Thermodynamic descriptions of the BaO-CaO, BaO-SrO, BaO-SiO2 and SrO-SiO2 systems

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 54 (2016) 107–116

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CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry journal homepage: www.elsevier.com/locate/calphad

Thermodynamic descriptions of the BaO-CaO, BaO-SrO, BaO-SiO2 and SrO-SiO2 systems Rui Zhang a,n, Huahai Mao b,c, Pekka Taskinen a a

Aalto University, School of Chemical Technology, Metallurgical Thermodynamics and Modeling Research Group, Espoo, Finland KTH Royal Institute of Technology, Department of Material Science and Engineering, Stockholm, Sweden c Thermo-Calc Software AB, Norra Stationsgatan 9, SE-113 64 Stockholm, Sweden b

art ic l e i nf o

a b s t r a c t

Article history: Received 17 April 2016 Received in revised form 27 June 2016 Accepted 28 June 2016

In order to provide an adequate basis for extrapolation into higher order oxide systems, a thermodynamic assessment was performed on the BaO-CaO, BaO-SrO, BaO-SiO2 and SrO-SiO2 binary systems by critically evaluating the available experimental data and previous thermodynamic modeling. Associate solution model was applied to describe the molten phase in the BaO-SiO2 and SrO-SiO2 systems. Two associates, Ba2SiO4 and BaSiO3, were tested and compared with the previous assessment with only one associate Ba2SiO4. A set of self-consistent thermodynamic parameters for the descriptions of each oxide system is presented. The phase diagrams, thermodynamic properties including activities, standard enthalpies of formation at 298.15 K and enthalpy increments were calculated according to the thermodynamic parameters acquired in the present work. For the BaO-SiO2 and SrO-SiO2 systems, the site fractions of species in the liquid were calculated to illustrate the chemical short-range order tendency of the compound(s) in the liquid phase. & 2016 Elsevier Ltd. All rights reserved.

Keywords: CALPHAD Associate solution model BaO

1. Introduction Glass ceramics are widely applied as the one of the candidates for producing high-energy storage materials due to the flexible adjustment of compositions and the free of porosity. Ferroelectric glass ceramics of the BaO-CaO-SrO-Nb2O5-SiO2-B2O3 system have the great potential for certain applications that have been recognized by Golezardi et al. [1]. By tailoring the composition of various components in this system, it facilitates to acquire the materials with desired dielectric and ferroelectric properties [2]. Melting-quenching and sol-gel methods are accepted as two conventional approaches to prepare the glass ceramics. However, the problems associated are (i) the complexity of the compounds or solid solutions formed and (ii) high melting points of some substances in the system. These give rise to the difficulties to understand the phase relations and thermodynamic properties of this multi-components system at certain temperatures during production. Additionally, a good knowledge of the BaO-CaO-SrO-SiO2 system contributes to complete and extend the MTOX oxide database used in smelting and refining [3]. However, even thermodynamic descriptions of the basic binary systems in this complicated oxide system are poorly available. By using CALculation of PHAse Diagram (CALPHAD) approach, thermodynamic modeling of various binary n

Correspondence to: P.O. Box 16200, FI-00076 Aalto, Finland. E-mail address: rui.2.zhang@aalto.fi (R. Zhang).

http://dx.doi.org/10.1016/j.calphad.2016.06.009 0364-5916/& 2016 Elsevier Ltd. All rights reserved.

systems in this complex system contributes to the extrapolation to higher order systems and establish the thermodynamic database to describe this complex oxide system. With the thermodynamic descriptions available, it is efficient and convenient to understand and predict the phase equilibria, chemical reactions and thermodynamic properties at various temperatures. The present work aims at (i) performing thermodynamic assessment of the BaO-CaO, BaO-SrO, BaO-SiO2 and SrO-SiO2 systems by the CALPHAD technique; (ii) achieving sets of thermodynamic parameters for the four binary systems to reproduce the phase diagram data and thermodynamic properties, such as, activities, enthalpy increments, enthalpies of formation; and (iii) testing the validity of the associate solution model with two associates in the BaOSiO2 case. For the sake of simplicity, symbols B and S were used as abbreviations of BaO and SrO (or SiO2), thus BS, B3S, B2S, B2S3, B5S8, B3S5, BS2, S3S, S2S and SS stand for BaSiO3, Ba3SiO5, Ba2SiO4, Ba2Si3O8, Ba5Si8O21, Ba3Si5O13, BaSi2O5, Sr3SiO5, Sr2SiO4 and SrSiO3 respectively throughout the paper if not stated otherwise.

2. Literature review 2.1. The BaO-CaO system Due to the high melting points of BaO and CaO, 2196 K and 2886 K respectively, few experimental data are available for the

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R. Zhang et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 54 (2016) 107–116

phase equilibrium of the BaO-CaO system. Flidlider et al. [4] mentioned a very low mutual solubility of BaO and CaO in the solid states of both ends when studying the heats of formation of the solid solutions of alkaline earth metal oxides. However, no values were reported in their work [4]. The thermodynamic assessment of the BaO-CaO system was performed by several authors. Van Der Kemp et al. [5] calculated the phase diagram of this system by evaluating the excess thermodynamic functions. Seo et al. [6] simulated the thermodynamic properties and calculated the phase diagram by molecular dynamic simulation (MDS). Based on the mathematical equation from the work by Blander [7], Shukla [8] estimated the solubility between the two oxides. The calculated possible eutectic reaction by Van Der Kemp [5], Seo [6] and Shukla [8] shows a large discrepancy as 2050 K [5], 2180 K [6] and 2082 K [8], respectively. All the previous assessments were compared with the present calculation. 2.2. The BaO-SrO system Jacob and Varghese [9] determined the miscibility gap in the BaO-SrO system on the basis of X-ray diffraction analysis. The subsolidus is slightly asymmetric with the critical point of 557 0.8 mol% SrO at 13567 4 K. By means of mass spectrometry, Van Der Kemp and Oonk [10] measured the excess molar Gibbs energy for SrO and BaO ranging from 1430 K and 1530 K. The phase diagram of the BaO-SrO system was calculated using this result combining with the excess molar enthalpy obtained in their work. Shukla [8] optimized the phase diagram of this system by assuming the liquid phase to be ideal and modeling the solid solution with a single sub-lattice substitutional model. Gong and Jin [11] reported the thermodynamically calculated phase diagram when assessing the BaO-SrO-TiO2 ternary system. The present thermodynamic modeling of the BaO-SrO system was based on the thermodynamic parameters acquired by Gong and Jin [11] by fitting the measurements made by Jacob and Varghese [9]. 2.3. The BaO-SiO2 system The phase equilibria data of the BaO-SiO2 system were reported in several studies [12–20]. The critical literature review can be found in the work by Zhang et al. [12]. It reports a flat liquidus existing in the SiO2-rich region in most of the measurements, and the flatness implies the possible existence of miscibility gap with its critical point close to the liquidus line. However, according to the calculated phase diagram by Shukla [8], a stable miscibility gap at higher temperature is presented. By considering the contradicted information, the miscibility gap at SiO2-rich side was not taken into account in the present work. In the work [12] by Zhang et al., the thermodynamic modeling of the BaO-SiO2 system using associate solution model with one associate Ba2SiO4 reproduces most of the experimental and thermodynamic data. Considering the liquid models used by Zaitsev et al. [21], Allendorf and Spear [22] and Hillert et al. [23] on the (Na2O, K2O, CaO)-SiO2 systems being composed of more than one silicate species, in the present work, thermodynamic re-assessment with the additional associate BaSiO3 was conducted and compared with the literature data to test the validity by using two associates. 2.4. The SrO-SiO2 system The phase diagram of SrO-SiO2 system was experimentally constructed by Eskola [24], ranging from 1573 K to 2018 K by means of quenching method. Two stoichiometric compounds, S2S and SS, were reported and the melting point of SS was determined to be 1853 K, in agreement with the work by Jaeger and Van

Klooster [19] of 1851 K. The phase diagram of the SrO-SiO2 system were established by Fields et al. [20] according to the determination of the liquidus in the SrO-rich region when investigating the BaO-SrO-SiO2 system. Based on the X-ray diffraction analysis results, three compounds, S3S, S2S and SS, were confirmed. At the same time, a phase transition, α-S2S-α’-S2S, was presented by Fields et al. [20] in the study of phase relations in the system Ba2SiO4-Sr2SiO4. The data strengthen the prediction by Hahn and Eysel [25] concerning the existence of such a phase transition. Experimental data of the molten phase in equilibrium with SiO2 and SS were reported by Ghanbari and Brett [26] in the study of the MgO-SiO2-SrO ternary system. The liquidus temperatures in the SiO2-rich corner were measured by Greig [18] and a liquid immiscibility above 1967 K was predicted. The miscibility gap in the SiO2-rich corner was observed by Kracek [27] when constructing the cristobalite liquidus in the alkali oxide-silica system (Mg, Ca, Sr, Ba, Li, Na, K, Rb and Sc). The same finding was provided by Ol'Shanskij [28] in the research of alkaline earth oxide-silica melts ranging from 1873 K to 2473 K. Later, by equilibration and quenching, Hageman and Oonk [29] determined the liquid immiscibility in the SrO-SiO2 system. The phase diagram of the SrSiO3-SiO2 system was constructed by Huntelaar et al. [30], based on the determination by differential thermal analysis (DTA). For all the literature data briefly introduced above, the details of the experimental techniques, analysis methods and identified phases and temperatures are summarized in Table 1. The phase stability data is poorly available for the phase S3S. On the basis of the investigation by Fields et al. [20], the S3S phase is stable above 1473 K. The phase stability of the Ba3SiO5 phase was experimentally investigated and thermodynamically calculated by Zhang et al. [12]. It decomposes into BaO and Ba2SiO4 at 1323 K. By considering the similarity of strontium with barium in the same group in the periodic table, the decomposition temperature of S3S is assumed to be around 1323 K. Further experiment is strongly required to confirm the phase stability of this phase. Shukla [8] performed a thermodynamic assessment by using a modified quasi-chemical model for the description of the liquid phase. The calculated phase diagram shows the polymorphic phase transition of S2S at 1973 K. By combining the experimental studies made by Fields et al. [20] and Hahn and Eysel [25], the S2S transition temperature was taken as 1973 K in the present work. The activities of SrO and SiO2 in glass and melts of the SrO-SiO2 system ranging from 1840 K to 1970 K were determined by Lopatin et al. [31] employing high temperature mass spectrometry. The activity data were taken into account in the present thermodynamic assessment. The standard molar enthalpies of formation 0 ) of SS (solid) and S2S (solid) were measured by Huntelaar ( ∆H298 et al. [33] and Barany et al. [34]. The values reported by Barany et al. [34] were regarded as uncertain by Huntelaar et al. [33] since the measurements were made in concentrated HF (aq) at 346.9 K and the absence of a pre-period and presence of SrF2 (s) precipitations influenced the final results. Róg et al. [35] derived the enthalpies of formation (from oxides) for the two phases, SS and S2S, on the basis of their measurements about the Gibbs energies of formation. However, for the SS and S2S in the SrO-SiO2 system and the BS and B2S in the BaO-SiO2 system, the measured Gibbs energies of formation by Róg et al. [35] were doubted by Shukla [8] based on critical evaluation and comparison with the calculations and others’ work as reported by Shukla [8]. The evidence of inaccurate measurements by Róg et al. [35] were discussed in the work by Zhang et al. [12] that the thermodynamic properties of the BaO-SiO2 system (in the same work of the SrOSiO2 system [35]) show an inconsistence by comparing Róg et al. [35]’s results with the calculations and other experimental work included in their thermodynamic assessment [12]. By dropping the melted samples into the ice calorimeter, the heat contents (HT-

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Table 1 Summary of the key experimental data in the literature. Type of data in various oxide system

Analysis technique*

Reference

The BaO-SrO system Solid state miscibility gap

XRD

[9]

The SrO-SiO2 system / Phase equilibria Liquidus and liquid immiscibility in the SiO2- Quenching rich corner Melting point of SS, 1853 K Voltage measurement Complete phase diagram and α-S2S-α’-S2S Quenching, XRD Partial phase diagram from 1573 K to 2018 K Quenching, OM α-S2S-α’-S2S XRD Liquid in equilibrium with SiO2 and SS EPMA; XRD respectively Liquidus of cristobalite of alkali oxide-siliQuenching cate mixtures Liquids in the SiO2-rich region from 1873 K Quenching to 2473 K Liquid immiscibility in the SiO2-rich region Quenching Phase diagram of SrSiO3-SiO2 system DTA

The SrO-SiO2 system/ Thermodynamic properties Activities of SrO and SiO2 in glasses and melts from 1840 K to 1970 K Standard molar enthalpies of formation

MS

[18] [19] [20] [24] [25] [26] [27] [28] [29] [30]

[31]

Fig. 1. Calculated phase diagram of the BaO-CaO system, compared with the literature data [5,6,8].

Solution calorimetry [33,34]

0 ) for S2S and SS ( ∆H298 Gibbs energy formation of Strontium EMF silicates Drop calorimetry Heat content (HT-H273) of liquid with the composition of SrO
2 SiO2 Enthalpy increments (HT-H298) of S2S and SS Drop calorimetry

[35] [36] [37]

* OM ¼Optical microscopy; XRD ¼ X-ray diffraction; EPMA ¼Electron probe microscopy analysis; DTA ¼ Differential thermal analysis; MS ¼Mass spectrometry; EMF ¼ electromotive force.

H273) were measured by Richet and Bottinga [36] for the SrO-SiO2 liquids at the composition of SrO
2SiO2. However, the standard enthalpy of formation at room temperature for this composition is not available in literature. In order to compare with the (HT-H273), extrapolation the thermodynamic properties of the liquid to 273 K was performed. By drop calorimetry, Huntelaar et al. [37] measured enthalpy increments (HT-H298) of the S2S and SS phases. The two sets of measured enthalpy increments were compared with

Table 2 Summary of thermodynamic parameters describing the liquid phase in the BaO-CaO, BaO-SrO, BaO-SiO2 and SrO-SiO2 systems, referred to stable element reference (T¼ 298.15 K, P ¼1 bar). All values are given in SI units (J, mol and K). The complete optimized thermodynamic parameters of BaO-CaO, BaO-SrO, BaO-SiO2 and SrO-SiO2 systems are available in the Appendices. The BaO-CaO system Liquid:

0

1

Halite:

0

1

The BaO-SrO system Halite:

0

1

The BaO-SiO2 system Liquid:

0

1

2

3

0

1

LBaO, CaO= -6175þ 6*T LBaO, CaO= 49700 þ3*T

LBaO, SrO= 31366.73-6.66*T

LSiO2, Ba2SiO4= 2284 þ1.4*T

LSiO2, Ba2SiO4= 96-7*T

LBaO, SiO2= 1142 þ0.7*T

LBaO, CaO= 2*T LBaO, CaO= -4800þ 2*T

LBaO, SrO= -2026.1 þ0.43*T

LSiO2, Ba2SiO4= -22532-13.6*T LSiO2, Ba2SiO4= 73.46-7.5*T

4

LSiO2, Ba2SiO4= 22,456

4

LBaO, SiO2= 11,228

LSiO2, BaSiO3= 11,228

LBaO, SiO2= - 11266-6.8*T

2

3

0

1

2

3

LSiO2, BaSiO3= 36.73-3.75 *T

4

0

1

LBaO, Ba2SiO4= 2000

2

0

1

2

3

0

1

0

1

LBaO, SiO2= 48-3.5*T LSiO2, BaSiO3= 1142þ 0.7*T

LSiO2, BaSiO3= 48-3.5*T

LBaO, Ba2SiO4= 1000

LBaO, SiO2= 36.73-3.75*T

LSiO2, BaSiO3= - 11266-6.8*T

The SrO-SiO2 system

LSiO2, Si2SiO4=  1 04936.5 þ6.97∗T

LSiO2, Si2SiO4=  2521.47  0.84∗T

LSrO, SiO2=  0.2  0.73∗T

LSrO, Sr 2SiO4= -24765.14

LSiO2, Si2SiO4= 138172.9-65.9*T LSiO2, Si2SiO4= 59375.94-0.16*T

LSrO, SiO2= 1572.1-0.55*T

LSrO, Sr 2SiO4= 23842.5

LBaO, Ba2SiO4= 1200

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where ΣHiSER is the sum of enthalpies of the elements at 298.15 K and 1 bar in their stable states (Stable Element Reference, denoted as SER); T is the absolute temperature. The Gibbs energy expressions for pure BaO SrO, CaO, and SiO2 were extracted from SGTE94 [38] and Mao et al. [39,40]. 3.2. Solution phases For the BaO-CaO and BaO-SrO systems, the substitutional solution model was employed to describe the liquid phase. Their Gibbs energy functions were described as: ∅ Gm∅ − H SER = xBaO 0GBaO + xi 0Gi∅ + RT ( xBaO lnxBaO + xi lnxi ) + EGm

(2)

where xBaO and x i are the mole fractions of BaO and the component i (i¼CaO and SrO), respectively. EGm is the excess Gibbs energy expressed by the Redlich-Kister (R-K) polynomials [41] as: E

Gm = xBaO xilLBaO ∙ i = xBaO xi [0L + 1L( xBaO − xi )]

Fig. 2. Calculated phase diagram of the BaO-SrO system, compared with the literature data [9,10].

(3)

where lLBaO ∙ i is the interaction parameter between BaO and the component i (i ¼CaO and SrO), which is the optimization parameter in the present work. The general linear temperature dependent form of the interaction parameter lL=a + bT was applied. For the BaO-SiO2 and SrO-SiO2 systems, the associate solution model was used for the description of the liquid phase. Since the thermodynamic assessment of the BaO-SiO2 system using one associate (B2S) was performed by Zhang et al. [12], in the present work, two associates (B2S and BS) were included in the associate solution model in order to test whether it can better describe the liquidus between the two stoichiometric compounds, B2S and BS. By the associate solution model with two associates, the liquid phase in the BaO-SiO2 system is assumed to be constituted of BaO, Ba2SiO4, BaSiO3 and SiO2. The Gibbs energy of liquid can be expressed as: Liq

Liq

GmLiq − ΣHiSER = yBaO 0G BaO + ySiO 0G SiO 2 + yBa 2

(

Liq

0 2SiO4

3

+ RT yBaO lnyBaO + ySiO lnySiO + yBa 2

+ yBaSiO lnyBaSiO 3

3

)

Liq

G Ba2SiO4 + yBaSiO 0G BaSiO3

2

2SiO4

lnyBa

2SiO4

E

+ Gm

(4)

where y represents the mole fractions of BaO, Ba2SiO4, BaSiO3 and 0 Liq Liq SiO2. The Gibbs energies of 0G Ba SiO and GBaSiO were extracted 2

4

3

from MTOX oxide database [3]. EGm is the excess Gibbs energy described by the R-K polynomials [41] as: E

Gm = yBaO ySiO

+ yBaO yB Fig. 3. Calculated phase diagram of the BaO-SiO2 system, compared with the literature data [12–20].

the present calculation. The thermodynamic data reviewed above were summarized in Table 1.

1

n

2S

+ yBaO yBS + yBS ySiO

n1

2

∑ n = 0 n3LBaO⋅ BS(xBaO − xBS )n3 3

n4

∑n 2

+ yB S ySiO 2

∑ n = 0 n2LBaO⋅ B2S( xBaO − x B2S ) 2

4=0

2

(

L BS ⋅ SiO 2 xBS − xSiO 2

n4

)

∑ n = 0 n5LB2S ⋅ SiO2(x B2S − xSiO2)n5

(5)

5

n2

n3

n4

n5

in which LBaO ∙ SiO2 , LBaO ∙ B2S , LBaO ∙ BS , LBS ∙ SiO2 and L B2S ∙ SiO2 are the interactions between different species to be optimized in the present work. After the proposal of Hillert et al. [23], the following relations are used among these interaction parameters, n5L B2S ∙ SiO2 ¼

3. Thermodynamic modeling 3.1. Unary oxides The Gibbs energy function of component o in phase φ , oGoφ ¼

Goφ( T ) - ΣHiSER , (o¼ BaO, CaO, SrO and SiO2, and i ¼Ba, Ca, Sr, Si, and O) was expressed by the equation:

Goφ( T ) = a + bT + cTlnT + dT2 + eT −1 + fT 3 + gT7 + hT −9

∑ n = 0 n1LBaO⋅ SiO2(xBaO − xSiO2)n1

2

(1)

2* n1LBaO ∙ SiO2 ¼ 2* n4LBS ∙ SiO2 , counting the amount of BaO or the corresponding negative charge of anions i.e. SiO4  4, SiO3  2 and O  2, respectively. The Gibbs energy function of the molten phase in the SrO-SiO2 system shares the same format as that in Eqs. (4) and (5), but replaces the associates in the Eq. (5) with SrO, Sr2SiO4 and SiO2. Liq The thermodynamic descriptions of the 0G Sr term were 2SiO4 achieved from the MTOX oxide database [3].

R. Zhang et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 54 (2016) 107–116

111

Fig. 4. Calculated activities of BaO and SiO2 in the melts at various temperatures, compared with the literature data [43]. The reference states are solid BaO and cristobalite.

Fig. 5. The calculated enthalpy increments (HT-H273) at the composition of BaO: SiO2 ¼ 1:3, compared with the literature data [8,36].

Fig. 6. The calculated site fractions of various associates in the BaO-SiO2 liquid phase at 1800 K.

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3.3. Binary oxide compounds For the BaO-SiO2 system, the Gibbs energy functions of the compounds BS, B3S, B2S, B2S3, B5S8, B3S5 and BS2 were evaluated in the same approach as can be found in the work by Zhang et al. [12], so the detailed description was skipped in the present work. For the SrO-SiO2 system, the existence of solid S3S, S2S and SS were experimentally confirmed. The Gibbs energy functions of these compounds were evaluated based on the thermodynamic parameters from the MTOX oxide database [3]. Generally, they were modeled as: 0

G SmSn − mHSrSER − nHSiSER − (m + n)HOSER = A + BT + GSmSn

(6)

where HiSER is the enthalpy of element i (i¼ Sr, Si and O) at 298.15 K and 1 bar. A and B are the parameters to be optimized based on selected literature data reviewed in the ‘literature review. GSmSn denotes the Gibbs energy function of the compound SmSn. They were directly adopted from the MOTX oxide database [3] for the compounds S2S, SS and S3S. Fig. 7. The calculated phase diagram of the SrO-SiO2 system, compared with the literature data [18,20,24,26,29,30].

3.4. Optimization The optimization of thermodynamic parameters in the present work was performed using PARROT module in the Thermo-Calc

Fig. 8. Calculated activities of SrO and SiO2 in the melts at various temperatures, compared with the literature data [31]. The reference states are solid SrO and cristobalite.

R. Zhang et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 54 (2016) 107–116

113

Fig. 9. Calculated enthalpy increments of the composition SrO
2 SiO2, compounds S2S and SS, compared with the literature data [33,36].

Figs. 1 to 10 and Tables 3 and 4. The detailed interpretations and discussions are provided system by system in the following paragraphs. 4.1. The BaO-CaO system As can be seen in Fig. 1, disagreement exists for the temperature of the eutectic reaction. In an unpublished work, the attempt by the authors was made to find the molten phase using equilibration-quenching technique. It was concluded that no liquid phase was observed at 1973 K (limitation of the furnace employed) based on the SEM/EDS results. The calculated eutectic temperature in the present work, 2149 K, locates between the reported values by the previous literature data. Further experiment is needed to acquire the data related with the molten phase in this system. 4.2. The BaO-SrO system

Fig. 10. The calculated site fractions of the associate in the liquid phase of the SrOSiO2 system at 1800 K.

software package [42]. Due to the poor availability of experimental data for the BaO-CaO and BaO-SrO systems, the modeling work was based on the assessments made by Seo [6], Shukla [8] and Gong and Jin [11]. For the BaO-SiO2 and SrO-SiO2 systems, they were started by fitting the liquidus data and thermodynamic properties such as activities of various components. Then the experimental data of the compounds were taken into account for thermodynamic assessment. The optimization was repeated by adjusting the weights given to each piece of experimental information. In order to achieve the overall fit, all the thermodynamic parameters were finally optimized simultaneously using all the evaluated experimental data.

4. Results and discussion According to the optimized thermodynamic parameters in the present work, as listed in Table 2, the phase diagrams, thermodynamic properties and invariant reactions of various oxide systems were calculated and compared with the literature data in

Due to the absence of experimental data of the liquid phase, in the present assessment, the interaction parameters in the liquid phase were excluded. The assessment was conducted according to the unique measurement by Jacob and Varghese [9]. The calculated phase diagram of the BaO-SrO system from room temperature to 3000 K is shown in Fig. 2. The measured solid state miscibility gap by Jacob and Varghese [9] supports the calculated results made by the present work and Van Der Kemp and Oonk [10] showing a symmetric shape, although the measurement by Jacob and Varghese [9] is slightly asymmetric shifting towards the SrO side. 4.3. The BaO-SiO2 system The interactions of BaO, B2S, BS and SiO2 were listed in Table 2. In the subsystem BaSiO3-SiO2, the interaction between BaSiO3 and SiO2 is important. In order to fit the flat cristobalite liquidus curve, which indicates an asymmetric metastable miscibility gap underneath, high-order terms in a Redlich-Kister polynomial is necessary. However, the introduction of this interaction makes the BaSiO3 less favorable relative to Ba2SiO4 and BaO at high SiO2 contents because the interaction gives a positive energy contribution. In order to avoid an unreasonable increase of those species (BaO and Ba2SiO4) in the SiO2-rich part of the system, the relation between these interaction parameters [23] were used. The implementation of such relations [23] ensures the present model

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Table 3 Calculated invariant reactions in the present work, compared with the literature data. Equilibrium

Temperature (K)

Reference

1696 1693

The present calculation [13,24]

Liquid 2 BS

1878 1873 1877

The present calculation [13] [20]

Liquid 2 B2S

2423 2423

The present calculation [20]

Liquid 2 B2S3

1728 1720 1723

The present calculation [13] [24]

Liquid 2 B5S8

1720 1719

The present calculation [13]

B3S5 2 B5S8 þ B2S3

1571 1577

The present calculation [14,15]

2610 2598

The present calculation [20]

Liquid 2 SS

1853 1853

The present calculation [24] [30]

Liquid 2 S3S

2428 2443

The present calculation [20]

Liquid 2 SS þ Tridymite

1631 1631 1615

The present calculation [24] [30]

Liquid 2 SS þ S2S

1852 1818 1840

The present calculation [20] [30]

Liquid 2 S3S þ S2S

2427 2423

The present calculation [20]

Liquid 2 S3S þ SrO

2371 2353

The present calculation [20]

The BaO-SiO2 system Liquid 2 BS2

The SrO-SiO2 system Liquid 2 S2S

experimental and modeling work with a good consistency. Compared with other modeling, the present calculation shows a good agreement with the experimental data by Roth and Levin [13]. New experimental data are needed to confirm the calculation concerning the eutectic reaction, liquid - B2S þ BS. Due to the high temperatures of conducting experiments, same difficulties of lack of experimental data concerning other eutectic reactions in this system give rise to the uncertainty about the calculated results in the present work. The priority was given to fit the congruent melting of the compounds in the system, and then the eutectic reactions in the system were considered via rough estimation made on the basis of other modeling work. The calculated oxide-component activities and enthalpy of increments of the composition at BaO:SiO2 ¼ 1:3 agree well the experimental measurements, as can be found in Figs. 4 and 5. As indicated in the work by Tyurnina et al. [43], the errors in the activities at 1970 K determined by the method of comparing ion currents are 5–10% for BaO and 8–15% for SiO2. By considering the uncertainties provided by Tyurnina et al. [43], small weights were given to the activity data during the optimization process. More measurements with small uncertainties are required to acquire accurate thermodynamic parameters in order to describe the activities of BaO and SiO2. In the work by Zhang et al. [12], the activities of BaO and SiO2 in the BaO-SiO2 system were also calculated. There is no significant difference between the calculated activities based on the two sets of thermodynamic parameters (a. with one associate and b. two associates). Therefore, only the present calculations were presented in Fig. 5. As can be observed from Fig. 6, the calculated site fractions of the associates, BS and B2S, are dominant in the vicinity of corresponding stoichiometry. However, it should be noted that the molten phase is assumed to be constituted of the B2S and BS associates without a full confirmation by experimental observation. So the associate solution model in this work is regarded as a mathematical expression for the Gibbs energy functions, and Fig. 6 is the graphical representation helping to understand the behavior of the two associates in the liquid. It may shine light on the shortrange order tendency in the silicate melts. It may also indicate the polymerization degree with the change of SiO2 content, for example Hillert et al. [23] evaluated the fraction of different kinds of oxygen atoms in the CaO-SiO2 system by the interpretation of the species SiO2 representing two unbroken oxygen bridges between Si atoms, each SiO3  2 represents one unbroken and two broken oxygen bridges, and each SiO4  4 represents four broken oxygen bridges. Further experiments are needed to confirm the behavior of the associates in the melts. 4.4. The SrO-SiO2 system

predict reasonable site fractions of constituents (see Fig. 6), especially BaSiO3 becomes the dominant species in the vicinity of the corresponding composition. In the subsystem BaO-Ba2SiO4, the experimental liquidus curve does not indicate evidently any metastable miscibility gap underneath. In order to fit the eutectic of BaO þ B3S less strong interaction parameters between BaO and Ba2SiO4 is sufficient. Table 2 shows in particular 1LBaO, Ba2SiO4 was almost one order of magnitude lower than 1LSiO2, Ba2SiO4 . To simplify the description, the interactions between BaO and BaSiO3 was ignored due to its negligible effect on the phase diagram and thermodynamic property. So they were excluded from thermodynamic modeling of the liquid phase and skipped in Table 2. The calculations compared with the literature data are presented in the Figs. 3 to 6 and Tables 3 and 4. In Fig. 3, the phase diagram calculated based on the present assessment can depict the

As shown in Fig. 7 and Table 3, most of the experimental data available can be well reproduced by the present thermodynamic assessment. In the previous assessment by Shukla [8], the miscibility gap in the SiO2-rich corner caused some difficulties to obtain a good fit with the measurements. The difficulties remain in the present work that the calculated results were a compromise of the experimental data measured by Ol'Shanskij [28] and Hageman and Oonk [29]. A monotectic point of 2066 K was reported by Ol'Shankij [28], while the value measured by Hageman and Oonk [29] was 180 K lower. By considering the modeling work conducted by Shukla [8], the present result of 2040 K may be regarded as a satisfactory one. The measured eutectic point by Fields et al. [20] in the S2S and SS subsystem is at 1818 K and 47 mol% SiO2, which is lower than the measurement by Huntelaar et al. [30] at 1840 K and calculated one in the present work at 1852 K. In the work by Fields et al. [20] with oxygen-acetylene torch employed, the possible formation of hydroxides may account for this discrepancy. The calculated liquidus in the SrO-rich region shows a

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115

Table 4 The calculated standard molar enthalpy of formation at 298.15 K in the present work, compared with the experimental literature data. Calculated from oxides by Shukla [8]

Calculated from elements by present work

Calculated from elements by Shukla [8]

Measurements by elements

Compound

Calculated from oxides by the present work

The BaO-SiO2 system BaSiO3

 174390.6

 158,454

 1633194.6

 1,617,258

Ba2SiO4

 265191.48

 285,500

 2272099.5

 2,292,422

1,606,4007 2600 [32] 1,617,8007 2400 [34] 2,292,2007 4200 [32] 2,276,5007 4300 [34]

BaSi2O5 Ba2Si3O8 Ba5Si8O21 Ba3Si5O13 Ba3SiO5

 250680.99  431999.8  1117231.6  681659.8  246271.08

    

173,696 344,912 869,414 517,434 245,000

 2,620,185  4260307.8  11,143,352  6879471.8  2801283.1

    

    – – – – –

The SrO-SiO2 system Sr2SiO4

 209010.51

 209,000

 2303782.5

 2,304,000

SrSiO3

 127346.35

 129,200

 1630082.3

 1,632,000

2,305,7007 2200 [33] 2,304,400 72200 [34] 2,226,8007 6000 [35] 1,635,3007 1800 [33] 1,633,6007 1400 [34] 1,581,700 73200 [35]

Sr3SiO5

 184060.39

 180,900

 2870868.4

 2,868,020

      –

0 (J/mol) ∆H298

discrepancy compared with the experimental data by Fields et al. [20]. The doubt was raised by Huntelaar et al. [31] that the erroneous liquidus measurements by Fields et al. [20] were subjected to a misuse of the melting point of SrO. The determined melting point of SrO by Noguchi [44] is 2872 720 K, while Fields et al. [20] reported it to be around 2700 K in the published phase diagram. Using the present thermodynamic parameters in Table 2, the activities of SrO and SiO2 in the melt and two types of enthalpy increments were calculated and compared with the literature data. As can be found in Figs. 8 to 10, the calculated results agree well with the experimental ones. In Fig. 8, negative deviations can be observed in the melt region, indicating the interactions of the components in the system to form new chemical compounds. However, in the SiO2-rich region, the measured SrO activities by Lopatin et al. [31] at various temperatures are much higher than the calculated ones in the present work. The same phenomenon was found in the assessment by Shukla [8], stating that small weights were given to the activity data measured by Lopatin et al. [31] for the reason that the measurements were unreasonably high. By comparing the results of activities in Figs. 4 and 8, for the BaO-SiO2 and SrO-SiO2 systems respectively, the degree of the negative deviation of the melts from the ideality seems depend on the basicity of BaO and SrO, so that more compounds tend to form in the BaO-SiO2 system with larger basicity of BaO. The site fractions of the constituents in the SrO-SiO2 liquid phase are calculated and shown in Fig. 10, implying the domination of the associate S2S in this binary system. With the assessed binary oxide systems, the further work will be concentrated on the extrapolation into higher order systems. The challenging part is the compatibility of the thermodynamic models employed in different binary systems. A successful application can be achieved in the MTOX oxide database [3]. The description of the molten phase in the BaO-Al2O3-SiO2 ternary system is based on (a) the substitutional solution model used in the BaO-Al2O3 and Al2O3-SiO2 systems, and (b) associate solution model adopted in the BaO-SiO2 system. The test will be made on the BaO-CaO-SiO2 and BaO-SrO-SiO2 systems in the future work.

2,543,200 4,173,220 10,895,534 6,715,246 2,800,000

5. Conclusion By means of the CALPHAD technique, the systems BaO-CaO, BaO-SrO, BaO-SiO2 and SrO-SiO2 were thermodynamically assessed. Due to the poor availability of experimental data, the BaOCaO and BaO-SrO systems were optimized based on few measurements and calculated liquidus from the previous work. The calculated phase diagrams of the two binary oxide systems are presented and further experimental information is suggested to verify the calculations in the present work. With two associates, Ba2SiO4 and BaSiO3, in the associate solution model to describe the liquid phase, the BaO-SiO2 system was re-assessed applying some relations of the interaction parameters between SiO2 and different constituents. According to the thermodynamic description obtained in the present assessment, the phase diagram, activities of BaO and SiO2 in the melts, enthalpy increments (HT-H273) at BaO:SiO2 ¼1:3, were calculated and they present a good agreement with the literature data. Experimental data on the invariant reactions above 1700 K are needed to facilitate further assessment, in order to acquire an accurate thermodynamic description at high temperatures. Based on the optimized thermodynamic parameters of the SrOSiO2 system in the present work, the calculated phase diagram, activities of SrO and SiO2, enthalpy increments (HT-H298) of Sr2SiO4 and SrSiO3 and enthalpy increments (HT-H273) in the liquid phase at the composition of SrO·2SiO2 can well reproduce the literature data. New experimental data are required for phase equilibria and activities of SrO in the SiO2-rich side to obtain a better description of the liquid immiscibility.

Acknowledgment This research was financially supported by Association of Finnish Steel and Metal Producers, Tekes and System Integrated Metal Processes (SIMP) program by FIMECC.

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