Thermodynamic investigation of ZrO₂-BaO system

GONG Wei-ping(龚伟平), CHEN Teng-fei(陈腾飞), JIN Zhan-peng(金展鹏)

State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China

Received 28 June 2006; accepted 11 January 2007

Abstract: Thermodynamic description of ZrO₂-BaO system was developed using the available experimental information. Special attention was paid to the modelling of the perovskite phase BaZrO₃ by a temperature-dependent polynomial to fit the experimental thermodynamic properties. The liquid phases, C_SS (cubic ZrO₂ solid solution) and T_SS (tetragonal ZrO₂ solid solution) were modelled with Redlich-Kister formula. The compounds Ba₂ZrO₄ and Ba₃Zr₂O₇ were treated as stoichiometric phases and the BaO_SS and M_SS (halite BaO and monoclinic ZrO₂ solid solutions) were treated as pure compounds. Comparisons between the calculated and the measured phase diagram as well as the thermodynamic quantities indicate that the most reliable experimental information is satisfactorily accounted for by the present thermodynamic calculation.

Key words: ZrO₂-BaO system; thermodynamic description; perovskite phase; Redlich-Kister formula

1 Introduction

Doped with certain amount of MgO, CaO, SrO, BaO, Y₂O₃ or CeO₂, the disruptive martensitic phase transformation of pure ZrO₂ from monoclinic to tetragonal can be suppressed, thus the mechanical properties are greatly improved[1]. While the mechanical properties of partially stabilized zirconia(PSZ) or tetragonal zirconia polycrystals(TZP) with a smaller amount than needed to produce fully stabilized zirconia, are quite different from each other[2-4]. Obviously, the knowledge of the phase diagram and thermodynamic properties is of fundamental importance to define the processing conditions for making these materials and subsequent treatments to obtain optimal engineering properties. Associated with the sluggish kinetics at low temperatures, the formation of meta-stable phases, and the difficulties in conducting experiments at high temperatures, etc, the phase equilibria in ZrO₂-included systems have been proved to be difficult to determine with certainty. Since only calorimetry, the electromotive force and mass spectrometry are practicable, measurements of the thermodynamic properties in ZrO₂-included systems are also not easy from the experimental point of view. When the present investigation was initiated, the literature experimentally dealing with the ZrO₂-BaO system gave an incomplete and confusing picture[5-8]. In this work, the Calphad technique was employed to determine the phase relations and thermodynamic properties in ZrO₂-BaO system with the aim to assess the thermodynamic properties of the various phases in the ZrO₂-BaO system and to provide the optimized thermodynamic parameters, which can reproduce the reliable experimental phase diagram, thermodynamic data and structural information satisfactorily.

2 Evaluation of experimental data in literature

2.1 Phase diagram information

PASCHOAL et al[6] and SHEVCHENKO et al[7] were responsible for the major contributions to understanding the ZrO₂-BaO liquidus phase diagram. By means of optical microscopy, X-ray diffraction(XRD) and differential thermal analysis(DTA) techniques, PASCHOAL et al[6] measured the liquidus in the BaO-rich side. Using the DTA method, SHEVCHENKO et al[7] constructed a series of the phase diagrams of ZrO₂/HfO₂-based systems, and the attention was paid to the ZrO₂-rich side. The ZrO₂-BaO liquidus equilibria reported by SHEVCHENKO et al[7] were in good agreement with those measured by WARTENBERG et al[8]. Based on the available experimental information, the ZrO₂-BaO system was characterized by BaZrO₃ and Ba₂ZrO₄ compounds, in which BaZrO₃ melted congruently at (2 978±10) K, and Ba₂ZrO₄ decomposed peritectically at about 2 600 K. The present work was mainly based on these experimental data to set up the liquidus equilibria, on the grounds that the high-purity specimens were employed, and experimental procedures were well described.

Both PASCHOAL et al[6] and SHEVCHENKO et al[7] did not report the compound Ba₃Zr₂O₇, while the available information on {(1-x)(BaO)+x(ZrO₂)} indicated the existence of Ba₃Zr₂O₇ in the ZrO₂-BaO system[8-9] and the phase diagram calculated by DASH et al[10] for {(1-x₁-x₂)(Ba)+x₁(Zr)+x₂(O)} indicated that Ba₃Zr₂O₇ co-existed with BaZrO₃ at 1 287 K. And more, Ba₃Zr₂O₇ was really prepared by the reaction of  BaCO₃(s) and ZrO₂(s) in the mole ratio of 3/2 in an alumina boat at   1 300 K for 400 h in dry air[10] and was found at 1 650 K[11]. Consequently, special attention was paid to the compound Ba₃Zr₂O₇ in this work with the aim to understand the difference existing in Refs.[6-11].

The maximum solubility of BaO in c-ZrO₂ (cubic ZrO₂) and t-ZrO₂ (tetragonal ZrO₂) is 0.025 mol [7]. This small solubility of BaO in ZrO₂ benefits the mechanical properties of zirconia very much and the measured data [7] were used to evaluate the thermodynamic properties of C_SS (cubic ZrO₂ solid solution) and T_SS (tetragonal ZrO₂ solid solution). The very limited solubility of ZrO₂ in halite BaO (about 0.005 mol)[6-8] was ignored. No experimental data were reported for the solubility of BaO in m-ZrO₂ (monoclinic ZrO₂).

2.2 Structural and thermodynamic information

The structural behavior and the thermodynamic properties of the perovskite phase BaZrO₃ have been the subjects of many investigations associated with the technological application[12-19]. Using high- temperature X-ray diffractometry, MATHEWS et al[12] measured the cell parameters, unit-cell volumes and the coefficients of volume thermal expansion of the zirconia CaZrO₃, SrZrO₃ and BaZrO₃ in the temperature range from 298 to 1 675 K. The linear variation of the unit-cell volume and the cell parameters without any discontinuity indicated that the compound BaZrO₃ did not take place any phase transition, and the structure of BaZrO₃ was cubic. Using electromotive force, JOCAB et al[13] reported the enthalpies of formation of both SrZrO₃ and BaZrO₃ from the component oxides in the temperature range from 960 to 1 210 K. Based on the slope of electromotive force, SrZrO₃ was detected to undergo a structural transformation at about 1 123 K, while no structural transformation was detected for the compound BaZrO₃[13]. Because the experimental procedures were well controlled and the experimental results were generally consistent with each other[12-13], the structure of BaZrO₃ was treated as cubic in the whole temperature range.

Several groups[13-19] investigated the thermo- dynamic properties of BaZrO₃. Using high-temperature differential calorimeter, NAGARAJAN et al[14] reported the enthalpy increments H(T)-H(298) for BaZrO₃ from  1 000 to 1 700 K. Drop calorimetry was used by LEVITSKII[15], for H(T)-H(298) measurements on BaZrO₃, respectively. BANERJEE et al[16] determined H(T)-H(298) of BaZrO₃ by a precise high-temperature Calvet micro- calorimeter in the temperature range from 365.7 to 981 K. CORDFUNKE et al[17] also reported the enthalpy values for BaZrO₃ in their compilations. GOSPODINOV et al[18] reported enthalpy data for BaZrO₃ in the temperature range between 298 and 500 K by differential scanning calorimeter(DSC). These experimental data[14-16] except those of Ref.[18] were in good agreement with each other and join smoothly with the adiabatic measurements carried out by KING et al[19]. They were used to evaluate the Gibbs energy of BaZrO₃. Data from GOSPODINOV et al[18] were too high to have any physical meaning and were excluded in this work. The estimated data from CORDFUNKE et al[17] were not adopted, since they were directly connected with the thermodynamic parameters.

The estimated thermodynamic properties at 298 K, i.e. the enthalpy of formation of BaZrO₃ ?_fH(298)=   (-1 768.58±2) kJ/mol[13,15], the molar heat capacity C_p(298)=(101.71±0.31) J/(mol?K)[19] and the standard entropy S^Θ(298)=(124.7±2) J/(mol?K)[19] were adopted so that the evaluation can be carried out practically, but a low weight factor was applied to them.

The Gibbs energies of formation of BaZrO₃ relative to the pure oxides in the temperature range from 960 to  1 210 K, and from 1 180 to 1 320 K were determined by JOCAB et al[13] and LEVITSKII[15] using electro- motive force, respectively. JOCAB et al[13] also reported the enthalpies of formation of BaZrO₃ from the component oxides in the temperature range from 960 to  1 210 K, which were in good agreement with the value at 1 060 K reported by MUROMACHI et al[20]. These data were not used in the optimization. However, they were compared with the calculated results in order to check the final modelling.

For the compounds Ba₂ZrO₄ and Ba₃Zr₂O₇, the enthalpies of formation from the component oxides at 298 K were determined[11, 21]. These data were adopted to optimize the parameters of the compounds.

All temperatures quoted in this work were converted into the International Temperature Scale of 1990[22]. The thermodynamic functions were calculated at the normal constant pressure.

3 Thermodynamic models

The Gibbs energy function =- for the component i (i=ZrO₂, BaO) in the phase F is expressed by

where  is the molar enthalpy of the component i at 298.15 K and 101 325 Pa in its standard element reference state, and T is the absolute temperature. The last two terms in Eqn.(1) are used only outside the ranges of stability, the term gT⁷ is relative to the liquid below the melting point and hT ^–9 to the solid phases above the melting point.

In the present work, the Gibbs energy functions of pure ZrO₂, and were taken from the assessments of DU et al[23]. The Gibbs energy functions of BaO, and  were consistent with those used by LU et al[24], which were little different from those of SGTE substance database since some modification was made. Here, l denotes liquid, c, t and m stand for cubic, tetragonal and monoclinic ZrO₂, respectively, h represents halite BaO. The Gibbs energy functions employed in this work are expressed as

Due to the lack of experimental information, the Gibbs energies of the hypothetical meta-stable ZrO₂ and BaO were expressed relative to those of their stable structures:

where  the coefficients A_i and B_i (i=1, 2) are to be assessed by checking their influence on the calculated phase equilibria.

The liquid phase and solid solutions C_SS and T_SS were described by Redlich-Kister polynomials. The Gibbs energy for the liquid was expressed by

where  H^Θ is the abbreviation of  R is the gas constant, and X is the molar fraction of BaO. The interactive parameters a₀, b₀, a₁ and b₁ are to be optimized. The C_SS and T_SS were described by an analogous equation. Due to the very limited solubility of ZrO₂ in halite BaO and BaO in m-ZrO₂, the BaO_SS (halite BaO solid solution) and M_SS (monoclinic ZrO₂ solid solution) were treated as pure compounds in this work.

The compounds Ba₂ZrO₄ and Ba₃Zr₂O₇ were modelled as stoichiometric phases due to the very limited information. The Gibbs energy of Ba₂ZrO₄ was given by

where  A₃ and B₃ are connected with the enthalpy and entropy of formation from pure oxides in solid state, which will be evaluated in the course of optimization. The analogous equation, Eqn.(14) can be written for the Gibbs energy of Ba₃Zr₂O₇:

Since there were experimental thermodynamic data for BaZrO₃ in a wide temperature range[12-19], it was preferable to express its Gibbs energies relative to the SER state, and the following equation was used:

where  the coefficients c₁, d₁ and e₁ can be evaluated mainly from the measured enthalpy increments[14-16].

4 Optimization procedure

The Thermo-calc software package was used to optimize the thermodynamic parameters. The critically selected experimental data were employed with some certain weights, and the weights can be changed systematically until most of the experimental data were accounted for within the claimed uncertainty limits.

Optimization was started with the perovksite phase BaZrO₃. By using the measured thermodynamic data [14-16] selected in the above section, the numerical values of the coefficients c₁, d₁ and e₁ in Eqn.(15) describing the Gibbs energy function of BaZrO₃ could be critically evaluated. Once c₁, d₁ and e₁ have been estimated, the coefficients a₁ and b₁ in Eqn.(15) could be estimated from the reported heat capacity, entropy, and enthalpy of formation of BaZrO₃ at 298 K[13, 19]. The obtained coefficients were subjected to further optimization, the calculated thermodynamic properties of BaZrO₃ at 298 K were compared with the literature available data[13,15, 19-20] in Table 1.

Table 1 Estimated thermodynamic properties of perovskite phase BaZrO₃ at 298 K compared with measured values

Since the liquidus has been measured over a wide composition and temperature region[6-8], the optimization for its thermodynamic parameters is very important to the successful description of the ZrO₂-BaO system. And since there are not any independent data for the liquid phase, such as experimental enthalpy of the mixture, the C_SS, T_SS and Ba₂ZrO₄ should be modelled to reproduce the liquidus throughout the system. In this case, a suitable number of the thermodynamic parameters for each phase was really important to the optimization. It was found that the parameters a₀, b₀, a₁ and b₁ in Eqn.(12) should be introduced to describe the properties of the liquid satisfactorily. For the C_SS and T_SS phases, the experimental data were few, so the regular substitutional parameters were introduced to describe the relative properties. The coefficients A₃ and B₃ in Eqn.(13), were used to describe the compounds Ba₂ZrO₄. With most of experimental data[5-8] reproduced quite well, special attention was paid to the compound Ba₃Zr₂O₇ to check the possibility of its existence. Because there were not any phase diagram data about the compound Ba₃Zr₂O₇, the estimated enthalpy of formation of Ba₃Zr₂O₇ from the component oxides at 298 K[11] was used to optimize the coefficients A₄ and B₄ in Eqn.(14).

All the thermodynamic parameters were finally evaluated together and slight adjustments were made to give the best description of the system.

5 Results and discussion

The present evaluated thermodynamic parameters of the ZrO₂-BaO binary system are as follows:

The interaction parameters of liquid:

a₀=-357 817.66, b₀=73.4

a₁=-282 549.78, b₁ = 93.9

The interaction parameters of the C_SS phase:

a₀=-104 672.96, b₀=-8.4

The interaction parameters of the T_SS phase:

A comparison between the calculated ZrO₂-BaO phase diagram and that measured by ADAMSON et al [5-8] is shown in Fig.1. The calculated invariant reaction temperatures are compared with the experimental ones[5-8] in Table 2. It can be seen from Table 2 that the present modelling can account for the measured invariant temperatures[5-8] quite well. The eutectoid reactions T_SSM_SS+BaZrO₃ at 1 454 K and the peritectiod reaction Ba₃Zr₂O₇Ba₂ZrO₄+BaZrO₃ at 1 650 K are the results of calculations. These reactions are not easy to be experimentally detected because of the following reasons: 1) it is not easy to detect Ba₃Zr₂O₇ from Ba₂ZrO₄ or BaZrO₃ due to the near composition; 2) it is very difficult for oxides to achieve equilibrium at a low temperature such as 1 454 K. Better knowledge on the phase equilibria at low temperatures is useful for further refinement of the ZrO₂-BaO system.

Fig.1 Comparison between calculated ZrO₂-BaO phase diagram and experimental data in Refs.[5-8]

Table 2 Comparison between calculated and measured coordinates of invariant temperatures in ZrO₂-BaO system

In Fig.2, the calculated H(T)-H(298) for BaZrO₃ is compared with the experimental values[14-16]. The agreement between the calculated and measured values of H(T)-H(298) is acceptable within the experimentaluncertainties.

Fig.2 Comparison of calculated H(T)-H(298) of BaZrO₃ with measured data [14-16]

The calculated Gibbs energy and enthalpy of formation for BaZrO₃ from the pure oxides are compared with the experimental data[13, 15, 19-20] in Tables 3 and 4, respectively. The calculation can describe these experimental data reasonably although they are not used in the present optimization.

Table 3 Gibbs energy of formation of BaZrO₃ from component oxides compared with measured values in Refs.[13, 15]

Table 4 Enthalpy of formation of BaZrO₃ from component oxides compared with measured values in Refs.[13, 20]

The present calculated enthalpy of formation for the compounds Ba₂ZrO₄ and Ba₃Zr₂O₇ from the component oxides at 298 K are compared with the literature data in Table 5, a good agreement is obtained.

Table 5 Comparison of enthalpy of formation for Ba₂ZrO₄ and Ba₃Zr₂O₇ from component oxides at 298 K

6 Conclusions

1) The thermodynamic function of the perovskite phase BaZrO₃ is critically evaluated with all reliable experimental data reproduced within the estimated experimental uncertainty. A set of reasonable and self-consistent thermodynamic parameters for the ZrO₂-BaO binary system is obtained. The calculated phase diagram and thermodynamic properties data are in good correspondence with the experimental information.

2) The compound Ba₃Zr₂O₇ decomposes to Ba₂ZrO₄ and BaZrO₃ at 1 650 K. Thermodynamic and phase diagram measurements on Ba₃Zr₂O₇ are useful for further refinement of the compound and the ZrO₂-BaO system.

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Foundation item: Project(33354) supported by the Natural Science Foundation of Guangdong Province, China

Corresponding author: CHEN Teng-fei; Tel: +86-731-8877242; E-mail: tengfei@mail.csu.edu.cn

(Edited by CHEN Wei-ping)