+, Co2+) (O2, Va)3 is used for the description of GdCoO3d, whereby each bracket refers to one crystal sublattice of the general perovskite structure ABO3. Following the compound energy formalism (CEF), the Gibbs energy of the perovskite phase reads: 

GPerov ¼ y Gd3þ y Co3þ y O2  GPerov m Gd3þ :Co3þ :O2 þ y Gd3þ y Co2þ y O2  GPerov Gd3þ :Co2þ :O2 þ y Gd3þ y Co3þ y Va  GPerov Gd3þ :Co3þ :Va þ y Gd3þ y Co2þ y Va  GPerov Gd3þ :Co2þ :Va

Fig. 4. Results of EDX line scan measurements on a quenched solid pellet sintered at 1513 K for 168 h in air at atmospheric pressure. The nominal composition of the pellet is 50 mol.% Gd2O3–50 mol.% CoO. The line scan is made across the phase (grain) boundary.

Fig. 5. Microstructure of the DTA sample with nominal composition 65 mol.% CoO–35 mol.% Gd2O3 which was first prepared as a pellet and heated to 1673 K in air at atmospheric pressure at a heating rate of 10 K min1 and subsequently cooled at the same rate. Dark regions: CoOrich phase that contains 0.21 mol.% of Gd2O3.

Table 2 Summary of the results of SEM measurements of the eutectic concentration; Images were evaluated using ImageJ program [20]. Sample

Area CoO

Area Gd2O3

Aver. area CoO ± Dr

Aver. area Gd2O3 ± Dr

CoO (mol.%/cat%)

018 016 015 013

43.166 41.609 42.583 39.744

56.834 58.391 57.417 60.255

41.7 ± 1.1

58.2 ± 1.1

0.75/0.60

Dr-standard deviation from area measurements (n = 4).

of Phase Diagrams (CALPHAD). Evaluation of an associate model [26] reveals an unphysical dependence of nonstoichiometry on the chosen size of the associates. Still, in specific cases, the associate model of defect chemistry can lead to a better physical description of oxygen non-

þ RT ðy Co3þ ln y Co3þ þ y Co2þ ln y Co2þ Þ þ RT ½3ðy O2 ln y O2 þ y Va ln y Va Þ þ E GPerov m

ð1Þ

where y represents the site fraction of a particular species on the respective sublattice. The second and third to last terms are the configurational entropies of mixing on the oxygen and cobalt sublattices. The last term takes into account the excess Gibbs energy of mixing. This term represents the deviation of the Gibbs energy from an ideal solution, and it is a measure for the magnitude of interactions between the ions in the solution. The equation can be visualized as corners of a compositional square representing four end-members of the perovskite phase, where each  G parameter in Eq. (1) represents one corner, as shown in Fig. 6. Only one neutral end-member exists representing a stoichiometric compound. All other corner end-members are charged and do not exist in nature. The line in Fig. 6 denotes possible compositions of a non-stoichiometric perovskite phase as it reduces from a stoichiometric compound to a fully reduced perovskite GdCoO2.5 allowed by the electroneutrality condition. The total Gibbs energy of the reduced perovskite can be modeled as 1 5  Perov GGdCo2þ O ¼  GPerov þ  GPerov þ A þ BT 3þ 3þ 2þ :Co2þ :O2 5=2 6 Gd :Co :Va 6 Gd  1 1 5 5 þ 3RT ln þ ln ð2Þ 6 6 6 6 where A and B are parameters to be optimized with experiments, representing the enthalpy of formation and the entropy of formation, respectively. The last term describes the configurational entropy which arises due to ideal mixing of O2 and Va on the anion site of the perovskite. The end-member with the highest charge is chosen as reference state, and it is given the value 3  Perov GGd3þ :Co3þ :Va ¼  GPerov   GGas ð3Þ Gd3þ :Co3þ :O2 2 O2 In order to solve Eqs. (2)–(4) unambiguously, an additional equation is required: according to Fig. 6, the center

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  all concentrations except Co0Co and concentration,  Va O are approximately 1 and can thus be  ignored.  Addi- tionally, the charge neutrality relation 2 Co0Co ¼ Va O must hold. Inserting this in Eq. (7) gives the proportional 1=6 ity Va O / p O2 . This result is not in agreement with experimental findings on deviation from oxygen stoichiometry for rare-earth cobaltites ACoO3d [27,31] as a function of oxygen partial pressures. From the experimental results, vacancy concentration dependence on pO2 is the oxygen  VaO / paO2 , where a is between 0.33 and 0.51. 5.3. Compound energy model of GdCoO3d using associates

Fig. 6. Compositional square representing four end-members of the GdCoO3d perovskite phase, where each corner represents the molar Gibbs energy  G of the corresponding end-member. The solid line denotes possible compositions of the non-stoichiometric perovskite phase as it reduces from a stoichiometric compound GdCoO3 to a fully reduced perovskite GdCoO2.5 allowed by the electroneutrality condition. The stoichiometric and fully reduced perovskite are denoted by the black dots.

composition denoted with C can be obtained by mixing equal amounts of either (Gd3+) (Co3+) (Va)3 and (Gd3+) (Co2+) (O2)3 or (Gd3+) (Co3+) (O2)3 and (Gd3+) (Co2+) (Va)3. A system that obeys such a relation is called a reciprocal system. Assuming a chemical reaction ðGd3þ ÞðCo3þ ÞðO2 Þ3 þ ðGd3þ ÞðCo2þ ÞðVaÞ3 $ ðGd3þ ÞðCo2þ ÞðO2 Þ3 þ ðGd3þ ÞðCo3þ ÞðVaÞ3

ð4Þ

the energy of the reciprocal reaction can be given as 

1 5 1 GdxGd þ CoxCo þ 3OxO $ GdxGd þ ðCo2 VaÞCo þ OxO þ O2 ðgÞ 2 2 4 ð9Þ The equilibrium constant of this reaction is 1=4

GPerov þ  GPerov   GPerov Gd3þ :Co3þ :O2 Gd3þ :Co2þ :Va Gd3þ :Co2þ :O2   GPerov ¼ DGr Gd3þ :Co3þ :Va

Following Grundy et al. [26] using the CEF, the perovskite phase can be given the sublattice formula ðGd3þ ÞðCo2 Va4þ ; Co2 O4þ Þ0:5 ðO2 Þ2:5 , where {Co2Va}4+ and {Co2O}4+ are associates; the former describing the fully reduced perovskite that contains only Co2+, and the latter describing the stoichiometric perovskite that contains only Co3+. Using these associates, the reduction reaction of stoichiometric perovskite reads 1 ðGd3þ ÞðCo3þ ÞðO2 Þ3 $ ðGd3þ ÞðCo2 Va4þ Þ0:5 ðO2 Þ2:5 þ O2 4 ð8Þ or using atomic Kro¨ger–Vink notation [32]:

Ka ¼ ð5Þ

If DGr is not equal to zero, the Gibbs energy surface takes on a saddle-like shape. This would result in the solid solution (Gd3+) (Co2+, Co3+) (O2, Va)3 having a positive deviation from ideality without introducing interaction parameters. For this reason, it is advisable to keep the Gibbs energy DGr of imaginary reciprocal reaction equal to zero. Setting the energy of the reciprocal reaction DGr to zero, Eqs. (2)–(4) can be solved, and the Gibbs energies of all ;  GPerov ;  GPerov , end-members  GPerov Gd3þ :Co3þ :O2 Gd3þ :Co2þ :O2 Gd3þ :Co2þ :Va  Perov and GGd3þ :Co3þ :Va are unambiguously determined. The following defect reaction for the reduction of the perovskite phase can be defined (in Kro¨ger–Vink atomic notation [32]): 1 1 1 ð6Þ CoxCo þ OxO ! Co0Co þ Va O þ O2 2 2 4 leading to the equilibrium constant  0  1=2 1=4 CoCo VaO a O2 ð7Þ Kr ¼     1=2 CoxCo OxO p

where aO2 ¼ pO 2 is the activity of the oxygen species, and pO2 O2

is the standard pressure of 1 bar. Assuming a small defect

½Co2 VaCo 1=2 aO2  x  x 3 CoCo ½OO 

ð10Þ

  For small defect concentrations, CoxCo ½OxO  is approxi1=2 mately equal to 1, and the slope ½Co2 VaCo  / aO2 is obtained. 5.4. Compound energy model of the solid solutions The Gd3+ ions are substituted by Co3+ ions on the cationic sublattice owing to the same charge and smaller radii of the ions [31–33]. Thus the simple model was chosen: ðGd3þ ; Co3þ Þ2 ðO2 Þ3

ð11Þ

resulting in the Gibbs energy of CoO-doped Gd2O3 being 

2 O3 2 O3 2 O3 GGd ¼ y Gd3þ  GGd þ y Co3þ  GGd m Co3þ :O2 Gd3þ :O2 2 O3 þ 2RT ðy Gd3þ ln y Gd3þ þ y Co3þ ln y Co3þ Þ þ E GGd m

ð12Þ 2 O3 GGd Gd3þ :O2

The Gibbs energy is given by the Gibbs energy of pure Gd2O3, and the second end-member is described as 1  Gas G þ AGd2 O3 þ BGd2 O3 T ð13Þ 2 O2 where the model parameter AGd2 O3 is the enthalpy of formation, and BGd2 O3 is the entropy of formation. Both are 

2 O3 GGd ¼ 2 GCoO þ Co3þ :O2

T. Ivas et al. / Acta Materialia 58 (2010) 4077–4087

optimized using a least-squares method by fitting experimental results. All polymorphic modifications of Gd2O3 are described with the same model. The solid solution of Gd2O3 in CoO is described by ðCo2þ ; Gd3þ ÞðO2 ; VaÞ

ð14Þ

leading to 

GCoO m

¼ y Co2þ



GCoO Co2þ :O2

þ y Gd3þ



 þ RT ðy Co2þ ln y Co2þ þ y Gd3þ ln y Gd3þ Þ

þ ðy O2 ln y O2 þ y Va ln y Va Þ þ E GCoO m

ð15Þ

where y Co2þ and y Gd3þ are site fractions of Co2+ and Gd3+ on the first sublattice. The second term describes the ideal-configurational entropy of mixing. The last term is the excess Gibbs energy of mixing due to the interaction of ions in the mixture. 5.5. Ionic liquid The two-sublattice ionic liquid model [34,35] is used to describe the liquid phase. Owing to a very strong electrostatic interaction between anions and cations in the ionic liquid, it is assumed that anions and cations occupy distinct lattices and are allowed to mix freely on their respective sublattices. The cobalt species considered in the liquid are Co2+ and Co3+. The Co4+ oxidation state is unlikely to exist in the liquid at normal oxygen partial pressure. It is thus sufficient to include Co2þ and Co3þ in the model, as well as hypothetic vacancies on the anionic sublattice to maintain charge neutrality as the liquid becomes gradually more metallic. In the Gd–Co–O system, the ionic liquid model is represented as ðGd3þ ; Co3þ ; Co2þ Þp ðO2 ; VaÞq , where p and q (the number of sites on the respective sublattice) must vary with composition in order to maintain charge neutrality. The values of p and q are calculated as follows: p ¼ 2y O2 þ qy Va q ¼ 3y Gd3þ þ 2y Co2þ þ 3y Co3þ The hypothetical vacancies have an induced charge equal to q. As pointed out by Hillert et al. [34,35], this model is unrealistic, particularly in the case when the number of ions on one of the sublattices decreases to low values. Still, this model proved valuable, as it yields a satisfactory thermodynamic description of the liquid phase in many ionic systems [35,36]. The molar Gibbs energy of the liquid is given by 

with the excess Gibbs energy E GLm being E

GLm ¼ y Co2þ y O2 y Va  Lliq Co2þ :O2 ;Va þ y Co3þ y O2 y Va  Lliq Co3þ :O2 ;Va þ y Gd3þ y Co3þ y O2  Lliq Gd3þ ;Co3þ :O2 þ y Gd3þ y Co2þ y O2  Lliq Gd3þ ;Co2þ :O2

2 O3 GGd Gd3þ :O2

GLm ¼ qy Gd3þ y Va  GLGd3þ :Va þ qy Co3þ y Va  GLCo3þ :Va þ qy Co2þ y Va  GLCo2þ :Va þ y Gd3þ y O2  GLGd3þ :O2

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ð17Þ

Only two interaction parameters,  Lliq and Gd3þ ;Co3þ :O2 were required to reproduce the experimental phase diagram data.  liq LGd3þ ;Co2þ :O2

5.6. Optimization of the model parameters The complete set of optimized thermodynamic parameters for the Gd2O3–CoO system is given in Table 3. The optimization was done using the PARROT module of the ThermoCalc program [37]. PARROT can take into account all the thermodynamic and phase diagram data simultaneously and minimizes the weighed sum of squared errors. The new temperature value for the decomposition of gadolinium cobaltite was used, together with the consistent thermodynamic data from Petrov et al. [38] and Subasri et al. [11] for the optimization of the A and B model parameters of the perovskite phase. Using the data for oxygen non-stoichiometry of the GdCoO3d [39], the A and B parameters of the reduced end-member were optimized. The available experimental data are well reproduced by the associate model, resulting in a slope of 1/2 for the concentrations of oxygen vacancies as a function of aO2 . This slope was also stated for LaCoO3d, which has similar thermophysical properties to GdCoO3d. Furthermore, the present results are in line with previous experimental findings for other rare-earth cobaltites, which consistently show slopes very close to 1/2 in a bi-logarithmic plot of the oxygen deficiency d as a function of aO2 . The model parameters of the solid solubility of CoO in Gd2O3, AGd2 O3 and BGd2 O3 in Eq. (13) were optimized using experimental data measured in this study. The experimentally determined eutectic temperature and compositions were used to optimize regular and sub-regular interaction parameters of the liquid phase. As it is assumed that interaction energies between Co2+–Gd3+ and Co3+–Gd3+ ions have comparable values in the oxide melt, both regular and sub-regular interaction parameters were given the same value. The regular interaction parameter was used to optimize the calculated eutectic temperature, and the sub-regular interaction parameter was used to reproduce the calculated eutectic composition. 6. Modeling results and discussion

þ y Co3þ y O2  GLCo3þ :O2 þ y Co2þ y O2  GLCo2þ :O2 þ pRT ðy Gd3þ ln y Gd3þ þ y Co2þ ln y Co2þ þ y Co3þ ln y Co3þ Þ þ qRT ðy O2 ln y O2 þ y Va ln y Va Þ þ E GLm ð16Þ

The calculated phase diagram is shown in Fig. 7, together with experimental solubility data obtained in this study. The calculated eutectic temperature is 1621 ± 1 K, and the eutectic composition is 60 ± 2 mol.% CoO. The

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Table 3 Thermodynamic parameters of the Gd2 O3 CoO systema. 

 CoO 2 O3 GGd CoO ¼ GCoO þ 14:24T



2 O3 GBGd ¼ 1858111 þ 620:0992T  114:534T lnðT Þ  0:007203T 2 þ 540000T 16 Gd2 O3



2 O3 GCGd ¼ 1868812 þ 660:0623T  119:1688T lnðT Þ  00006438T 2 þ 772000T 16 Gd2 O3

A  Gd2 O3 : ðGd3þ ; Co3þ Þ2 ðO2 ; VaÞ3 

2 O3 2 O3 GAGd ¼  GBGd þ 6300  20579T Gd:O Gd2 O3



2 O3 2 O3 GAGd ¼ 12  GO2 Gas þ 2 GGd CoO Gd:O

B  Gd2 O3 : ðGd3þ ; Co3þ Þ2 ðO2 ; VaÞ3 

2 O3 2 O3 GBGd ¼  GCGd Gd:O Gd2 O3



 Gd2 O3 2 O3 GBGd ¼ 12 GGas O2 þ 2 GCoO Co:O

C  Gd2 O3 : ðGd3þ ; Co3þ Þ2 ðO2 ; VaÞ3 

2 O3 2 O3 GCGd ¼  GCGd Gd:O Gd2 O3



 Gd2 O3 2 O3 GCGd ¼ 12  GGas O2 þ 2 GCoO Co:O

H  Gd2 O3 : ðGd3þ ; Co3þ Þ2 ðO2 ; VaÞ3 

2 O3 2 O3 GHGd ¼  GBGd þ 41000  16:565T Gd:O Gd2 O3



Gd2 O3 2 O3 GHGd ¼ 12 GGas O2 þ 2GCoO Co:O

X  Gd2 O3 : ðGd3þ ; Co3þ Þ2 ðO2 ; VaÞ3 

Gd2 O3 2 O3 GXGd:O ¼  GBGd þ 53031  21:134T Gd2 O3



Gd2 O3 Gd2 O3 GXCo:O ¼ 12  GGas O2 þ 2GCoO

CoO : ðCo2þ ; Gd3þ ; VaÞ1 ðO2 Þ1 

 CoO GCoO Co:O ¼ GCoO



1  CGd2 O3 GCoO  14 GGas Gd:O ¼ 2 GGd2 O3 O2 þ 95930 þ 10764T



1  Gas GCaO Va:O ¼ 0 þ 2 GO2

Perovskite GdCoO3 : ðGd3þ ÞðCo2þ ; Co3þ ÞðO2 ; VaÞ3 

1 Gas 2 O3 GGdCo3 ¼ 12  GBGd þ GCoO CoO þ 4 GO2  65739 þ 4091T Gd2 O3



GPerov ¼ GGdCoO3 Gd3þ ;Co2 :O2



1 Gas 2 O3 GPerov ¼ 12  GBGd þ GCoO CoO þ 4 GO2 þ 131635  550062T Gd2 O3 Gd3þ ;Co2 :O2



GPerov ¼ GGdCoO3  32 GGas O2 Gd3þ :Co3þ :Va



5 Gas 2 O3 GPerov ¼ 12  GBGd þ GCoO CoO  4 GO2 þ 11:238T Gd2 O3 Gd3þ :Co2þ :Va

Perovskite(Associate model) GdCoO3 : ðGd3þ ÞðCo2 Va4þ ; Co2 O4þ Þ0:5 ðO2 Þ2:5  

GAPerov Gd3þ:Co GAPerov Gd3þ :Co

2O

2O

4þ

4þ

:O2

:O2

2  CoO 2 O3 ¼ 12  GBGd þ 12 GGas O2 þ GCoO  63850 þ 39:08T þ 0:03T Gd2 O3 2 O3 ¼ 12  GBGd þ GCoO CoO  16236:2 þ 25:44T Gd2 O3

Liquid: ðGd3þ ; Co2þ ; Co3þ Þp ðO2 ; VaÞq  Liq LCo2þ :O2 ;Va ¼ 182675  30:556T  Liq LCo3þ :O2 ;Va ¼ 54226  20T  Liq LGd3þ :Co3þ :O2 ¼ 47526 1 Liq LGd3þ :Co3þ :O2 ¼ 70365  Liq LGd3þ :Co2þ :O2 ¼ 47526 a

All parameters are in SI units: J, mol and K.

calculated Gibbs energy of formation for GdCoO3d is compared with the experimental results in Fig. 8. The use of experimental data from Petrov et al. [38] and Subasri et al. [11] for the optimization of model parameters resulted

in the smallest discrepancies between calculated results and experimental data. The experimental data of Patil et al. [10] are in disagreement with previous experimental data and thus were not used for the optimization.

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Fig. 7. (a) Isothermal section of the Gd–Co–O phase diagram at 1373 K. The dashed lines correspond to the quasi-binary section Gd2O3–CoO at an oxygen content in air. (b) Optimized quasi-binary Gd2O3–CoO phase diagram at atmospheric pressure, compared with experimental data. , , Phase boundaries determined by EDX; , , , phase transitions analyzed by DSC measurements at 25%, 50% and 75 mol.% Co, respectively.

Fig. 8. Calculated Gibbs energy of formation of GdCoO3 by the reaction 1/2Gd2O3 + CoO + 1/4O2(g) ? GdCoO3 as a function of temperature.

Many studies proposed the disproportionation of trivalent Co to Co2+ and Co4+ to describe the variation of the electrical conductivity, magnetic susceptibility and Mo¨ssbauer spectra [14,40]. In contrast to this, the XAS spectra of Co-ions in ACoO3 show that the formal charge of Co remains Co3+ up to temperatures of 1073 K, and it was not possible to obtain clear evidence for the charge disproportionation of the Co ions [27]. Sehlin et al. [40] argued that the electron hopping frequency for an adiabatic small

polaron conductor is larger than the relevant phonon frequency, and thus only average valence or spin states can be observed. Experimental findings of charge disproportionation in ACoO3 perovskites are inconclusive, and more investigations with higher-energy resolution spectra are necessary to probe the state of the Co-ions via LII,III X-ray adsorption [27]. As proposed by Grundy et al. [26], the defect chemistry of the perovskite phases can be modeled using the associate model. When using the associate model, the choice of associates is somewhat arbitrary, as in most cases these are not physically meaningful entities. However, choosing associates based on sound physical arguments is essential for good approximation of a real system. In a recent work, Zuev et al. [41] measured the Seebeck coefficient and electronic conductivity in undoped and doped lanthanum cobaltites. The non-linear fit of the Seebeck coefficient data gives a small negative value for the non-configurational entropy term in doped and undoped lanthanum cobaltites. This indicates the possibility of the formation of the defect associate fCo0Co Va g in the LaCoO3d perovskite owing to the following considerations: at the high temperature of 1323 K, the non-configurational entropy has a lowest value and increases with decreasing temperature. Hence, at lower temperatures the oxygen vacancy will frequently be nearby two Co2+ ions, forming the “imaginary” associate {Co2Va}4+. The charge 4+ stems from the CALPHAD convention that vacancies do not carry any charge. This puts the choice of {Co2Va}4+ as the dominant defect in the associate model on a physically meaningful base. The associate model of GdCoO3d correctly describes the defect chemistry from high towards low oxygen partial pressures. In contrast to the description of Yang et al. [32],

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Fig. 9. Deviation from oxygen stoichiometry of GdCoO3d perovskite modeled using the associate and compound energy model plotted for 1073 K, 1173 K and 1273 K as a function of pO2 , with experimental data included (symbols). The slopes of 1/2 (associate model) and 1/6 (CEF model) of the calculated oxygen non-stoichiometry are indicated by triangles.

who required a very large charge disproportionation of Co3+ to Co2+ and Co4+ in order to reproduce the non-stoichiometry data correctly, the associate model used in this work does not take into account charge disproportionation. This is reasonable, since the occurrence of significant disproportionation of Co3+ to Co2+ and Co4+ in rare-earth cobaltites is doubtful [15]. The associate model correctly employed in this study describes the experimentally determined defect chemistry of GdCoO3d, as shown in Fig. 9. The slope in the log(d ) vs. logðaO2 Þ diagram is determined by the configurational entropy of the model description. As the concentration of defects is small, the slope cannot be influenced by introducing interaction parameters. The physical situation that the associate model describes in the case of the GdCoO3d perovskite is that two Co0Co and one Va O defects act like a single particle even at low concentrations, meaning that there must be a strong interaction between the two defects. The CEF model, in contrast, assumes that the two defects are independent of one another, so they both contribute to the configurational entropy leading to the slope of 1/6 in the log(d) vs. logðaO2 Þ diagram. The model that is most appropriate for a given case is the one that reproduces the experimental data best. In the case of GdCoO3d, the associate model is more appropriate, indicating that there is a strong interaction between the oxygen vacancy and two Co0Co defects. It is also known for some other ionic systems that the CEF description leads to entropies that are too high. In

the Zr–O system, the description (Zr4+, Zr3+) (O2, Va)2 of the fluorite phase leads to a pronounced maximum in the calculated melting temperature of the non-stoichiometric fluorite phase that is in contradiction with experimental data. This maximum is caused by an entropic stabilization of the fluorite phase, indicating that the configurational entropy is overestimated when describing the phase with this model. Chen et al. [45] amended this problem by describing the fluorite phase using the description (Zr4+, Zr0) (O2, Va)2, which reduced the configurational entropy. Another possibility would have been to describe the phase using an associate description. The associate description would assume that the oxygen vacancies remain associated with the reduced Zr even at low defect concentrations. However, the calculation of defect chemistry using the model (Gd3+) (Co3+, Co2+)(O2, Va)3 leads to a slope of 1/6, which is in contradiction to experimental data. However, previous modeling showed that CEF can be used to describe a wide range of defect chemistries in the perovskite phases. The compound energy model (Av+, Va) (Bv+, Va) (O2, Va)3 illustrated by the work of Grundy et al. [42,43] on LaMnO3 and (La, Sr)MnO3 and the work of Yang et al. [44] on LaCoO3–d demonstrated that the CEF is capable of modeling oxygen deficiency, cation deficiency and charge disproportionation of perovskite phases. The main advantages and disadvantages of the CEF compared with the associate model have been discussed comprehensively in a paper by Grundy et al. [26]. In the case of ionic materials where many different defects can arise as a result of multiple valence states of ions, the CEF model might be more appropriate, as for the LaMnO3 perovskite, for example [43]. A remaining open question for further studies is how CEF and associate models can be combined in a consistent way to reproduce several types of interactions between defects. 7. Conclusions The limits of mutual solid solubilities of Gd2O3 and CoO have been determined as a function of temperature using combined EDX and XRD measurements up to 1513 K. DSC measurements were performed to determine the eutectic temperature and composition. The eutectic composition was determined by measuring the eutectic volume fraction in SEM images of different samples close to the eutectic concentration. Further, the decomposition temperature of gadolinium cobaltite has been determined in air, T = 1538 ± 5 K, and at different oxygen partial pressures. Using these experimental data and selective data from the literature, the authors optimized the model parameters of the Gd2O3–CoO system and calculated the phase diagram. The calculated phase diagram is in very good agreement with the experiments. Two different descriptions of the defect chemistry of GdCoO3d have been presented: the CEF does not reproduce the experimental oxygen non-stoichiometry data of

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gadolinium cobaltite. However, it was shown that the associate model satisfactorily reproduces the experimental results, with a smaller number of optimized parameters compared with the CEF model. It remains to be tested whether the associate model can be applied also to ACoO3 (A = La, Pr, Sm, Nd, Eu) perovskites, especially at lower temperatures were the charge disproportionation of cobalt is fairly small. Acknowledgements The authors acknowledge financial support by the Swiss National Foundation (SNF Project Nr. 200021-109707/1). References [1] Godickemeier M. Solid State Ionics 1996;86:691. [2] Godickemeier M, Sasaki K, Gauckler LJ, Riess I. J Electrochem Soc 1997;144:1635. [3] Chen M. Understanding the thermodynamics at the LaMnO3–YSZ interface in SOFC. Department of Materials, ETH Zurich; 2005. [4] Jud E, Gauckler LJ. J Electroceram 2005;15:159. [5] Zinkevich M. Private communication; 2006 [6] Zinkevich M, Djurovic D, Aldinger F. 7th European SOFC Forum Lucerne 2006; Paper P0512. [7] Chen M, Hallstedt B, Gauckler LJ. J Phase Equilib 2003;24:212. [8] Kropanev AY, Petrov AN. Inorg Mater 1983;19:1782. [9] Kitayama K. J Solid State Chem 1988;76:241. [10] Patil A, Dash S, Parida SC, Venugopal V. J Alloys Compd 2004;384:274. [11] Subasri R, Pankajavalli R, Sreedharan OM. J Alloys Compd 1998;269:71. [12] Kropanev AY, Petrov AN, Zhukovskii VM. Zh Neorg Khim 1983;28:2938. [13] Bhide VG, Rajoria DS, Reddy YS. Phys Rev Lett 1972;28:1133. [14] Raccah PM, Goodenough JB. Phys Rev 1967;155:932. [15] Abbate M, Fuggle JC, Fujimori A, Tjeng LH, Chen CT, et al. Phys Rev B 1993;47:16124. [16] Casalot A, Dougier P, Hagenmuller P. J Phys Chem Solids 1971;32:407. [17] Goodenough JB. Mater Res Bull 1971;6:967. [18] Korotin MA, Ezhov SY, Solovyev IV, Anisimov VI, et al. Phys Rev B 1996;54:5309.

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