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Phase equilibria in the CoO–SiO2 system
L
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Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 127–132
1 9 7 3
www.elsevier.com/locate/calphad
Phase equilibria in the CoO–SiO2 system Leszek A. Zabdyra, Grzegorz Garzela, Olga B. Fabrichnayab,∗ a Institute of Metallurgy and Materials Science, Polish Academy of Sciences, Reymonta Str. 25, Krakow, 30-059, Poland b Max-Planck-Institut f¨ur Metallforschung and Universit¨at Stuttgart, Institut f¨ur Nichtmetallische Anorganische Materialien, Pulvermetallurgisches
Laboratorium, Heisenbergstr. 3, D-70569 Stuttgart, Germany Received 18 February 2003
Abstract The emf method was employed to determine thermodynamic properties of cobalt orthosilicate, taking into account two different crystallographic forms of silica: amorphous and quartz. Results were then compared to available literature data and used along with other experimental information of the system to evaluate a thermodynamic description by the CALPHAD method. © 2003 Elsevier Ltd. All rights reserved.
1. Introduction Knowledge of the phase equilibria in the system CoO–SiO2 is essential for understanding reactions and processes taking place during pyrometallurgical treatment of some copper ores containing cobalt. The constitutional study on the system cobalt oxide–silica was made by Masse and Muan [1] using the quenching technique supported by microscopic and X-ray examination. They also reviewed all the earlier studies on this subject, and as a result of their work the phase diagram of the CoO–SiO2 system in air was presented. According to [1], there is a large liquid miscibility gap on the silica-rich side of the system. The only intermediate phase in the system is cobalt orthosilicate Co2 SiO4 , with olivine-type structure, as a line compound melting congruently at 1688 K. There are two eutectics on both sides of it: 63 wt.% CoO at 1654 K, and 72 wt.% CoO at 1680 K, respectively. Some thermodynamic data for the CoO–SiO2 system are available, especially a number of works on cobalt orthosilicate formation. They were critically evaluated by Kale and Jacob [2], and recently by Kopyto et al. [3], underlining the considerable scatter of experimental data. In this situation a careful examination of orthosilicate formation reaction is needed over a wide temperature range, and with special attention paid on the explicitly defined crystal structures ∗ Corresponding author. Tel.: +49-711-689-3106; fax: +49-711-689-
3131. E-mail addresses: [email protected] (L.A. Zabdyr), [email protected] (O.B. Fabrichnaya). 0364-5916/$ - see front matter © 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0364-5916(03)00048-8
of reactants. Results are to be combined with the available experimental data on both thermodynamics and constitution of the system for a critical assessment by the CALPHAD method. 2. Experimental details The background of the emf technique employed in this study was similar to that used by [3], but for higher temperatures involved, different equipment was used. Differences also occurred in sample preparation. The scheme of the galvanic cell used was: Co, SiO2 , Co2 SiO4 |CSZ| air
(1)
where: CSZ—calcia-stabilized zirconia; air—reference electrode and with the overall cell reactions: 2Co + O2 + SiO2 (quartz) = Co2 SiO4 (olivine)
(2)
2Co + O2 + SiO2 (glass) = Co2 SiO4 (olivine)
(3)
for two forms of silica, respectively. The Gibbs energy change of such a cell reaction is directly related to its measured electromotive force E by the well-known relation: G 0T = RT ln pO2 − z F E.
(4)
In the case of air reference electrode Eq. (4) is equal to: G 0T = −12.975T − 4F E.
(5)
The schematic sketch of the cell arrangement is shown in Fig. 1. The vertical molybdenum furnace was used to
128
L.A. Zabdyr et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 127–132
achieve the required upper temperature limit of 1650 K, and the molybdenum winding was protected by the N2 –10% H2 gas mixture, supplied by the unique semiautomatic system; the patent procedure of this installation is currently under way. Temperature was controlled by a EUROTHERM 2404 device, and emf readings were taken by a high-resistance Keithley 2000 multimeter. A computer-controlled emf data acquisition system was used for both heating and cooling cycles within the temperature interval of 1150–1650 K.
Argon
Alumina shield tube CSZ electrolyte tube
Table 1 Crystallographic data and thermodynamic models for stable phases in the CoO–SiO2 system Phase
Pearson symbol, prototype
Model
CoO
cF8, NaCl
(Co+2 )(O−2 )
SiO2 quartz SiO2 tridymite SiO2 cristobalite
hP9, quartz hP12, tridymite cF24, cristabolite
SiO2 SiO2 SiO2
Co2 SiO4
oP28, olivine
(Co+2 )2 (Si+4 )(O−2 )4
Liquid
Pt current lead Pt current lead Moly furnace Working electrode
Thermocouple
(Co+2 )P (O−2 , SiO−4 4 , SiO2 )Q
Air
The source materials for sample preparation were as below:
Fig. 1. The scheme of the cell assembly.
– cobalt powder 99.9 + %, −100 mesh, from Johnson Mattey Inc. (USA); – cobalt oxide containing at least 72 wt.% of Co, “pure”, from POCH (Poland); – silicon acid, SiO2 ·H2 O, “pro analysis”, from CIECH (Poland); – quartz crystal of gem quality.
700
650
600
550 1100
3. Results Gibbs energy changes of the reactions (2) and (3) were calculated from measured emf values by means of relation (5) within investigated temperature intervals as below: −1
G 2 (±1521) = −506 124 + 162.09T J mol 1175–1574 K
(6)
−1
G 3 (±1494) = −513 999 + 169.66T J mol 1162–1624 K
(7)
SiO2 - amorphous SiO2 - quartz
750
E, mV
Silicon acid was fired in the air at 1300 K for 130 h, and after cooling the sample was analysed using X-ray examination. It was then used as a substrate in reaction (3) and for orthosilicate synthesis; quartz crystal was ground in the agate mortar. Appropriate amounts of amorphous silica and cobalt oxide were ground, pelletized and fired under argon at 1620 K for 6 h. The operation was repeated twice and the product was then checked by X-ray and by EPMA to confirm the olivine structure.
800
1200
1300
1400 T, K
1500
1600
1700
Fig. 2. Emf vs. temperature.
where: numbers in parentheses are single standard deviations, and the respective graphical plots are shown in Fig. 2. The value of G 2 calculated at 1273 K: −300 kJ mol−1 agrees excellently with −302.3 kJ mol−1 obtained by [2] and −302.6 kJ mol−1 from O’Neil [5]; the relative error is less than 1%.
L.A. Zabdyr et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 127–132
−5
260 240
[7] [8]
[2] [12] [14]
220
− 10 ∆Gf, ox kJ/mol
Cp, J/(mol.K)
129
200 180
− 15
160 140
600
900 Temperature, K
1200
− 20 800
1500
Fig. 3. The calculated heat capacity for Co2 SiO4 together with experimental data.
− 260 − 270
exp. - [1] 2300 2200 Liq1 + Liq2 2100 Temperature, K
∆Gf, el kJ/mol
1800
2400 [5] [3] [13] [11] [this study]
− 280 − 290 − 300 − 310 − 320
2000
Liq
1900 SiO2 (Cr) + Liq 1800 1700
− 330
CoO + Liq SiO2 (Tr) + Liq
1600
− 340
1500
− 350 − 360 800
1600
Fig. 5. Calculated Gibbs energy of formation of olivine from oxides together with experimental data.
− 240 − 250
1400 1200 Temperature, K
1000
SiO2 (Tr) + OL
1400 1000
1200 1400 Temperature, K
1600
1800
Fig. 4. Calculated Gibbs energy of formation of Co2 SiO4 from Co, oxygen and quartz together with experimental data.
The thermodynamic data for the CoO are from the SGTE database [6]. The heat capacity data are accepted from dropcalorimetry measurements of [7], which are in a good agreement with data of [8] obtained by adiabatic calorimetry. The standard entropy data from [8], solution calorimetry data of [9, 10], emf measurements from different works [2, 3, 5, 11, 12] along with results of the present study and gas equilibria [13, 14] were used to optimise standard entropy and enthalpy of formation of olivine. The thermodynamic parameters of liquid were assessed from the liquidus
0 SiO2
0.2
OL-Co 2 SiO4
120 300
0.4 0.6 Weight fraction CoO
OL + CoO
0.8
1.0 CoO
Fig. 6. Calculated phase diagram of the CoO–SiO2 system at air condition together with experimental data. Cr—cristobalite; Tr—tridymite; OL—olivine.
data of [1] and activity data of [15]. Data for SiO2 polymorphs come from [16]. 4. Thermodynamic modelling The phases stable in the CoO–SiO2 system and models used for their description are presented in Table 1. All solid phases are treated as stoichiometric compounds. The liquid phase is described by the partially ionic sublattice model [4]: (Co+2 )P (O−2 , SiO−4 4 , SiO2 )Q where P and Q
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Table 2 Thermodynamic description of the CoO–SiO2 system Quartz SiO2 298.15–6000
G(Quartz, SiO2 ) = GSIO2S
Tridymite SiO2 298.15–6000
G(Tridymite, SiO2 ) = GTRIDYM
Cristobalite SiO2 298.15–6000
G(Cristobalite, SiO2 ) = GCRISTOB
Halite CoO 298.15–6000
G(Halite,CoO) = GCOO S
Olivine Co2 SiO4 298.15–6000
G(Olivine, Co2 SiO4 ) = GCO2SIO4 S
IONIC LIQ
(Co+2 )P (O−2 , SiO−4 4 , SiO2 )Q
298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000
G(IONIC LIQ, Co+2 : O−2 ) = 2 · GCOO L
G(IONIC LIQ, Co+2 : SiO−4 4 ) = 4 · GCOO L + 2 · GSIO2LIQ − 46 768 G(IONIC LIQ, SiO2 ) = GSIO2LIQ
L0 (IONIC LIQ, Co+2 : O−2 , SiO2 ) = LCOSI0
L1 (IONIC LIQ, Co+2 : O−2 , SiO2 ) = LCOSI1 L2 (IONIC LIQ, Co+2 : O−2 , SiO2 ) = LCOSI2 L0 (IONIC LIQ, Co+2 : O−2 , SiO−4 4 ) = 31 398
L0 (IONIC LIQ, Co+2 : SiO−4 4 , SiO2 ) = 2 · LCOSI0 L1 (IONIC LIQ, Co+2 : SiO−4 4 , SiO2 ) = 2 · LCOSI1 L2 (IONIC LIQ, Co+2 : SiO−4 4 , SiO2 ) = 2 · LCOSI2
Functions 298.15–400
GCOO S = −255 168.144 + 363.157 222T − 63.3385T · ln T + 0.013 681 885T 2
400–2090
−258 744.641 + 374.407 411T − 63.869 86T · ln T + 0.009 143 755T 2 − 1.898 08 × 10−6 T 3 + 478 979.6/T
2090–4000
−270 112.723 + 414.705 451T − 67T · ln T
298.15–6000
GCOO L = GCOO + 40 000 − 19.138 756T
298.15–1690
GCO2SIO4 S = −1 473 594 + 1033T−170.8327T · ln T − 0.013 908T 2 + 2013 908.5/T
1690–1900
−1552 902.88 + 1591.07T−242.67T · ln T
298.15–373
GCRISTOB = −601 467.73 − 8140.2255T + 1399.8908T · ln T − 2.857 9085T 2 + 0.001 040 8145T 3 − 13 144 016/T
373–453
−1498 711.3 + 13 075.913T − 2178.3561T · ln T + 3.493 609T 2 − 0.001 076 2132T 3 + 29 100 273/T
453–543
−3224 538.7 + 47 854.938T − 7860.2125T · ln T + 11.817 149T 2 − 0.003 365 1832T 3 + 1.275 0272 × 108 /T
543–3300
−943 127.51 + 493.260 56T − 77.5875T · ln T + 0.003 040 245T 2 − 4.631 18 × 10−7 T 3 + 2 227 125/T
3300–4000
−973 891.99 + 587.056 06T − 87.373T · ln T
298.15–540
GSIO2S = −900 936.64 − 360.892 175T + 61.1323T · ln T − 0.189 203 605T 2 + 4.950 9742 × 10−5 T 3 − 854 401/T
540–770
−1091 466.54 + 2882.672 75T − 452.1367T · ln T + 0.428 883 845T 2 − 9.091 770 6 × 10−5 T 3 + 12 476 689/T
770–848
−1563 481.44 + 9178.586 55T − 1404.5352T · ln T + 1.284 044 26T 2 − 2.350 476 57 × 10−4 T 3 + 56 402 304/T
848–1800
−928 732.923 + 356.218 325T − 58.4292T · ln T − 0.005 159 95T 2 − 2.47 × 10−10 T 3 − 95113/T
1800–2960
−924 076.574 + 281.229 013T − 47.451T · ln T − 0.012 003 15T 2 + 6.78127 × 10−7 T 3 + 665 385/T
2960–4000
−957 997.4 + 544.992 084T − 82.709T · ln T
298.15–388
GTRIDYM = −918 008.73 + 140.559 25T − 25.1574T · ln T − 0.014 871 4T 2 − 2.279 183 3E-05T 3 + 66 331/T
388–433
−921 013.31 + 224.538 08T − 37.8701T · ln T − 0.023 685 35T 2 − 1.6835 × 10−7 T 3
433–900
−919 633.42 + 210.516 51T − 35.605T · ln T − 0.030 499 85T 2 + 4.6255 × 10−6 T 3 − 162 026/T
900–1668
−979 377.7 + 848.3098T − 128.434T · ln T + 0.0338 7055T 2 − 3.786 883 × 10−6 T 3 + 7070 800/T
1668–3300
−943 685.26 + 493.580 35T − 77.5875T · ln T + 0.003 040 245T 2 − 4.63 118 × 10−7 T 3 + 222 7125/T
3300–4000
−974 449.74 + 587.375 85T − 87.373T · ln T
298.15–2980
GSIO2LIQ = −923 689.98 + 316.247 66T − 52.17T · ln T − 0.012 002T 2 + 6.78 × 10−7 T 3 + 665 550/T
2980–4000
−957 614.21 + 580.014 19T − 87.428T · ln T
298.15–6000
LCOSI0 = 288.84 + 16.97T
298.15–6000
LCOSI1 = −170 735.36 + 90.95T
298.15–6000
LCOSI2 = 96 827.44
Parameters optimised in this study are in bold.
L.A. Zabdyr et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 127–132
+ Q RT (yO−2 ln yO−2 + ySiO−4 ln ySiO−4
(a)
4
1.1 [17]
+ ySiO2 ln ySiO2 ) +
T = 1723 K
1.0
E
4
Gm
(8)
where: E
0.9
G m = yCo+2 yO−2 ySiO2 L Co+2 :O−2 ,SiO2
+ yCo+2 ySiO−4 ySiO2 L Co+2 :SiO−4 ,SiO2 4
0.8 a (CoO)
131
4
+ yCo+2 yO−2 ySiO−4 L Co+2 :O−2 ,SiO−4 4
0.7
(9)
4
and L A,B:C parameters described by the Redlich–Kister polynomial are assessed in this study
0.6
L A,B:C = L 0 (y A − y B ) + L 1 (y A − y B ) + L 2 (y A − y B )2 . 0.5
(10)
0.4
5. Results 0.3 0.50
0.55
0.65
0.60 X (Liq, CoO)
0.70
(b)
The thermodynamic description of the CoO–SiO2 system is presented in Table 2.
1.0 [17]
Table 3 The enthalpy and entropy data for Co2 SiO4
T = 1773 K
0.9
a (CoO)
0.8
T (K)
Property
Experimental
Reference
965
∆H f,ox, kJ mol−1
−21.6 ± 2.1
[9]
−21.43
−23.3 ± 0.8
[10]
−21.15
142.6 ± 0.2
[8]
142.12
986
0.7
298.15
0 , J(mol−1 K−1 ) S298
Calculated
0.6 Table 4 The invariant reactions in the system CoO–SiO2
0.5
Reaction
Calculated T K/wt.% CoO in the liquid
Experimental T K/wt.% CoO in the liquid
Liquid = Olivine + Tridymite
1637/63.0
1653/63
Liquid = CoO + Olivine
1689/72.7
1680/72
Fig. 7. Calculated activities of CoO in liquid along with experimental data for 1723 K (a) and 1773 K (b), respectively.
Liquid = Olivine
1690
1688
Cristobalite = Tridymite + Liquid
1744/61.5
1743/62
are numbers of sites on the cation and anion sublattice, respectively. The P and Q vary with composition to maintain electroneutrality: yi (−vi ) + yV a Q and Q= yjvj P=
Liquid 2 = Liquid 1 + Cristobalite
1965/1.2, 55.5
1978/3.0, 55
0.4 0.3 0.50
0.55
0.60 X (Liq, CoO)
i
0.65
0.70
j
where: νi is the valency of ion i . Summation over i is made for all anions and summation over j is made for all cations; vacancies, V a, are not considered here, hence yV a = 0. According to this model the Gibbs energy for the liquid phase is given by: G m = yCo+2 yO−2 0 G (Co+2 )2 (O−2 )2 + yCo+2 ySiO−4 0 G (Co+2 ) 4
−4 4 (SiO4 )2
+ ySiO2 0 G SiO2
The calculated heat capacity together with experimental data are presented in Fig. 3. The standard entropy and enthalpy of formation from oxides for olivine along with experimental data are presented in Table 3. Calculated parameters of the invariant reactions of the system are listed in Table 4 along with their experimental equivalents. The calculated Gibbs energy for reaction (2) and the reaction of formation of Co2 SiO4 from oxides are presented in Figs. 4 and 5 together with experimental data. The comparison with experimental data shows a good
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L.A. Zabdyr et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 127–132
agreement of calculated thermodynamic values with those experimentally measured in Fig. 4. The differences between calculations and experimental data presented in Fig. 5 are within uncerainty limits of experimental data and they are partially due to differences in thermochemical data for oxides used by [2, 12, 14] and those employed in this study. The calculated phase diagram of the CoO–SiO2 system along with data of [1] is presented in Fig. 6. The obtained thermodynamic description reproduces the experimental phase diagram reasonably well. The calculated activity of CoO in the liquid at temperatures 1723 and 1773 K is shown in Fig. 7a and b along with experimental data [15]. The calculated values agree with experimental data within uncertainty limits. References [1] D.P. Masse, A. Muan, Trans. AIME 233 (1965) 1448.
[2] G.M. Kale, K.T. Jacob, Trans. Inst. Min. Metall. (Section C) 98 (1989) C117. [3] M. Kopyto, L.A. Zabdyr, K. Fitzner, Arch. Metallurgy 46 (4) (2001) 447. [4] M. Hillert, J. Alloys Comp. 320 (2001) 161. [5] H.St.C. O’Neil, Am. Mineral. 72 (1987) 280. [6] 98SGTE, Thermocalc Database SSUB98. [7] H. Watanabe, in: S. Akimoto, M.H. Manghnani (Eds.), High-Pressure Research in Geophysics, Tokyo, 1982, p. 441. [8] R.A. Robie, H.B. Hemingway, Am. Mineral. 67 (1982) 470. [9] A. Navrotsky, J. Inorg. Nucl. Chem. 33 (1971) 4035. [10] A. Navrotsky, F.S. Pintchovski, S. Akimoto, Phys. Earth Planet. Inter. 19 (1979) 275. [11] G. Rog, B. Langauke, G. Borhardt, H. Schmalzried, J. Chem. Thermodyn. 6 (1974) 1113. [12] A. Kozlowska-Rog, G. Rog, Polish J. Chem. 58 (1979) 2083. [13] B.G. Lebedev, V.A. Levitski, V.A. Burtsev, Russ. J. Phys. Chem. 36 (1962) 460. [14] E. Aukrust, A. Muan, J. Am. Ceram. Soc. 46 (1963) 358. [15] I.B. Smith, C.R. Masson, Canad. J. Chem. 49 (1971) 683. [16] B. Hallstadt, CALPHAD 16 (1992) 53.
P
H
A
A
C
D
Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 127–132
1 9 7 3
www.elsevier.com/locate/calphad
Phase equilibria in the CoO–SiO2 system Leszek A. Zabdyra, Grzegorz Garzela, Olga B. Fabrichnayab,∗ a Institute of Metallurgy and Materials Science, Polish Academy of Sciences, Reymonta Str. 25, Krakow, 30-059, Poland b Max-Planck-Institut f¨ur Metallforschung and Universit¨at Stuttgart, Institut f¨ur Nichtmetallische Anorganische Materialien, Pulvermetallurgisches
Laboratorium, Heisenbergstr. 3, D-70569 Stuttgart, Germany Received 18 February 2003
Abstract The emf method was employed to determine thermodynamic properties of cobalt orthosilicate, taking into account two different crystallographic forms of silica: amorphous and quartz. Results were then compared to available literature data and used along with other experimental information of the system to evaluate a thermodynamic description by the CALPHAD method. © 2003 Elsevier Ltd. All rights reserved.
1. Introduction Knowledge of the phase equilibria in the system CoO–SiO2 is essential for understanding reactions and processes taking place during pyrometallurgical treatment of some copper ores containing cobalt. The constitutional study on the system cobalt oxide–silica was made by Masse and Muan [1] using the quenching technique supported by microscopic and X-ray examination. They also reviewed all the earlier studies on this subject, and as a result of their work the phase diagram of the CoO–SiO2 system in air was presented. According to [1], there is a large liquid miscibility gap on the silica-rich side of the system. The only intermediate phase in the system is cobalt orthosilicate Co2 SiO4 , with olivine-type structure, as a line compound melting congruently at 1688 K. There are two eutectics on both sides of it: 63 wt.% CoO at 1654 K, and 72 wt.% CoO at 1680 K, respectively. Some thermodynamic data for the CoO–SiO2 system are available, especially a number of works on cobalt orthosilicate formation. They were critically evaluated by Kale and Jacob [2], and recently by Kopyto et al. [3], underlining the considerable scatter of experimental data. In this situation a careful examination of orthosilicate formation reaction is needed over a wide temperature range, and with special attention paid on the explicitly defined crystal structures ∗ Corresponding author. Tel.: +49-711-689-3106; fax: +49-711-689-
3131. E-mail addresses: [email protected] (L.A. Zabdyr), [email protected] (O.B. Fabrichnaya). 0364-5916/$ - see front matter © 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0364-5916(03)00048-8
of reactants. Results are to be combined with the available experimental data on both thermodynamics and constitution of the system for a critical assessment by the CALPHAD method. 2. Experimental details The background of the emf technique employed in this study was similar to that used by [3], but for higher temperatures involved, different equipment was used. Differences also occurred in sample preparation. The scheme of the galvanic cell used was: Co, SiO2 , Co2 SiO4 |CSZ| air
(1)
where: CSZ—calcia-stabilized zirconia; air—reference electrode and with the overall cell reactions: 2Co + O2 + SiO2 (quartz) = Co2 SiO4 (olivine)
(2)
2Co + O2 + SiO2 (glass) = Co2 SiO4 (olivine)
(3)
for two forms of silica, respectively. The Gibbs energy change of such a cell reaction is directly related to its measured electromotive force E by the well-known relation: G 0T = RT ln pO2 − z F E.
(4)
In the case of air reference electrode Eq. (4) is equal to: G 0T = −12.975T − 4F E.
(5)
The schematic sketch of the cell arrangement is shown in Fig. 1. The vertical molybdenum furnace was used to
128
L.A. Zabdyr et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 127–132
achieve the required upper temperature limit of 1650 K, and the molybdenum winding was protected by the N2 –10% H2 gas mixture, supplied by the unique semiautomatic system; the patent procedure of this installation is currently under way. Temperature was controlled by a EUROTHERM 2404 device, and emf readings were taken by a high-resistance Keithley 2000 multimeter. A computer-controlled emf data acquisition system was used for both heating and cooling cycles within the temperature interval of 1150–1650 K.
Argon
Alumina shield tube CSZ electrolyte tube
Table 1 Crystallographic data and thermodynamic models for stable phases in the CoO–SiO2 system Phase
Pearson symbol, prototype
Model
CoO
cF8, NaCl
(Co+2 )(O−2 )
SiO2 quartz SiO2 tridymite SiO2 cristobalite
hP9, quartz hP12, tridymite cF24, cristabolite
SiO2 SiO2 SiO2
Co2 SiO4
oP28, olivine
(Co+2 )2 (Si+4 )(O−2 )4
Liquid
Pt current lead Pt current lead Moly furnace Working electrode
Thermocouple
(Co+2 )P (O−2 , SiO−4 4 , SiO2 )Q
Air
The source materials for sample preparation were as below:
Fig. 1. The scheme of the cell assembly.
– cobalt powder 99.9 + %, −100 mesh, from Johnson Mattey Inc. (USA); – cobalt oxide containing at least 72 wt.% of Co, “pure”, from POCH (Poland); – silicon acid, SiO2 ·H2 O, “pro analysis”, from CIECH (Poland); – quartz crystal of gem quality.
700
650
600
550 1100
3. Results Gibbs energy changes of the reactions (2) and (3) were calculated from measured emf values by means of relation (5) within investigated temperature intervals as below: −1
G 2 (±1521) = −506 124 + 162.09T J mol 1175–1574 K
(6)
−1
G 3 (±1494) = −513 999 + 169.66T J mol 1162–1624 K
(7)
SiO2 - amorphous SiO2 - quartz
750
E, mV
Silicon acid was fired in the air at 1300 K for 130 h, and after cooling the sample was analysed using X-ray examination. It was then used as a substrate in reaction (3) and for orthosilicate synthesis; quartz crystal was ground in the agate mortar. Appropriate amounts of amorphous silica and cobalt oxide were ground, pelletized and fired under argon at 1620 K for 6 h. The operation was repeated twice and the product was then checked by X-ray and by EPMA to confirm the olivine structure.
800
1200
1300
1400 T, K
1500
1600
1700
Fig. 2. Emf vs. temperature.
where: numbers in parentheses are single standard deviations, and the respective graphical plots are shown in Fig. 2. The value of G 2 calculated at 1273 K: −300 kJ mol−1 agrees excellently with −302.3 kJ mol−1 obtained by [2] and −302.6 kJ mol−1 from O’Neil [5]; the relative error is less than 1%.
L.A. Zabdyr et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 127–132
−5
260 240
[7] [8]
[2] [12] [14]
220
− 10 ∆Gf, ox kJ/mol
Cp, J/(mol.K)
129
200 180
− 15
160 140
600
900 Temperature, K
1200
− 20 800
1500
Fig. 3. The calculated heat capacity for Co2 SiO4 together with experimental data.
− 260 − 270
exp. - [1] 2300 2200 Liq1 + Liq2 2100 Temperature, K
∆Gf, el kJ/mol
1800
2400 [5] [3] [13] [11] [this study]
− 280 − 290 − 300 − 310 − 320
2000
Liq
1900 SiO2 (Cr) + Liq 1800 1700
− 330
CoO + Liq SiO2 (Tr) + Liq
1600
− 340
1500
− 350 − 360 800
1600
Fig. 5. Calculated Gibbs energy of formation of olivine from oxides together with experimental data.
− 240 − 250
1400 1200 Temperature, K
1000
SiO2 (Tr) + OL
1400 1000
1200 1400 Temperature, K
1600
1800
Fig. 4. Calculated Gibbs energy of formation of Co2 SiO4 from Co, oxygen and quartz together with experimental data.
The thermodynamic data for the CoO are from the SGTE database [6]. The heat capacity data are accepted from dropcalorimetry measurements of [7], which are in a good agreement with data of [8] obtained by adiabatic calorimetry. The standard entropy data from [8], solution calorimetry data of [9, 10], emf measurements from different works [2, 3, 5, 11, 12] along with results of the present study and gas equilibria [13, 14] were used to optimise standard entropy and enthalpy of formation of olivine. The thermodynamic parameters of liquid were assessed from the liquidus
0 SiO2
0.2
OL-Co 2 SiO4
120 300
0.4 0.6 Weight fraction CoO
OL + CoO
0.8
1.0 CoO
Fig. 6. Calculated phase diagram of the CoO–SiO2 system at air condition together with experimental data. Cr—cristobalite; Tr—tridymite; OL—olivine.
data of [1] and activity data of [15]. Data for SiO2 polymorphs come from [16]. 4. Thermodynamic modelling The phases stable in the CoO–SiO2 system and models used for their description are presented in Table 1. All solid phases are treated as stoichiometric compounds. The liquid phase is described by the partially ionic sublattice model [4]: (Co+2 )P (O−2 , SiO−4 4 , SiO2 )Q where P and Q
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Table 2 Thermodynamic description of the CoO–SiO2 system Quartz SiO2 298.15–6000
G(Quartz, SiO2 ) = GSIO2S
Tridymite SiO2 298.15–6000
G(Tridymite, SiO2 ) = GTRIDYM
Cristobalite SiO2 298.15–6000
G(Cristobalite, SiO2 ) = GCRISTOB
Halite CoO 298.15–6000
G(Halite,CoO) = GCOO S
Olivine Co2 SiO4 298.15–6000
G(Olivine, Co2 SiO4 ) = GCO2SIO4 S
IONIC LIQ
(Co+2 )P (O−2 , SiO−4 4 , SiO2 )Q
298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000 298.15–6000
G(IONIC LIQ, Co+2 : O−2 ) = 2 · GCOO L
G(IONIC LIQ, Co+2 : SiO−4 4 ) = 4 · GCOO L + 2 · GSIO2LIQ − 46 768 G(IONIC LIQ, SiO2 ) = GSIO2LIQ
L0 (IONIC LIQ, Co+2 : O−2 , SiO2 ) = LCOSI0
L1 (IONIC LIQ, Co+2 : O−2 , SiO2 ) = LCOSI1 L2 (IONIC LIQ, Co+2 : O−2 , SiO2 ) = LCOSI2 L0 (IONIC LIQ, Co+2 : O−2 , SiO−4 4 ) = 31 398
L0 (IONIC LIQ, Co+2 : SiO−4 4 , SiO2 ) = 2 · LCOSI0 L1 (IONIC LIQ, Co+2 : SiO−4 4 , SiO2 ) = 2 · LCOSI1 L2 (IONIC LIQ, Co+2 : SiO−4 4 , SiO2 ) = 2 · LCOSI2
Functions 298.15–400
GCOO S = −255 168.144 + 363.157 222T − 63.3385T · ln T + 0.013 681 885T 2
400–2090
−258 744.641 + 374.407 411T − 63.869 86T · ln T + 0.009 143 755T 2 − 1.898 08 × 10−6 T 3 + 478 979.6/T
2090–4000
−270 112.723 + 414.705 451T − 67T · ln T
298.15–6000
GCOO L = GCOO + 40 000 − 19.138 756T
298.15–1690
GCO2SIO4 S = −1 473 594 + 1033T−170.8327T · ln T − 0.013 908T 2 + 2013 908.5/T
1690–1900
−1552 902.88 + 1591.07T−242.67T · ln T
298.15–373
GCRISTOB = −601 467.73 − 8140.2255T + 1399.8908T · ln T − 2.857 9085T 2 + 0.001 040 8145T 3 − 13 144 016/T
373–453
−1498 711.3 + 13 075.913T − 2178.3561T · ln T + 3.493 609T 2 − 0.001 076 2132T 3 + 29 100 273/T
453–543
−3224 538.7 + 47 854.938T − 7860.2125T · ln T + 11.817 149T 2 − 0.003 365 1832T 3 + 1.275 0272 × 108 /T
543–3300
−943 127.51 + 493.260 56T − 77.5875T · ln T + 0.003 040 245T 2 − 4.631 18 × 10−7 T 3 + 2 227 125/T
3300–4000
−973 891.99 + 587.056 06T − 87.373T · ln T
298.15–540
GSIO2S = −900 936.64 − 360.892 175T + 61.1323T · ln T − 0.189 203 605T 2 + 4.950 9742 × 10−5 T 3 − 854 401/T
540–770
−1091 466.54 + 2882.672 75T − 452.1367T · ln T + 0.428 883 845T 2 − 9.091 770 6 × 10−5 T 3 + 12 476 689/T
770–848
−1563 481.44 + 9178.586 55T − 1404.5352T · ln T + 1.284 044 26T 2 − 2.350 476 57 × 10−4 T 3 + 56 402 304/T
848–1800
−928 732.923 + 356.218 325T − 58.4292T · ln T − 0.005 159 95T 2 − 2.47 × 10−10 T 3 − 95113/T
1800–2960
−924 076.574 + 281.229 013T − 47.451T · ln T − 0.012 003 15T 2 + 6.78127 × 10−7 T 3 + 665 385/T
2960–4000
−957 997.4 + 544.992 084T − 82.709T · ln T
298.15–388
GTRIDYM = −918 008.73 + 140.559 25T − 25.1574T · ln T − 0.014 871 4T 2 − 2.279 183 3E-05T 3 + 66 331/T
388–433
−921 013.31 + 224.538 08T − 37.8701T · ln T − 0.023 685 35T 2 − 1.6835 × 10−7 T 3
433–900
−919 633.42 + 210.516 51T − 35.605T · ln T − 0.030 499 85T 2 + 4.6255 × 10−6 T 3 − 162 026/T
900–1668
−979 377.7 + 848.3098T − 128.434T · ln T + 0.0338 7055T 2 − 3.786 883 × 10−6 T 3 + 7070 800/T
1668–3300
−943 685.26 + 493.580 35T − 77.5875T · ln T + 0.003 040 245T 2 − 4.63 118 × 10−7 T 3 + 222 7125/T
3300–4000
−974 449.74 + 587.375 85T − 87.373T · ln T
298.15–2980
GSIO2LIQ = −923 689.98 + 316.247 66T − 52.17T · ln T − 0.012 002T 2 + 6.78 × 10−7 T 3 + 665 550/T
2980–4000
−957 614.21 + 580.014 19T − 87.428T · ln T
298.15–6000
LCOSI0 = 288.84 + 16.97T
298.15–6000
LCOSI1 = −170 735.36 + 90.95T
298.15–6000
LCOSI2 = 96 827.44
Parameters optimised in this study are in bold.
L.A. Zabdyr et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 127–132
+ Q RT (yO−2 ln yO−2 + ySiO−4 ln ySiO−4
(a)
4
1.1 [17]
+ ySiO2 ln ySiO2 ) +
T = 1723 K
1.0
E
4
Gm
(8)
where: E
0.9
G m = yCo+2 yO−2 ySiO2 L Co+2 :O−2 ,SiO2
+ yCo+2 ySiO−4 ySiO2 L Co+2 :SiO−4 ,SiO2 4
0.8 a (CoO)
131
4
+ yCo+2 yO−2 ySiO−4 L Co+2 :O−2 ,SiO−4 4
0.7
(9)
4
and L A,B:C parameters described by the Redlich–Kister polynomial are assessed in this study
0.6
L A,B:C = L 0 (y A − y B ) + L 1 (y A − y B ) + L 2 (y A − y B )2 . 0.5
(10)
0.4
5. Results 0.3 0.50
0.55
0.65
0.60 X (Liq, CoO)
0.70
(b)
The thermodynamic description of the CoO–SiO2 system is presented in Table 2.
1.0 [17]
Table 3 The enthalpy and entropy data for Co2 SiO4
T = 1773 K
0.9
a (CoO)
0.8
T (K)
Property
Experimental
Reference
965
∆H f,ox, kJ mol−1
−21.6 ± 2.1
[9]
−21.43
−23.3 ± 0.8
[10]
−21.15
142.6 ± 0.2
[8]
142.12
986
0.7
298.15
0 , J(mol−1 K−1 ) S298
Calculated
0.6 Table 4 The invariant reactions in the system CoO–SiO2
0.5
Reaction
Calculated T K/wt.% CoO in the liquid
Experimental T K/wt.% CoO in the liquid
Liquid = Olivine + Tridymite
1637/63.0
1653/63
Liquid = CoO + Olivine
1689/72.7
1680/72
Fig. 7. Calculated activities of CoO in liquid along with experimental data for 1723 K (a) and 1773 K (b), respectively.
Liquid = Olivine
1690
1688
Cristobalite = Tridymite + Liquid
1744/61.5
1743/62
are numbers of sites on the cation and anion sublattice, respectively. The P and Q vary with composition to maintain electroneutrality: yi (−vi ) + yV a Q and Q= yjvj P=
Liquid 2 = Liquid 1 + Cristobalite
1965/1.2, 55.5
1978/3.0, 55
0.4 0.3 0.50
0.55
0.60 X (Liq, CoO)
i
0.65
0.70
j
where: νi is the valency of ion i . Summation over i is made for all anions and summation over j is made for all cations; vacancies, V a, are not considered here, hence yV a = 0. According to this model the Gibbs energy for the liquid phase is given by: G m = yCo+2 yO−2 0 G (Co+2 )2 (O−2 )2 + yCo+2 ySiO−4 0 G (Co+2 ) 4
−4 4 (SiO4 )2
+ ySiO2 0 G SiO2
The calculated heat capacity together with experimental data are presented in Fig. 3. The standard entropy and enthalpy of formation from oxides for olivine along with experimental data are presented in Table 3. Calculated parameters of the invariant reactions of the system are listed in Table 4 along with their experimental equivalents. The calculated Gibbs energy for reaction (2) and the reaction of formation of Co2 SiO4 from oxides are presented in Figs. 4 and 5 together with experimental data. The comparison with experimental data shows a good
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L.A. Zabdyr et al. / Computer Coupling of Phase Diagrams and Thermochemistry 27 (2003) 127–132
agreement of calculated thermodynamic values with those experimentally measured in Fig. 4. The differences between calculations and experimental data presented in Fig. 5 are within uncerainty limits of experimental data and they are partially due to differences in thermochemical data for oxides used by [2, 12, 14] and those employed in this study. The calculated phase diagram of the CoO–SiO2 system along with data of [1] is presented in Fig. 6. The obtained thermodynamic description reproduces the experimental phase diagram reasonably well. The calculated activity of CoO in the liquid at temperatures 1723 and 1773 K is shown in Fig. 7a and b along with experimental data [15]. The calculated values agree with experimental data within uncertainty limits. References [1] D.P. Masse, A. Muan, Trans. AIME 233 (1965) 1448.
[2] G.M. Kale, K.T. Jacob, Trans. Inst. Min. Metall. (Section C) 98 (1989) C117. [3] M. Kopyto, L.A. Zabdyr, K. Fitzner, Arch. Metallurgy 46 (4) (2001) 447. [4] M. Hillert, J. Alloys Comp. 320 (2001) 161. [5] H.St.C. O’Neil, Am. Mineral. 72 (1987) 280. [6] 98SGTE, Thermocalc Database SSUB98. [7] H. Watanabe, in: S. Akimoto, M.H. Manghnani (Eds.), High-Pressure Research in Geophysics, Tokyo, 1982, p. 441. [8] R.A. Robie, H.B. Hemingway, Am. Mineral. 67 (1982) 470. [9] A. Navrotsky, J. Inorg. Nucl. Chem. 33 (1971) 4035. [10] A. Navrotsky, F.S. Pintchovski, S. Akimoto, Phys. Earth Planet. Inter. 19 (1979) 275. [11] G. Rog, B. Langauke, G. Borhardt, H. Schmalzried, J. Chem. Thermodyn. 6 (1974) 1113. [12] A. Kozlowska-Rog, G. Rog, Polish J. Chem. 58 (1979) 2083. [13] B.G. Lebedev, V.A. Levitski, V.A. Burtsev, Russ. J. Phys. Chem. 36 (1962) 460. [14] E. Aukrust, A. Muan, J. Am. Ceram. Soc. 46 (1963) 358. [15] I.B. Smith, C.R. Masson, Canad. J. Chem. 49 (1971) 683. [16] B. Hallstadt, CALPHAD 16 (1992) 53.