Critical assessment and thermodynamic modeling of the Cu–O and Cu–O–S systems

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 59–70

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Critical assessment and thermodynamic modeling of the Cu–O and Cu–O–S systems Denis Shishin, Sergei A. Decterov n ´cole Polytechnique, Montre´al, Que´bec, Canada Centre de Recherche en Calcul Thermochimique (CRCT), De´p. de Ge´nie Chimique, E

a r t i c l e i n f o

abstract

Article history: Received 8 February 2012 Received in revised form 17 April 2012 Accepted 19 April 2012 Available online 9 May 2012

Critical evaluation, thermodynamic modeling and optimization of the Cu–O and Cu–O–S systems are presented. The liquid phase over the whole composition range from metallic liquid to sulfide melt to oxide melt is described by a single model developed within the framework of the quasichemical formalism. The model reflects the existence of strong short-range ordering in oxide, sulfide and oxysulfide liquid. Two ranges of maximum short-range ordering in the Cu–O system at approximately the Cu2O and CuO compositions are taken into account. Parameters of thermodynamic models are optimized to reproduce all available thermodynamic and phase equilibrium data within experimental error limits. The optimization of the Cu–O and Cu–O–S systems performed in the present study is of particular importance for the description of the solubility of oxygen in matte and liquid copper. The obtained self-consistent set of model parameters can be used as a basis for development of a thermodynamic database for simulation of copper smelting and converting. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Copper smelting Matte Slag Thermodynamic modeling Phase diagram

1. Introduction The present study is part of an ongoing research project which is aimed at developing a thermodynamic database for simulation of copper extraction from sulfide concentrates. The major phases that form during copper smelting and converting are blister copper (a liquid metal phase rich in Cu), matte (a molten sulfide phase containing mainly Cu, S and Fe), slag (a molten oxide phase) and gas. In principle, all the three liquid phases represent just one liquid with miscibility gaps. Liquid metal, matte and slag can be completely miscible over certain ranges of temperature and composition, even though this normally does not happen under industrial conditions. It is desirable to have one general thermodynamic model which can describe all the three liquid phases simultaneously, but this is very difficult to achieve because the model must reflect quite different atomic interactions that are intrinsic to metallic, sulfide and oxide phases. In early studies, matte was often modeled as a mixture of stoichiometric sulfides Cu2S–FeS. Sometimes, stoichiometric oxide components were also added to account for the solubility of oxygen in the matte phase [1]. In reality, the composition of matte can substantially deviate from the stoichiometric sulfides, even though matte exhibits strong short-range ordering (SRO) which results from the fact that metal-sulfur nearest-neighbor

n

Corresponding author. Tel.: þ1 514 340 4711x5796; fax: þ 1 514 340 5840. E-mail addresses: [email protected] (D. Shishin), [email protected] (S.A. Decterov). 0364-5916/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.calphad.2012.04.002

pairs are energetically favored over metal–metal and sulfur– sulfur pairs. This was successfully described by the modified quasichemical model (MQM) [2,3]. However, matte and blister copper were modeled as two different phases in the resulting thermodynamic database that was developed for simulation of copper smelting and converting [3]. Later, Waldner and Pelton [4,5] applied the generalized version of the MQM [6,7] to describe matte and liquid metal in the Cu– Fe–S system as one continuous solution. The present work was undertaken to add oxygen to this solution with a view to account for appreciable solubility of oxygen in industrial matte and liquid copper [8,9] which is of practical importance. The second objective was to explore the possibility of describing all three phases, liquid metal, matte and slag, by one solution. To this end, all oxygen-containing subsystems of the Cu–Fe–O–S system must be optimized using the Calphad technique. The optimizations of the Cu–O and Cu–O–S systems are presented in this article, and the other subsystems will be reported elsewhere. In a thermodynamic ‘‘optimization’’ of a system, all available thermodynamic and phase diagram data are evaluated simultaneously in order to obtain one set of model equations for the Gibbs energies of all phases as functions of temperature and composition. From these equations, all of the thermodynamic properties and the phase diagrams can be back-calculated. In this way, all the data are rendered self-consistent and consistent with thermodynamic principles. Thermodynamic property data, such as activity data, can aid in the evaluation of the phase diagram, and phase diagram measurements can be used to deduce thermodynamic properties. Discrepancies in the available data can often be resolved, and

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D. Shishin, S.A. Decterov / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 59–70

interpolations and extrapolations can be made in a thermodynamically correct manner. A small set of model parameters is obtained. This is ideal for computer storage and calculation of properties and phase diagrams. In the present study, all calculations were carried out using the FactSage thermochemical software and databases [10].

2. Thermodynamic models 2.1. Liquid solution Modeling of the liquid phase in the Cu–O–S system is a challenging task. No attempts were found in the literature to model this liquid over the entire composition range from liquid metal to oxysulfide melt. The thermodynamic model must describe drastic changes in the activity of sulfur and oxygen which are the result of strong short-range ordering at the Cu2S and Cu2O compositions, respectively. Furthermore, in the Cu–O system, there must be a maximum in short-range ordering at the CuO composition as well, even though no experimental data are available in this region because the oxygen pressure is too high. Schmid [11] and later Clavaguera-Mora et al. [12] modeled the Cu–O liquid using an associated solution model. Schmid [11] optimized 7 temperature-dependent parameters, whereas Clavaguera-Mora et al. [12] described the liquid with one excess parameter, but only up to the composition of Cu2O. In the Cu–O system, Hallstedt et al. [13,14] successfully used the twosublattice ionic liquid model with Cu þ 1 and Cu þ 2 on the first sublattice and O  2 and charged vacancy on the second one. Schramm et al. [15] added Cu þ 3 on the first sublattice to better describe the CuO liquidus at high oxygen pressures. In the present work, a model for the liquid phase is developed within the framework of the quasichemical formalism [6,7]. It has just one sublattice containing four species: CuI, CuII, S and O, where CuI and CuII correspond to two oxidation states of copper atoms. In the Cu–O system, the fraction of the CuI–O pairs goes through a maximum at about the Cu2O composition, while the CuII–O pairs are most abundant at the CuO composition. All species are not charged, so the condition of electroneutrality is not imposed and the model represents the liquid phase from metal to nonmetals. Figs. 1 and 2 illustrate the concept of two oxidation states of Cu which bring about two compositions of maximum short-range ordering in Cu–O liquid. The calculated entropy of mixing between pure liquid Cu and hypothetical pure liquid oxygen has two local minima which correspond to maximum short-range ordering at the Cu2O and CuO compositions. There are no reliable experimental data on the oxidation states of copper in the liquid phase, but the drastic transition of CuI to CuII between the Cu2O and CuO compositions seems physically reasonable. The curves in Figs. 1 and 2 were calculated using the optimized model parameters for the liquid phase; for the sake of simplicity, the miscibility gap in the liquid and formation of all other phases were suppressed. To explain the meaning of parameters of the quasichemical formalism, let us consider a binary solution formed by components A and B. The formulae and notations of the quasichemical formalism were described in detail elsewhere [6,7] and only a brief summary is given here. In the pair approximation of the modified quasichemical model, the following pair exchange reaction is considered: ðA2AÞ þ ðBBÞ ¼ 2ðA2BÞ; Dg AB

ð1Þ

where (i–j) represents a first-nearest-neighbor pair and Dg AB is the non-configurational Gibbs energy change for the formation of two moles of (A–B) pairs. When the solution is formed from pure components A and B, some (A–A) and (B–B) pairs break to form (A–B) pairs, so the Gibbs

Fig. 1. Calculated entropy of mixing in Cu–O liquid at 1200 1C.

Fig. 2. Calculated distribution of copper between CuI and CuII in Cu–O liquid at 1200 1C.

energy of mixing is given by [6]:

Dg mix ¼ gðnA g 3A þnB g 3B Þ ¼ T DSconfig þ

n  AB

2

Dg AB

ð2Þ

where g 3A and g 3B are the molar Gibbs energies of pure liquid components; nA , nB and nAB are the numbers of moles of A, B and (A–B) pairs and DSconfig is the configurational entropy of mixing given by randomly distributing the (A–A), (B–B) and (A–B) pairs. Since no exact expression is known for the entropy of this distribution in three dimensions, an approximate equation is used which was shown [6] to be an exact expression for a one dimensional lattice (Ising model) and to correctly reduce to the random mixing point approximation (Bragg Williams) expression when Dg AB is equal to zero.

D. Shishin, S.A. Decterov / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 59–70

ði þ jÞ Z 1

Dg 3AB

g ijAB

and are the parameters of the model which can be where functions of temperature. In practice, only the parameters g i0 AB and g 0j need to be included. AB The composition of maximum short-range ordering is determined by the ratio of the coordination numbers. Let Z A and Z B be the coordination numbers of A and B. These coordination numbers can vary with composition as follows [6]:     1 1 2nAA 1 nAB ¼ A þ A ð4Þ ZA Z AA 2nAA þ nAB Z AB 2nAA þ nAB     1 1 2nBB 1 nAB ¼ B þ B ZB Z BB 2nBB þnAB Z BA 2nBB þnAB

ð5Þ

where Z AAA and Z AAB are the values of Z A when all the nearest neighbors of an A are As, and when all the nearest neighbors of an A are Bs, respectively, and where Z BBB and Z BBA are defined similarly. For example, in order to set the composition of maximum short-range ordering at the molar ratio nA =nB ¼ 2, one can set the ratio Z BBA =Z AAB ¼ 2. Values of Z BBA and Z AAB are unique to the A–B binary system, while the value of Z AAA is common to all systems containing A as a component. Even though the model is sensitive to the ratio of the coordination numbers, it is less sensitive to their absolute values. We have found by experience that selecting values of the coordination numbers which are smaller than actual values often yields better results. This is due to the inaccuracy introduced by an approximate equation for the configurational entropy of mixing which is only exact for a one dimensional lattice. The smaller coordination numbers partially compensate this inaccuracy in the model equations, being more consistent with a one dimensional lattice. Therefore, the ‘‘coordination numbers’’ in our model are essentially treated as model parameters which are used mainly to set a physically reasonable composition of maximum short-range ordering. There are ten possible pairs formed by the species CuI, CuII, O, and S in the Cu–O–S liquid phase. The fractions of all pairs are calculated by the Gibbs energy minimization procedure built into the FactSage software [10] using the optimized model parameters. CuI–CuI, O–O and S–S are the predominant pairs at compositions close to pure Cu, O and S, respectively. The CuI–O, CuII–O and CuI–S pairs are dominant in the oxide and sulfide liquids, whereas the fractions of the CuI–CuII, CuII–CuII, O–S and CuII–S pairs are small at all compositions of interest. Extrapolation of binary terms into the CuI–CuII–O–S system is done by an asymmetric ‘‘Toop-like’’ method [7]. The components are divided into two groups: metals (CuI and CuII) and nonmetals (S and O). By this means in every ternary subsystem, one component belongs to a different group than the other two. ‘‘Toop-like’’ extrapolation is applied, taking this ‘‘different’’ component as an asymmetric component. Except for the binary terms, the model can have ternary terms, Dg ABðCÞ , which give the effect of the presence of component C upon the energy Dg AB of pair exchange reaction (1). Ternary terms are also expanded as empirical polynomials having model parameters g ijk ABðCÞ . The formulae for ternary terms and for extrapolation of binary and ternary terms into a multicomponent system are discussed in detail elsewhere [7].

Bragg–Williams random mixing model was used with the following formula (per mole of atoms): g ¼ ðX Cu g oCu þ X O g oO þ X S g oS Þ þRTðX Cu ln X Cu þX O ln X O þ X S ln X S Þ þ X Cu X S LCu,S þ X Cu X O LCu,O

are the mole fraction and molar Gibbs energy of where X i and component i, Li,j represents an interaction energy between i and j, which can be a function of temperature and composition. 2.3. Digenite Digenite is a copper sulfide mineral with the formula Cu2  xS. In the present study, this name is reserved for the solid solution which is stable above about 73 1C and has a cubic structure, space group Fm3m. Digenite containing a substantial amount of dissolved iron is called bornite. The nature of the nonstoichiometry in digenite and bornite is complex and can be explained by the formation of different defects, for example by the substitution of one Cu2 þ cation and a vacancy for two Cu1 þ cations or by the substitution of a charged vacancy for one Cu1 þ cation. The digenite solid solution was described by Waldner and Pelton [5] using a simple Bragg–Williams random mixing model applied to the formula unit (Cu2,Va)S: g ¼ ðX Cu2 S g oCu2 S þ X VaS g oVaS Þ þRTðX Cu2 S ln X Cu2 S þ X VaS ln X VaS Þ n X LkCu2 S,VaS ðX VaS X Cu2 S Þk þ X Cu2 S X VaS

Sulfur and oxygen are soluble to some extent in Cu metal, which has an FCC structure at the conditions of interest. Simple

ð7Þ

k¼0

where X i and g 3i are the mole fraction and molar Gibbs energy of component i, and the last term represents an expansion of the interaction energy between i and j in a Redlich–Kister power series. A Bragg–Williams random mixing model applied to the formula unit (Cu,Va)2S has also been tested, but it required twice the number of parameters for a similar description of the data on sulfur potential. Furthermore, the first formula unit written as (Cu2,Fe,Va)S appeared to be more suitable for expansion to the bornite solid solution [5]. The solubility of oxygen in digenite was not modeled due to the lack of experimental data.

3. The Cu–S system The Cu–S system was optimized by Waldner and Pelton [5]. The phase diagram is shown in Fig. 3 along with the experimental data [16–29] and the optimized model parameters are given

2000 1800

L1 -5 -4

1600

log10 (P(S2), atm) -3

-2 -1 0 +1 +2 L1 (Cu-liq) + L2 (Matte)

L2 (Matte)

1400

[21] [22] [23] [24] [25] [26] [27] [28] [29]

[16] [17] [18] [19] [20]

1200 1000

L1 (Cu-liq) + Digenite

L2 (Matte) + L3 (Sulfur)

800 L3 (Sulfur) + Digenite

fcc + Digenite 600 400

L3 (Sulfur) + CuS(s) fcc + Cu2S(s2)

200

Digenite + CuS(s)

fcc + Cu2S(s)

0

2.2. Solid FCC copper

ð6Þ

g 3i

Temperature, °C

Dg AB can be expanded as an empirical polynomial in terms of the mole fractions of pairs [6]: X ij i j Dg AB ¼ Dg 3AB þ g AB X AA X BB ð3Þ

61

0

0.1

0.2

CuS(s) + S(s2) CuS(s) + S(s)

0.3

0.4 0.5 0.6 Molar ratio S/(Cu + S)

0.7

0.8

0.9

1

Fig. 3. Calculated phase diagram of the Cu–S system along with experimental data [16–29] and S2 isobars. The formation of the gas phase is suppressed.

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D. Shishin, S.A. Decterov / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 59–70

Table 1 Calculated invariant points in the Cu–O–S system. T (1C)

Cu

O

S

log10[P(O2) (atm)]

log10[P(S2) (atm)]

log10[P(SO2) (atm)]

0.66951 0.98671 0.66139 0.97668 0.65202 0.66206 0.64789 0.63094 0.63241 0.65064

0.00935 0.00081 0.16056 0.01697 0.09398 0.07388 0.06867 0.36869 0.36689 0.02082

0.32114 0.01248 0.17806 0.00635 0.25400 0.26406 0.28344 0.00037 0.00070 0.32854

 8.12

 7.12

 1.43

 5.61

 7.82

0.82

 7.27  8.49  5.19  1.22  1.30  4.20

 8.06  9.43  5.05  8.71  8.25  2.41

2.93 0.27 4.30 3.70 3.81 5.33

1

Digeniteþ L1 þL2 þ fcc

1070.1

2

Cu2O þL1 þ L2 þfcc

1060.6

3 4 5 6 7 8

Cu2O þdigenite þ Cu2SO4 þ L2 Cu2O þdigenite þ fccþL2 Cu2SO4 þCuSO4 þ digeniteþ L2 (CuO)(CuSO4) þCu2Oþ CuSO4 þ L2 Cu2O þCu2SO4 þ CuSO4 þ L2 CuSO4 þL2 þ digeniteþ L3

773.8 819.9 920.7 1170.5 1175.5 1026.4

in Table 2. Solid CuS, S and low-temperature Cu2S were assumed to be stoichiometric phases, while FCC and digenite (high-temperature Cu2S) were modeled as solid solutions. Contrary to Cu–O liquid, the Cu–S liquid phase was modeled in such a way that Cu exists almost exclusively as CuI over the whole composition range from metal to sulfur. This is because CuS is much less stable than solid CuO and there is no experimental evidence for strong short-range ordering in the liquid phase at the CuS composition which corresponds to very high S2 partial pressures. Contradictory experimental data have been reported for the miscibility gap on the Cu-rich side of the phase diagram. Waldner and Pelton [5] gave preference to the data suggesting a wider miscibility gap with high convolution temperature. This choice resulted in correct prediction of thermodynamic properties and phase equilibria in the Cu–Fe–S ternary system from the binaries without introducing ternary parameters. Details of the optimization will be reported elsewhere.

4. The Cu–O system 4.1. Phase diagrams The phase diagram of the Cu–O system is shown in Fig. 4. This system has been much studied experimentally for compositions between Cu and Cu2O. There is more uncertainty in experimental measurements over the range of mole fractions of oxygen from 0.33 to 0.45 and no data are available beyond X O ¼0.45. The Cu–O system was critically assessed by Hallstedt et al. [13,14] who suggested the following invariant points [13]: A. B. C. D. E. F. G. H.

Eutectic: L (Cu liquid)$Cu (FCC)þ Cu2O Monotectic: L (oxide liquid)$L (Cu liquid)þCu2O Congruent melting point of Cu2O: Cu2O$L (oxide liquid) Eutectic: L (oxide liquid)$Cu2OþCuO Melting of Cu2O in air: Cu2OþO2$ L (oxide liquid) Melting of CuO in oxygen: CuO$L (oxide liquid) þO2 Convolution point: L (Cu liquid) þL (oxide liquid)$L Congruent melting point of CuO: CuO$L (oxide liquid)

These points and experimental data [30–49] are shown in Figs. 4 and 5. The scatter of the experimental data collected by Hallstedt et al. [13] for each invariant point is shown by bars. No data are available for point H because the oxygen pressure is too high to suppress the formation of the gas phase and measure the melting temperature. 4.2. Solid Cu2O and CuO Thermodynamic properties of solid stoichiometric compounds Cu2O and CuO have been well studied. A comprehensive review of the experimental data was reported by Hallstedt et al. [13] and

their optimized thermodynamic functions of solid Cu2O and CuO were accepted in the present study. 4.3. Liquid phase A drastic increase of the oxygen potential is observed in the liquid phase near the Cu2O composition, as can be seen from Fig. 6. This is the result of short-range ordering. Hallstedt et al. [13] recalculated the EMF vs. T data of Taskinen [34,41] into isotherms log10 P(O2) vs. X O which are plotted in Fig. 6. The equilibrium oxygen contents of the liquid phase higher than 0.34 were measured at fixed P(O2) as a function of temperature [36,46]. The nearly linear shape of these isobars (see Fig. 4) makes it possible to interpolate the X O values to a given temperature and plot the data as log10 P(O2) vs. X O isotherms, as shown in Fig. 6. The solubility of oxygen in liquid copper at high dilution has been studied repeatedly. The most thorough are the latest measurements of Otsuka and Kozuka [50] and Taskinen [34,41]. The equality of the chemical potentials of oxygen in the liquid and gas phase can be written as

mO ¼ 0:5mOþ2 ðTÞ þ RT lnðgO X O Þ ¼ 0:5½mOþ2 ðTÞ þ RT ln PðO2 Þ

ð8Þ

þ O2

where m is the Gibbs energy of ideal O2 gas at 1 atm, gO is the activity coefficient of oxygen in the liquid phase and PðO2 Þ is the equilibrium oxygen partial pressure in atm. Hence ln gO ¼ 0:5 lnPðO2 Þln X O

ð9Þ

In the Cu-rich region up to X O  0:1, ln gO changes nearly linearly with composition. Hallstedt et al. [13] suggested recalculating all available experimental data in this region into ln gO and expressing it as a linear function: ln gO ¼ lnðg3O ðTÞÞþ eO O ðTÞX O

ð10Þ

is the activity coefficient of oxygen at infinite dilution where g and eO O ðTÞ is the first-order interaction coefficient. It is common practice to recalculate g3O ðTÞ into the ‘‘Gibbs energy of dissolution of oxygen in liquid Cu at infinite dilution with 1 mol% O liquid and 1 atm O2 gas as reference states’’ defined as  3  g ðTÞ DG31%OðliqÞ ðTÞ  RT ln O ð11Þ 100 3 O ðTÞ

Substitution of Eq. (9) and (10) into Eq. (11) gives " !# 100X O 3 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DG1%OðliqÞ ðTÞ ¼ lim RT ln X O -0 PðO2 Þ,atm

ð12Þ

DG31%OðliqÞ ðTÞ is convenient because it is a nearly linear function of

temperature. The first-order interaction coefficient, eO O ðTÞ, is close to be a linear function of inverse temperature (in K). These functions are presented in Figs. 7 and 8. The lines calculated from the model parameters optimized in the present study are shown along with

D. Shishin, S.A. Decterov / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 59–70

63

Table 2 Optimized properties of stoichiometric compounds and model parameters for the liquid phase, fcc and digenite solid solutions in the Cu–O–S system (J mol  1 and J mol  1 K  1). Compounds

Temperature range (K)

DHo298:15

So298:15

C P ðTÞ

CuO (tenorite) Cu2O CuS (covellite)

 155,192.1  170,258.2  48,575.8

43.0626 92.6796 75.8612

 83,515.5

116.7648

 81,278.2

122.1507

0.0000

32.05400

361.6

33.02366

 769,982.0  752,850.0

109.25395 182.42240

(CuO)(CuSO4)

298–3000 298–3000 298–1000 41000 298–376 4376 298–923 4923 298–368.3 368.3–1300 41300 298–388.36 388.36–1300 41300 298–2000 298–1000 41000 298–1500

 927,593.0

157.31802

49.0300 þ 0.006940T  780,000T  2 66.2600 þ 0.015920T  748,000T  2 43.6710 þ0.020136T  4.7200  10  9T2  210,120T  2 63.5925 53.0000 þ 0.078743T 82.6073 111.0000  0.0307524T 82.6155 11.0070 þ 0.053058T  4.6526  10  5T2 17.9418 þ0.021790T  8.4153  10  6T2  79,820T  2 32.0000 17.3180 þ0.020243T 21.1094 þ0.017208T  6.7085  10  6T2  241,480T  2 32.0000  38.4487 þ 0.030146T þ13,239,629T  2  192,652.41T  1 þ 10,802.62175T  0.5 99.5792 þ0.069454T 169.0336  43.4719 þ 0.065865T þ 10,404,443.8T  2  184,939.21T  1 þ11,535.83175T  0.5

Solutions

Temperature range (K)

Cu2S (chalcocite) Cu2S (high T chalcocite) S (orthorhombic)

S (monoclinic)

CuSO4 Cu2SO4

Modified quasichemical model (CuI, CuII, O, S), grouping: CuI, CuII in group 1; O, S in group 2

Liquid (metal, oxide, sulfide). I

II

Molar Gibbs energy g(T)

I

II

Cu Cu O S Z Cu ¼ Z Cu ¼ Z SSS ¼ Z O OO ¼ Z CuI CuII ¼ Z CuII CuI ¼ Z OS ¼ Z SO ¼ 6, CuI CuI CuII CuII

I

Z Cu ¼ 1:5, CuI S

Z SSCuI ¼ 3,

I

Z Cu ¼ 1:6, CuI O

ZO ¼ 3, OCuI

II

Z SSCuII ¼ Z Cu ¼ 3, CuII S

II

ZO ¼ Z Cu ¼2 OCuII CuII O

g 3CuI

298–2990 2990–3500 298–1358

121,184.8 þ136.0406T  24.50000T ln T  9.8420  10  4T2  0.12938  10  6T3 þ322,517T  1 102,133.3 þ231.9844T  36.20000T ln T 5194.4 þ120.9752T  24.11239T ln T  0.00265684T2 þ 0.12922  10  6T3 þ52,478T  1  5.83932  10  21T7

g 3CuII

1358–3500 298–3500

 46.9þ 173.8837T  31.38000T ln T g 3CuI þ 4781.5

g 3O

g 3S

298–388.36 388.36–428.15 428.15–432.25 432.25–453.15 453.15–717 717–3500

Dg 3CuI S

 4001.5 þ 77.9057T  15.50400T ln T  0.0186290T2  0.24942  10  6T3  113,945T  1  5,285,183.2 þ 118,449.6004T  19,762.4000T ln T þ32.79275100T2  10221.417  10  6T3 þ 264,673,500T  1  8,174,994.8 þ 319,914.0872T  57,607.2990T ln T þ 135.3045000T2  52,997.333  10  6T3  219,408.8 þ 7758.8558T  1371.8500T ln T þ 2.8450351T2  1013.8033  10  6T3 92,539.8  1336.3502T þ202.9580T ln T  0.2531915T2 þ 51.8835  10  6T3  8,202,200T  1  6890.0 þ 176.3709T  32.0000T ln T  67,166.116  8.695398T

g 10 CuI S

55,282.59  5.6751299T

g 20 CuI S

7511.4858

g 30 CuI S

 24,638.853

g 90 CuI S

 836.8 þ2.5104T

g 01 CuI S

11,621.957

g 02 CuI S

36,336.6  15.02049T

g 04 CuI S

33,205

Dg 3CuI O

 189,802.98 þ 2.21752T

g 10 CuI O

43,618.2  13.598T

g 20 CuI O

 4142.16

g 50 CuI O

7252.2667  2.3709333T  228,446.4  16.736T

Dg 3CuII O Dg 3CuI CuII

83,680  217,568

g 011 CuI OðSÞ FCC (solid Cu)

Bragg–Williams (Cu, O, S)

g 3Cu

298–1358 1358–2000 298–368.3 368.3–2000 298–2000

g 3S g 3O LCu,S LCu,O

 7770.5 þ130.4854T  24.1124T ln T  0.002657T2 þ0.12922  10  6T3 þ 52,478T  1  13,542.3 þ 183.8042T  31.3800T ln T þ 3.64643  1029T  9 60,442.6 þ67.0953T  11.0070T ln T  0.026529T2 þ2.3  10  5T  1 59,932.6 þ103.2150T  17.9418T ln T  0.010895T2 þ 1.40256  10  6T3 þ 39,910T  1 120,184.8 þ139.1406T  24.5000T ln T  9.8420  10  4T2–0.12938  10  6T3 þ322,517T  1  62,550.39  38.424305T  170,498  21.00368T

Digenite

Bragg–Williams (Cu2, vacancy)S

g 3Cu2 S

298–1450

 99,688.1 þ 420.44593T  83.0000T ln T

g 3VaS

298–363.3 363.3–1300

L1Cu,Va:S

60,853.7 þ65.02737T  11.0070T ln T  0.026529T2 þ 7.754333  10  6T3 59,568.9 þ104.30253T  17.9418T ln T  0.010895T2 þ1.402558  10  6T3 þ39,910T  1  70,031.8 þ15.712907T

L2Cu,Va:S

59,052.83

The Gibbs energy of formation of a compound from elements in their standard state at a temperature of T (K) and a pressure of 1 atm is given by DG ¼ DHo298:15 TSo298:15 þ RT RT o o 298:15 C P ðTÞdTT 298:15 C P ðTÞ=TdT, where DH298:15 is the enthalpy of formation of the compound at 1 atm and 298.15 K, S298:15 is the entropy of the compound at 1 atm and 298.15 K, and C P ðTÞ is the heat capacity at constant pressure.

64

D. Shishin, S.A. Decterov / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 59–70

-5 -4 -3 . 5

1400

-3

log10(P (O2 ), atm)

L

-2 -1 0

1

2

P (O2) = 0.21 atm

1450

G

1350

H

-0.5

1200 1150 1100 A

1050 1000 0

0.1

0.2

0.3 Molar ratio O/(Cu+O)

0.4

0.5

0.6

Fig. 4. Calculated phase diagram of the Cu–O system along with experimental points [30–45] and invariant points from assessment [15]. Dashed lines are calculated oxygen isobars. The scatter of the experimental data collected by Hallstedt et al. [13] for each invariant point is shown by bars. Gas phase is suppressed.

-2.5

-3.5

-4.5

-5.5 0

0.1

0.2 0.3 0.4 Molar ratio O/(Cu+O)

0.5

0.6

Fig. 6. Calculated oxygen potential in Cu–O liquid expressed as isotherms along with experimental points [34,36,41,46].

-0.60

optimized in [15] [49] [48] [47] [45] [36] [33], [46] [44] [38] [40] [34] [39]

-0.62 -0.64 -0.66

-1

[P (O ), atm]

1250

–1000/T, K

[34], [41] 1100 °C 1150 °C 1200 °C 1250 °C 1300 °C 1350 °C 1400 °C 1450 °C [36] 1350 °C 1150 °C, interpolated 1350 °C, interpolated [46] 1200 °C, interpolated 1300 °C, interpolated

-1.5 [30] C [31],[32] L1 (Cu-liq) + L2 (Oxide) [33] B B [34] [35] L (Cu-liq) + Cu 2 O [36] [37] [38] Cu2 O + L (Oxide) E L + CuO [39] [40] F [41] [42] D [43] Cu2 O + CuO [44] P (O 2 ) = 0.21 atm fcc (Cu-solid) + Cu 2 O [45] Optimized in [15]

log

Temperature, °C

1300

-0.68

G

L (Oxide) C

-73.0

B

-73.5

-0.70

-74.0

E L (Cu-liquid)

-74.5

-0.72 F -0.74

-75.0

D A

-0.76

Cu 2O

CuO

-75.5

fcc (Cu-solid)

-76.0

-0.78

-76.5

-0.80 -8

-6

-4 -2 log10 [P (O2), atm]

0

2

Fig. 5. Calculated potential phase diagram of the Cu–O system along with experimental points [33,34,36,38,39,44–49] and invariant points from assessment [15]. The scatter of the experimental data collected by Hallstedt et al. [13] for each invariant point is shown by bars. The gas phase is suppressed.

the assessment of Hallstedt et al. [13] and selected experimental data [34,36,41,50] recalculated by Hallstedt et al. [13]. The Gibbs energy of formation of liquid Cu2O from liquid copper and O2 gas at 1 atm was estimated by Taskinen [41] from EMF studies. His data along with the results of other authors are shown in Fig. 9. He also measured the Gibbs energy of formation of solid Cu2O by an EMF technique. From the temperature dependencies of these Gibbs energies, the enthalpy of melting of Cu2O was evaluated to be 73 kJ/mol [41]. A more direct measurement of the enthalpy of melting was reported by Mah et al. [51] who studied the heat content of Cu2O. The heat content data [51,52] are shown in Fig. 10. The enthalpy of congruent melting of Cu2O derived from the measurements of Mah et al. [51] is 64.7 kJ/mol, which is in good agreement with the value of 64.4 kJ/mol optimized in the present study. The optimized model parameters are given in Table 2. The end members of the liquid phase are pure liquid CuI, CuII and hypothetical pure liquid oxygen which should not be confused with real molecular liquid oxygen. The Gibbs energy of pure liquid copper, g 3CuI , was taken from the SGTE database [54]. g 3CuII is essentially the

-77.0 -77.5 -78.0 1100

1200

Present study [34] [13], assessment

1300 Temperature, °C

1400

1500

[50] [41] Others reviewed in [13]

Fig. 7. Gibbs energy of dissolution of oxygen in liquid Cu at infinite dilution with 1 mol % O liquid and 1 atm O2 gas as reference states. Dotted and dashed lines represent the experimental data [34,41,50] and the assessment of Hallstedt et al. [13]. Thin solid lines show other series of experimental data reviewed by Hallstedt et al. [13].

same, but a positive value is added to suppress its formation in pure Cu (see Fig. 2). A positive excess parameter Dg 3CuI CuII is added for the same purpose. The Gibbs energy of pure liquid oxygen, g 3O , is not known and was estimated in the present study from the thermodynamic properties of liquid oxides in the FactSage database [10]. For example, the standard entropy of liquid oxygen at 298.15 K, S3298 ðOÞ, can be obtained as a first approximation from the entropies of liquid Mn2O3 and MnO, assuming the additivity of entropies:S3298 ðOÞ ¼ S3298 ðMn2 O3 Þ2S3298 ðMnOÞ. Other pairs of liquid oxides were also considered: TiO2 and Ti2O3, CuO and

D. Shishin, S.A. Decterov / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 59–70

-4

65

180 Cu O, [51]

160 -5

Cu O, [52]

H (T) - H (25 °C), kJ/mol

140 -6

-7

-8

Present study 120

Optimized in [13]

100 80 60 40

-9 0.70

0.68

0.66 0.64 1000/T, K-1

Present study [34] [13], assessment

0.62

0.60

[36] [41] Others reviewed in [13]

Fig. 8. First-order interaction coefficient for O in liquid Cu. Dotted and dashed lines represent the experimental data [34,36,41] and the assessment of Hallstedt et al. [13]. Thin solid lines show other series of experimental data reviewed by Hallstedt et al. [13].

-50 Present study [36] cited in [41] [38] cited in [41] [53] cited in [41] [41]

-51

Gf, kJ/mol

-52 -53 -54 -55 -56 -57 -58 1220

1240

1260 1280 1300 Temperature, °C

1320

1340

20 0 0

200

400

600 800 1000 Temperature, °C

1200

1400

Fig. 10. Heat content of Cu2O: experimental points [51,52] and calculated lines indicating optimizations of the present study and of Hallstedt et al. [13].

Several optimization attempts have been made with different values of g 3O . The resulting excess parameters were rather different, but the thermodynamic properties of the liquid phase at X O r 0:5 were almost the same. This means that the Gibbs energy of the liquid phase is well constrained by the experimental data which are adequately fitted by the model. Large negative parameters Dg 3CuI O and Dg 3CuII O were required to reproduce the liquidus in the Cu2O–CuO region. It is the balance between Dg 3CuI O and Dg 3CuII O that defines the shape of the liquidus and P(O2) in this region. The miscibility gap between metallic and oxide liquid is created by a positive parameter g 10 . During the CuI O optimization, all available experimental points were considered simultaneously and two more excess parameters were required to adequately reproduce all of them. The optimized parameters are strongly correlated and, therefore, are given in Table 2 with relatively large numbers of significant digits. As can be seen from Figs. 4–10, the experimental data are well reproduced by the model. The composition of maximum shortrange ordering between CuI and O was moved from XO ¼0.333 to 0.348 in order to prevent the P(O2) vs. X O isotherms in Fig. 6 from rising too early. These isotherms still look a little too steep at X O from 0.30 to 0.33, but the error does not exceed 0.4 in log10 P(O2) which is less than the estimated accuracy of the measurements. 4.4. FCC solid solution

Fig. 9. Gibbs energy of formation of liquid Cu2O from liquid copper and O2 gas at 1 atm. The solid line is calculated from the model parameters for the liquid phase optimized in the present study. The other lines were derived by Taskinen [41] from EMF measurements [36,38,41,53].

Cu2O, and FeO and Fe2O3. The heat capacity of pure liquid oxygen can be estimated similarly. The properties of supercritical fluid oxygen reported by Stewart et al. [55] provide the upper limit for S3298 ðOÞ and the lower limit for C P ðOÞ. Finally, the slope of the heat content data above the melting temperature of Cu2O shown in Fig. 10 is well reproduced by the model, which indicates that the estimated heat capacity of pure liquid oxygen gives the right heat capacity of the liquid phase at the Cu2O composition.

The solubility of oxygen in solid Cu which has an FCC structure is shown in Fig. 11. The experimental data were assessed by Hallstedt et al. [13] and Clavaguera-Mora [12] who concluded that studies [56–60] reporting lower solubility of oxygen were more reliable than the earlier measurements [61–63]. One temperature-dependent model parameter, LCu,O , was optimized to fit these data. It is given in Table 2. The Gibbs energy of hypothetical oxygen with an FCC structure, g oO , was fixed assuming that the transition O(FCC)-O(liq) occurs at 50 1C with the enthalpy of melting equal to 1 kJ/mol. This is in line with the trend of decreasing melting temperatures and enthalpies of melting in a series Te, Se, S, O. The heat capacities of hypothetical FCC and liquid oxygen were assumed to be the same. Of course, the stable

66

D. Shishin, S.A. Decterov / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 59–70

O

1100

L 0.9 0.8

L + fcc (Cu-solid)

900

0.7 0.5

Ox ide )

Fig. 11. Solubility of oxygen in FCC (solid Cu) phase: experimental points [56–63] and calculated lines.

0.3 0.1

L1

Cu

(

Cu

L2 (Matte) + Gas

0.9

Molar ratio O/(Cu + O)

0.4

L3 ( Cu -liq )+ 0.00025

0.2

0.00020

L1 (

0.00015

s Ga

0.8

0.00010

)+ liq

0.7

0.00005

0.6

500 0.00000

Cu2O

0.5

600

0.4

[56] [57] [58] [61] [62] [59] [63] [60]

700

L3 (Oxide) + Gas

0.6

Present study

800

0.3

fcc (Cu-solid) + Cu2O

0.2

Temperature, °C

fcc (Cu-solid)

0.1

1000

L1 (Cu-liq) + L2 (Matte) 0.9

0.8

0.7 0.6 0.5 0.4 Cu2S mole fraction

0.3

0.2

S

0.1

Fig. 12. Calculated isothermal section of the Cu–O–S phase diagram at 1250 1C and P¼ 1 atm.

0.00 0

0.1

0.2

0.3

0.4

+ Gas L2 (Matte) + Digenite L2 (Matte) + Gas

0.04

L2 (Matte)

0.06

0.02

0.5

0.6

Molar ratio S/Cu 0.10

0.06

0.04

0.02

0.00 0

L2 (Matte) + Gas

1250 °C

+ Gas L1 (Cu-liq)

0.08

Molar ratio O/Cu

There are three ternary compounds in the Cu–O–S system, CuSO4, (CuO)CuSO4 and Cu2SO4, which decompose with formation of the gas phase before melting at ambient pressure. Three liquids may appear in the system: liquid copper with some solubility of oxygen and sulfur, liquid matte expanding from molten Cu2S towards Cu2O and oxide liquid based on molten Cu2O. Liquid metal may coexist with oxysulfide melt, but at ambient pressure formation of the gas phase containing mainly SO2 separates matte and oxide liquid. The evaluated phase diagram of the Cu–O–S system at 1250 1C and a total pressure of 1 atm is shown in Fig. 12. The Cu–O–S system is rather well studied in the region of liquid metal and matte at pressures up to 1 atm. No experimental data has been found on the solubility of sulfur in liquid Cu2O and on equilibrium between liquid metal and liquid oxide in the Cu–O–S system. The lack of experimental data is due to high P(SO2) in this region. Schmiedl [64] equilibrated liquid copper with matte at controlled P(SO2) and temperatures ranging from 1100 to 1250 1C. In both phases, he measured the oxygen content by the hydrogen reduction method and the sulfur content by the combustion method. The experimental compositions at 1100 and 1250 1C are shown in Fig. 13(a) and (b). Kuxmann and Benecke [65] measured the oxygen content of Cu–O–S matte equilibrated with liquid copper at fixed P(SO2). The sulfur content was not measured, so it is not possible to determine the matte phase boundary from their data. Equilibrium P(SO2) over liquid metalþmatte tie-lines rises with increasing oxygen content and finally becomes more than 1 atm, as shown in Fig. 14. Weight percent of oxygen is chosen as the X-axis in Fig. 14(a) to compare the results of Schmiedl [64] and Kuxmann and Benecke [65]. Points of Kuxmann and Benecke [65] at 1200 and 1250 1C were obtained by linear interpolation of their P(SO2) isobars. The latter are shown in Fig. 14(b) along with the interpolated points of Schmiedl [64].

Molar ratio O/Cu

5.1. Phase diagrams

L2 (Matte) + Digenit e + Gas Digenite + Gas

0.08

1100 °C L1 (Cu-liq) + L2 (Matte) + Gas m at ), 2 [64] O 0 (S 1. .9 0 8 P 0..7 0 0.6 0 .5 0.4 ) ) e t 0.3 at liq 2 (M uL + 0.2 C ( liq) CuL1 L1 ( 0.1 05 0. te ni ige L2 (Matte) + D L1 (Cu-liq) + 0.01

L2 (Matte )

5. The Cu–O–S system

L1 (Cu-liq ) + Gas

0.10

L1 (Cu-liq) + Cu2O + Gas

form of oxygen at all temperatures and pressures of interest is gaseous O2.

L1 (Cu-liq) + L2 (Matte) + Gas [64] tm ),a P 1.0.9 0 .8 0 .7 0 6 0. 0.5 0 .4 ) q 0.3 -li u 0.2 (C ) 1 e L 2 (Matt L + 0.1 ) iq -l L1 (Cu 0.05 0.01 O (S

0.1

0.2

2

0.3

0.4

L2 (Matte)

0.5

0.6

Molar ratio S/Cu Fig. 13. Liquid metalþ matte region on the Cu–O–S isothermal sections at P¼ 1 atm: experimental points [64] and calculated lines. The corresponding P(SO2) is indicated for each metal–matte tie-line. (a) 1100 1C, (b) 1250 1C.

Equilibrium P(O2) and P(S2) over liquid metal þmatte tie-lines was studied by Jalkanen and Tikkanen [66,67]. The compositions of metal and matte were not measured. The gas equilibrated with

D. Shishin, S.A. Decterov / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 59–70

1.2

-5.0

[66] ,1200 °C Calc., 1200 °C [66], 1250 °C [67], 1250 °C Calc., 1250 °C [66], 1300 °C Calc., 1300 °C

-5.5 1.0

-6.0

0.6

0.4

0.2

0.0 0.0

0.5

1.0 1.5 weight % O in matte

2.0

-8.0 -8.5

-10.0 -6.5

-6.0 log

-5.5 [P (S ), atm]

-5.0

Fig. 15. P(S2) vs. P(O2) dependence in the liquid metalþmatte region of the Cu–O–S system: experimental points [66,67] and calculated lines.

1.8 weight % O in matte

-7.5

-9.5

2.5

2.0

-7.0

-9.0

1.6 1.4

1250

1.2

1200

1.0 0.6 0.4 0.2 0.0 1000

1100

1200 1300 1400 Temperature, °C

[65], P(SO ) = 0.93 atm [64], P(SO ) = 0.93 atm Calc., P(SO ) = 0.93 atm [65], P(SO ) = 0.48 atm [64], P(SO ) = 0.48 atm Calc., P(SO ) = 0.48 atm

1500

1600

[65], P(SO ) = 0.18 atm [64], P(SO ) = 0.18 atm Calc., P(SO ) = 0.18 atm [65], P(SO ) = 0.05 atm Calc., P(SO ) = 0.05 atm

L2 (Oxysulfide) Cu2O + L2

1100

L2 (Oxysulfide) + Cu2O + L1 (Cu-liquid)

1050 1000

L2

L2 (Oxysulfide) + L1 (Cu-liq)

1150

0.8 Temperature, °C

P(SO ), atm

[64], 1250 °C [65], 1250 °C Calculated, 1250 °C [64], 1200 °C [65], 1200 °C Calculated, 1200 °C [64], 1150 °C [65], 1150 °C Calculated, 1150 °C [64], 1100 °C [65], 1100 °C Calculated, 1100 °C

log [P (O ), atm]

-6.5

0.8

67

L2 + Digenite L2 (Oxysulfide) + fcc (Cu-solid)

L2 (Oxysulfide) + Cu2O + fcc (Cu-solid)

950 900

L2 + fcc + Digenite

850 800

Digenite (Cu2S-solid) + Cu2O + fcc (Cu-solid)

750 0

0.2

0.4

0.6

0.8

1

Molar ratio Cu 2S/(Cu 2S + Cu 2O)

Fig. 14. (a) Equilibrium P(SO2) over liquid metalþ matte tie-lines in the Cu–S–O system. (b) Solubility of oxygen in Cu–S–O matte in equilibrium with liquid copper and SO2/N2 gas mixtures. Experimental points [64,65] and calculated lines.

Fig. 16. Cu2O–Cu2S isopleth. Formation of the gas phase is suppressed. Circles represent the phase diagram estimated by Oelsen [68], lines are calculated from the model parameters optimized in the present study.

two liquids was analyzed by gas chromatography for CO, CO2 and SO2, which allowed P(O2) and P(S2) to be calculated. The results are shown in Fig. 15. If formation of the gas phase is suppressed by applying high total pressure, continuous oxysulfide liquid will exist from Cu2O to Cu2S. Oelsen [68] reported a schematic representation of the ‘‘Cu2O–Cu2S’’ phase diagram and estimated the equilibrium pressure of SO2 along this join at different temperatures. The maximum P(SO2) at 1200 1C was suggested to be 7.0 atm. These results are shown in Figs. 16 and 17. Oelsen [68] provided no details on how his estimations were made. He only cited the work of Lange [69] who, in turn, quoted Reinders and Goudriaan [70]. The latter two publications deal with temperatures up to 730 1C and do not have any information about the liquid phase. Nevertheless, the diagram of Oelsen [68] was accepted and later cited by several authors [65,71] as the ‘‘Cu2O–Cu2S phase diagram in equilibrium with copper’’. The partial pressures of SO2 shown in Fig. 17 were not calculated exactly for compositions located on the Cu2O–Cu2S section, but rather for compositions (1 X)Cu2OþXCu2Sþ0.5Cu, so that these P(SO2) correspond to tie-lines between solid or liquid

metallic copper and oxysulfide phases which are slightly shifted off the Cu2O–Cu2S join. Recently Trofimov and Mikhailov [72] estimated P(SO2) over Cu2O–Cu2S melts. Without providing sufficient information on the estimation method, they concluded that the SO2 partial pressure over oxysulfide liquid at 1200 1C can reach several thousand atmospheres which is much higher than estimated by Oelsen [68].

5.2. Solubility of oxygen in liquid copper and matte The solubility of oxygen and sulfur in liquid copper was measured in several studies [64,73,74] at fixed P(SO2). These data are presented in Fig. 18 which shows the enlarged stability region of liquid Cu from Fig. 12. The phase boundary between the liquid Cu and (Cuþmatte) field measured by Schmiedl [64] at fixed P(SO2) is also shown in Fig. 18. The SO2 isobars of Johannsen and Kuxmann [73] extrapolated up to this phase boundary are in agreement with P(SO2) reported by Schmiedl [64].

68

D. Shishin, S.A. Decterov / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 59–70

15

0.0014

1200

[68] 0.0012

750 °C 900 °C

0.0010 (P(O2), atm)1/2

1060 °C 10 P (SO ), atm

1200 °C

1060

5

0.0008 0.0006 0.0004

[74], 1300 °C, P(SO2) = 0.01 atm Calc., 1300 °C, P(SO2) = 0.01 atm [74], 1200 °C, P(SO2) = 0.01 atm [75], 1206 °C, P(SO2) = 0.005÷0.03 atm Calc., 1200 °C, P(SO2) = 0.01 atm

900 0.0002

750

0.0000 0.000

0 0

0.2

0.4 0.6 0.8 Molar ratio Cu S/(Cu S + Cu O)

Fig. 17. P(SO2) over tie-lines between metallic Cu phases and oxysulfide phases located approximately along the Cu2O–Cu2S join. Formation of the gas phase is suppressed. Full lines are calculated from the model parameters optimized in the present study, the other lines represent P(SO2) estimated by Oelsen [68].

[O/(Cu+O), mol]

log

Phase boundaries, 1150 °C, P = 1 atm [64], 1150 °C, L1/(L1+L2) boundary [73], 1150 C, P(SO ) = 1 atm Calc., 1150 C, P(SO ) = 1atm [73], 1150 C, P(SO ) = 0.13 atm Calc., 1150 C, P(SO ) = 0.13 atm [73], 1150 C, P(SO ) = 0.53 atm Calc., 1150 C, P(SO ) = 0.53 atm

-2.0

-2.5

-2.5 [S/(Cu+S), mol]

-1.5

Fig. 18. Liquid copper region of the Cu–O–S phase diagram: experimental points [64,73,74] and calculated phase boundaries and P(SO2) isobars.

Sano and Sakao [75] equilibrated liquid copper with flowing gas at a given P(SO2) and a certain CO/CO2 ratio at 1206 1C. After quenching, copper was analyzed for O and S. Since no special attempts were made to move along SO2 isobars, the resulting points are scattered over the stability field of liquid copper. A more systematic approach was taken by Johannsen and Kuxmann [73] and Oishi et al. [74]. They equilibrated liquid copper containing various amounts of sulfur and oxygen with SO2–N2 or SO2–Ar gas mixtures, respectively. The O and S content of every sample changed, so that the final composition lies on a certain SO2 isobar. These isobars are shown in Fig. 18. In addition, Oishi et al. [74] measured P(O2) at every point by an oxygen sensor with a CaO–stabilized ZrO2 electrolyte. The P(O2) values measured by Oishi et al. [74] can be compared with the ones calculated from CO/CO2 ratios reported by Sano and Sakao [75]. As can be seen from Fig. 19, the results of these two studies are in good agreement. It is worth noting that the lines in Fig. 19, cannot be

0.3

0.31

0.32

0.33

0.34

-2.0 Recalculated from [77], 1150 °C [75], 1206 °C

-2.5

[76], 1150 °C

-3.0

[76], 1250 °C Calc., x = 0.0006, 1150 C Calc., x = 0.0006, 1200 C Calc., x = 0.0006, 1250 C

-4.0

log

0.010

L1 (Cu-liq)

-3.5

-3.5

0.008

-1.5

-3.0

-3.5 -4.5

0.006

Fig. 19. Relationship between P(O2) and oxygen content of liquid copper in the Cu–O–S system at fixed P(SO2). Experimental points [74,75] and calculated lines.

[74], 1300 C, P(SO ) = 0.01 atm Calc., 1300 C, P(SO ) = 0.01 atm Phase boundaries, 1200 °C, P = 1 atm [64], 1200 °C, L1/(L1 + L2) boundary [74], 1200 C, P(SO ) = 0.01 atm Calc., 1200 C, P(SO ) = 0.01 atm [74], 1200 C, P(SO ) = 0.005 atm Calc., 1200 C, P(SO ) = 0.005 atm

0.004

Molar ratio O/(Cu + S + O)

0.29 -1.0

-1.0

-1.5

0.002

1

-4.5 0

0.01

0.02 0.03 Molar ratio S/(Cu + S)

L2 (Matte) 0.04

0.05

Fig. 20. Activity coefficient of oxygen in Cu–O–S liquid: experimental points [75–77] and calculated lines. The break in the X-axis is introduced to enlarge the liquid metal and matte regions.

extrapolated to zero oxygen content because they correspond to a P(SO2) isobar: as the mole fraction of oxygen in liquid copper decreases, the sulfur content increases, which finally results in the phase transition L1-L1þL2 as shown in Fig. 18. Otsuka and Chang [76] studied the equilibrium oxygen partial pressure over liquid copper and matte using EMF determinations on the galvanic cell, Oðin Cu2S meltsÞ9ZrO2 ð þ CaOÞ9air, Pt

ð13Þ

The oxygen content was measured by coulometric titration and it was always less than 0.2 mol%. The sulfur content was determined before the experiment from the starting materials and after the equilibration by combustion and analysis. These data recalculated to ln gO as defined by Eq. (9) are shown in Fig. 20 along with the results of Sano and Sakao [75].

D. Shishin, S.A. Decterov / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 38 (2012) 59–70

Janke and Fisher [77] used an EMF cell similar to (13), but they did not report the method of analysis for oxygen and sulfur. They proposed the following linear approximation for ln gO :

L3 (Oxide)

P (SO2 ) = 1 atm

L2 (Matte)

-0.7

( L1

L4 (Sulfur)

) -liq Cu

CuO

-0.8

ð14Þ -0.9 -1

where X O and X S are the mole fractions of oxygen and sulfur in Cu–O–S melt, respectively. Janke and Fisher [77] did not report the measured oxygen partial pressures and compositions, but rather plotted the third term from Eq. (14) as a function of X S at 1150 1C. To compare these data with the results of Otsuka and Chang [76] and Sano and Sakao [75], one has to evaluate the value of lnðg3O ðTÞÞ. It should be noted that since the oxygen contents were very low in all three studies, the second term in Eq. (14) has almost no effect on ln gO . From a separate experiment in the Cu–O system performed by Janke and Fisher [77], the value lnðg3O ð1150 o CÞÞ ¼ 1:61 can be obtained, which corresponds to DG31%OðliqÞ ð1150 o CÞ ¼ 73:6 kJ=mol according to Eq. (11). As can be seen from Fig. 7, the latter value is substantially higher than the optimized value DG31%OðliqÞ ð1150 o CÞ ¼ 75:7 kJ=mol. Therefore, we used the corresponding optimized value lnðg3O ð1150 o CÞÞ ¼ 1:79 to recalculate the plot of Janke and Fisher [77] into ln gO . As can be seen from Fig. 20, the results of studies [75–77] for the activity coefficient of oxygen in liquid copper are in fairly good agreement.

Digenite

–1000/T, K

S ln gO ¼ lnðg3O ðTÞÞ þ eO O ðTÞX O þ eO ðTÞX S

69

(C fcc

Cu 2O

) olid u-s

-1

C O)( (Cu

O 4) uS

-1.1 -1.2 -1.3

Cu2S (chalcocite)

CuSO4

-1.4 Cu 2SO4 -1.5 -18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

log10 [P (O2), atm]

Fig. 21. Calculated potential phase diagram of the Cu–O–S system at P(SO2)¼ 1 atm.

5.3. Results of optimization The thermodynamic description of the Cu–S system [5] was combined with the model parameters for the Cu–O system optimized in the present study to predict the thermodynamic properties and phase equilibria in the Cu–O–S system. All available experimental data in the liquid metal region were in agreement with the calculations, but in the metal þmatte region the calculated P(SO2) increased faster with rising oxygen content than suggested by the measurements shown in Fig. 14(a). The maximum P(SO2) over tie-lines between metallic Cu phases and oxysulfide phases at 1200 1C (Fig. 17) calculated without ternary parameters was around 15 atm. One ternary parameter g 011 was introduced to fit the data of CuI OðSÞ Schmiedl et al. [64] by affecting the properties of the liquid phase in the matte region. This parameter has virtually no effect on the liquid metal region. The measurements of Kuxmann and Benecke [65] shown in Fig. 14(b) are also described better with this parameter. Furthermore, the calculated Cu2O–Cu2S isopleth (Fig. 16) and the calculated P(SO2) curves in Fig. 17 became similar to the estimations of Oelsen [68]. Even though the P(SO2) isotherms calculated for the compositions located exactly on the Cu2O–Cu2S section have higher maxima than shown in Fig. 17 (for example, the maximum P(SO2) equals to 83 atm at X Cu2 S ¼ 0:13 and 1200 1C), these values are still much lower than several thousand atmospheres estimated by Trofimov and Mikhailov [72]. The final description of the available experimental data is shown by the calculated lines in Figs. 12–20. The agreement is within experimental error limits. The P(SO2) vs. composition data of Sano and Sakao [75] for the metallic liquid region are also well reproduced by the model. The thermodynamic properties of stoichiometric CuSO4 and (CuO)(CuSO4) were taken from JANAF [78]. The thermodynamic functions of Cu2SO4 estimated by Barin et al. [79] were accepted in the present study, but the enthalpy of formation was made more negative to be consistent with the experimental observations of Jacinto et al. [80], who found traces of Cu2SO4 at ambient pressure and temperatures up to 500 1C during non-equilibrium reduction of CuSO4. Cu2SO4 is stable up to 450 1C on the calculated potential diagram at P(SO2)¼1 atm shown in Fig. 21. The thermodynamic properties of all stoichiometric compounds and model parameters are given in Table 2.

Fig. 22. Calculated liquidus projection for the Cu–O–S system in the oxysulfide liquid region. Gas phase is suppressed.

The calculated liquidus projection in the oxysulfide liquid region is shown in Fig. 22 and the calculated invariant points are given in Table 1. As can be seen from the liquidus projection, the Cu2O–Cu2S section crosses the primary phase regions of FCC and liquid Cu. The corresponding phase boundaries separating the fields L2(Oxysulfide), L2(Oxysulfide)þFCC(Cu-solid) and L2(Oxysulfide)þL1(Cu-liquid) appear on the Cu2O–Cu2S isopleth shown in Fig. 16. On the other hand, the compositions of the oxysulfide liquid phase in equilibrium with L1(Cu-liquid) or fcc(Cu-solid) are shifted off the Cu2O–Cu2S section, so P(SO2) shown in Fig. 17 corresponds to the compositions of oxysulfide liquid on the corresponding isotherms in Fig. 22.

6. Conclusions A complete critical evaluation and optimization of the Cu–O and Cu–O–S systems has been performed. A model for the liquid phase has been developed within the framework of the quasichemical formalism. This model describes simultaneously metallic liquid, sulfide liquid (matte) and oxide liquid (slag). For the Cu–O system, the model reflects the existence of two ranges of maximum short-range ordering at approximately the Cu2O and CuO compositions. All available thermodynamic and phase equilibrium data have been critically evaluated to obtain one set of

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optimized model parameters for the Gibbs energies of all phases that can reproduce the experimental data within experimental error limits. The present study forms a basis for development of a thermodynamic database for the simulation of copper smelting and converting. In particular, the model developed for the liquid phase and the optimized model parameters can be used to provide a description of the solubility of oxygen in matte and liquid copper. Additional major components such as Fe, Si and Ca are being added to the database as well as Al, Mg and other minor components.

Acknowledgments Valuable discussions with Professor E. Jak from the Pyrometallurgy Research Centre at The University of Queensland, Australia, are gratefully acknowledged.

Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.calphad.2012.04.002.

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