J. MATER. CHEM., 1995,5(7), 1059-1062 1059

Solid-state Miscibility Gap and Thermodynamics of the System BaO-SrO

K. T. Jacob* and Viji Varghese Department of Metallurgy, lndian lnstitute of Science, Bangalore 560 072, lndia

A solid-state miscibility gap in the pseudo-binary system BaO-SrO is delineated by X-ray diffraction studies on samples equilibrated either in vacuum or under flowing inert gas at temperatures between 1073 and 1423 K. For the Sr,Ba, -xO solid solution an asymmetric phase boundary, characterized by a critical temperature of 1356 ( k 4 ) K and composition x = 0.55 ( 0.008), is obtained. Thermodynamic mixing properties of the solid solution, derived from the experimental phase boundary compositions and temperatures, can be represented by the expression:

AGE =x(l -x){33 390 - 7.09T)x + (29 340 -6.23T)(1 -x)} J mol -' It is necessary to include excess entropy terms to obtain a good fit to the experimental data. The chemical spinodal

curve is computed from the thermodynamic parameters.

Many high-temperature oxide superconductors contain alka- line-earth-metal oxide components. The thermal and transport properties of the superconductors can be altered for specific applications by appropriate cation substitution. Barium can often be substituted for strontium and vice versa. A knowledge of phase relations is useful for optimizing the parameters for synthesis and processing of superconductors. However, a prerequisite for the study of phase relations in complex systems is the adequate definition of the phase diagrams for the pseudo-binary and ternary subsystems. As part of a series of systematic studies on the phase equilibria and thermo- dynamic properties of systems relevant to the development of high- T, oxide superconductor^,'-'^ miscibility gap and mixing properties in the pseudo-binary system BaO-SrO are explored. Because of the relatively large difference in cationic radius [r(Ba2')=0.136 nm and r(Sr2+)=0.116 nm on the Shannon-Prewitt scale14 for six-fold coordination], a com- plete range of solid solubility is not expected in this system at lower temperatures. However, there is no report in the literature on the experimental determination of binodal and spinodal boundaries of the BaO-SrO system. Previous studies on Sr,Ba, -,O solid solutions include acid solution calorimetry by Flidlider et ~ 1 . ' ~ and mass spectrometric analysis of the equilibrium vapour composition at elevated temperatures.16

Study of the pseudo-binary system BaO-SrO requires careful control of the gas phase. Both of the alkaline-earth- metal monoxides react with oxygen to form the corresponding peroxides. At elevated temperatures, there is significant mutual solubility of the monoxide and peroxide phase^.'^.'' Thus, a low oxygen potential has to be maintained in the gas phase to prevent the incorporation of excess oxygen into the monox- ide phase at high temperatures. Moreover, both oxides readily react with moisture and oxides of carbon and sulfur present in the air. To prevent contamination, processing of the oxides was carried out in an inert-gas glove box. In this study, the samples are annealed at high temperature either in vacuum or in a stream of prepurified argon gas.

Experimental Materials

The starting materials were BaCO, and SrCO, of 99.99% purity. The monoxide solid solutions were prepared by ball- milling appropriate mixtures of carbonates for 2 h, and then decomposing the mixed carbonate in vacuum at 1073 K. A

platinum crucible was used to hold the carbonate mixture. The resulting oxide mixtures were compacted into pellets using a steel die in an inert-gas glove box. The pellets were heat-treated under flowing inert gas at 1573 K for two days and rapidly cooled to room temperature. The formation of solid solutions is confirmed by X-ray diffraction (XRD). The samples were kept in a closed sample holder during X-ray analysis.

Argon gas of 99.99% purity was passed over NaOH to remove trace C 0 2 and over anhydrous Mg(C104), and P205 to remove trace H 2 0 . The inert gas was then deoxygenated by passing it through columns of Cu wool at 723 K and Ti granules at 1150 K.

Operations and Procedures

The variation of the lattice parameter of the solid solution Sr,Ba, -,O with composition was established by XRD analysis of the samples quenched from 1573 K. The X-ray diffraction patterns were obtained using Cu-Ka radiation. Metallic silicon was mixed with the powder sample for XRD, and this acted as an internal standard so that accurate cell dimensions could be obtained by least-squares refinement of the d-spacings.

For the determination of the phase diagram, homogeneous single-phase samples of equimolar composition were annealed at 11 temperatures between 1073 and 1423 K, for various periods of time. At 1073 K the samples were equilibrated for 60 days, while at 1423 K they were annealed for three days. The equilibration periods at various temperatures were chosen so as to ensure that phase separation goes to completion, as judged on the basis of X-ray analysis. Larger annealing times do not cause any further change in the lattice parameters of coexisting phases. The equilibration was carried out either in vacuum or in flowing argon. A small mass loss was detected for samples heat-treated in vacuum at temperatures above 1523 K. The oxygen partial pressure in the inert gas was determined to be 3 x lop7 Pa, using an oxygen sensor based on stabilized zirconia. The lattice parameters of the coexisting solid solutions for a given thermal treatment were used to deduce the respective solvus compositions. Further confir- mation about the solvus temperature can be obtained by heat-treating samples containing between 20 and 80 mol% SrO at different temperatures and ascertaining whether they are single or two-phase. A few samples were examined under a scanning electron microscope (SEM) with energy-dispersive analysis of X-rays (EDAX) capability. The composition and

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1060 J. MATER. CHEM., 1995, VOL. 5

homogeneity of adjacent grains can be checked using SEM and EDAX.

Results and Discussion Lattice Parameters

The variation of the lattice parameter for the monoxide phase with composition at room temperature is shown in Fig. 1. The accuracy of the lattice parameter measurement is +0.0001 nm. The results exhibit a small positive deviation from Vegard's law. However, molar volume is a linear function of composition within experimental uncertainty limits, in accordance with Retger's law. Fig. 1 is used subsequently as the calibration curve for determining phase compositions from the measured lattice parameters of phase-separated samples.

Miscibility Gap

A solid-state miscibility gap is observed in the system BaO-SrO at temperatures below 1356 (+4) K. The same composition of coexisting phases at a given temperature is obtained when the samples are equilibrated in vacuum or in flowing argon gas. Fig. 2 shows the phase diagram determined primarily on the basis of lattice parameter measurements. The miscibility gap is asymmetric, with the critical composition corresponding to 0.55 (k0.008). No attempt is made in this study to follow the kinetics of phase separation. To confirm the phase boundary, several compositions were heat-treated at temperatures above the solvus and one composition was treated below the solvus. All the compositions lying above the miscibility gap were found to be single phase. To locate the critical temperature, solid solution samples characterized by x=0.55 were heat-treated at two temperatures below 1356 K. These were found to decompose into two phases with identical space group, but differing lattice parameters.

EDAX results for several large grains of each unexsolved solid solution indicated that the composition was uniform (&0.5%). The analysis of the coexisting phases after exsolution was less accurate (& 5 % ) because of the finer microstructural features. After prolonged annealing at 1315 K to coarsen the microstructure, the coexisting phases were found to be charac-

0*560 I"'"''''

0.510 1 BaO 0.2 0.4 0.6 0.8 5

X 0

Fig. 1 Variation of the lattice parameter of the solid solution Sr,Ba, -,O with composition. ( - - - ) Vegard's law.

1500!7-7--7 1400

1300 -

1200 -

1100 -

1000 -

900 -

E

BaO 0.2 0.4 0.6 0.8 SrO X

Fig. 2 Experimental phase boundary compositions (0 ) for the system BaO-SrO (Sr,Ba, -xO). (0) single-phase region samples; (m) two- phase region samples. The computed binodal and spinodal curves using subregular (- - - ) and pseudo-subregular (-) models are compared.

terised by x = 0.38 (t- 0.06) and x = 0.73 (f 0.05), in reasonable agreement with the solvus in Fig. 1. The compositions from EDAX are less precise than those obtained by XRD.

Thermodynamic Properties

The phase diagram can be used to derive the thermodynamic mixing properties of the solid solution. Since the miscibility gap is asymmetric, the simplest formalism that can be used is the subregular solution model proposed by Hardy," which contains two parameters to describe the enthalpy of mixing. The strictly subregular model, with ideal entropy of mixing of the cations, does not give a good fit to the experimental miscibility gap. If the model parameters are derived using the critical temperature and composition as inputs, the calculated miscibility gap is narrower than the experimental curve as shown in Fig. 2. To improve the fit the excess entropy terms are introduced. Four parameters of the model have to be derived from the experimental phase boundary compositions. To reduce the number of parameters to three, the ratio (t) of the enthalpy term in the expression for the excess Gibbs energy of mixing to the corresponding excess entropy term is kept at a fixed value. Each excess entropy term can then be expressed as the product of the corresponding enthalpy and the ratio (z). It is well established that the value of z is approximately constant for systems of similar type.20,21 In this scheme, the enthalpy and entropy have the same sign, in accordance with the general enthalpy compensation prin- ciple.20*2' Using an optimization procedure, values of the two enthalpy terms and z are obtained from the measured phase boundary compositions. The optimized value for z is 4710 K. This corresponds to a fictitious temperature at which the solution becomes ideal. The derived temperature does not have a real physical significance, since the parameters obtained by fitting the experimental phase boundary in the temperature range 1073-1356K cannot obviously be used to predict the behaviour at 4710 K. The optimized parameters are then used to calculate the phase diagram. The computed phase diagram is shown in Fig. 2.

The excess Gibbs energy of mixing obtained by an optimiz-

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J. MATER. CHEM., 1995, VOL. 5 1061

ation procedure, can be represented as:

AGE=X(l - ~ ) ( ( 3 3 390-7.09T)x+(29 340-6.23T) (1-x)}

J mol-' (1)

The temperature-independent terms give the enthalpy of mixing, while the temperature-dependent terms correspond to excess entropy. Only a fraction of the enthalpy of mixing is manifested as excess Gibbs energy at high temperatures. The solution exhibits positive deviations from ideality. The extent of deviation decreases with temperature. The chemical spino- dal curves calculated using the strictly subregular and pseudo- subregular solution models are compared in Fig. 2. The spinodal curves for each model lies inside the corresponding binodal curves. Along the spinodal curves, a2G/ax2 = 0.

The pseudo-subregular model gives the best fit to the experimental input. Van der Kemp et aLI6 measured the ion intensity ratio, R = (ISr+/lBa +), as a function of temperature for eight compositions of the solid solution with rock-salt structure. Since the slopes of log R us. the reciprocal of absolute temperature did not exhibit systematic variation with composition, only the excess Gibbs energy of mixing at 1490 K was deduced from the data.16 The excess Gibbs energy given by eqn. ( 1 ) is compared with the data obtained by Knudsen- cell mass spectrometry at 1490 K in Fig. 3. Although the mass spectrometric measurements have been interpreted in terms of a regular solution model with symmetric excess Gibbs energy, in contrast to the subregular solution model used in this study, there is fair agreement between the two sets of data.

The enthalpy of mixing obtained in this study is compared with calorimetric data" in Fig. 4. The function AH/x( 1 -x) is plotted against composition. The calorimetric data show an asymmetric heat of mixing, with more positive values for BaO-rich compositions. This is unlikely, since the replacement of a smaller cation by a larger one generally results in a more pronounced positive enthalpy change than substitution of a larger cation by a smaller one. The values deduced in this study are in agreement with theoretical expectations. The calorimetric data may be affected by the possible contami- nation of the monoxide sample by peroxide. The monoxide is unstable at room temperature and a coating of peroxide phase on the surface is expected if special precautions are not taken.

E3aO 0.2 0.4 0.6 0.8 SrO X

Fig.3 Comparison of the excess Gibbs energy of mixing for the system BaO-SrO (Sr,Ba,_,O) obtained in this study (-) with data obtained by Knudsen-effusion mass spectrometry ( - - - ) at 1490 K16

7 I

*O t 1 t 01 ' 1 1 ' 1 ' ' ' J 6aO 0.2 0.4 0.6 0.8 SrO

X

Fig. 4 Comparison of the enthalpy of mixing for the system BaO-SrO (Sr,Ba,-,O) deduced from analysis of the phase diagram (-) with calorimetric data (0) of Flidlider et al." and the estimate ( - - - ) of Van der Kemp et ~ 1 . ' ~

There is also the possibility of contamination by hydroxide, carbonate and sulfate as result of interaction with moisture, C 0 2 and SO2 present in air. Van der Kemp et ~ 1 . ' ~ have evaluated a symmetric expression for the enthalpy of mixing based on the calorimetric data of Flidlider et a l l5 This value is also shown in Fig. 4; however, the rationale for their evaluation'6 is unclear.

Summary The subsolidus miscibility gap in the BaO-SrO system is determined. The phase boundary is slightly asymmetric, with the critical composition occurring at 55 (k0.8) mol% SrO. The critical temperature is 1356 (+4) K. A pseudo-subregular solution model, with excess entropy terms, is found to fit the experimental data. The excess Gibbs energy at 1490 K obtained from phase diagram analysis is found to be in reasonable agreement with recent data obtained using Knudsen-cell mass spectrometry.'6

References

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K . T. Jacob and T. Mathews, J . Am. Ceram. Soc., 1992,75,3225. T. Mathews, J. P. Hajra and K. T. Jacob, Chem. Muter., 1993, 5, 1669. G. M. Kale and K. T. Jacob, Chem. Muter., 1989,1,515. K. T. Jacob, T. Mathews and J. P. Hajra, Metall. Trans., Sect. A, 1993,24,1655. T. Mathews and K. T. Jacob, J . Am. Ceram. Soc., 1994,77, 133. T. Mathews and K. T. Jacob, J. Muter. Rex , 1993,8, 3015. K. T. Jacob, T. Mathews and J. P. Hajra, High Temp. Muter. Process., 1993, 12,251. K. T. Jacob, T. Mathews and J. P. Hajra, J . Muter. Chem., 1993, 3, 1025. T. Mathews and K. T. Jacob, Metall. Trans., Sect. A , 1992, 23, 3325. G. M. Kale and K. T. Jacob, Solid State lonics, 1989,34, 167. K. T. Jacob and T. Mathews, J . Muter. Chem., 1991,1,545. K. T. Jacob and Y. Waseda, J. Phase Equilibr., 1994,15,401. K. T. Jacob and P. M. Raj and Y. Waseda, J . Phase Equilibr., 1995, 16, in the press. R. D. Shannon and C. T. Prewitt, Acta Crystallogr., Sect. B, 1969, 25,925.

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15 G. V. Flidlider, T. V. Kovtunenko, E. V. Kiseleva and 19 H. K. Hardy, Acta Metall., 1953, 1, 202. A. A. Bundel, Russ. J . Phys. Chem., 1966,40, 1329.

16 W. J. M. Van der Kemp, H. A. J. Oonk, C. Bergman and R. Chastel, J . Chem. Thermodyn., 1992,24, 857.

17 0. V. Kedrovskii, I. V. Kovtunenko, E. V. Kiseleva and Academic Press, London, 1974, vol. 1, p. 167; 185. A. A. Bundel, Russ. J. Phys. Chem., 1967,41,205.

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Paper 4/07628A; Received 14th December, 1994

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