thermodynamic reassessment of the bao-b2o3 system

Thermodynamic Reassessment of the BaO-B2O3 SystemH. Yu, Q. Chen, and Zh. Jin

(Submitted 21 November 1998; in revised form 29 May 1999)

The BaO-B2O3 pseudobinary system is assessed. A two-sublattice ionic solution model, (Ba2+)P(O2–,BO3

3−, B4O72−, B3O4.5)Q, is adopted to describe the liquid phase. All the solid phases are treated as

stoichiometric compounds. A set of parameters consistent with most of the available experimentaldata on both phase diagram and thermodynamic properties is obtained by using CALPHAD tech-nique. A comparison between the calculated results and experimental data as well as a previous as-sessment is presented.

Introduction

Among alkali and alkaline earth borate systems, the BaO-B2O3 system is well known because of the discovery of theBBO crystal (βBaB2O4). It is important as an end-member ofmany higher-order borate systems, which may contain new fa-vorable crystals. As with other borate systems, the knowledgeof phase equilibria in this system is limited due to experimentalrestrictions. With the aid of the CALPHAD technique, thermo-dynamic assessment plays an important role in obtaining a pre-cise phase diagram and reliable thermochemical information.Moreover, this work is also a vital part of setting up a databaseon functional crystals.

The complicated structure of the borate amorphous phaseresults in numerous difficulties in the selection of a liquidmodel for borate systems. In previous assessments of CaO-B2O3 and BaO-B2O3 by [95Che], a two-sublattice ionic solu-tion model (Me2+)P(O2–, BO3

3−, B2O3)Q Me = Ca or Ba, wasadopted. Although the calculations in these systems can fit ex-perimental data within reasonable deviations, this model stillhas some limitations and failed to produce an acceptable resultin Li2O-B2O3 [97Yu1]. Hence, the authors modified this modelinto (Men+)P(O2–, BO3

3−, B4O72−, B3O4.5)Q, where Men+ repre-

sents metal cation, and assessed Li2O-B2O3 successfully[97Yu1].

In order to both unify the liquid model and confirm its fea-sibility in alkaline earth borate systems, the authors reassessedCaO-B2O3 [97Yu2]. Although the results do not differ from theprevious calculation significantly, which is natural because pa-rameters can be adjusted to fit the experimental data to someextent, improvements are still noticed, especially in the calcu-lated immiscibility region. In this article, the authors reassessBaO-B2O3 for the sake of unifying the liquid model in alkaliand alkaline earth borate systems.

Experimental Data

The shortage and scatter of experimental data in BaO-B2O3causes difficulties in the assessment. [49Lev] were the first to

report a relatively complete phase diagram of BaO-B2O3; fourcompounds—BaO⋅4B2O3, BaO⋅2B2O3, BaO⋅B2O3, and3BaO⋅B2O3—were found. Temperature measurements werelater repeated [53Lev]. Additionally, [58Ham] determinedseveral liquidus points in this system; their results are gener-ally in accordance with [53Lev].

Many researchers have contributed to the investigation ofthe liquid immiscibility region in BaO-B2O3 system, including[58Lev], [82Oht], [81Cle], [79Hag], and [87Hag]. Unfortu-nately, serious discrepancies among these data exist, and thedetermined critical temperatures vary within a temperaturerange of more than 200 K . This may be caused by experimentaldifficulties.

[53Lev] initially reported that BaB2O4 (BaO⋅B2O3), has anα ↔ β transformation at a temperature between 100 and 400°C. However, [69Hub] measured the temperature to be 925 ± 5°C. This is supported by later studies, 920 ± 10 °C by [82Jin]and 925 °C by [96Hik]. Thus, the authors adopted 925 °C inthe present work. Additionally, [96Hik] also determined themetastable melting point of βBaB2O4 to be 1372 K. These datawere also included in the optimization. This temperature isvery close to that of αBaB2O4, 1378 K, which indicates only asmall difference in the thermodynamic properties betweenthem.

Thermodynamic data for the BaO-B2O3 system are verylimited. [63Ste] determined heat capacities of glassy and crys-talline BaO⋅2B2O3 and BaO⋅4B2O3. [89Mul] measured themixing enthalpy of liquid at 1551 K. The authors includedthese data in the optimization.

Thermodynamic Model

The two-sublattice ionic solution model, (Men+)P(O2–,BO3

3−, B4O72−, B3O4.5)Q, were adopted for this article. The value

of subscripts P and Q in the formulation are changeable:

P = ∑ yi (−γi) = 2yO2− + 3yBO33− + 2yB

4O

72− (Eq 1)

Q = ∑ yj γj = yBa2+ = 2 (Eq 2)

where yi and γi and yj and γj represent the site fractions andcharges of anion i and cation j, respectively. The Gibbs energyof the liquid is expressed as:

H. Yu, Q. Chen, and Zh. Jin, Department of Materials Science and Engi-neering, Central South University of Technology, Changsha, Hunan410083, P.R. China. Present address for Q. Chen: Department of MaterialScience and Engineering, Royal Institute of Technology, S-10044, Stock-holm, Sweden. Contact e-mail: [email protected].

Basic and Applied Research: Section I

Journal of Phase Equilibria Vol. 20 No. 5 1999 479

GmL = yO2− 0GBa2+:O2− + yBO

33− 0GBa2+:BO

33− + yB

4O

72− 0GBa2+:B

4O

72−

+ 1.5 yB3O

4.5 0GB

2O

3 + R T(yO2− ln yO2− + yBO

33− ln yBO

33−

+ yB4O

72− ln yB

4O

72− + yB

3O

4.5 ln yB

3O

4.5) + Gm

ex (Eq 3)

where 0GBa2+:O2− and 0GB2O

3 represent the Gibbs energy of the

pure liquid BaO and B2O3, which come from the SGTE substancedatabase. 0GBa2+:BO

33− and 0GBa2+:B

4O

72− are the Gibbs energy of

the associates Ba3(BO3)2 and Ba2(B4O7)2 in the liquid respec-tively. R is gas constant; T is temperature. 0GBa2+:BO

33− is given

by Neumann-Kopp’s rule:

0GBa2+:BaO33− = 0G3BaO⋅B

2O

3

S + A + B T (Eq 4)

Because heat capacity curves of glassy and crystallineBaO⋅2B2O3 and BaO⋅4B2O3 have been found to be similar[63Ste], 0GBa2+:B

4O

72− is thus expressed as:

0GBa2+:B4O

72− = 2 0GBaO⋅2B

2O

3

S + C + D T (Eq 5)

where 0GBaO⋅2B2O

3

S is the Gibbs energy of crystallineBaO⋅2B2O3.

In Eq 3, Gmex is the excess Gibbs energy of liquid. For simpli-

fying this expression, one assumes that the same interactionsexist between neutral and anionic species, weighted per nega-tive charge. Additionally, another interaction parameter be-tween BO3

3− and B4O72− is used to avoid unrealistic

immiscibility in the region between them. Therefore, Gmex is de-

scribed by:

Table 1 Parameters for the BaO-B2O3 system (J/mole of formula units)

Liquid

0GBa2+:O2− = 2GBAOL0GB

3O

4.5 = 1.5GB2O3L

0GBa2+:BO33− = 3GBAOL + GB2O3L − 425,964.944 + 99.9297008 T

0GBa2+:B4O

72− = 2 0GBaO⋅2B

2O3 + 182,149.0308 − 9.660453 T

0L = –63,560.6090 – 60.6513205 T1L = –74,213.28602L = 13,899.73840LBa2+:BO

33−⋅B

4O

72− = −366,110.345

Solid B2O3

0GB2O

3

S = GB2O3S

BaO⋅4B2O3

0GBaO⋅4B2O3

= −5,880,719.74 + 1641.911415 T − 290.953517 T ln T − 0.111427633 T 2 + 2.65849867 × 106 T −1

BaO⋅2B2O3

0GBaO⋅2B2O3

= −3,316,249.845 + 975.6467177T − 172.663804 T ln T − 0.0532353780T 2 + 1.03216951 × 106 T −1

αBaO⋅B2O3

0GαBaO ⋅ B2O3

= GBAOS + GB2O3S − 168,651.488

βBaO⋅B2O3

0GβBaO ⋅ B2O3

= GBAOS + GB2O3S − 170,590.593 + 1.61868986 T

3BaO⋅B2O3

0G3BaO ⋅ B2O3

= 3GBAOS + GB2O3S − 371,288.073 + 71.8050568 T

Solid BaO

0GBaOS − GBAOS

Functions:

GB2O3L =–1,269,394.89 + 501,184.624 T –1 + 198.313176 T – 35.6509435 T ln T –0.0739858812 T 2 + 1.10697483 × 10–5 T 3 (298.14 < T < 400.00)–1,272,805.86 + 732,599.572 T –1 + 256.720618 T – 44.8913912 T ln T –0.0628129276 T 2 + 8.37141693 × 10–6 T 3 (400.00 < T < 723.00)–1,305,592.36 + 820.788302 T – 129.704 T ln T (723.00 < T < 3000.00)GB2O3S =–1,293,465.45 + 501,184.624 T –1 + 231.605779 T – 35.6509435 T ln T –0.0739858812 T 2 + 1.10697483 × 10–5 T 3 (298.14 < T < 400.00)–1,296,876.42 + 732,599.572 T –1 + 290.013221 T – 44.8913912 T ln T –0.0628129276 T 2 + 8.37141693 × 10–6 T 3 (400.00 < T < 723.00)–1,329,662.91 + 854.080905 T – 129.704 T ln T (723.00 < T < 3000.00)GBAOL = GBAOS + 58,576 – 26.623797 TGBAOS =–563,212.303 + 238.213889 T – 45.367112 T ln T – 0.0088301228 T 2 + 9.53812533 × 10–7T 3 + 126,373.536 T –1 (298.14 < T < 900.00)–566,075.47 + 277.305539 T – 51.308392 T ln T – 0.003335694 T 2 + 7.57304 × 10–9T 3 + 390,471.8 T –1 (900.00 < T < 2286.00)–584,226.131 + 398.668889 T – 66.944 T ln T (2286.00 < T < 2400.00)

Section I: Basic and Applied Research

480 Journal of Phase Equilibria Vol. 20 No. 5 1999

Gmex = 2 yO2−

yB3O

4.5

[0L + 1L(yO2− − yB3O

4.5) + 2L(yO2− − yB

3O

4.5)2]

+ 3 yBO33− yB

3O

4.5[0L + 1L(yBO

33− − yB

3O

4.5) + 2L(yBO

33− − yB

3O

4.5)2]

+ 2 yB4O

72− yB

3O

4.5 [0L + 1L(yB

4O

72− − yB

3O

4.5) + 2L(yB

4O

72− − yB

3O

4.5)2]

+ yBO33− yB

4O

72−

0LBa2+:BO33−,B

4O

72− (Eq 6)

All the compounds in BaO-B2O3 are stoichiometric. Sincethe heat capacities of BaO⋅2B2O3 and BaO⋅4B2O3 are avail-able, their Gibbs energy functions can be written as:

0G = a + bT + cT ln T + dT + eT −1 (Eq 7)

As to the other crystalline phases, the Gibbs energy is ex-pressed according to Neumann-Kopp’s rule:

0GxBaO⋅yB2O

3

S = x 0GBaOS + y 0GB

2O

3

S + A + BT (Eq 8)

Optimization and Calculation

All the optimizations and calculations are carried out withinTHERMO-CALC. The parameters are given in Table 1. Thecalculated BaO-B2O3 phase diagram is shown in Fig. 1, and de-tailed comparisons between the present and previous calcula-tion are also presented in Fig. 2 and 3.

As shown in Fig. 2, the calculated boundary of the miscibil-ity gap at low temperature is in agreement with the previouswork and fits most experimental data very well. Although thecalculated critical point is about 80 K lower than the previouscalculation and much closer to recent researches [87Hag], itdoes not indicate an improvement due to the scatter of experi-mental data. Such a difference can be eliminated by the adjust-ment of parameters; the calculation should be regarded as acompromise between those data and other information includ-ing thermochemical and phase equilibria data.

Fig. 1 Calculated phase diagram of the BaO-B2O3 system

Fig. 2 Comparison between the present and previously (dashedline) calculated miscibility gap together with experimental data

Table 2 Experimental and calculated invariant reactions in BaO-B2O3 system

[49Lev, 53Lev] [63Ste] [82Oht] [95Che] This workReactions T, K X(B2O3) T, K T, K X(B2O3) T, K X(B2O3) T, K X(B2O3)

L → BaO + Ba3B 1643 0.127 … … … 1619 0.107 1645 0.111L → Ba3B 1656 … … … … 1674 … 1654 …L → Ba3B + βBaB 1188 0.221 … … … 1191 0.226 1188 0.225L → αBaB 1378 … … … … 1378 … 1378 …L → βBaB + BaB2 1177 0.443 … … … 1166 0.424 1177 0.446L → BaB2 1183 … 1183 … … 1187 … 1183 …L → BaB2 + BaB4 1142 0.594 … … … 1144 0.574 1145 0.570L → BaB4 1162 … 1162 … … 1157 … 1161 …L1 → BaB4 + L2 1151 0.980 … 1151 0.989 1154 0.981 1154 0.983

… 0.700 … … 0.704 … 0.699 … 0.714

BaxBy represents crystalline phase xBaO⋅yB2O3. X, mole fraction



There are also some differences between the calculatedliquidus and that in the previous work; this is presented in Fig.3. The calculated liquidus of BaO⋅B2O3 is significantly im-proved, whereas that of 3BaO⋅B2O3 becomes worse. Accord-ing to the previous calculation, the temperature of the eutecticreaction L ↔ BaO + 3BaO⋅B2O3 was low and the meltingpoint of 3BaO⋅B2O3 was high, deviating markedly from the ex-perimental data. Sacrificing those data for invariant reactions,the previous calculation produced a very sharp liquidus for3BaO⋅B2O3 so that it would fit the data for the 3BaO⋅B2O3liquidus; this is believed to be unnecessary in the present work.Reasonably, the authors have paid more attention to tempera-tures of invariant reactions in the present assessment, as indi-cated in Table 2.

The calculated mixing enthalpy of the liquid phase at 1551K is presented in Fig. 4. The present assessment obtains nearlythe same results as the previous work. A large difference be-

tween the experimental data near the B2O3 end still exists.Besides large experimental errors in this region, such devia-tion is also caused by the same factors as in the earlier CaO-B2O3 assessment. The experimentally determined mixingenthalpy suggests a strong immiscibility tendency in the vi-cinity of B2O3. If so, the calculated miscibility gap is likelyto extend to an extremely high temperature, which is obvi-ously unrealistic. To some extent, the calculation could beregarded as a compromise between mixing enthalpy andmiscibility gap.

Figures 5 and 6 show the calculated heat content ofBaO⋅2B2O3 and BaO⋅4B2O3 together with related experimen-tal data from [63Ste]. Calculated thermodynamic propertiesincluding H298, S298, ∆Hfus, and ∆Sfus of crystalline phases arelisted in Table 3 together with previous work. Without any ex-perimental data, different results for BaO⋅B2O3 andBaO⋅3B2O3 are predicted by the two assessments.

Table 3 Calculated thermochemical properties of crystalline phases (standard reference state)

H298, S298, ∆Hfus, ∆Sfus,Phase J/mol J/mol ⋅ K J/mol J/mol ⋅ K Reference

BaO⋅4B2O3 5,766,278 402.979 115,183 99.253 This work5,753,792 433.230 115,389 99.700 [95Che]

115,583 99.469 [63Ste]BaO⋅2B2O3 3,253,140 224.050 85,719 72.435 This work

3,245,025 252.884 87,054 73.318 [95Che] 85,726 72.465 [63Ste]

BaO⋅B2O3(a) 1,992,195 124.369 72,294 52.475 This work1,965,852 166.213 43,838 31.812 [95Che]

3BaO⋅B2O3 3,289,115 198.568 183,488 110.913 This work3,321,172 264.995 201,244 120.247 [95Che]

(a) H298, S298 refer to βBaO⋅B2O3 and ∆Hfus, ∆Sfus refer to αBaO⋅B2O3

Fig. 3 Comparison between the present and previously (dashedline) calculated liquidus together with experimental data

Fig. 4 Calculated and experimentally determined [89Mul] mix-ing enthalpy of liquid at 1551 K (referred to liquid B2O3 and crys-talline BaO)



Figures 7 and 8 depict the calculated heat contents of liquidat the compositions of BaO⋅2B2O3 and BaO⋅4B2O3; they agreewith the experimental data very well at high temperature. Byextrapolating down to room temperature, they are also com-pared with the available information on glassy phases. The de-viations at lower temperature are caused by the differencesbetween glassy phase and supercooled liquid; as yet the glasstransformations cannot be dealt with.

Conclusions

The BaO-B2O3 pseudobinary system is assessed thermody-namically in this work. A two-sublattice ionic solution model

denoted (Ba2+)P(O2–, BO33−, B4O7

2−, B3O4.5)Q, is adopted to de-scribe the liquid. All solid phases are treated as stoichiometriccompounds. A set of parameters consistent with most of theavailable experimental data on both phase diagram and ther-modynamic properties is obtained through optimization. De-tailed comparison with previous work is also presented.

Acknowledgment

The authors wish to thank Prof. B. Sundman for providingthe software Thermo-Calc. This work is financially supportedby the National Advanced Materials Committee of China(NAMCC).

Fig. 5 Heat content of crystalline BaO⋅2B2O3 Fig. 6 Heat content of crystalline BaO⋅4B2O3

Fig. 7 Heat content of glass and liquid at XBaO = 0.333 (referredto crystalline BaO⋅2B2O3 at 298 K)

Fig. 8 Heat content of glass and liquid at XBaO = 0.2 (referred tocrystalline BaO⋅4B2O3 at 298 K



References

49Lev: E.M. Levin and H.F. McMurdie, The System BaO-B2O3, J.Res. Nat. Bur. Std., Vol 42 (No. 2), 1949, p 131-138

53Lev: E.M. Levin and G.M. Ugrinic, The System Barium Ox-ide-Boric Oxide-Silica, J. Res. Nat. Bur. Std., Vol 51 (No. 1),1953, p 37-56

58Ham: E.H. Hamilton, G.W. Cleek, and O.H. Grauer, Some Prop-erties of Glasses in the System Barium Oxide-Boric Oxide-Silica,J. Am. Ceram. Soc., Vol 41 (No. 6), 1958, p 209-215

58Lev: E.M. Levin and G.W. Cleak, Shape of Liquid ImmiscibilityVolume in the Barium Oxides-Boric Oxide-Silica, J. Am. Ceram.Soc., Vol 41 (No. 5), 1958, p 175-179

63Ste: D.R. Stewart and G.E. Rindone, High-Temperature En-ergy Relations in Borates: Alkaline-Earth and Lead BorateCompounds and Their Glasses, J. Am. Ceram. Soc., Vol 46 (No.12), 1963, p 593-596

69Hub: K.H. Hubner, Neues Jahrb. Min. Monatsh., 1963, p 33579Hag: V.B.M. Hageman and H.A.J. Oonk, The Region of Liquid

Immiscibility in the System B2O3-BaO, Phys. Chem. Glasses, Vol20 (No. 6), 1979, p 126-129

81Cle: K. Clemens, M. Yoshiyagawa, and M. Tomozawa, Liquid-Liquid Immiscibility in BaO-B2O3, J. Am. Ceram. Soc., Vol 64(No. 6)C, 1981, p 91-92

82Jin: J.-K. Liang, Y.-L. Zhang, and Q.-Z. Huang, The Kinetic Studyof BaB2O4 Phase Transition, Acta Chim. Sin., Vol 40 (No. 11),1982, p 994-1000

82Oht: Y. Ohta, K. Morinaga, and T. Yanagase, Liquid-Liquid Im-miscibility in Several Binary Borate Systems, J. Ceram. Soc. Jpn.,Vol 90 (No. 9), 1982, p 511-516

87Hag: V.B.M. Hageman and H.A.J. Oonk, Liquid Immiscibility inthe system B2O3-MgO, B2O3-CaO, B2O3-SrO and B2O3-BaOSystems, Phys. Chem. Glasses, Vol 28 (No. 5), 1987, p 183-187

89Mul: F. Müller and S. Demirok, Thermochemical Study of theLiquid Systems BaO-B2O3 and CaO-B2O3, Glastech. Ber., Vol 62(No. 4), 1989, p 142-149

95Che: Q. Chen, Ph.D. thesis, CSUT, Changsha, Hunan, P.R. China,1995

96Hik: K. Hikaru, K. Yasuhiko, S. Katesumi, et al., High Tempera-ture Powder X-Ray Diffraction Study of Barium MetaborateBaB2O4, Rep. Res. Lab. Eng. Mater., Tokyo Inst. Technol., Vol 19,1994, p 9-17; Ceram. Abstr., Vol 75 (No. 3), 1996, p 382, 75-06240A

97Yu1: H. Yu, Zh. Jin, Q. Chen, and M. Hillert, Thermodynamic As-sessment of Li2O-B2O3 System, submitted for publication in J.Am. Ceram. Soc.

97Yu2: H. Yu, Q. Chen, and Zh. Jin, Thermodynamic Reassessmentof CaO-B2O3 System, accepted for publication in Calphad



thermodynamic reassessment of the bao-b2o3 system

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