Critical Assessment and Thermodynamic Modelingof the Fe-O-S SystemDenis Shishin, Evgueni Jak, and Sergei A. Decterov

(Submitted December 23, 2014; in revised form February 13, 2015; published online March 13, 2015)

The Fe-O-S system has been assessed over the whole composition range to produce a self-consistent set of thermodynamic properties of all condensed phases from 298 K to above theliquidus temperatures at ambient pressure. The liquid phase from metallic liquid to sulfide meltto oxide melt is described by a single model developed within the framework of the quasi-chemical 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 Fe-O systemat approximately FeO and Fe2O3 compositions are taken into account. Parameters of thermo-dynamic models have been optimized to reproduce all available thermodynamic and phaseequilibrium data. The thermodynamic modeling of the Fe-O-S system performed in the presentstudy is of particular importance for the description of the solubility of oxygen in matte.

Keywords CALPHAD approach, critical assessment, liquidus,optimization, phase diagram, thermodynamicmodeling, thermodynamic properties

1. Introduction

The present study is part of an ongoing research projectwhich is aimed at developing a thermodynamic database forsimulation of copper extraction from sulfide concentrates.The previous article dealt with the Cu-O-S system.[1] Themajor phases that form during copper smelting and con-verting are: blister copper (a liquid metal phase rich in Cu),matte (a molten sulfide phase containing mainly Cu, S andFe), slag (a molten oxide phase) and gas. In principle, allthree liquid phases represent just one liquid with miscibilitygaps. Liquid metal, matte and slag can be completelymiscible over certain ranges of temperature and composi-tion, even though this normally does not happen underindustrial conditions. It is desirable to have one generalthermodynamic model which can describe all three liquidphases simultaneously, but this is very difficult to achievebecause the model must reflect quite different atomicinteractions that are intrinsic to metallic, sulfide and oxidephases.

As in the case of slags, mattes exhibit strong first-nearest-neighbor (FNN) short-range ordering (SRO). Metal-sulfurpairs in matte are energetically favored over metal-metal andsulfur-sulfur pairs, but contrary to oxide melts, such as CaO-SiO2, where the ratio O/(Ca + 2Si) is always very close to 1,the composition of matte can substantially deviate fromstoichiometric sulfides both towards metals and nonmetals.In the Fe-S system there is even no miscibility gap betweenliquid metal and liquid sulfide.

This study presents the thermodynamic modeling andoptimization of model parameters for the Fe-O-S system,which complete ‘‘optimization’’ of all binary and ternarysubsystems of the Cu-Fe-O-S system using the Calphadtechnique. The results of the present study can be combinedwith the optimizations of the Cu-Fe-S,[2–4] Cu-O-S,[1] Fe-O[5] and Cu-Fe-O[6] systems to predict thermodynamicproperties and phase equilibria in the Cu-Fe-O-S quaternarysystem. Comparison of these predictions with the availableexperimental data will be reported elsewhere.

In the present study, all calculations were carried out usingthe FactSage thermochemical software and databases.[7]

2. Thermodynamic Models

The models for the liquid phase, monoxide, bcc and fccsolid solutions are discussed below. The models for spinel(magnetite) and pyrrhotite (Fe1�xS) were reported earlier.

[2,8]

2.1 Liquid Solution

No attempts were found in the literature to model theliquid phase in the Fe-O-S system over the entire compo-sition range from liquid metal to oxysulfide melt. Thethermodynamic model must describe drastic changes in theactivities of sulfur and oxygen which are the result of strongSRO at the FeS and FeO compositions, respectively.Furthermore, in the Fe-O system, a second maximum inSRO is to be expected at the Fe2O3 composition, even

Denis Shishin, Centre de Recherche en Calcul Thermochimique(CRCT), Deep. de Geenie Chimique, E cole Polytechnique, Montreal,QC, Canada; Evgueni Jak, PYROSERCH (PyrometallurgyResearch), School of Engineering, The University of Queensland,Brisbane, QLD, Australia; and Sergei A. Decterov, Centre deRecherche en Calcul Thermochimique (CRCT), Deep. de GeenieChimique, Ee cole Polytechnique, Montreal, QC, Canada andPYROSERCH (Pyrometallurgy Research), School of Engineering,The University of Queensland, Brisbane, QLD, Australia.Contacte-mails: d.shishin@uq.edu.au,e.jak@uq.edu.au, and sergei.decterov@polymtl.ca

JPEDAV (2015) 36:224–240DOI: 10.1007/s11669-015-0376-41547-7037 �ASM International

224 Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015

though no experimental data are available in this regionbecause of very high equilibrium oxygen pressures.

Thermodynamic modeling of the liquid phase and theavailable experimental data for the Fe-O and Fe-S systemswere reviewed by Hidayat et al.[5] and Waldner andPelton,[2] respectively.

In the present study, a model for the liquid phase isdeveloped within the framework of the quasichemicalformalism.[9,10] It has one sublattice containing four species:FeII, FeIII, S and O, where FeII and FeIII correspond to twooxidation states of Fe. In the Fe-O system, the fraction of theFeII-O pairs goes through a maximum close to the FeOcomposition, while the FeIII-O pairs are most abundant at theFe2O3 composition. All species are not charged, so thecondition of electroneutrality is not imposed and the model iscapable to represent the liquid phase frommetal to nonmetals.

The formulae and notations of the quasichemical for-malism have been described in detail elsewhere[9,10] andonly a brief summary is given here. To explain the meaningof parameters of the quasichemical formalism, let usconsider a binary solution formed by components A andB. In the pair approximation of the modified quasichemicalmodel, the following pair exchange reaction is considered:

ðA-AÞ þ ðB-BÞ ¼ 2ðA-BÞ; DgAB ðEq 1Þ

where (i–j) represents a FNN pair and DgAB is the non-configurational Gibbs energy change for the formation oftwo moles of (A-B) pairs.

When the solution is formed from pure components Aand B, some (A-A) and (B-B) pairs break to form (A-B)pairs, so the Gibbs energy of mixing is given by[9]:

DGmix ¼ G� ðnAg�A þ nBg�BÞ ¼ �TDSconfig þ nAB

2

� �DgAB

ðEq 2Þ

where G is the Gibbs energy of the solution, g�A and g�B arethe molar Gibbs energies of pure liquid components; nA, nBand nAB are the numbers of moles of A, B and (A-B) pairsand DSconfig is the configurational entropy given byrandomly mixing the (A-A), (B-B) and (A-B) pairs. Sinceno exact expression is known for this entropy of mixing inthree dimensions, an approximate equation is used whichwas shown[9] to be an exact expression for a one dimen-sional lattice (Ising model) and to correctly reduce to therandom mixing point approximation (Bragg Williamsmodel) when DgAB is equal to zero.

DgAB can be expanded as an empirical polynomial interms of the mole fractions of pairs[9]:

DgAB ¼ Dg�AB þX

ðiþjÞ�1

gijABXiAAX

jBB ðEq 3Þ

where Dg�AB and gijAB are the parameters of the model whichcan be functions of temperature. In practice, only theparameters gi0AB and g0jAB need to be included.

The composition of maximum SRO is determined by theratio of coordination numbers. Let ZA and ZB be thecoordination numbers of A and B. These coordinationnumbers can vary with composition as follows[9]:

1

ZA¼ 1

ZAAA

2nAA2nAA þ nAB

� �þ 1

ZAAB

nAB2nAA þ nAB

� �ðEq 4Þ

1

ZB¼ 1

ZBBB

2nBB2nBB þ nAB

� �þ 1

ZBBA

nAB2nBB þ nAB

� �ðEq 5Þ

where ZAAA and ZA

AB are the values of ZA when all nearestneighbors of an A are As, and when all nearest neighborsof an A are Bs, respectively, and where ZB

BB and ZBBA are

defined similarly. For example, in order to set thecomposition of maximum SRO at the molar rationA=nB ¼ 2, one can set the ratio ZB

BA=ZAAB ¼ 2. Values of

ZBBA and ZA

AB are unique to the A-B binary system, whilethe value of ZA

AA is common to all systems containing A asa component.

Even though the model is sensitive to the ratio of thecoordination numbers, it is less sensitive to their absolutevalues. We have found by experience that selecting valuesof the coordination numbers that are smaller than actualvalues often yields better results. This is due to theinaccuracy introduced by an approximate equation for theconfigurational entropy of mixing which is only exact for aone dimensional lattice. The smaller coordination numberspartially compensate this inaccuracy in the model equations,being more consistent with a one dimensional lattice.Therefore, the ‘‘coordination numbers’’ in our model areessentially treated as model parameters which are usedmainly to set a physically reasonable composition ofmaximum SRO.

There are ten possible pairs formed by the species FeII,FeIII, O and S in the Fe-O-S liquid phase. The fractions ofall pairs are calculated by the Gibbs energy minimizationprocedure built into the FactSage software[7] using theoptimized model parameters. FeII-FeII, O-O and S-S are thepredominant pairs at compositions close to pure Fe, O andS, respectively. The FeII-O, FeIII-O and FeII-S pairs aredominant in the oxide and sulfide liquids, whereas thefractions of the FeII-FeIII, FeIII-FeIII, O-S and FeIII-S pairsare small at all compositions of interest.

‘‘Coordination-equivalent’’ fractions (Ym) are defined as

Ym ¼ Zmnm=X

ðZiniÞ ðEq 6Þ

In addition to the binary terms, the model can haveternary terms, DgABðCÞ, which give the effect of thepresence of component C upon the energy DgAB of pairexchange reaction (1). Ternary terms are expanded asempirical polynomials either in terms of the mole fractionsof pairs (with model parameters gijkABðCÞ) or in terms of the‘‘coordination-equivalent’’ fractions (with model pa-rameters qijkABðCÞ). In the quasichemical formalism, it isalso possible to have Bragg Williams ternary terms, whichare essentially the same as qijkABðCÞ terms, except for theyare not taken into account in the calculation of the amountsof pairs.

Extrapolation of binary terms into the FeII-FeIII-O-Ssystem is done by an asymmetric ‘‘Toop-like’’ method.[10]

The components are divided into two groups: metals (FeII

Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015 225

and FeIII) and nonmetals (S and O). By this means in everyternary subsystem, one component belongs to a differentgroup than the other two. ‘‘Toop-like’’ extrapolation isapplied, taking this ‘‘different’’ component as an asymmet-ric component. The formulae for ternary terms and forextrapolation of binary and ternary terms into a multicom-ponent system are discussed in detail elsewhere.[10]

2.2 Solid FCC and BCC Iron

Sulfur and oxygen are soluble to some extent in Fe metal,which has an fcc or bcc structure at the conditions ofinterest. The Bragg-Williams random mixing model wasused for both phases with the following formula (per moleof atoms):

g ¼ ðXFegoFe þ XOg

oO þ XSg

oSÞ þ RTðXFe lnXFe

þ XO lnXO þ XS lnXSÞþXFeXSLFe;S þ XFeXOLFe;O

ðEq 7Þ

where Xi and g�i are the mole fraction and molar Gibbsenergy of component i, Li;j represents the interaction energybetween i and j, which can be a function of temperature andcomposition.

2.3 Monoxide (wustite)

Vogel and Fulling[11] carried out equilibration andquenching experiments followed by analysis and reportedthat FeO and FeS are immiscible. Johto et al.[12] alsoreported that sulfur was not soluble in wustite based onequilibration/quenching/EMPA experiments. Hence, sulfurwas assumed to be insoluble in monoxide.

The simplest polynomial model that was used for wustitein the Fe-O system[5] is accepted in the present study. Itdescribes the nonstoichiometry of the wustite phase towardsoxygen using the Bragg-Williams approximation and as-suming random mixing of Fe2+ and Fe3+ ions on cationsites. This assumption does not correspond to the realstructure of wustite, which is rather complex and notcompletely understood. However, it was shown in theassessment of the Fe-O system[5] that different models givealmost identical representations of the entropy of wustite asa function of composition, provided that the modelsadequately reproduce the absolute entropies of wustite atseveral compositions and 25 �C, which were obtained bythe integration of the experimental low-temperature heatcapacities.

The Gibbs energy per mole of components FeO andFeO1.5 is given by

g ¼ ðXFeOgoFeO þ XFeO1:5g

oFeO1:5

Þþ RTðXFeO lnXFeO þ XFeO1:5 lnXFeO1:5Þþ XFeOXFeO1:5

LFeO;FeO1:5

ðEq 8Þ

where goM and XM are the Gibbs energy and mole fraction ofpure component M, respectively. The molar interactionenergy LM ;N between components M and N is expanded as apolynomial in the mole fractions of the components:

LM ;N ¼Xi;j�0

qijM ;NXiMX

jN ðEq 9Þ

where qijM ;N are the binary model parameters.

3. The Fe-S System

The Fe-S system was optimized byWaldner and Pelton.[2]

The phase diagram is shown in Fig. 1. Comparisons with theexperimental data, descriptions of thermodynamic modelsand optimized model parameters for all phases are given inRef 2. The description of the Fe-S liquid phase optimized byWaldner and Pelton[2] was accepted in the present study withminor modifications. Contrary to the Fe-O liquid, the Fe-Sliquid phase was modeled in such a way that Fe exists almostexclusively as FeII over the whole composition range frommetal to sulfur. This is because solid Fe2S3 is not stable andthere is no experimental evidence for strong SRO in the liquidphase at the Fe2S3 composition which corresponds to veryhigh S2 partial pressures.

A small modification of the Dg�FeIIS

parameter for theliquid phase was made in the present study to improve thedescription in the liquid iron region at 1500-1600 �C. Theresulted changes in the description of the system below1500 �C are minimal compared to the original study ofWaldner and Pelton.[2] Even though some of the experimen-tal data in the temperature range of 1600-1730 �C seem tobe fitted not as good as by Waldner and Pelton,[2] the regionfrom 1500 to 1600 �C is more important for industrialapplications and the experimental measurements are moreaccurate there. The differences are discussed in more detailelsewhere.[13]

4. The Fe-O System

The Fe-O system was reevaluated recently[5] and theoptimized phase diagram is shown in Fig. 2.

5. The Fe-O-S System

5.1 Phase diagrams

There are two ternary compounds in the Fe-O-S system,FeSO4 and Fe2(SO4)3, which decompose forming the gasphase before melting at ambient pressure. Subsolidusreactions were studied by Skeaf and Espelund,[14] Hsiehand Chang,[15] Rosenqvist and Hofseth,[16] Musbah andChang,[17] Schaefer[18] and Espelund and Jynge[19] using theEMF technique in flowing SO2. Their data are summarizedin Fig. 3. Most likely, these experiments do not correspondto equilibrium with the gas phase, which can contain othergaseous species such as SO3, S2 and O2, but rather to a fixedpotential of SO2, i.e. the other gaseous species do not form

226 Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015

fast enough to significantly change the composition offlowing SO2. If the equilibrium with the gas phase wereattained, it would be almost pure SO2 over the range ofP(O2) from 10�4 to 10�14 atm. At higher oxygen potentials,amounts of SO3 and O2 become substantial, while at lowerP(O2) the partial pressure of S2 starts to increase. Thecomposition of the gas flowing out of the furnace was notanalyzed, but our calculations showed that large amounts ofcondensed phases in EMF cells would have to react in orderto produce the gas phase of equilibrium composition, whichis not what happened in the experiments.

Rosenqvist and Hynne[20] carried out equilibration,quenching and analysis experiments and reported that FeSdoes not dissolve in Fe3O4 spinel.

Liquid that appears in the system expands from moltennonstoichiometric FeS towards FeO. At high temperatures italso spreads to liquid metal. The evaluated phase diagram ofthe Fe-O-S system at 1200 �C and at the total pressure of1 atm is shown in Fig. 4.

Phase equilibria in the Fe-S-O system were studiedrepeatedly.[11,12,21–29]

Naldrett[25] determined the iron-wustite-troilite-liquid (Fe-‘‘FeO’’-‘‘FeS’’-L) ternary eutectic temperature by meltingpyrrhotite, wustite and iron in silica, iron or silver crucibles.Experiments in silica and iron crucibles gave 915± 2 �C,while in silver crucibles the eutectic temperature wasmeasured to be 905± 2 �C. The composition of this eutecticwas determined by melting in silver crucibles and is shown inFig. 5. Even though the eutectic temperature obtained insilver crucibles was lower, the author claimed that thepresence of Ag had only a small effect on the Fe:S:O ratio inthe liquid phase at the eutectic temperature. Naldrett[25] alsoreported the temperature and composition of the magnetite-

wustite-troilite-liquid (‘‘Fe3O4’’-‘‘FeO’’-‘‘FeS’’-L) ternaryperitectic. The experiments were conducted in evacuatedand sealed silica tubes, hence it was possible to study meltswith high equilibrium vapor pressures without affecting thecomposition. The results obtained in contact with silica tubesshould probably be interpreted as corresponding to the Fe-O-S-Si system at SiO2 saturation. Naldrett suggested that sincethe presence of SiO2 did not affect much the temperature ofthe Fe-‘‘FeO’’-‘‘FeS’’-L eutectic, it should not have a strongeffect on the ‘‘Fe3O4’’-‘‘FeO’’-‘‘FeS’’-L invariant tem-perature and composition. The temperature was found to be934± 2�C and the composition is shown in Fig. 5.

The experiments of Hilty and Crafts[21] involved meltingmixtures of FeS and Fe2O3 in iron crucibles. The meltingwas carried out in Ar, assuming that the O:S ratio in thesamples did not change significantly due to low P(SO2) andP(S2) in the iron-saturated system. Taking into account thefluctuations of cool Ar flow, the accuracy in temperaturedetermination suggested by the authors was ±10 �C.Preliminary studies were conducted to prove that thereaction time of 2 h was sufficient for equilibration. Afterequilibration, samples were quenched in water and studiedby chemical analysis and microscopic examination. Theresults are plotted in Fig. 5 and 6(a-f).

Darken and Gurry (cited in Ref 22) melted the charge ofpyrrhotite and wustite. The composition of pyrrhotitecorresponded to FeS0.942 and that of wustite—to FeO1.054.Samples were placed in iron crucibles in an atmosphere ofpurified N2 and annealed at controlled temperature. Nospecial precautions were made in order to keep the sampleson the FeS0.942-FeO1.054 section, so the initial compositionscould have changed due to dissolution of iron from thecrucibles or evaporation of oxygen and sulfur into the gas

fcc + Liquid

Liquid 2 Liquids

Pyrrhotite (Fe 1-xS) + bcc

Pyrrhotite (Fe 1-xS) + Liquid

FeS2 + LiquidPyrrhotite

FeS2 + S(s)

FeS2 + S(s2)

bcc + Liquid

bcc + FeS

'Fe7S8'Fe9S10Fe10S11Fe11S12

+ FeS2

Pyr

rhot

ite

+2+10-1-2-3-4

-5

log10[P(S2), atm]

+2

+1

0-1-2-3-4-5

Molar ratio S/(Fe + S)

Tem

pera

ture

, °C

0 0.2 0.4 0.6 0.8 10

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

Fig. 1 Calculated phase diagram of the Fe-S system with superimposed S2 isobars. Formation of the gas phase is suppressed

Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015 227

phase. The phase boundaries corresponding to precipitationof the pyrrhotite and wustite phases were obtained bymicroscopic examination of samples quenched into mer-cury. The structural characteristics of the polished samplesmade it possible to determine whether quenching was madefrom the temperatures above or below these phase bound-aries. The compositions of the liquid phase were notmeasured, which increases the uncertainty of the determined

phase boundaries. These experimental points are plotted inFig. 7, assuming that the samples were in equilibrium withiron and that the O:S ratio in the samples did not changeduring the experiments.

Vogel and Fulling[11] used corundum crucibles to meltmixtures of Fe, Fe2O3 and S in Ar. Quenched sampleswere examined microscopically. The temperature of920 �C was measured for the Fe-‘‘FeS’’-‘‘FeO’’-L eutec-

2 Liquids

L2 + bcc

WüstiteL2 + fcc

Wüstite + fcc

Spinel

Wüstite + bcc

Spinel + bcc

L2 + gas

Spinel+gas

Fe2O

3+

gas

Fe2O

3+

spin

el

Wüs

tite

+ sp

inel

-24

-20

-16

-12

-10

-8

-6

Molar ratio O/(Fe + O)

Tem

pera

ture

, °C

0 0.1 0.2 0.3 0.4 0.5 0.6500

700

900

1100

1300

1500

1700

1900

2100

2300

2500

L2 (Oxide)

Wüs

tite

+ fc

c

Spi

nel

Slag + Spinel

Spinel + Wüstite

Wüstite

Wüs

tite

+ bc

c

2 Li

quid

s

Spi

nel +

Fe

2O3

-24

-20

-16

-16

-12

-12

-10

-10

-8

-8

-6

-4

-2

0

log10[P(O2), atm]

L2 +

bcc

L2 +

fcc

Mass ratio Fe2O3/(FeO+Fe2O3)

Tem

pera

ture

, °C

0 0.2 0.4 0.6 0.8 1500

700

900

1100

1300

1500

1700

(a)

(b)

Fig. 2 (a) Optimized phase diagram of the Fe-O system.[5] The dashed lines are calculated oxygen isobars. The gas phase is sup-pressed. (b) Enlarged FeO-Fe2O3 part of the same diagram

228 Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015

tic. The composition of this eutectic is shown in Fig. 5.The authors also reported the ‘‘FeO-FeS’’ section of theFe-O-S phase diagram, but it remains unclear how muchthe actual compositions of their samples deviated fromthis section. As can be seen from Fig. 5, iron must haveprecipitated from the initial compositions along most ofthe FeO-FeS section to produce oxysulfide liquid inequilibrium with monoxide (wustite). Hence, the monox-ide liquidus reported by Vogel and Fulling[11] can becompared with the calculated phase diagram in equilib-rium with iron shown in Fig. 7.

Yazawa and Kameda[28] presented the Cu2S-FeO-FeSphase diagram at iron saturation. The extrapolation of theirliquidus to the FeO-FeS section is given in Fig. 7.

Rosenqvist and Hartvig[23] equilibrated oxysulfide liquidwith magnetite and the SO2-S2 gas flow with controlledP(S2) at a total pressure of 1 atm and 1135 or 1185 �C.Crucibles were made from alumina lined with magnetite.The liquid phase was analyzed for Fe, S and O byconventional methods: precipitation of iron as Fe2O3,electro-deposition of S as BaSO4 and determination of theoxygen content by the hydrogen-reduction method (heatingthe sample in hydrogen to convert oxygen into water, which

[1980Ros][1988Mus]

Fe2O3

Spinel

L

Fe2(SO4)3

FeSO4

FeS2

Pyrrhotite

[1980Sch][1977Esp]

[1973Ske][1986Hsi]

P(SO2) = 1 atm

Monoxide

1000/T,K

log 1

0[P(

O2)

, atm

]

0.6 0.8 1.0 1.2 1.4 1.6-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Fig. 3 Potential phase diagram of the Fe-O-S system at P(SO2) = 1 atm

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.10.20.30.40.50.60.70.80.9

0.10.2

0.30.4

0.50.6

0.70.8

0.9

L + Gas

L + Spinel + Gas

Fe2O3 + Gas

L + fcc

L

L+

Monox

ide+

fccL+

Mon

oxide

Fe2O

3+

Spine

l +G

as

L + Spinel

O

Fe Smole fraction

O

Fe Smole fraction

Fig. 4 Calculated isothermal section of the Fe-O-S phase dia-gram at 1200 �C and P = 1 atm

0.58

0.56

0.54

0.52

0.48

0.46

0.44

0.42

0.44

0.46

0.48

0.52

0.54

0.56

FeO FeS

1000 °C

1100 °CPyrrhotite

1200 °C

fcc

Monoxide

1300 °CSpinel

1400 °C

1500 °C

L (Metal)

bcc

947 °C

918 °C

FeSO4

Invariants, this studyFcc-Mono-Pyrr-L[2013Joh], 915-920 °C[1969Nal], 915 °C[1952Hil], 920 °C[1948Vog], 920 °CMono-Pyrr-Spin-L[1969Nal], 934 °CUnivariant lines

Fig. 5 Liquidus projection of the Fe-O-S system (FeO-FeS re-gion). Formation of the gas phase is suppressed. Points show thecompositions of invariant points reported in studies[11,12,21,25]

Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015 229

was absorbed with P2O5). The compositions of the liquidphase in equilibrium with magnetite and SO2-S2 gas areplotted in Fig. 6(c,d).

Bog and Rosenqvist[24] prepared the H2S-H2O-H2 gasmixtures of certain composition and equilibrated them withiron sulfide at 1120 �C, i.e. both P(O2) and P(S2) were fixed inthese experiments. The crucible material was not reported. Thecomposition of resulting melt was determined by unspecifiedchemical methods. Some experiments were conducted at iron

saturation. The compositions of the samples in equilibriumwith iron along with oxygen and sulfur isobars are plotted inFig. 6(c).

Ueda et al.[27] melted mixtures of Fe, Fe2O3 and FeS iniron crucibles at 1000-1400 �C. The oxygen partial pressurewas measured using the following oxygen concentrationcell:

Pt j Ni,NiOj ZrO2ðCaO) jspecimenj RejPt ðEq 10Þ

[2008Ued] Darken in [1971Tur]L/(L + fcc)

L + MonoxideL+fcc+Monoxide

L + Monoxide + fcc

L + fcc

Spinel + Pyrrhotite + Gas

Pyrrhotite + Gas

Spinel + PyrrhotiteL + Spinel + Pyrrhotite

L + Spinel

L + Pyrrhotite

L

L + Monoxide

L + Spinel + Monoxide

[1952Hil]1000 °C(interpolated)

L/(L+Monoxide)

[2013Joh]

L/(L+fcc+Monoxide)

Molar ratio (S/Fe)

Mol

ar r

atio

(O/F

e)

0 0.2 0.4 0.6 0.8 1.00

0.2

0.4

0.6

0.8

1.0

[2008Ued]

Darken in [1971Tur]

L/(L + fcc)L + fcc + Monoxide

L + Monoxide + fcc

L + fcc

Pyrrho

tite+ Gas

L + Spinel

L + Pyrrhotite

L

L + Monoxide

L + Spinel + Monoxide

[1952Hil]1100 °C

(interpolated)L/(L + Monoxide)

L + Gas

L + Pyrrho

tite+ Gas

L + Spinel + Gas

L + Spinel + MonoxideL + Spinel

Molar ratio (S/Fe)

Mol

ar r

atio

(O/F

e)

0 0.2 0.4 0.6 0.8 1.00

0.2

0.4

0.6

0.8

1.0

(a)

(b)

Fig. 6 Isothermal sections of the Fe-S-O phase diagram with superimposed O2 and S2 isobars at the total pressure of 1 atm and (a)1000 �C, (b) 1100 �C, (c) 1120 �C, (d) 1200 �C, (e) 1300 �C, (f) 1400 �C and (g) 1450 �C. Experimental points are from Ref 21–24,26, and 27. The solid lines are the calculated phase boundaries. The dotted and dashed lines in figures (c to e) are the calculated O2 andS2 isobars, respectively. The experimental tie-lines in figures (f and g) are shown by the dotted lines

230 Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015

After equilibration, the crucible was quenched in a waterbath. Compositions of the specimens were determined bychemical analysis. Oxygen and sulfur contents were deter-mined by reduction with hydrogen. Iron was determined bytitration methods and from the mass balance. The phaseequilibrium results are shown in Fig. 6(a,b,d,e,f) and theoxygen potential measurements are given in the nextSection in Fig. 8 and 9.

Takeda[26] melted the Fe-S-O mixtures in iron cruciblesat 1200 and 1300 �C and measured the oxygen potential

with a sensor similar to cell (10). The method used forchemical analysis was not reported. The results are shown inFig. 6(d,e) and in the next Section in Fig. 9.

Johto et al.[12] heated mixtures of the pure Fe, FeS andFe2O3 powders in crucibles lined with iron foil. Theexperiments were conducted either in an Ar atmosphere orat P(O2) controlled by the CO/CO2 gas flow. After heattreatment, the samples were quenched. Microscopic obser-vations showed that the Fe-‘‘FeS’’-‘‘FeO’’-L eutectic shouldbe between 915 and 920 �C. The iron and sulfur contents of

L/(L + fcc)

L + Monoxide + fcc

L + fcc

L + Pyrrhotite

LL + Gas

[1959Bog]

L + Spinel + Gas Log10[P(O2), atm]Log10[P(S2), atm][1959Bog]

-5.6-5.4-5.0-4.4

-15.0-14.5-14.0-13.3

1120 °C

[1958Ros]

L/(L + Spinel), 1135 °C

Molar ratio (S/Fe)

Mol

ar r

atio

(O/F

e)

0 0.2 0.4 0.6 0.8 1.00

0.2

0.4

0.6

0.8

1.0

exp. calc. exp. calc.

[2008Ued]

Darken in [1971Tur]

L/(L + fcc)L + Monoxide

L + fcc + Monoxide

L + fcc

L

[1952Hil]1200 °C

L/(L + Monoxide)

L + Gas

L + Spinel + Gas

L + Spinel + MonoxideL + Spinel

[1958Ros]

[1997Tak]

L/(L + Spinel), 1185 °C

(interpolated)

-14

[2013Joh]

L/(L + Monoxide)L/(L + fcc + Monoxide)L/(L + Spinel + Monoxide)

Molar ratio (S/Fe)

Mol

ar r

atio

(O/F

e)

0 0.2 0.4 0.6 0.8 1.00

0.2

0.4

0.6

0.8

1.0

(c)

(d)

Fig. 6 continued

Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015 231

the liquid phase in equilibrium with solid phases weredetermined by EMPA analysis. The oxygen content was notmeasured directly and was obtained by difference, whichmakes the reported compositions relatively less accurate.The position of the eutectic point suggested by Johtoet al.[12] is shown in Fig. 5 and 7. The compositions of theliquid phase in equilibrium with solids are plotted inFig. 6(a, d). The dependence of the liquid composition onP(O2) is discussed in the next Section and plotted in Fig. 9.

Lee et al.[29] equilibrated mixtures of ‘‘FeO’’, FeS andAg in iron crucibles under the flow of CO/CO2. After

equilibration, silver was analyzed for sulfur and ‘‘eachcomponent’’ of oxysulfide liquid was determined ‘‘by a gasanalyzer and titration method’’. Since the results of analysesare not provided, it is not possible to evaluate the extent ofcontamination of the oxysulfide phase by silver. Themeasured compositions of oxysulfide liquid in equilibriumwith iron were plotted by Lee et al.[29] in the Fe-S-Otriangle. These compositions have much higher sulfurcontent than reported by Hilty and Crafts,[21] Uedaet al.,[27] Takeda[26] and even Johto et al.,[12] which maybe due to the presence of silver in the liquid phase. Hence,

[2008Ued]

Darken in [1971Tur]

L/(L + fcc)L + Monoxide

L + fcc + Monoxide

L + fcc

L

[1952Hil]

1300 °C

L/(L + Monoxide)

L + Gas

L + Spinel + MonoxideL + Spinel

[1997Tak]

(interpolated)

-5

Molar ratio (S/Fe)

Mol

ar r

atio

(O/F

e)

0 0.2 0.4 0.6 0.8 1.00

0.2

0.4

0.6

0.8

1.0

[2008Ued]L/(L + bcc)

L + bcc

L

[1952Hil]1400 °C

L + Gas

L1 + L2

L1 + L2

Molar ratio (S/Fe)

Mol

ar r

atio

(O/F

e)

0 0.2 0.4 0.6 0.8 1.00

0.2

0.4

0.6

0.8

1.0

(e)

(f)

Fig. 6 continued

232 Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015

the results of Lee et al.[29] were not used in the presentoptimization.

As can be seen from Fig. 5 and 6, the phase relations inthe Fe-S-O system are complex and somewhat unusual. Theliquid phase substantially deviates from the FeO-FeS joinboth towards iron and nonmetals. It splits into two liquids athigh temperatures. The miscibility gap becomes wider ratherthan narrower with an increase in temperature. The mea-sured compositions are not very accurate, which is evidentfrom the wide scatter of the experimental points corre-sponding to the L/(L + fcc) phase boundary shown inFig. 6. The reported FeO-FeS phase diagram[11,22,28] wasmeasured at iron saturation rather than by studying thecompositions along the FeO-FeS section, which inevitablyshifts the composition of the liquid phase from the FeO-FeSjoin (see Fig. 5). The calculated phase diagram at ironsaturation is shown in Fig. 7.

5.2 Solubility of Oxygen and Sulfur in Oxysulfide Liquid

The solubility of oxygen and sulfur in oxysulfide liquidwas measured by Bog and Rosenqvist,[24] Dewing andRichardson,[30] Nagamori and Kameda,[31] Kameda andYazawa,[32] Stofko et al.,[33] Mintsis et al.,[34] Blatovet al.,[35] Nagamori and Yazawa,[36] Rose and Brenan,[37]

Fonseca et al.,[38] Ueda et al.[27] and Johto and Henao.[12]

Dewing and Richardson[30] heated small samples of thecondensed phase in a stream of N2-S2-SO2. The melts wereheld in a platinum spiral. After attaining equilibrium, thesamples were quenched and analyzed by treatment inhydrogen. The resulting H2S was absorbed by the zincacetate solution. Residual metal was dissolved in acid givingthe iron content. Insoluble platinum was weighted. It wasfound that the quenched samples contained up to 2 mol% of

platinum sulfide at high P(S2). Thus, iron, sulfur andplatinum were determined directly and oxygen by differ-ence. Most data points were obtained at 1206 �C. Thepartial pressures of S2 and SO2 were reported by the authorsand equilibrium P(O2) was calculated in this study. The dataare plotted in Fig. 8.

Nagamori and Kameda[31] equilibrated Fe-O-S melts withCO-CO2-SO2 gas mixtures at 1200 �C in alumina crucibles.The quenched samples were analyzed for the iron content bytitration with KMnO4, for sulfur by precipitation as BaSO4,and for oxygen by the hydrogen reduction method. No initialgas compositions were reported by the authors, only calcu-lated P(S2) and P(O2). The results are presented in Fig. 8.

Kameda and Yazawa[32] equilibrated Cu-Fe-O-S liquidwith CO-CO2-SO2 gas mixtures at 1150 to 1225 �C inalumina crucibles. The copper, iron and sulfur contents weredetermined analytically and the oxygen content was mea-sured by the hydrogen reduction method. Even though tendifferent CO/CO2/SO2 ratios were used, only the results forone gas composition were reported and used in the presentstudy to calculate equilibrium P(O2) and P(S2). The copper-free point is plotted in Fig. 8.

Stofko et al.[33] studied Fe-S-O melts in equilibrium withN2-S2-SO2 gas at 1200 �C in alumina crucibles. Thequenched samples were analyzed for the iron content bytitration with KMnO4, for sulfur by precipitation as BaSO4,and for oxygen by the hydrogen reduction method. Noinitial gas compositions were reported by the authors,instead, the calculated P(S2) and P(O2) were given. The dataare plotted in Fig. 8.

Mintsis et al.[34] equilibrated Fe-O-S melts and CO-CO2-SO2 gas mixtures at 1200 and 1300 �C. The iron and sulfurcontents in the quenched samples were obtained by

L + bcc

L

[1952Hil]1450 °C

L + Gas

L1 + L2

L1 + L2

Molar ratio (S/Fe)

Mol

ar r

atio

(O/F

e)

0 0.2 0.4 0.6 0.8 1.00

0.2

0.4

0.6

0.8

1.0

(g)

Fig. 6 continued

Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015 233

chemical analysis. The oxygen content was determined bydifference in some samples and by an unspecified analyticalmethod in controlled samples. The CO/CO2/SO2 ratios werereported and used in the present study to calculate P(O2) andP(S2). The results for 1200 �C are presented in Fig. 8.

Nagamori and Yazawa[36] equilibrated Fe-O-S melts withCO-CO2-SO2 gas mixtures at 1200 �C in alumina crucibles.The molten samples were quenched and analyzed foroxygen, sulfur and iron. Sulfur and iron were determinedgravimetrically: sulfur as BaSO4 and iron as Fe2O3. Oxygenwas analyzed by the hydrogen reduction method. Theanalytical results and compositions of ingoing CO-CO2-SO2

gas were reported. The data are given in Fig. 8.Fonseca et al.[38] equilibrated Fe-O-S melts with CO-

CO2-SO2 gas mixtures at 1200 to 1400 �C in silicacrucibles. Electron microprobe analysis (EMPA) was usedto measure the contents of all elements, including oxygen, inthe quenched samples. The CO/CO2/SO2 ratios werereported. The results for 1200 �C are presented in Fig. 8.

Blatov et al.[35] and Rose and Brenan[37] equilibrated Fe-O-S melts with CO-CO2-SO2 gas mixtures at 1300 �C. Thecrucible material and analytical methods were not reportedin the former paper. In the latter work, San Carlos olivinemega crystal was used as a crucible and the samples wereanalyzed by EMPA, even for oxygen. The CO/CO2/SO2

ratios were reported in both studies.From Fig. 8 it is evident that there are some discrepan-

cies between the results of different authors at 1200 �C.Nagamori and Kameda[31] suggest lower sulfur contents andhigher oxygen contents than Dewing and Richardson,[30]

Kameda and Yazawa[32] and Stofko et al.[33] On thecontrary, Fonseca et al.[38] give higher sulfur contents andlower oxygen contents compared to the same stud-ies.[30,32,33] The data of Stofko et al.[33] are rather scattered,

so that the dependence on P(S2) is mostly within theexperimental scatter, while the results of Mintsis et al.[34]

suggest that the solubility of sulfur is essentially indepen-dent of P(S2). The experimental data at higher tem-peratures[34,35,37,38] are even more scattered. The scatter isprobably due to difficulties in attaining equilibrium betweenthe liquid and gas phases when two partial pressures arefixed, especially at high P(S2).

The experimental results for the oxygen partial pressureover liquid saturated with solid iron[12,24,26,27] are summa-rized in Fig. 9. These data are much more reliable andconsistent.

5.3 Solubility of Oxygen and Sulfur in Liquid Iron

The solubility of oxygen and sulfur in metallic liquid wasmeasured by Hilty and Crafts,[21] Hayashi and Uno,[39]

Schenck and Hinze.[40]

Hilty and Crafts[21] studied the equilibrium between Fe-rich liquid (liquid iron, L1) and FeO-rich liquid (slag, L2) inthe Fe-S-O system using a rotating furnace at 1450 to1650 �C. Samples were melted in magnesia crucibles underan Ar atmosphere. Slag was contaminated with MgO fromthe crucible material (up to 2.5 wt.%) and by SiO2 from thethermocouple protection tube (up to 4 wt.%), though this ismuch less than the equilibrium solubility of MgO and SiO2

in slag under the conditions of the experiments. Samples ofliquid iron were analyzed: oxygen was determined by avariant of the vacuum-fusion method and sulfur wasmeasured gravimetrically. The experimental results areplotted in Fig. 10.

Hayashi and Uno[39] equilibrated liquid iron with H2S-H2O-H2-Ar mixtures at 1500 to 1600 �C in aluminacrucibles. Oxygen and sulfur were analyzed by the vacuum

L + fcc

L + fcc + Monoxide

Monoxide + Pyrrhotite + bcc

L + bcc L1 + L2

L + Pyrrhotite + fcc[1955Yaz], extrap. from Cu2S-FeS-FeO

Darken and Gurry cited in [1971Tur][1952Hil], misc. gap[2008Ued], misc. gap

L1 + L2 + bcc

L

918.0 oC914.3 oC (bcc -> fcc)

[1948Vog]

[2013Joh], eutectic

Molar ratio FeS/(FeS + FeO)

Tem

pera

ture

, °C

0 0.2 0.4 0.6 0.8 1800

900

1000

1100

1200

1300

1400

1500

Fig. 7 Projection of the Fe-S-O phase diagram in equilibrium with iron on the FeS-FeO section through the Fe corner. Experimentalpoints from Ref 12, 21, 22, 27, and 28

234 Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015

fusion method. The obtained alloy compositions are shownin Fig. 10. The equilibrium P(O2) and P(S2) were calculatedfrom the experimental gas compositions. The activitycoefficient of oxygen defined as

ln cO ¼ 0:5 lnPðO2Þ � lnXO ðEq 11Þ

is plotted in Fig. 11. The activity coefficient of sulfur wascalculated in a similar way:

ln cS ¼ 0:5 lnPðS2Þ � lnXS ðEq 12Þ

The results are shown in Fig. 12.Schenck and Hinze[40] equilibrated liquid iron with CO/

CO2 gas of known composition in alumina crucibles at 1600and 1650 �C. The quenched samples were analyzed foroxygen content by gas chromatography. No analysis for Safter equilibration was reported, it was assumed that theinitial S content from FeS did not change. The experimentswere first made using sulfur-free samples, and then theeffect of sulfur on the oxygen content was measured byaddition of known amounts of FeS. The activity coefficientof oxygen in the liquid phase, fO, was defined using weightrather than mole fractions as it is normally done in thetechnical literature[41]:

lO ¼ 0:5lþO2ðTÞ þ RT lnðfOWOÞ ¼ 0:5½lþO2

ðTÞþ RT lnPðO2Þ�

ðEq 13Þ

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50 60 70

Po = [P(O2), atm]1/2 106

[1974Sto], Ps = 0.14[2008Fon], Ps = 0.00 0.03 [1988Min], Ps = 0.15[2001Nag], Ps = 0.02 0.03 [1974Sto], Ps = 0.15 0.17[2001Nag], Ps = 0.05 [2008Fon], Ps = 0.17[1965Nag], Ps = 0.05 [1965Nag], Ps = 0.17[1960Dew], Ps = 0.06 [1974Sto], Ps = 0.18 0.20[1960Dew], Ps = 0.07 [1965Nag], Ps = 0.18[1965Nag], Ps = 0.08 [1988Min], Ps = 0.20 0.21[1988Min], Ps = 0.09 [2008Fon], Ps = 0.23[1965Nag], Ps = 0.09 [1974Sto], Ps = 0.25[1970Kam], Ps = 0.09 [1988Min], Ps = 0.27 0.28[1988Min], Ps = 0.11 [1965Nag], Ps = 0.30

Ps = 0.02Ps = 0.05 Ps = 0.06Ps = 0.08 Ps = 0.09Ps = 0.12 Ps = 0.16Ps = 0.19 Ps = 0.24Ps = 0.30

0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60 70

Po = [P(O2), atm]1/2 106

Ps = [P(S ), atm]21/2

Fig. 8 Solubility of oxygen and sulfur in Fe-O-S oxysulfidemelt at 1200 �C

19

18

17

16

15

14

13

12

11

10

9

0 0.1 0.2 0.3 0.4 0.5

Log 1

0[P(O

2),atm

]

Molar O/(Fe + O + S)

Present study, 1000 °C Present study, 1100 °CPresent study, 1120 °C Present study, 1200 °CPresent study, 1300 °C Present study, 1400 °C[2008Ued], 1400 °C [2008Ued], 1300 °C[2008Ued], 1200 °C [2008Ued], 1100 °C[2008Ued], 1000 °C [1959Bog], 1120 °C[1997Tak], 1200 °C [1997Tak], 1300 °C[2013Joh], 1000 °C [2013Joh], 1200 °C

Fig. 9 Partial pressure of oxygen for oxysulfide liquid in equi-librium with iron in the Fe-O-S system: experimentalpoints[12,24,26,27] and calculated lines. The kink and horizontalpart of the calculated line at 1400 �C reflect the presence of themiscibility gap

Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015 235

where lþO2is the Gibbs energy of ideal O2 gas at 1 atm, WO

is the weight fraction of oxygen and PðO2Þ is theequilibrium oxygen partial pressure in atm. The compositiondependence of the activity coefficient was represented bythe following equation

log10ðfOÞ ¼ log10 f �OðTÞ� �

þ eOOðTÞ � wt:% O

þ eSOðTÞ � wt:% SðEq 14Þ

and the first-order interaction coefficient eSO was obtained.This value was adopted by the Steelmaking data source-book.[41] The dashed lines in Fig. 11 were calculated using

bcc prim. field

1450 °C1500 °C1550 °C1600 °C1650 °C

1500 °C

1550 °C

1600 °C

1650 °C

1450 °C

[1982Hay], L1 [1952Hil], L1/(L1 + L2) border

L2 (Oxide) primary field

Molar ratio (S/Fe)

Mol

ar r

atio

(O/F

e)

0 0.02 0.04 0.06 0.08 0.100

0.01

0.02

0.03

Fig. 10 Liquidus projection of the Fe-S-O system near the Fe corner. Experimental points[21,39] and calculated lines

6.5

6.0

5.5

5.0

4.5

4.0

3.5

3.0

0.005 0.015 0.025 0.035 0.045 0.055Molar S/(Fe + O + S)

Present study, X(O) = 0.001, 1500 °CPresent study, X(O) = 0.003, 1500 °CPresent study, X(O) = 0.001, 1550 °CPresent study, X(O) = 0.005, 1550 °CPresent study, X(O) = 0.001, 1600 °CPresent study, X(O) = 0.005, 1600 °C[1966Sch], X(O) = 0.001, 1500 °C[1966Sch], X(O) = 0.001, 1550 °C[1966Sch], X(O) = 0.001, 1600 °C

1n γ

o

Fig. 11 Effect of sulfur on the activity coefficient of oxygen inFe-O-S metallic liquid: experimental points[39] and calculatedlines. The amounts of oxygen for the experimental points are ap-proximately the same as for the calculated lines of the same col-or; the solid and open points correspond to the solid and dashedlines, respectively. The dotted lines were calculated using pa-rameters of Eq 14 obtained by Schenck and Hinze[40]

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

0 0.002 0.004 0.006

Molar O/(Fe + O + S)

Present study, X(S) = 0.03, 1500 °CPresent study, X(S) = 0.05, 1500 °CPresent study, X(S) = 0.01, 1550 °CPresent study, X(S) = 0.05, 1550 °CPresent study, X(S) = 0.01, 1600 °CPresent study, X(S) = 0.03, 1600 °C

1n γ

s

Fig. 12 Effect of oxygen on the activity coefficient of sulfur inFe-O-S metallic liquid: experimental points[39] and calculatedlines. The amounts of sulfur for the experimental points are ap-proximately the same as for the calculated lines of the same col-or; the solid and open points correspond to the solid and dashedlines, respectively

236 Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015

Tab

le1

Optimized

properties

ofstoichiometriccompou

ndsan

dmod

elparam

etersforliquid

andsolidsolution

sin

theFe-O-S

system

(Jmol

21)

Com

pou

nds

Tem

perature

range

(K)an

dreference

Molar

Gibbsenergy

gðTÞ

Fe 2O3(hem

atite)

[5]

S[1]

FeS

(troilite),FeS

2(pyrite)

‘Fe 7S8’(monoclinic

pyrrho

tite)Fe 9S10,Fe 1

0S11,Fe 1

1S12

[2]

FeSO4

298-80

0�76

6593

.6+12

96.461

6T�19

2.54

87TlnT�0.0116

0265

T2+3.62

6209

10�6T3�22

1846

5.7T

�1�43

771.41

3llnT

800-20

00�99

5911.2

+92

7.07

02T�15

0.78

43Tln

T�0.00

571347

T2+33

6612

0.1T�1

>20

00�10

1203

2.9+10

85.463

19T�17

1.95

52TlnT

Fe 2(SO4) 3

298-80

0�21

6237

5.9+33

89.584

2T�50

2.12

94TlnT�0.03

361654T2+1.0028

6910

�5T3�57

5363

3.2T

�1�1137

14.9841lnT

800-20

00�25

3694

3.7+19

11.110

0T�34

6.04

60TlnT�0.01

728174T2+47

8656

2.7T

�1�61

977.2609

lnT+12

668.5367T0.5

>20

00�28

0198

7.7+28

67.986

1T�45

2.61

04TlnT

Solutions

Liquid(m

etal,oxide,

sulfide)

Modified

quasichemical

model:(FeII ,FeIII,O,S);Group

ing:

FeII ,FeIIIin

group1andO,Sin

grou

p2

ZFeII

FeII FeII¼

ZFeIII

FeIIIFeIII¼

ZS SS¼

ZO OO¼

ZFeII

FeII FeIII¼

ZFeIII

FeIIIFeII¼

ZO OS¼

ZS SO¼

6,ZFeII

FeII S¼

ZS SFeII¼

2,ZFeII

FeII O

¼2,

ZO OFeII¼

2,ZS SFeIII¼

3,ZFeIII

FeIIIS¼

2,ZO OFeIII¼

3,ZFeIII

FeIIIO¼

2

g� O

[1]

g� FeII

298-18

11[43]

13265.9+117.57

56T�23

.514

3TlnT�0.00

439752T2�5.8926

9910

�8T3+77

358.5T

�1�3.67

515519

10�21T7

1811-6000[43]

–10838

.8+29

1.30

20T-46

.0000T

lnT

g� FeIII

298-35

00g� FeII+62

76.0

g� S

[1]

Dg� FeII S

[2]

–10488

8.10

+0.3388

T

Thisstud

y–1

2233

4.14

+112.4659T�13

.758

2TlnT

g01 FeII S,g02 FeII S,g03 FeII S,g10 FeII S,g20 FeII S,g40 FeII S

[2]

Dg� FeII O

�39

1580

.56

g10 FeII O

129778

.63�30

.334

0T

Dg� FeIIIO

–39455

1.20

+12

.552

0T

g20 FeIIIO

83680.00

q001 FeII FeIIIðO

ÞBragg-W

illiam

sparameter

30543.20

�44

.004

14T

Dg� FeII FeIII

83680.00

q102 SOðFeII Þ

Bragg-W

illiam

sparameter

292567

.68�20

4.28

04T

g001

FeII SðO

Þ22

044.34

�17

.804

26T

g002

FeII SðO

Þ27

764.62

�22

.255

32T

g101

FeII O

ðSÞ

–23012

.00

g901

FeII O

ðSÞ

–41553

.40+41

.840

00T

g002

FeIIIOðSÞ

–21756

.80

fcc(Solid

Fe)

Bragg-W

illiam

s(Fe,

O,S)

g� Fe

298-18

11[43]

–236.5

+13

2.41

56T�24

.664

3TlnT�0.0037

58T2+77

359.0T

�1�5.8927910

�8T3

1811-6000[43]

–27097

.2+30

0.25

21T�46

.000

0TlnT�2.7885

4910

31T�9

g� S

[1]

g� O

[1]

LFe;S

–59070

.74�34

.612

18T

LFe;O

–31565

2.63

�27

.614

40T

Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015 237

Tab

le1

continued

Com

pou

nds

Tem

perature

range

(K)an

dreference

Molar

Gibbsenergy

gðT

Þ

Magneticprop

erties

ofFe

[44]

TNeel=67

K

Magneticmom

entb=0.70

Structure-dependent

parameter

P=0.28

bcc(Solid

Fe)

Bragg-W

illiam

s(Fe,

O,S)

g� Fe

298-18

11[43]

10375.2+114.5502

T�23

.514

3TlnT�0.0043

98T2+77

359.0T

�1�5.8927910

�8T3

g� S

298-36

8.3[2]

19725.8+41

.094

5T�11.0070T

lnT�0.0265

29T2+7.75

4333910

�6T3

368.3-1300

[2]

18441.0+80

.369

7T�17

.941

8TlnT�0.01

0895T2+1.4025

58910

�6T3+39

910T

�1

g� O

Sam

eas

infcc[1]

LFe;S

–29973

.6�11.742

68T

LFe;O

–31514

9.19

+20

.693

49T

Magneticprop

erties

ofFe

[44]

TCurie=10

43K

Magneticmom

entb=2.22

Structure-dependent

parameter

P=0.40

Pyrrhotite(‘‘Fe 1

–xS’’)

[2]

Wustite

(Fe 1

–xO

)[5]

Spinel(m

agnetite,Fe 3

�xO

4)

[8,5]

The

thermodynam

icproperties

ofgaseousspeciesweretakenfrom

theFactSagepure

substancedatabase

[7]

Tab

le2

Calculatedinvarian

tpoints

intheFe-O-S

system

Reactionupon

cooling

T,�C

Com

positionof

liquid

(mole)

log 1

0[P(O

2),atm]

log 1

0[P(S

2),atm]

log 1

0[P(SO

2),atm]

Fe

OS

Lfi

Pyrrhotite+mon

oxide+fcc

918.0

0.5051

40.15711

0.3377

5–1

6.39

–7.60

–8.14

Lfi

Pyrrhotite+mon

oxide+Spinel

947.1

0.4941

80.1894

90.3163

4–1

3.88

–5.15

–4.78

L(sulfur)+spinel

fipy

rrho

tite

+FeSO4

982.0

0.0014

60.0000

10.9985

3–7

.82

1.79

4.31

L(m

etal)+L(oxysulfide)fi

L(oxy

sulfide)+bcc

1366.9

0.7826

90.0058

30.2114

8–1

2.28

–4.76

–6.95

238 Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015

the parameters of Eq 14 from the Steelmaking datasourcebook,[41] assuming that eSO is independent of tem-perature.

5.4 Optimization

The database for the Fe-S system[2] was combined withthe model parameters for the Fe-O system[5] to predict thethermodynamic properties and phase equilibria in the Fe-O-S system. The thermodynamic properties of stoichiometricFeSO4 and Fe2(SO4)3 were taken from the NIST-JANAFthermochemical tables.[42]

The phase relations in the Fe-O-S system predicted usingonly binary parameters for the liquid phase were qualita-tively correct, but the agreement with the experimental datawas not satisfactory quantitatively. Ternary parametersg001FeIISðOÞ and g002

FeIISðOÞ were introduced to raise the monoxideliquidus and the eutectic temperature shown in Fig. 7. Onemore ternary parameter, g101

FeIIOðSÞ, and a Bragg-Williamsparameter, q102

SOðFeIIÞ, were required to suppress the lowtemperature immiscibility between liquid FeS1�x and FeOand to increase the iron content in iron-saturated liquid (seeFig. 6). Another ternary parameter, g002

FeIIIOðSÞ, was added toshift the phase boundary L/(L + Spinel + Gas) in Fig. 6(b)and (d) to higher S and O contents.

The binary parameter Dg�FeIIS

was adjusted to raise cS iniron-rich Fe-S liquid at 1500 to 1600 �C in order to improvethe description of the data of Hayashi and Uno[39] shown inFig. 12. This did not impair the overall description of theexperimental data in the Fe-S system. An additionalparameter, g901

FeIIOðSÞ, was used to raise cO and cS in liquidiron (see Fig. 11, 12). However, the solubility of oxygen inliquid iron equilibrated with slag falls when cO increases,which made the description of the data of Hilty andCrafts[21] shown in Fig. 10 less accurate. A better fit of thedata of Hayashi and Uno[39] and of Schenck and Hinze[40]

would result in a large disagreement with the solubility dataof Hilty and Crafts,[21] and also with the miscibility gap inFig. 6(f,g) as reported by Hilty and Crafts[21] and Uedaet al.[27] And vice versa, if the miscibility gap betweenliquid iron and liquid oxysulfide were described moreaccurately, the activity coefficient of oxygen in Fig. 11would fall dramatically. To resolve this contradiction, moreexperimental studies are required in the liquid iron region ofthe Fe-O-S system. In the present study, the modelparameters were optimized to attain a reasonable compro-mise between the data on the activity coefficients of oxygenand sulfur in liquid iron[39,40] and the data on phaseequilibria with oxysulfide liquid.[21,27]

The resulting description of the available experimentaldata is shown by the calculated lines in Fig. 3-12. In mostcases the agreement is within the experimental error limits.However, the calculated miscibility gap L1 + L2 shown inFig. 6(e, f) and 16 expands less rapidly with increasingtemperature than suggested by the data of Hilty andCrafts[21] and Ueda et al.[27] The experimentalL1 + L2 + bcc triangles at 1400 and 1450 �C are close tothe calculated ones at 1470 and 1505 �C, respectively.

From the data on the solubility of oxygen and sulfur atfixed P(O2) and P(S2) summarized in Fig. 8, oxygen and

sulfur isobars over the matte region can be calculated. Inparticular, these isobars at 1200 and 1300 �C are presentedin Fig. 6(d, e).

The thermodynamic properties of all stoichiometriccompounds and the values of the optimized model pa-rameters are given in Table 1. The optimized parameters arestrongly correlated and, therefore, are given in Table 1 withrelatively large numbers of significant digits. The calculatedinvariant points are listed in Table 2.

6. Conclusions

A critical assessment and thermodynamic modeling havebeen performed for the Fe-O-S system over the wholecomposition range. A model for the liquid phase has beendeveloped within the framework of the quasichemicalformalism. This model describes simultaneously metallicliquid, sulfide liquid (matte) and oxide liquid (slag). For theFe-O system, the model reflects the existence of two rangesof maximum SRO at approximately FeO and Fe2O3

compositions. Parameters of thermodynamic models forthe liquid and solid phases have been optimized to providethe best description of all available thermodynamic andphase equilibrium data. The obtained self-consistent set ofmodel parameters can be used to calculate the solubility ofoxygen and sulfur in liquid and solid iron. The stabilityrange of oxysulfide liquid can also be calculated at differenttemperatures along with the equilibrium oxygen and sulfurpartial pressures at each composition.

The model parameters obtained in the present study arebeing used for development of a thermodynamic databasefor simulation of copper smelting and converting. Inparticular, the model and optimized properties of the liquidphase are essential for description of the solubility ofoxygen in matte. The present study completes the opti-mization of all binary and ternary subsystems of the Cu-Fe-O-S quaternary system. The experimental data available forthe Cu-Fe-O-S system were compared with the predictionsfrom the combined database. Even though the agreementwas fair, it was found that the Cu-Fe-S[2–4] optimizationneeds some improvement. Just a few additional modelparameters that reflect interactions, which are present onlyin the quaternary system, may also be added to improve thedescription. The optimization of the Cu-Fe-O-S quaternarysystem will be reported elsewhere.

References

1. D. Shishin and S.A. Decterov, Critical Assessment andThermodynamic Modeling of Cu-O and Cu-O-S Systems,CALPHAD, 2012, 38, p 59-70

2. P. Waldner and A.D. Pelton, Thermodynamic Modeling of theFe-S System, J. Phase Equilib. Diff., 2005, 26, p 23-28

3. P. Waldner, Thermodynamic Modeling of the Cu-S System,Internal Report, Ecole Polytechnioque de Montreal, Montreal,QC, 2005

Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015 239

4. P. Waldner and A.D. Pelton, Thermodynamic Modeling of theCu-S System, Internal Report, Ecole Polytechnioque deMontreal, Montreal, QC, 2006

5. T. Hidayat, D. Shishin, E. Jak, and S. Decterov, ThermodynamicReevaluation of the Fe-OSystem,Calphad, 2015, 48, p 131-144

6. D. Shishin, T. Hidayat, E. Jak, and S. Decterov, CriticalAssessment and Thermodynamic Modeling of Cu-Fe-O Sys-tem, CALPHAD, 2013, 41, p 160-179

7. C.W. Bale, E. Belisle, P. Chartrand, S.A. Decterov, G.Eriksson, K. Hack, I.-H. Jung, Y.-B. Kang, J. Melancon,A.D. Pelton, C. Robelin, and S. Petersen, FactSage Thermo-chemical Software and Databases—Recent Developments,CALPHAD, 2009, 33(2), p 295-311

8. S.A. Decterov, E. Jak, P.C. Hayes, and A.D. Pelton, Experimen-tal Study and Thermodynamic Optimization of the Fe-Zn-OSystem, Metall. Mater. Trans. B, 2001, 32B(4), p 643-657

9. A.D. Pelton, S.A. Decterov, G. Eriksson, C. Robelin, and Y.Dessureault, The Modified Quasichemical Model. I—BinarySolutions, Metall. Mater. Trans. B, 2000, 31B(4), p 651-659

10. A.D. Pelton and P. Chartrand, The Modified QuasichemicalModel. II—Multicomponent Solutions, Metall. Mater. Trans.A, 2001, 32A(6), p 1355-1360

11. R. Vogel and W. Fulling: The System Iron-Iron Sulfide (FeS)-Wustite (FeO), Festskr. J. Arvid Hedvall, 1948, p 597-610

12. H. Johto, H.M. Henao, E. Jak, and P. Taskinen, ExperimentalStudy on the Phase Diagram of the Fe-O-S System, Metall.Mater. Trans. B, 2013, 44(6), p 1364-1370

13. D. Shishin, ‘‘Development of a thermodynamic database forcopper smelting and converting’’, Ph. D. thesis, EcolePolytechnique of Montreal, 2013

14. J.M. Skeaff and A.W. Espelund, Electromotive Force Methodfor the Determination of Sulfate-Oxide Equilibria Results forthe Magnesium, Manganese, Iron, Nickel, Copper and ZincSystems, Can. Metall. Q., 1973, 12(4), p 445-454

15. K.C. Hsieh and Y.A. Chang, A Solid-State Emf Study ofTernary Nickel-Sulfur-Oxygen, Iron-Sulfur-Oxygen, andQuaternary Iron-Nickel-Sulfur-Oxygen, Metall. Trans. B,1986, 17B(1), p 133-146

16. T. Rosenqvist and A. Hofseth, Phase Relations and Thermo-dynamics of the Copper-Iron-Sulfur-Oxygen System at 700-1000 �C, Scand. J. Metall., 1980, 9(3), p 129-138

17. O.A. Musbah and Y.A. Chang, A Solid-State EMF Study ofthe Fe-S-O and Co-S-O Ternary Systems, Oxid. Met., 1988,30(5–6), p 329-342

18. S.C. Schaefer, Electrochemical Determination of Gibbs Energiesof Formation of Manganese Sulfide and Iron Sulfide(Fe0.9S), RI,8486, Albany Res. Cent. Bur. Mines, Albany, OR, 1980

19. A.W. Espelund and H. Jynge, The Zinc-Iron-Sulfur-OxygenSystem Equilibriums Between Sphalerite or Wurtzite, Pyr-rhotite, Spinel, Zinc Oxide and a Gas Phase, Scand. J. Metall.,1977, 6(6), p 256-262

20. T. Rosenqvist and P.H. Hynne, The Reaction Between IronSulfide and Sulfur Dioxide, Tidsskr. Kjemi. Bergves. Metall.,1953, 13, p 196-200

21. D.C. Hilty and W. Crafts, Liquidus Surface of the Iron-Sulfur-Oxygen System, J. Metals, 1952, 194, p 1307-1312

22. E.T. Turkdogan, G.J.W. Kor, L.S. Darken, and R.W. Gurry,Sulfides and Oxides in Iron-Manganese Alloys. I. PhaseRelations in Iron-Manganese-Sulfur-Oxygen System, Metall.Trans., 1971, 2(6), p 1561-1570

23. T. Rosenqvist and T. Hartvig, The Thermodynamics of Fe-CuMattes, and Their Equilibrium with Magnetite, Norges Tek.-Naturvitenskapelige Forskiningsrud Met. Kom. Meddel, 1958,12, p 21-52

24. S. Bog and T. Rosenqvist, A Thermodynamic Study of IronSulphide-Iron Oxide Melts. Nat. Phys. Lab. Symp. No. 9,NPL, Teddington, 1959

25. A.J. Naldrett, A Portion of the System Fe-S-O Between 900and 1080 �C and Its Application to Sulfide Ore Magmas, J.Petrol., 1969, 10(2), p 171-201

26. Y. Takeda, Oxygen potential measurement of iron silicate slag-copper-matte system. Proceedings of International ConferenceMolten Slags, Fluxes Salts ‘97, 5th. Iron and Steel Society,Warrendale, PA, 1997

27. S. Ueda, K. Yamaguchi, and Y. Takeda, Phase Equilibrium andActivities of Fe-S-O Melts, Mater. Trans., 2008, 49(3), p 572-578

28. A. Yazawa and M. Kameda, Fundamental Studies on CopperSmelting. III. Partial Liquidus Diagram for Cu2S-FeS-FeOSystem, Technol. Rep. Tohoku Univ., 1955, 19(2), p 239-250

29. Y.S. Lee, S.M. Jung, and D.J. Min, Thermodynamic Study onPhase Equilibria in the Liquid Fe-S-O System, Steel Res.,2002, 73(11), p 461-466

30. E.W. Dewing and F.D. Richardson, Thermodynamics ofMixtures of Ferrous Sulphide and Oxide, J. Iron Steel Inst.,1960, 194, p 446-450

31. M. Nagamori and M. Kameda, Equilibriums Between the Fe-S-O System Melts and CO-CO2-SO2 Gas Mixtures at 1200�,Trans. Inst. Metals (Jpn.), 1965, 6, p 21-30

32. M. Kameda and A. Yazawa: Effects of Partial Pressures ofOxygen and Sulfur on the Oxygen Content in Copper Matte.Studies in Met. (Commemoration for Prof. Matoba), TohokuUniversity, 1970

33. M. Stofko, J. Schmiedl, and T. Rosenqvist, Thermodynamicsof Iron-Sulfur-Oxygen Melts at 1200 �C, Scand. J. Metall.,1974, 3(3), p 113-118

34. V.P. Mintsis, A.G. Ryabko, L.S. Tsemekhman, G.P. Grodin-skii, and Y.V. Fisher, Equilibrium in the Iron-Sulfur-OxygenSystem, Izv. Akad. Nauk SSSR Met., 1988, 1, p 28-32

35. I.A. Blatov, B.P. Burylev, L.S. Tsemekhman, and S.L.Litvinov, Thermodynamics of the Interaction of Componentsof the Fe-S-O System in Equilibrium with the CO-CO2-SO2

Gas Phase at 1300 �C, Metally, 1997, 6, p 34-3636. M. Nagamori and A. Yazawa, Thermodynamic Observations

of the Molten FeS-FeO System and Its Vicinity at 1473 K,Metall. Mater. Trans. B, 2001, 32B(5), p 831-837

37. L.A. Rose and J.M. Brenan, Wetting Properties of Fe-Ni-Co-Cu-O-S Melts Against Olivine: Implications for Sulfide MeltMobility, Econ. Geol., 2001, 96(1), p 145-157

38. R.O.C. Fonseca, I.H. Campbell, H.S.C. O’Neill, and J.D.Fitzgerald, Oxygen Solubility and Speciation in Sulphide-RichMattes,Geochim. Cosmochim. Acta, 2008, 72(11), p 2619-2635

39. S. Hayashi and T. Uno, Activities of Sulfur and Oxygen inLiquid Iron, Tetsu to Hagane, 1982, 68(13), p 1728-1736

40. H. Schenck and H. Hinze, Equilibriums of the Iron-Carbon-Oxygen System in the Temperature and Concentration Rangeof Molten Steel and the Effect of Phosphorus, Manganese, andSulfur, Arch. Eisenhuettenwes., 1966, 37(7), p 545-553

41. Steelmaking Data Sourcebook. Japan Society for the Promo-tion of Science, 19th Comm. On Steelmaking, Gordon &Breach Science, New York, NY, 1988, 312 pp

42. M. Chase, NIST-JANAF Thermochemical Tables, 4th ed.,NIST, Gaithersburg, 1998

43. A.T. Dinsdale, SGTE Data for Pure Elements, CALPHAD,1991, 15, p 317-425

44. I. Ansara and A. Jansson, Assesment of the Copper-IronSystem, Materials Research Center, The Royal Institute ofTechnology, Stockholm, Sweden, 1993

240 Journal of Phase Equilibria and Diffusion Vol. 36 No. 3 2015