Evaluation of thermodynamic data and phase equilibria in the system Ca–Cr–Cu–Fe–Mg–Mn–S part I: Binary and quasi-binary subsystems

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Evaluation of thermodynamic data and phase equilibria in the system Ca–Cr–Cu–Fe–Mg–Mn–S part I: Binary and quasi-binary subsystems Tatjana Jantzen a,n, Klaus Hack a, Elena Yazhenskikh b, Michael Müller b a b

GTT-Technologies, Kaiserstraße 103, D-52134 Herzogenrath, Germany Forschungszentrum Jülich GmbH, IEK-2, D-52425 Jülich, Germany

art ic l e i nf o

a b s t r a c t

Article history: Received 10 March 2016 Received in revised form 26 April 2016 Accepted 27 April 2016

The Ca–Cr–Cu–Fe–Mg–Mn–S system has been thermodynamically assessed using all available experimental data. The thermodynamic description of the high-temperature phase Chromium and Iron Pyrrhotite is described using a two-sublattice model which allows the description of the stability range of this phase in the binary Fe–S and Cr–S systems and also the solubility of such elements as Cu, Mg and Mn in the binary systems. Particular attention was given also to the phases Oldhamite and Digenite, which exhibit very wide solubility with respect to the metal elements. In this part of the report binary and quasi-binary subsystems are presented. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Sulfide Phase diagrams Thermodynamic modeling Pyrrhotite Oldhamite Digenite

1. Introduction Sulfur is commonly contained as an essential component in many natural and manufactured materials. Sulfide glasses can be used for high refractory index materials. Sulfur species are present in radioactive and toxic wastes. Sulfides are in focus of attention due to their importance for ferrous and copper metallurgical processes. The thermal properties and stability ranges of sulfide containing systems is necessary for understanding and control of the processes of desulfurization of molten alloys and formation of the sulfides during the solidification process. In the present work the most important metal sulfur systems Me–S (Me ¼Ca, Cr, Cu, Fe, Mg, Mn) are considered in terms of evaluation of thermodynamic properties and phase equilibria. The experimental information on the thermodynamic properties of the sulfide systems (phase diagram, phase transition etc.) are used for the generation of Gibbs energy datasets for all available phases and compounds. The database consists of the optimized thermodynamic parameters for all phases using suitable thermodynamic models for each phase. The datasets are used for the reproduction and calculation of thermodynamic properties and the prediction of value in multicomponent systems in known as well as in unknown regions of temperature and composition. Some phase diagrams and thermodynamic data assessments are n

Corresponding author. E-mail address: [email protected] (T. Jantzen).

available in the literature for sulfide systems with copper [1], iron [2,3], chromium [4,5] and manganese [2,6–8]. Both, the modified quasichemical model for short-range ordering [9], for example in [2,3], and the two-sublattice ionic liquid model [4,7,8,10] have been used for the molten sulfides. The modified associate species model [11], which has successfully been applied for the oxide liquid phase (slag) [12,13] is also applicable for sulfur-containing systems [14,15]. In order to obtain compatibility between the thermodynamic description of the liquid phase (slag) for oxides and sulfides we purpose to apply the modified associate species approach with suitable thermodynamic parameters for Me–S systems (Me ¼ Fe, Ca, Mn, Cr, Mg, Cu). The solid solutions found in the system under consideration are described using two- or three-sublattice models. The present work includes several solid solubilities which are so far not described in the literature. The thermodynamic dataset containing all phases for complete Me–S systems will be introduced into the complete database for complex systems relevant to slags and ashes. In a subsequent paper, the thermodynamic assessments of the corresponding ternary sulfide systems will be discussed.

2. Thermodynamic models All calculations and optimizations in this work were done using the FactSage thermochemical software package [16,17]. The Sulfide database contains a gas phase, a multi-component liquid phase, 6 solid solutions and several solid stoichiometric compounds

http://dx.doi.org/10.1016/j.calphad.2016.04.011 0364-5916/& 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: T. Jantzen, et al., Evaluation of thermodynamic data and phase equilibria in the system Ca–Cr–Cu–Fe–Mg–Mn– S part I: Binary and quasi-binary subsystems, Calphad (2016), http://dx.doi.org/10.1016/j.calphad.2016.04.011i

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Table 1 Crystal structure data of sulfides [19,20]. Sulfide

Pearson symbol

Space group

Strukturbericht designation

Prototype

CaS

cF8

NaCl

mC8 hP4 hP20

Fm 3̅ m C2/c P63/mmc P 3̅ 1c

B1

Cr1.03S CrS Cr2S3(I)

B81

NiAs Cr2S3(I)

Cr2S3(II)

hR10

Cr3S4 Cr5S6

mI14 hP22

Cr7S8

hP4

Cu2S-HT

cF12

Cu2S(MT) Cu2S(LT) CuS FeS-HT FeS-MT

hP6 mP144? hP12 hP4 hP24

FeS2

cP12

Fe7S8 Fe9S10 Fe10S11 Fe11S12 MgS

hP45 hP* oC* hP* cF8

MnS

cF8

MnS2

cP12

Cr2S3(II)

R 3̅ I2/m P 3̅ 1c P 3̅ m1 Fm 3̅ m P63/mmc P21/c P63/mmc P63/mmc P 6̅ 2c

Cr3S4 Cr5S6

2.1. Liquid phase

Cr7S8 C1

CaF2

B82 B18 B81

InNi2 CuS NiAs

C2

FeS2(pyrite)

Fm 3̅ m

B1

Fe7S8 Fe9S10 Fe10S11 Fe11S12 NaCl

Fm 3̅ m Pa 3̅

B1

NaCl

C2

FeS2(pyrite)

Pa 3̅ P3121

including the elements themselves. The Gibbs energies of the pure elements and some known sulfides were taken from the SGTE Pure Substance database [18], the missing compounds are modeled using the compound energy formalism. The crystal structure data of the pure stoichiometric sulfides are collected in the Table 1. The thermodynamic descriptions of the stoichiometric sulfides according to [19,20] are presented in Table 2. All phases in the metal–sulfur systems considered in the present work are given in Tables 3–6, and are described below in more detail.

Cmca

Liquid Me–S solutions exhibit short-range ordering (SRO) resulting from the fact that metal–sulfur pairs are usually predominant over metal-metal and sulfur-sulfur pairs. The compositions of the associate sulfide species correspond to those of maximum short-range ordering and correlate with solid neutral metal sulfides. For example, the liquid Fe–S solution shows a strong SRO near XS E0.5 corresponding to FeS, while the liquid Cu–S shows SRO near XS E0.333 corresponding to Cu2S. The SRO compositions were confirmed by experimental observation of the sulfur potential [21]. Similar to the binary iron-sulfur system, very stable compounds of MeS composition are considered as SRO composition of liquid Me–S solutions with Me ¼Mg, Mn, Ca, Cr. Accordingly, the pure liquid metals and sulfur along with associate

Table 2 Thermodynamic properties of pure stoichiometric sulfides used in the present work. Compound

0 J/mol ΔH298, f

0 J/mol K S298

CaS

 475,000

Cr2.06S2 (Cr1.03S)

 295,100

CrS

 135,000

Cr2S3(s1)

 343,456

132.827

Cr2S3(s2)

 335,140

138.473

Cr3S4

 484,764.8

198.357

Cr5S6

 772,212

310.47

Cr7S8

 1,059,266.2

CuS FeS(s1)

 55,000  101,000

FeS(s2)

 97,170

56.5 103.754

65

422.6086 67.47 60.31

69.429

FeS2 Fe7S8

 172400*  758,254

52.93 499.31

Fe9S10

 956,492

636.81

 1,056,568  1,156,907  348,000

700.5 763.23 50.33

Fe10S11 Fe11S12 MgS MnS

 214,200

78.199

MnS2

 223,844

99.914

T (K)

Cp, J/mol K

References

298–2800 2800–5500 298–450 450–1840 1840–3000 298–450 450–1840 1840–3000 298–450 450–1840 1840–3000 298–450 450–1840 1840–3000 298–450 450–1840 298–450 450–1840 298–450 450–1840 298–1000 298–420 420–440 440–590 298–420 420–440 440–590 298–1500 298–589 590–1400 298–589 590–1400 298–589 298–589 298–2500 2500–4000 298–1803 1803–2200 298–700

46.29021 þ0.008369608*T  118819* T  2 þ 1.181295E-10*T2 67 þ63.54928 þ0.10112578*T þ49702.08*T  2  7.41389796E-6*T2 þ103.41966þ0.00973533*T -528.195**T  2 þ1.57066296E-9*T2 134 þ31.77464 þ 0.05056289*T þ 24851.04**T  2  3.706949E-6*T2 þ51.70983þ 0.004867665*T  264.0975**T  2 þ7.853315E  10*T2 67 þ79.4366 þ0.126407225*T þ 62127.6**T  2  9.26737245E 6*T2 þ129.274575þ0.0121691625*T -660.24375**T  2 þ 1.9633287E-9*T2 þ167.5 þ79.4366 þ0.126407225*T þ62127.6**T  2  9.26737245E-6*T2 þ129.274575þ0.0121691625*T  660.24375**T  2 þ 1.9633287E-9*T2 þ167.5 þ111.21124þ 0.176970115*T þ 86978.64**T  2  1.297432145E-5*T2 þ180.984405 þ 0.0170368275*T  924.34125**T  2 þ2.7486602E-9*T2 þ174.76052 þ 0.278095895*T þ 136680.72**T  2  2.038821945E  5*T2 þ284.404065þ0.0267721575*T  1452.53625 **T  2 þ4.3193232E  9 *T2 þ238.3098 þ 0.379221675*T þ186382.8**T  2  2.780211745E  5*T2 þ387.823725 þ0.0365074875*T  1980.73125**T  2 þ 5.8899862E-9*T2 þ43.671þ 0.0201363*T  210120**T-2  4.72E-9*T2 þ2437.406-9.902902*T  41129850**T  2 þ 0.01156859*T2 þ83.00001 þ321.888  1.065128*T þ 686570**T  2 þ 0.001119891*T2 þ2437.406-9.902902*T  41129850**T  2 þ 0.01156859*T2 þ83.00001 þ321.888  1.065128*T þ 686570**T  2 þ 0.001119891*T2 þ72.387 þ0.0088501*T  1142790**T  2 þ7.3E  10*T2 þ1594.497 4.2376349*T  32367990**T  2 þ 0.00443408773*T2 þ304.251þ 0.1284715*T þ 19966170**T  2  2.315771E-5*T2 þ2101.867 5.6531299*T  42776390 **T  2 þ 0.00591211673 *T2 þ 381.539 þ 0.1683453 *T þ27002490 **T  2  3.087719E  5 *T2 þ 2355.552  6.3608774*T  47980590**T  2 þ0.00665113123*T2 þ 2609.237 7.0686249*T  53184790**T  2 þ 0.00739014573*T2 þ45.54407 þ 0.008756547*T  230669.9**T  2 þ1.816489E  10*T2 67 þ47.6976 þ0.0075312*T þ66.944 þ69.70544 þ0.01765648*T  435136**T  2

[18] This work

[18]

This work

This work

This work This work This work [18] [18]

[18]

[18], *- this work This work This work This work This work [18] [18] [18]

Please cite this article as: T. Jantzen, et al., Evaluation of thermodynamic data and phase equilibria in the system Ca–Cr–Cu–Fe–Mg–Mn– S part I: Binary and quasi-binary subsystems, Calphad (2016), http://dx.doi.org/10.1016/j.calphad.2016.04.011i

T. Jantzen et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Table 3 Modeling of binary S-containing phases. System

Phase

Description

Used data

Ca–S Cr–S

Liquid Liquid Cr1.01S Cr2S3(I) Cr2S3(II) Cr3S4 Cr5S6 Cr7S8 Pyrrhotite Liquid Cu2S-I Cu2S-II Digenite CuS Liquid FeS (s1, s2) FeS2 Pyrrhotite Liquid Liquid

(Ca, CaS, S) (Ca, CrS, S) Stoichiometric Stoichiometric Stoichiometric Stoichiometric Stoichiometric Stoichiometric (Cr, Va)S (Ca, Cu2S, S) (Cu, Va)(Cu,Va)(S) (Cu, Va)(Cu,Va)(S) (Cu, Va)(Cu,Va)(S) Stoichiometric (Fe, FeS, S) Stoichiometric Stoichiometric (Fe, Va) (S) (Mg, MgS, S) (Mn, MnS, S)

MnS MnS2 Oldhamite Oldhamite Oldhamite Digenite Digenite Oldhamite Pyrrhotite Oldhamite Pyrrhotite Oldhamite

Stoichiometric Stoichiometric (Ca, Fe) (S) (Ca, Mg) (S) (Ca, Mn) (S) (Cu, Va) (Cu, Mg, Va) (S) (Cu, Va) (Cu, Mn, Va) (S) (Mg, Mn) (S) (Fe, Mg, Va) (S) (Fe, Mg) (S) (Fe, Mn, Va) (S) (Fe, Mn) (S)

This work This work This work This work This work This work This work This work This work, CrS [18] this work this work, Cu2S(s1) [18] this work, Cu2S(s2) [18] this work, Cu2S(s3) [18] [18] [7] o50%S this work 450%S [18] (Hf, Cp) [18] [24] this work [7] o50%S this work 450%S [18] [18] This work This work This work This work This work This work This work This work This work This work

Cu–S

Fe–S

Mg–S Mn–S

CaS–FeS CaS–MgS CaS–MnS Cu2S–MgS Cu2S–MnS MgS–MnS FeS–MgS FeS–MnS

species with formula MeS (Me ¼ Ca, Cr, Fe, Mg, Mn) and copper sulfide Cu2S are considered as liquid solution constituents in the present study. In addition, interactions between solution species were introduced in order to fine tune the thermodynamic description especially with respect to miscibility gaps in the liquid.

3

To provide equal weighting of each associate species with regard to its entropic contribution in the ideal mixing term, each species contains one atom of sulfur. The molar Gibbs energy of the solution is presented by a threeterm expression with contributions of the reference part, the ideal and the excess part taking into account binary interactions as follows:

Gm =

∑ xi Gi0 + RT ∑ xi ln xi + ∑ ∑ xi xj ∑ Lij(v) (xi − xj )v i
(1)

v=0

where xi is the mole fraction of phase constituent i (including the associate species), Gi° is the molar Gibbs energy of the pure phase constituent and L ij(v) is an interaction coefficient between components i and j, according to the Redlich–Kister polynomial. Gi0 and L ij(v) with v ¼ 0, 1, 2 are temperature dependent in the same way according to equation:

Gi0, L ij(v) = A + B⋅T + C⋅T ⋅ ln T + D⋅T 2 + ….

(2)

Thermodynamic data for the pure liquid components have been taken from the SGTE Pure Substance database [18].

2.2. High-temperature pyrrhotite The Iron sulfide phase, commonly called Troilite, and the CrS modification at high temperature have the same crystal structure (space group P63/mmc, NiAs prototype) and Pearson symbol hP4 [19,20] and form a continuous solid solution. This solid solution phase can be described using the two-sublattice model (Cr, Fe, Va) S assuming that one sublattice can be occupied by Fe, Cr and vacancies (Va) while the other contains only sulfur atoms. This allows to describe the deviation from the stoichiometry towards higher S-contents according to the formula Fe1  xS and Cr1  xS. The molar Gibbs energy of this phase was expressed using the compound energy formalism derived by Hillert and Staffansson [22] and generalized by Sundman and Ågren [23] as follows:

Table 4 Calculated and experimentally assessed invariant reactions in Cr–S system. Reaction

Reaction type

Composition, at% S

L2(Cr)

Melting

0

0

L12L2 þ(Cr)

Monotectic

L22CrS þ (Cr)

Eutectic

L22CrS

Congruent

L22CrS þ L3

Monotectic

CrS þL32Cr2S3(II)

Peritectic

CrS þCr2S3(II)2Cr2S3(I)

Peritectoid

CrS þCr2S3(I)2Cr3S4

Peritectoid

(Cr) þ CrS2Cr1.03S

Peritectoid

CrS þCr3S42Cr5S6

Peritectoid

CrS þCr5S62Cr7S8

Peritectoid

CrS2Cr1.03Sþ Cr7S8

Eutectoid

L2(S)

Melting

3.5 4.0 4.77  44 44.4  50 0.505  67 58.58  58.5 54.18  58 54.06  58 53.95 0 0  53.9 52.43  52.2 52.39  52 52.07 100

0 0 0  50 50  50 0.505 59 54.01  100 99.16  60 60  58.5 60  51 50.01  56 57.14  53.7 54.54  49.3 49.26 100

38 30.4 28.5 0

100 98.31  60 0.60  59 60  58.2 57.1  49.3 49.26 54 54.54  53.3 53.33  53.3 53.33

Temperature,°C

Reference

1863 1906.8 1550 1760 1844 1350 1350 1565 1562  1300 1356 1250 1252 1200 1200 1152 1150 597 598 327 327 317 316 277 269 115 115

[31] [18] [31] [33] This [31] This [31] This [31] This [31] This [31] This [31] This [31] This [31] This [31] This [31] This [31] [18]

work work work work work work work work work work work

Please cite this article as: T. Jantzen, et al., Evaluation of thermodynamic data and phase equilibria in the system Ca–Cr–Cu–Fe–Mg–Mn– S part I: Binary and quasi-binary subsystems, Calphad (2016), http://dx.doi.org/10.1016/j.calphad.2016.04.011i

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Table 5 Calculated and experimentally assessed invariant reactions in Cu–S system. Reaction

Reaction type

Composition, at% S

L2Digenite

Congruent

L22 L1 þ Digenite

Monotectic

L2(Cu)þ Digenite

Eutectic

L22Digeniteþ L3

Monotectic

DigeniteþL2CuS

Peritectic

(Cu) þDigenite2Cu2S(II)

Peritectoid

(Cu) þCu2S(II)2Cu2S(I)

Peritectoid

33.32 33.33 32.9 33.16 1.48 1.44 41 38.61 36.6 36.7 0 0 0 0

33.32 33.33 2  1.66 0.0225 0  36.4 36.27  100  100 33.344 33.35 33.33 33.33

I I I G m = yCr ySII oGCr:S + yFe ySII oG Fe:S + yVa y SII oG Va:S I I I I I I + RT (yCr + yFe + yVa ) ln yCr ln yFe ln yVa ex + RTySII ln ySII + Gm

(3)

where yI and yII represent the site fractions of the components in the first and second sublattices, respectively. The oGCr:S and oGFe:S are the Gibbs energies of the pure stoichiometric sulfides without any defects, oGVa:S is the molar Gibbs energy of a hypothetical compound, pure sulfur with pyrrhotite structure, and is taken from [24]. n ex I I Gm = yCr ⋅yVa ⋅ySII

∑ L(kCr,Va:S) (yCrI

I k − yVa )

k=0 n I I + yFe ⋅yVa ⋅ySII

I k ) ∑ L(kFe,Va:S) (yFeI − yVa k=0 n

I I + yCr ⋅yFe ⋅ySII

∑ L(kCr,Fe:S) (yCrI

33.4 33.36 33.4 33.36 99.83 98.71 50 50 33.34 33.33 33.33 33.33

Temperature,°C

Reference

1129 1120 1105 1105 1067 1069 813 814 507 506 435 436 104 103

[48] This [48] This [48] This [50] This [51] This [51] This [52] This

work work work work work work work

MgS ¼Niningerite and MnS ¼Alabandite. The structure is simple, the metal atoms are located on the first octahedral sublattice, and the sulfur atoms occupy the second face centered cubic sublattice. This fact permits to describe this phase MeS as one phase using a two-sublattice model with the proposed formula (Mg, Ca, Mn) S. This monosulfide phase is called Oldhamite in the present database. The solubility of Fe in Oldhamite is strongly temperature dependent and varies considerably depending on the solvent system. In CaS-rich systems the solubility of FeS in Oldhamite is quite low and amounts to  2 wt% at 1100 °C, in comparison in MgS- and MnS-rich systems the solubility is much larger and reaches up to 80 wt% at the same temperature [25]. The Gibbs energy of the phase Oldhamite was described as follows with the formula (Fe, Mg, Ca, Mn) S assuming that Fe atoms dissolve on the metal lattice: I o I o I o I o Gm = yFe GFe : S + yMg GMg : S + yCa GCa :: S + yMn GMn : S

I k − yFe )

(

I I I I I I I I + RT yFe ln yFe + yMg ln yMg + yCa ln yCa + yMn ln yMn

(4)

k=0

The L (kMe,Va:S) and L (kCr,Fe:S) parameters can be expressed as a function of temperature (see Eq. (2)). The Pyrrhotite solid solution dissolves a significant amount of Manganese, from 5 at% at 600 °C to 7.4 at% at 1000 °C [25] . Also Copper and Magnesium show solubility in this phase, although to a lesser extent. Copper, Magnesium and Manganese are introduced into the thermodynamic description of Pyrrhotite as (Cu, Cr, Fe, Mg, Mn, Va) S in order to describe the entire solubility in iron sulfide-metal sulfide (where metal ¼Cu, Mg, Mn) systems. The complete Gibbs energy of Pyrrhotite containing all dissolved elements using (3) simplified under the condition ySII =1 can be written as I o I o I o I o I o G m = yCr GCr:S + yFe G Fe:S + yVa G Va:S + yCu GCu:S + yMg G Mg:S

(

I o I I I I I I + yMn G Mn:S + RT yCr ln yCr + yFe ln yFe + yVa ln yVa

)

I I I I I I ex + yCu ln yCu + yMg ln yMg + yMn ln yMn + Gm

(5)

where oGCu:S, oGMg:S and oGMn:S are the Gibbs energies of fictive metallic sulfides in the Pyrrhotite structure and are derived using available experimental data involving the solubility of the respective elements. 2.3. Oldhamite According to [19,20] (see Table 1) calcium, magnesium and manganese monosulfides have identical Pearson Symbol cF8, Space group Fm3m and Prototype NaCl, although all three endmember sulfides have different mineral names: CaS ¼Oldhamite,

o

+

I I yFe yMg LFe, Mg : S

+

I I yCa yMn L Ca, Mn : S o

+

I I yFe yCa LFe, Ca : S

+

I I yFe yMn LFe, Mn : S

+

)

I I yCa yMg L Ca, Mg : S

(6) o

GCa:S , GMg:S and GMn:S are the Gibbs energies of the pure metallic sulfides. oGFe:S is the Gibbs energy of a fictive FeS compound in Oldhamite Structure and is derived from the solubility of iron in the Oldhamite phase. The LMe1,Me2:S -parameters are the interaction parameters between two different metal atoms on the first sublattice and are represented by the following equation: I I LMe1,Me2:S = L (0Me1,Me2:S) + L (1Me1,Me2:S) (yMe1 − yMe2 )

(7)

The LMe1,Me2:S -parameters have been assessed in this work to describe both the low temperature immiscibility in Oldhamite in the CaS–MgS and CaS–MnS systems and the solubility of iron in the corresponding systems. 2.4. Digenite Three copper sulfides with composition close to Cu2S exist in different temperature and composition ranges. The high-temperature phase Digenite is characterized by a wide composition range, from 33.33 mol% S according to the stoichiometric compound Cu2S on the Cu-rich side to 38.40 mol% S at the monotectic temperature (813 °C) [26]. Two further modifications of Copper sulfide called low- and high-chalcolite have near-stoichiometic composition of Cu2S. Sundman in [1] and [24] has described Digenite using a three-sublattice model with a formula (Cu, Va)2(Cu, Va)1S1. According to [1] the first and the third sublattices are

Please cite this article as: T. Jantzen, et al., Evaluation of thermodynamic data and phase equilibria in the system Ca–Cr–Cu–Fe–Mg–Mn– S part I: Binary and quasi-binary subsystems, Calphad (2016), http://dx.doi.org/10.1016/j.calphad.2016.04.011i

T. Jantzen et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Table 6 Thermodynamic descriptions of the liquid and solid solution phases. Parameter value, J/mol

Reference

Liquid: (Ca, Cr, Cu, Fe, Mg, Mn, S, CaS, CrS,Cu2S, FeS, MgS, MnS) °GCa=°GLiq − Ca

* [68]

SGPS °GCr=°GLiq − Cr

[18]

SGPS °GCu=°GLiq − Cu

[18]

SGPS °GFe=°GLiq − Fe

[18]

SGPS °GMg=°GLiq − Mg

[18]

SGPS °GMn=°GLiq − Mn

[18]

SGPS °GS=°GLiq −S

[18]

SGPS °GCaS=°GLiq − CaS

*

SGPS + 6325 − 3*T °GCrS = °GCrS

[18]

SGPS °GCu2S =°GLiq − Cu

[18]

SGPS °GFeS =°GLiq − FeS

[18]

SGPS °GMgS =°GLiq − MgS

[18]

SGPS °GMnS =°GLiq − MnS

*

liq °L Cr,CrS =

+141776 − 70 * T

*

1 liq L Cr,CrS

= + 26432 − 32 * T

*

2 liq L Cr,CrS

= − 6432 + 4 * T

*

liq °LS,CrS =

+53145 − 19 * T

*

2S

1 liq LS,CrS

= − 38200

*

2 liq LS,CrS

= − 13000

*

liq °L Cu,Cu = +48000 2S liq °LS,Cu = +57160 − 2S

*

28. 6 * T

*

1 liq LS,Cu S= −35400 2 2 liq LS,Cu S° = −21000 2

*

liq °LFe,FeS =

[7]

+31761 − 9. 202 * T

*

1 liq LFe,FeS

= − 10761 − 0. 477 * T

[7]

liq °LS,FeS =

+49145 − 19 * T

*

1 liq LS,FeS

= − 59900 + 13 * T

*

2 liq LS,FeS

= + 7000

*

liq °LMn,MnS = +60357

*

1 liq LMn,MnS

*

liq °LS,MnS =

= − 19701 +33145 − 19 * T

[7]

1 liq LS,MnS

= − 37000 − 7 * T

*

2 liq LS,MnS

= − 22000

*

0 liq L CaS,FeS

= − 17800

0 liq L CaS,MnS

= − 23000

* *

0 liq L Cu S,MgS 2 0 liq L Cu S,MnS 2

= + 18570 − 23 *T

*

= + 86907 − 59 * T

*

1 liq L Cu S,MnS 2 2 liq L Cu S,MnS 2

= − 55079 + 33 * T

*

= + 58920 − 40 * T

*

0 liq LFeS,MgS

= + 12283 − 11 * T

*

1 liq LFeS,MgS

= − 7000

*

0 liq LFeS,MnS

= + 12200

*

0 liq LMgS,MnS

= − 9000

*

Digenite: (Cu, Va)(Cu, Fe, Mn, Mg, Va)(S) SGPS °GCu:Cu:S=°GCu S (s3) 2

°GCu:Fe:S= −12357. 481 + 205. 22704 * T − 54. 250439 * T * ln ( T )

* [18] *

 0.0054301*T2  .25335363E-05*T3 þ 117269*T  1 (298.15o T o 368.3)  11715.073þ 185.58946*T  50.78302*T*ln(T)  0.013247*T2 þ 0.642351*10  6*T3 þ 97314*T  1 (368.3 o T o1300)

°GCu:Mn:S= −174533. 16 + 431. 2711 * T − 84. 70354 * T * ln ( T )

*

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6

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Table 6 (continued ) Parameter value, J/mol

Reference

þ 0.009499*T2  .38771663E-05*T3(298.15o T o368.3)  173890.75 þ411.63352*T  81.236121*T*ln(T) þ0.00168196*T2  .70127898E-06*10  6*T3  19955*T  1 (368.3 o T o 1300) ⎡⎣ 7⎤⎦ +°GFeS −0.5*GVAVAS + 170000 2 ( s3) SGPS SGPS − 0.5*GVAVAS + 170000 0.5*°GCu +°GMnS 2S (s3)

*

SGPS SGPS °GCu:Mg:S= + 0.5*°GCu S (s3) +°GMgS − 0.5*GVAVAS + 170000

*

SGPS °GCu:Fe:S= + 0.5*°GCu S

°GCu:Mn:S= +

2 SGPS °GCu:Va:S= + 0.5*°GCu +0.5*GVAVAS 2S (s3) SGPS °GVa:Cu:S= + 0.5*°GCu +0.5*GVAVAS ( ) S s3 2 ⎡⎣ 7⎤⎦ °GVa:Fe:S=°GFeS +10000 SGPS + 10000 °GVa:Mn:S=°GMnS SGPS + 20000 °GVa:Mg:S=°GMgS

*

* * * * *

0 Digenite L Cu,Va:Cu:S=

−56200 + 35 * T

* *

0 Digenite L Cu:Cu,Va:S=

°GVa:Va:S=GVAVAS−50000

−56200 + 35 * T

*

0 Digenite L Cu:Cu,Mg:S=

−37000 + 13 * T

*

0 Digenite L Cu:Cu,Mn:S=

−27000

*

Cu2S-II: (Cu, Va) (Cu, Fe, Va)(S) SGPS °GCu:Cu:S=°GCu S (s2) 2

* [18]

⎡⎣ 7⎤⎦ 2 SGPS 0.5*°GCu +0.5*GVAVAS 2S (s2)

*

SGPS °GVa:Cu:S= + 0.5*°GCu S (s2) + 0.5*GVAVAS

*

SGPS °GCu:Fe:S= + 0.5*°GCu S (s2) +°GFeS − 0.5*GVAVAS + 170000

°GCu:Va:S= +

2 ⎡⎣ 7⎤⎦ °GVa:Fe:S=°GFeS +20000

°GVa:Va:S=GVAVAS 0 Cu2S − II L Cu,Va:Cu,Va:S=

−50000

Cu2S-I: (Cu, Va) (Cu, Fe, Va)(S) SGPS °GCu:Cu:S=°GCu S (s1) 2

*

* * * * *

⎡⎣ 7⎤⎦ 2 SGPS 0.5*°GCu +0.5*GVAVAS 2S (s1)

*

SGPS °GVa:Cu:S= + 0.5*°GCu S (s1) + 0.5*GVAVAS

*

SGPS °GCu:Fe:S= + 0.5*°GCu S (s1) +°GFeS − 0.5*GVAVAS + 170000

°GCu:Va:S= +

2 ⎡⎣ 7⎤⎦ °GVa:Fe:S=°GFeS +20000

°GVa:Va:S=GVAVAS 0 Cu2S − II L Cu,Va:Cu,Va:S=

−50000

Pyrrhotite: (Cr, Cu, Fe, Mg, Mn, Va)(S) SGPS °GCr:S=°GCrS s2

( )

*

* * * * * [18]

SGPS + 68000 °GCu:S=°GCuS s

*

SGPS °GFe:S=°GFeS ( s4)

[18]

SGPS + 19000 °GMg:S=°GMgS

*

⎡⎣ 7⎤⎦ °GMn:S=°GMnS+19915

*

°GVa:S=GVAS

()

0 Pyrrhotite LFe,Va:S =

−190667 − 7. 16 * T

[24] *

0 Pyrrhotite LFe,Mg:S =

+23000 − 6 * T

*

1 Pyrrhotite LFe,Mg:S =

+5000

*

0 Pyrrhotite LFe,Mn:S =

+5839

*

1 Pyrrhotite LFe,Mn:S =

+6224 − 3 * T

*

0 Pyrrhotite LFe,Cu:S =

−120700

*

0 Pyrrhotite L Cr,Va:S =

−172014 − 33 * T

*

1 Pyrrhotite L Cr,Va:S =

−23000 + 53 * T

*

2 Pyrrhotite L Cr,Va:S =

−43000

*

0 Pyrrhotite L Cr,Mn:S =

+23000 + 23 * T

*

Oldhamite : (Ca, Cr, Fe, Mg, Mn)(S) SGPS °GCa:S=°GCaS SGPS + 20480 °GCr:S=°GCrS (s1)

* * [18] *

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7

Table 6 (continued ) Parameter value, J/mol

Reference

⎡⎣ 7⎤⎦

*

°GFe:S=°GFeS + 192 SGPS °GMg:S=°GMgS

[18]

SGPS °GMn:S=°GMnS

[18]

0 Oldhamite LFe,Mg:S =

+15984 − 10 * T

*

1 Oldhamite LFe,Mg:S =

−3000

*

0 Oldhamite L Ca,Mn:S =+33000

*

− 7. 28 * T

1 Oldhamite L Ca,Mn:S =

−2000

*

0 Oldhamite LFe,Mn:S =

+6300

*

1 Oldhamite LFe,Mn:S =

+11865 − 5 * T

*

0 Oldhamite LFe,Ca:S =

+45700

*

0 Oldhamite L Ca,Mg:S =

+38000 − 11. 21 * T

*

1 Oldhamite L Ca,Mg:S =

−2000

*

0 Oldhamite L Cr,Mn:S =

−17000

*

GVAVAS ¼ þ 134820.43þ 55.417759*T  11.007*T*ln(T)  0.026528999*T2 þ 7.7543327E-06*T3 (298.15o T o368.3) þ 133535.61 þ94.692923*T  17.941839*T*ln(T)-0.010895125*T2 þ 1.402558E 06*T3 þ 39910*T  1 (368.3 o T o 1300) GVAS ¼ þ 100974.04þ87.401761*T  11.007*T*ln(T)  0.026529*T2 þ 7.754333E 06*T3 (298.15o T o 368.3) þ 99689.224þ 126.67692*T  17.941839*T*ln(T)  0.010895125*T2 þ1.402558E  06*T3 þ 39910*T*  1 (368.3 o T o1300) *

This work.

occupied by Cu and S atoms, respectively, while the second sublattice represents an interstitial position. Assuming that iron, manganese and magnesium atoms can be dissolved in Digenite, the following three-sublattice model with slightly different stoichiometry as in [1] was proposed in the present work (Cu, Va)1(Cu, Fe, Mg, Mn, Va)1(S)1. This formula allows describing the unsymmetrical phase boundaries, the Cu-rich boundary is approximately at Cu2S stoichiometry, the phase range extends to the sulfur side and the S-rich boundary can be described as Cu2  xS. The major components on the first and on the second sublattice respectively are copper atoms, the composition thus corresponding to the ideal stoichiometric compound Cu2S. Iron, manganese and magnesium atoms are introduced on the second sublattice to describe their solubility in Digenite, while the vacancies on the first sublattice were introduced to describe the neutral fictive sulfides FeS, MgS and MnS. The molar Gibbs energy of this phase is expressed as follows: I II o I II o I II o G m = yVa yVa G Va:Va:S + yVa yCu G Va:Cu:S + yVa yFe G Va:Fe:S I II o + yVa yMg G Va:Mg:S I II o I II o I II o + yVa yMn G Va:Mn:S + yCu yVa GCu:Va:S + yCu yCu GCu:Cu:S I II o + yCu yFe GCu:Fe:S I II o I II o + yCu yMg GCu:Mg:S + yCu yMn GCu:Mn:S I I I I + RT (yVa + yCu ) ln yVa ln yCu II II II II II II II II + RT (yVa + yCu + yFe + yMg ln yVa ln yCu ln yFe ln yMg II II ex + yMn ) + Gm ln yMn o

(8)

G j : k :S is the Gibbs energy of hypothetical compounds where the first and second sublattices are occupied by appropriate components j and k, oGCu:Cu:S is the Gibbs energy of Cu2S(HT) and is taken from the SGTE Pure Substance database [18].

3. Assessments Thermodynamic data sources used for the current database are collected in Table 3. The assessment on each binary and quasi-binary system presented here was performed using all available experimental information on the phase diagrams and component activities. The interaction parameters L ij(v) between species both in the liquid and solid solutions have being optimized. The introduction of nonideal interactions between the solid respectively liquid solution components was required, in order to obtain correct representations of the solubility regions. Under these conditions satisfactory descriptions of the solid solutions could be obtained. The optimization of the chosen solution parameters based on the available experimental data was performed using the optimizer module OptiSage included in the FactSage [16,17] software. 3.1. The Cr–S system The phase diagram used for the optimization was taken from [27], which is based on the experimental data reported by [28–32]. The system is characterized by two regions of liquid immiscibility: one between liquid chromium and “sulfide”-rich compositions, and the other between “sulfide”-rich und sulfur-rich liquids. The monotectic reaction between metal-rich and sulfide-rich liquids is assumed to have a temperature of 1550 °C and liquid compositions of 3.5 and 38.0 at% S according to [28], the critical point of the miscibility gap is unknown. These data for the monotectic reaction actually contradict the experimental investigations of two-liquid separation by Griffing and Healy [33] where the monotectic temperature is estimated to be higher than 1760 °C. The second region of liquid immiscibility between the “sulfide”-rich and sulfur-rich liquids is experimentally not well determined and proposed to extend at the monotectic temperature  1300 °C from 68 to 97 at%

Please cite this article as: T. Jantzen, et al., Evaluation of thermodynamic data and phase equilibria in the system Ca–Cr–Cu–Fe–Mg–Mn– S part I: Binary and quasi-binary subsystems, Calphad (2016), http://dx.doi.org/10.1016/j.calphad.2016.04.011i

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S [27]. Jellinek [29] reported very small solubility of sulfur in solid Cr and also the existence of several intermediate phases CrS, Cr7S8, Cr5S6, Cr3S4 as well as two modifications of Cr2S3 which was confirmed later by other researchers [30–32]. The temperatures of the invariant equilibria containing the near-stoichiometric phases Cr1.03S, Cr2S3, Cr3S4, Cr5S6 and Cr7S8 are taken from [31] who studied the chromium sulfides in the composition range 0.5 oXS o0.533 using high X-ray diffraction and differential thermal analysis (DTA). According to [32,34,35] the sulfide Cr1  xS displays a wide homogeneity range and melts congruently at 1565 °C at approximately 50 mol% S [27]. El Goressy and Kullerud have experimentally determined the Cr–S phase diagram [30] using DTA and reported the eutectic reaction between chromium and Cr1  xS at 1350 °C and 43.9 at% S which is in accordance with the data published by [27], whereas the melting point of CrS is  1650 °C which is considerably higher than found by [28] (1565 °C). The solubility range of Pyrrhotite is smaller than that investigated by Rau [32] and ranges for example at 1000 °C from  50.3 to 53.9 at% S ([32] 50.3 and 57.4 at% S). For the optimization of the solubility range of Pyrrhotite the data of [30] are chosen to keep the peritectoid character of melting of the following compounds Cr3S4, Cr5S6 and Cr7S8 given by [27] and also the melting temperature of Cr3S4 to be 1150 °C (1152 °C [31]). In the present work the solubility range of Pyrrhotite extends from 50.01 to 53.44 at% S at 1000 °C. Thermodynamic descriptions of the Cr–S system were recently proposed by Oikawa [4] up to 50 at% S and by Waldner [5] in the whole range of composition. Oikawa has described the liquid phase using the two-sublattice model proposed by Hillert and Staffansson [10], whereas Waldner [5] applied the quasichemical model [36]. The present assessment of the Cr–S system contains a description of the liquid phase using the modified associate species model [11], Pyrrhotite as a solid solution phase and 5 compounds. The latter, exhibiting very small homogeneity ranges, were modeled as stoichiometric phases Cr1.03S, Cr2S3, Cr3S4, Cr5S6 and Cr7S8 approximating the experimentally determined compositions by [29]. The heat capacity functions of the compounds Cr1.03S, Cr2S3, Cr3S4, Cr5S6 and Cr7S8 are estimated using the heat capacity function of CrS by weighting with corresponding stoichiometric factors as was proposed in [5]. The Gibbs energy of the compound CrS is taken from the SGTE Pure Substance database [18] and used for the description of Pyrrhotite, the other compounds (Cr1.03S, Cr2S3, Cr3S4, Cr5S6 and Cr7S8) are modeled in the present work considering their thermal stability given by [31]. The enthalpy of formation data for all compounds recalculated per

Fig. 2. Calculated Cr–S phase diagram compared with experimental data.

1 g-atom are presented in Fig. 1 compared with the data given by other researchers. The data presented in this work especially for the compounds CrS (Δ H 0f ¼  67.5 kJ/g-atom) and Cr2S3

(Δ H 0f ¼  67.28 kJ/g-atom) are nearly identical to those by [37] ( 67.5 and  67), and also in good agreement with the values for the Cr2S3 (Δ H 0f ¼  69.4 kJ/g-atom and Δ H 0f ¼ 68.2 kJ/g-atom) according to [38] and [39]. The values assessed by [5] are considerably higher, for example the value for the Cr2S3 amounts to Δ H 0f ¼ 95.228 kJ/g-atom, which, however, is in accordance with the results by Stolyarova [40]. According to [29] there are two modifications of the compound Cr2S3, El Goresy and Kullerud [30] reported also an allotropic phase transition in Cr2S3 from trigonal Cr2S3(I) to rhombohedral Cr2S3(II) structure. The temperature of transformation was chosen to be 1200 °C as proposed by [27]. The assessed invariant reactions in Cr–S system are compared with available experimental data and given in Table 4. The agreement between the experimental and calculated phase diagram is satisfactory as can be seen from Fig. 2. It should be mentioned that the calculated monotectic temperature on the chromium-rich side is higher than determined by Vogel and Rheinbach [28] and also higher but closer to the temperature found by Griffing and Healy [33]. The difference can be explained with undercooling effects. When the lines determining the liquid immiscibility are extrapolated below the monotectic reaction, the experimental points investigated by [33] are located on the metastable two-liquid separation. 3.2. The Cu–S system

Fig. 1. Heat of formation of the compounds in Cr–S system.

A complete review of thermodynamic properties of the Cu–S binary system was published by Chakrabarti and Laughlin [26]. The Cu–S phase diagram is similar to the Cr–S phase diagram and indicates two relatively large miscibility gaps in liquid, between copper and copper sulfide and between copper sulfide and sulfur liquids. The monotectic reaction on the Cu-rich side occurs at 1105 °C, on the S-rich side, the temperature of the monotectic reaction is lower and is equal to 813 °C [26]. Chakrabarti and Laughlin [26] reported the existence of six intermediate phases: Digenite Cu2  δS with wide solubility range, Covellite CuS, low-Chalcolite and high-Chalcolite at stoichiometric composition Cu2S, Djurleite of nominal composition Cu1.96S and Anilite of stoichiometry Cu1.75S. According to [26] Digenite is the most stable solid solution phase in the system and melts congruently at 1130 °C, the near-stoichiometric compounds Covellite, high-Chalcolite, low-Chalcolite, Djurleite and Anilite melt at 507°,

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435°, 103°, 93° and 75 °C respectively. The Cu–S system was critical assessed by Decterov [41, 42] using the quasi-chemical model for liquid and by Lee and Sundman [1] using the associate model for liquid. Lee and Sundman have modeled Digenite as solid solution phase (Cu, Va)2(Cu, Va)1(S)1 and all five stoichiometric compounds existing in the system, Decterov and Pelton in [41] and [42] have taken into account the following restricted number of phases: Digenite as solid solution phase with formula (Cu2S, Va2S) and the stoichiometric compounds Covellite (CuS), high-Chalcolite and low-Chalcolite (Cu2S). In the present work three solid solution phases Digenite, highChalcolite and low-Chalcolite as well as one stoichiometric compound Covellite CuS are included. The Gibbs energies for the three modifications of Cu2S as well as for CuS were taken from the SGTE Pure Substance database [18]. The Gibbs energy data for Cu2S were used for the description of high- and low-Chalcolite (Cu, Va)1(Cu, Fe, Va)1(S)1 as well as for Digenite. The following description proposed for Digenite (Cu, Va)1(Cu, Va)1(S)1 allows to treat the broad unsymmetrical phase field of the phase. On the Cu-rich boundary from 435 °C up to the melting at 1130 °C the composition of Digenite is near stoichiometric Cu2S [26], the Gibbs energy data for Cu2S(s3) was taken as oGCu:Cu:S according to Eq. (8). In the temperature range from 507 °C to 813 °C toward the sulfur-rich side Digenite extends and attains the compositions 36.6 and  36.4 at% S respectively [26]. The calculated values are in accordance with those given by [26] and are at the corresponding temperatures 507 °C and 813 °C 36.7 at% S and 36.3 at% S respectively. Schuhmann and Moles in [43] have carried out sulfur partial pressure measurements in Cu2S-rich liquids at 1150 °C, 1250 °C and 1350 °C, from the edge of the immiscibility area at about 32.5 at% S up to the composition of 35.5 at% S. Bale and Toguri [21] investigated the sulfur activity in the liquid in the composition range 0–40 at%S at the temperatures 1150–1250 °C in both copper-rich and copper sulfide-rich liquids. Both investigations are in general agreement. The calculated composition dependence of the sulfur activity in the liquid at different temperatures are compared with experimental values in Fig. 3, the agreement is very satisfactory. In the Cu-rich liquids the sulfur activity decreases only insignificantly with decreasing amount of sulfur, while in the copper sulfide area the composition dependence of the sulfur partial pressure is considerable. These two different regions are separated by a miscibility gap in the liquid, corresponding to the horizontal lines in Fig. 3. Sick and Schwerdtfeger in [44] have investigated the nonstoichiometry of Digenite as a function of PH2S/PH2 at 800 °C. In

9

Fig. 4. Concentration dependence of partial sulfur pressure in Digenite in Cu–S system.

Fig. 5. Calculated Cu–S phase diagram compared with experimental data.

Fig. 4 the calculated sulfur activity in non-stoichiometric Digenite is presented as ratio between the partial pressures of H2S and H2 ( PH2S/PH2) compared with the experimental data. As shown in Figs. 3 and 4 the experimentally determined sulfur activity in the liquid as well as in the Digenite phase can be reproduced well using the current thermodynamic database. The calculated phase diagram Cu–S is shown in Fig. 5 compared with experimental information [21,26,45–51]. The calculated and experimentally assessed in [48,50–52] invariant reactions in the Cu–S system are collected in Table 5, the agreement is satisfactory. 3.3. The Fe–S system

Fig. 3. Concentration dependence of partial sulfur pressure in liquid in Cu–S system.

The Fe–S system is characterized by the presence of seven intermediate phases, Fe1  xS, FeS, Fe7S8, Fe9S10, Fe10S11, Fe11S12, FeS2 and a eutectic reaction between iron and iron sulfide and a miscibility gap in the liquid on the sulfur-rich side. According to [20,53,61,65] iron sulfide Fe1  xS (Pyrrhotite) melts congruently at 1188 °C, exhibiting a broad homogeneity range toward excess S, and has two low temperature modifications β-Fe1  xS below 315 °C and α-Fe1  xS below 138 °C. Iron disulfide FeS2 melts incongruently at 743 °C [53]. The remaining polysulfide phases all dissociate peritectoidly in the range 100–318 °C [58,61]. The miscibility gap on the high sulfur side exhibits a monotectic reaction at 1082 °C. In comparison, the liquidus behavior on the Fe-rich side

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10

Fig. 6. Calculated Fe–S phase diagram compared with experimental data.

is quite flat thus indicating a tendency to immiscibility even between iron and iron sulfide liquids. The Fe–S system has been thermodynamically modeled first by Hillert and Staffansson [54] who applied a simple (Fe, Va)(S, Va) two-sublattice model for the liquid phase. A modified two-sublattice model for liquid was used by Ohtani and Nishizawa [55], and later by Guillermet [56] who also applied a two-sublattice model for the pyrrhotite phase. Oikawa and Mitsui [4] have described the Gibbs energy of the liquid phase in the Fe–FeS system by a two-sublattice model. Waldner and Pelton [3] have used the extended modified quasi-chemical model for the liquid and also a sublattice model for pyrrhotite. Lee, Sundman, Kim and Chin [1] have thermodynamically assessed the Fe–Cu–S system using an associate solution model for liquid and a two-sublattice model for Pyrrhotite. Miettinen and Hallstedt [7] investigated the Fe–FeS–Mn–MnS system using a two-sublattice model for the liquid phase. Their thermodynamic description of the liquid in the Fe–S system from 0 to 50 at% S was adopted for the associate model used in the present work. The miscibility gap in the S-rich area is modeled using available experimental data. According to [53] the monotectic reaction between the iron sulfide and sulfur-rich liquids occurs at 1082 °C and extends from 63 at% to 99.7 at% S. The description of the Gibbs energy of pure sulfur as component in the phase Pyrrhotite proposed by [24] was accepted for this work. The thermal stability of such iron sulfides as Fe7S8, Fe9S10 and Fe11S12 studied by Nakazawa, Morimoto [58] and GrØnvald, Haraldsen [61] was used for the optimization. For the modeling of Pyrrhotite the experimental homogeneity range investigated by GrØnvald, Haraldsen [61], Jensen [63] and Arnold [65] was taken into account. The calculated Fe–S phase diagram is shown in Fig. 6 compared with data given by [20,57–66]. 3.4. The Mn–S system The Mn–MnS system was investigated by Vogel and Hotop [67] using thermal and microscopic methods in the concentration range of 0–50 mol% of S. The limitations of the experimental data are caused by the high temperature of melting of MnS and formation of immiscible liquids. According to [67] the measured melting point of MnS lies at about 1600 710 °C. They also report the monotectic reaction between Mn and MnS in the range of 0.5– 46 at% S and a temperature of 1580 °C. The eutectic was measured [67] to be very close to the melting point of manganese [Teut ¼1230 °C and Tm(Mn) ¼1244 °C]. The solid transitions of pure Mn were determined at 1191 °C and 742 °C, whereas the last transformation at 742 °C was not noticeable by cooling. It should be

noted that the melting point of Mn (1246 °C) given in the SGTE unary database [68] corresponds to the measurements done by [67] while the experimentally determined solid–solid transitions in Mn are not in accordance with [68]. The melting behavior of MnS was re-investigated using the DTA technique by Staffansson [6], who has also calculated the phase diagram using the new experimental information. The solubility of S in liquid Mn was measured at different temperatures by Dashevsky and Kashin [69]. Previous assessments have been carried out by different authors [2,6–8]. Staffansson in [6] applied the two-sublattice model to the liquid phase. The binary thermodynamic parameters from [6] were re-optimized and expanded by Miettinen and Hallstedt [7] to get a good agreement between calculated and experimental immiscibility in the Mn–MnS system. The liquid phase has been modeled in the latest works using the modified quasi-chemical [2] and the ionic two-sublattice [8] model respectively. In the framework of the associate species approach stoichiometric liquid MnS is considered as a component in the liquid phase. In case of the Mn–S system there are no experimental data regarding the composition of SRO as mentioned in reference [2], but since the manganese sulfide MnS is a very stable solid compound, the composition XS E0.5 of sulfur can be taken as SRO in the system Mn–S. The description given by Miettinen and Hallstedt [7] for the system Mn–S with sulfur content o50 at% S has been adopted in the present work. The interaction parameters in the liquid 450 at% S have been optimized in order to reproduce the available experimental information from the literature. The thermodynamic functions on stoichiometric manganese sulfides are taken from the SGTE Pure Substance database [18]. The low temperature heat capacity measurements indicated a ferromagnetic transformation of MnS (Alabandite) at 147 K [70] or 152 K [71]. However, this behavior has not been considered in the present work, because the present thermodynamic description is focused on temperatures above 25 °C. On the other hand, the formation entropy of MnS was derived using the above-mentioned heat capacity measurements [70] and accepted in the SGTE Pure Substance thermodynamic database [18]. Coughlin [72] reported the heat content of MnS measured by drop-calorimetry. The melting point of MnS found at 1530 °C [72] seems to be too low, but the fusion enthalpy was used in the thermodynamic database [18]. The calculated heat content for the composition of 50 mole percent of S along with the experimental points [72] is shown in Fig. 7a. A jump in the heat content at 1530 °C was attributed by Coughlin to the melting point, but the value of 1655 °C obtained by Staffansson [6] seems to be more correct because of a very low partial pressure of oxygen applied during the experiments of [6]. In the present assessment the compound MnS is calculated to melt at 1643 °C as shown in the calculated complete phase diagram of the Mn–S binary system (Fig. 7b) with inset showing the Mn-rich concentration range with solubility of S in Mn compared with experimental data [69]. Good agreement with the experimental phase diagram data [6,67,69,72] is observed. MnS2 decomposes into a sulfur melt and MnS at 388 °C. The miscibility gap in the Mn-rich melts is calculated according to available literature data [6,67] with a monotectic temperature of 1571 °C. The assessment of the immiscibility between MnS and S must be considered as preliminary (see Fig. 7b) due to a lack of reliable experimental information. 3.5. The systems Ca–S and Mg–S Experimental data on the Ca–S system is very limited, probably due to the high melting point of Oldhamite (CaS). Although CaS is known as an excellent luminescent material [73], the thermodynamic data is very scarce, there is for instance no phase diagram Ca–S available. According to the review of Massalski [20] calcium

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thermodynamic description for the system Ca–S was given by Lindberg and Chartrand [75], who proposed the interaction parameters in the liquid phase to be similar to those in the systems with Ca–CaO and Ca–CaC2. These authors have also introduced the calcium polysulfides in order to allow the (Ca–S) liquid phase to obtain compositions more sulfur-rich than CaS. In the present work liquid calcium sulfide along with pure liquid calcium and sulfur are considered as components of an associate liquid. Regarding the solid phases only oldhamite CaS is taken into account. The Gibbs energy data for CaS are taken from the SGTE Pure Substance database [18] including the melting point at 2526 °C and melting enthalpy of 70 kJ/mol. The proposed phase diagram Ca–S is shown in Fig. 8. The calculated eutectic between Ca and CaS is at 0.97 mole percent of S and 830 °C. Regarding the binary system containing Mg no phase diagram data is available [76]. Similar to the system Ca–S the magnesium sulfide with cubic structure of NaCl is known to melt congruently. The thermodynamic data for MgS are taken from the SGTE Pure Substance database [18]. The calculated phase diagram is very similar to that for Ca–S and, therefore, is omitted here. The calculated melting point of MgS is about 2223 °C, the eutectic point between Mg and MgS lies at 0.5 mole percent of S and at 645 °C. For both systems Ca–S and Mg–S systems the liquid phase is modeled as an ideal associated solution. 3.6. Binaries with Oldhamite: CaS–MgS, CaS–MnS, MgS–MnS

Fig. 7. (a) Temperature dependence of heat content for the composition of 50 at% S in the Mn–S system along with experimental data. (b) Calculated Mn–S phase diagram compared with experimental data. Inset shows the phase equilibria in the Mn-rich part of the diagram.

Fig. 8. Calculated Ca–S phase diagram.

sulfide belongs to the NaCl-type crystal structure and melts at a temperature of 2525 °C. The formation of polysulfides mentioned in [20] could not be confirmed because of difficulties with the identification of the reaction products as reported Robinson and Scott [74]. They observed CaS as single solid product. A

The binary systems CaS–MgS, CaS–MnS, MgS–MnS are characterized by complete solubility between the corresponding sulfides with similar NaCl-structure: CaS (oldhamite), MgS (niningerite) and MnS (alabandite). Primak and Kaufman [77] studied the interaction of CaS and MgS by heating their mixtures with flux of NaCl at temperatures of 1000–1100 °C and investigated the reaction products by X-ray diffraction. The change of lattice parameter for CaS and MgS in the mixture after heating indicated the mutual solid solubility of the sulfides in each other. The estimated solubility values were about 12 mole percent of CaS in MgS and 14 mole percent MgS in CaS. Skinner [25] has considered the solid solution based on the different sulfides (Ca, Mg, Mn, Fe)S. According to him the stability of the solid solutions in the systems CaS–MgS and CaS–MnS is strongly dependent on the temperature. The low temperature immiscibility tends to close up at high temperatures with possible existence of complete solid solution in the sub-solidus range. The highest solvus was not defined. Later, the complete mutual solubility of the solid solutions based on CaS and MnS in the temperature range between 1150 °C and 1500 °C was confirmed experimentally by Leung [78]. According to him the liquidus minimum (azeotropic point) occurs at 26% CaS and 1500 °C. The solid–solid miscibility gap determined by X-ray diffraction method [78] agreed with data published by Kiessling and Westman [79]. Since the solid solutions based on the components sulfides CaS, MgS and MnS with NaCl- structure show similar behavior, the features of the phase diagram proposed for the system CaS–MnS [25,78,79] are accepted for all binary systems with Oldhamite. The calculated phase diagrams with the solubilities in liquid and solid states are presented along with the available phase diagram data for the systems CaS–MgS, CaS–MnS and MgS–MnS in Figs. 9, 10, and 11, correspondingly. Based on the solubility boundary data for the system CaS–MgS at temperatures below 1000 °C published in [25,80] immiscibility between two Oldhamites is assumed along with continuous equilibrium between solid solution and the liquid phase shown in Fig. 9. The miscibility gap in the system CaS–MnS (Fig. 10) is calculated in good agreement with experimental points of [25,78,79]. The Oldhamite solution in the system MgS–MnS is assumed to be ideal (Fig. 11) based on the information by [25] that MnS and MgS form

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Fig. 9. Calculated phase diagram of the pseudo-binary system CaS–MgS compared with available experimental data.

Fig. 12. Activities of CuS0.5 and MnS in the liquid phase in the system Cu2S–MnS at 1200 °C compared with experimental data.

Fig. 10. Calculated phase diagram of the pseudo-binary system CaS–MnS compared with available experimental data.

Fig. 13. Calculated phase diagram of the pseudo-binary system CuS0.5-MnS.

3.7. Binaries with Digenite: Cu2S–MgS, Cu2S–MnS

Fig. 11. Calculated phase diagram of the pseudo-binary system MgS–MnS.

a completely miscible solid solution at all temperatures between 600° and 1000 °C. The possible immiscibility in the Oldhamite solution under 600 °C was not studied experimentally.

The Cu2S–MnS system has been studied by Lei and Yoshikawa [81] using a confocal scanning laser microscope (CSLM), electron probe micro analyzer (EPMA) and chemical equilibration technique. They have determined solidus and liquidus temperatures in the system, mutual solubility in Digenite and MnS and also the activity of the components CuS0.5 and MnS in the liquid phase at 1200 °C. These activities were obtained using an equilibration method with molten Cu as a reference. As shown in Fig. 12 the calculated activities of CuS0.5 and MnS in the liquid phase indicate positive deviations from ideality which is in agreement with the experimental investigations by [81]. According to [81] the phase diagram is eutectic with mutual solubility between Cu2S (Digenite) and MnS. Based on the formation temperatures of the liquid, the eutectic temperature was determined to be 1021 722 °C at 3471 at% MnS [81]. The corresponding calculated values are 1020 °C and  32 at% MnS respectively. The calculated phase diagram of the system Cu2S–MnS is given in Fig. 13. The agreement with experimental data is well. The Cu2S–MgS system has been investigated in detail by Andreev, Sikerina and Solov’eva [82,83] over the whole composition range and from room temperature up to 1510 °C. The compositions

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Fig. 14. Calculated phase diagram of the pseudo-binary system Cu2S-MgS.

Fig. 15. Calculated phase diagram of the pseudo-binary system CaS–FeS in equilibrium with Fe.

of the phases were determined using X-ray powder diffraction and microscopy. The phase transition temperatures were investigated using differential thermal analysis (DTA). According to [82] there is a invariant reaction at 1139 °C, with the calculated temperature at 1132 °C; the solubility of MgS in Digenite is lower than 1 mol% MgS. The calculated phase diagram is presented in Fig. 14 compared with the experimental data by [83], the agreement is good.

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are positioned close to the iron sulfide side. In the FeS–MgS system the invariant reaction is of peritectic type, in FeS–MnS system it has an eutectic character. The Oldhamite phase based on MgS or MnS extends toward the iron-rich side and reaches a maximum at the temperature of the invariant equilibrium. FeS dissolves in MgS up to  75 mol% at the peritectic point, in MnS the solubility of FeS reaches 72 at% at the eutectic temperature. In both systems the solubility of MgS and MnS respectively in Pyrrhotite (FeS) is quite less and lower than 10 mol%. Critical evaluations and thermodynamic optimizations of the Fe–Mn–S system over the entire composition range were carried out by Kang [86] using the modified Quasichemical model for the liquid. Miettinen and Hallstedt [7] and Ohtani, Oikawa and Ishida [87] described the liquid phase using a two-sublattice model for liquid (Fe, Mn)(S, Va) which is identical to the ionic two-sublattice model (Fe þ 2, Mn þ 2)p(S  2, Va  Q)q at p¼ q¼ 2 used by [8]. Phase equilibria in the FeS–MgS system were determined by various authors using different X-ray methods [88–90], XRD [25], [91] and Mössbauer spectroscopy methods [92,93]. Experimental investigations on the phase relations in the whole range of concentration were carried out by Andreev et. al. [94] using X-ray powder diffraction analysis, visual polythermal analysis (VPTA) and DTA. According to [94] the system exhibits a peritectic phase transformation at  1197 °C, which is in contradiction to the eutectic reaction at 1070 720 °C published by Skinner [25]. The maximum solubility of MgS reached 2 mole percent at the peritectic point, while Skinner [25] reported the limit of MgS in FeS below  1 mol%. Experimental investigations done by Andreev [94] imply that the MgS-based solid solution is a substitutional solid solution. Andreev et al. determined the solidus line relating to the MgS solid solution during thermal analysis of homogeneous samples. The extension of MgS toward the Fe-rich side is extensive and temperature dependent [25], this behavior was confirmed later by Andreev [94]. The solubility of FeS increases significantly with increasing temperature, at 497 °C the solubility of FeS amounts to 35 mol%, at 1143 °C 58 at% and at 1197 °C reaches  75 mol% [94]. These data were simultaneously used for the optimization of the model parameters for the liquid, the Oldhamite and the Pyrrhotite phase. As shown in Fig. 16, the calculated phase diagram agrees well with the experimental data. In contrast to the FeS–MgS system the FeS–MnS system has been studied more intensively and carefully because of its importance for understanding desulfurization of molten steel and

3.8. Binaries with Pyrrhotite: CaS–FeS, FeS–MgS and FeS–MnS The FeS-rich concentration range of the phase diagram of the system CaS–FeS was studied by Vogel [84] and Heumann [85]. The eutectic point was found at approximately 14 mole percent of CaS at 1100 °C and the solubility FeS in CaS was about 2 mole percent. Based on these data, the phase diagram is proposed as shown in Fig. 15, also taking into account the limited solubility of FeS in Oldhamite. In order to reproduce the equilibrium with pure iron also in the calculation a small amount of excess Fe was added. The calculated eutectic is at 10 mole percent of CaS and at T ¼1051 °C. The CaS-based Oldhamite dissolves up to 1.8 mol% of the iron sulfide at 1100 °C, which agrees well with data of Heumann [85]. The phase diagrams FeS–MgS and FeS–MnS exhibit very similar behavior, where the invariant equilibria involving the liquid phase

Fig. 16. Calculated phase diagram of the pseudo-binary system FeS–MgS in equilibrium with Fe.

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agreement is satisfactory, especially at higher temperatures. The calculated phase diagram compared with available experimentally determined phase boundaries is shown in Fig. 18. The experimental eutectic is reported with temperatures between 1110 and 1181 °C and eutectic compositions between 6 and 10 mol% MnS according to [25,96–101]. In the present work the eutectic reaction occurs at 1135 °C and 6.8 mol% MnS which is in good accordance with the experiments.

4. Conclusions

Fig. 17. Calculated equilibrium ratios p(H2S)/p(H2) over Oldhamite in equilibrium with metallic iron in Fe–Mn–S system in the temperature range from 1100 °C to 1400 °C with experimental data.

A thermodynamic database for the system Ca–Cu–Cr–Fe–Mg– Mn–S has been generated. The liquid phase covering metallic, sulfidic and sulfuric compositions as well as miscibility gaps between them has been described using the non-ideal associate solution approach. Solid solubilities between sulfides including Digenite, Pyrrotite, Oldhamite have been evaluated using sublattice models taking into account the available experimental information. The solubility of sulfur in the various solid metals has been taken into account were possible. The general agreement between the calculated phase equilibria as well as thermodynamic properties and the respective experimental data is good. A comparison of the calculated and experimental equilibria for the ternary subsystems will be given in separate publication.

Acknowledgment Financial support of this work by Scientific Group Thermodata Europe, Nr. 11-2014 is gratefully acknowledged.

References

Fig. 18. Calculated phase diagram of the pseudo-binary system FeS–MnS in equilibrium with Fe.

formation of sulfides during the solidification process [7]. Most investigations enclosed the complete Fe–FeS–Mn–MnS composition range where the FeS–MnS section in equilibrium with metallic iron explains a part of the whole system. The FeS–MnS phase diagram is eutectic with different mutual solubility in the sulfide solid solution phases Oldhamite (MnS) and Pyrrhotite (FeS). The solubility of FeS in MnS is much higher than that of MnS in FeS. The composition ranges of the coexisting solid solution phases were determined at 600 °C, 700 °C, 800 °C, 900 °C and 1000 °C by Skinner [25] using microprobe analysis and cell edge determinations. According to [25] the FeS composition in Oldhamite existing in equilibrium with Pyrrhotite contains 53.6 at% FeS at 600 °C, and increases linearly with increasing temperature, amounting to 73.8 at% at 1000 °C. For the Gibbs energy optimization of the phase Oldhamite the sulfur potential data depending on the amount of Mn in Oldhamite measured by Fischer and Schwerdtfeger [95] were also used. They have determined the equilibrium partial pressure ratios p(H2S)/ p(H2) of a gas phase coexisting with metallic iron and Oldhamite in the temperature range from 1100 °C to 1400 °C. Calculated p(H2S)/p(H2) ratios in equilibrium with iron containing sulfur and manganese at different temperatures are presented in Fig. 17 compared with data given by [95], the

[1] B.-J. Lee, B. Sundman, S.I. Kim, K.-G. Chin, Thermodynamic calculations of the stability of Cu2S in low carbon steels, ISIJ Int. 47 (1) (2007) 163–171. [2] Y.-B. Kang, Critical evaluations and thermodynamic optimizations of the Mn– S and the Fe-Mn-S systems, Calphad 34 (2) (2010) 232–244. [3] P. Waldner, A.D. Pelton, Thermodynamic modeling of the Fe–S System, J. Phase Equilib. Diffus. 26 (1) (2005) 23–38. [4] K. Oikawa, H. Mitsui, H. Ohtani, K. Ishida, Thermodynamic calculation of phase equilibria in the Fe–Cr–S System, ISIJ Int. 40 (2) (2000) 182–190. [5] P. Waldner, W. Sitte, Thermodynamic modeling of the Cr–S system, Int. J. Mater. Res. (Former. Z. Met. ) 102 (2011) 1216–1225. [6] L.-I. Staffansson, On the Mn–MnS phase diagram, Metall. Trans. B 7B (3) (1976) 131–134. [7] J. Miettinen, B. Hallstedt, Thermodynamic assessment of the Fe–FeS–MnS– Mn system, Calphad 22 (2) (1998) 257–273. [8] D. Dilner, H. Mao, M. Selleby, Thermodynamic assessment of the Mn–S and Fe–Mn–S systems, Calphad 48 (2015) 95–105. [9] A.D. Pelton, S.A. Decterov, G. Eriksson, C. Robelin, Y. Dessureault, The modified quasichemical model I – binary solutions, Metall. Mater. Trans. B 31B (4) (2000) 651–659. [10] M. Hillert, L.-I. Staffanson, A thermodynamic analysis of the phase equlibria in the Fe–Mn–S system, Metall. Trans. B 7 (2) (1976) 203–211. [11] T.M. Besmann, K.E. Spear, Thermodynamic modelling of oxide glasses, J. Am. Ceram. Soc. 85 (12) (2002) 2887–2894. [12] E. Yazhenskikh, K. Hack, M. Müller, Critical thermodynamic evaluation of oxide systems relevant to fuel ashes and slags, Part 5: potassium oxidealumina-silica, Calphad 35 (2011) 6–19. [13] E. Yazhenskikh, T. Jantzen, K. Hack, M. Müller, Critical thermodynamic evaluation of oxide system relevant to fuel ashes and slags: potassium oxidemagnesium oxide-silica, Calphad 47 (2014) 35–49. [14] R.C. Sharma, Y.A. Chang, Thermodynamics and phase relationships of transition metal-sulfur systems: Part III. Thermodynamic properties of the Fe–S liquid phase and the calculation of the Fe–S phase diagram, Metall. Trans. B 10 (1) (1979) 103–108. [15] Y.Y. Chuang, K.C. Hsieh, Y.A. Chang, Thermodynamics and phase relationships of transition metal-sulfur systems: Part V. A reevaluation of the Fe–S system using an associated solution model for the liquid phase, Metall. Trans. B 16 (2) (1985) 277–285. [16] FactSage, Ecole Polytechnique, Montréal, 〈www.factsage.com〉. [17] C.W. Bale, E. Bélisle, P. Chartrand, S.A. Decterov, G. Eriksson, K. Hack, I.H. Jung, Y.-B. Kang, J. Melançon, A.D. Pelton, C. Robelin, S. Petersen, FactSage thermochemical software and databases – recent developments, Calphad 33 (2) (2009) 295–311.

Please cite this article as: T. Jantzen, et al., Evaluation of thermodynamic data and phase equilibria in the system Ca–Cr–Cu–Fe–Mg–Mn– S part I: Binary and quasi-binary subsystems, Calphad (2016), http://dx.doi.org/10.1016/j.calphad.2016.04.011i

T. Jantzen et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry ∎ (∎∎∎∎) ∎∎∎–∎∎∎ [18] SGTE, Pure Substance Database, SGTE, Grenoble, 2011. [19] W.B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, Pergamon Press, Oxford, 1967. [20] T.B. Massalski (Ed.), Binary Alloy Phase Diagrams, Second ed.,ASM International, Metals Park, OH, 1990. [21] C.W. Bale, J.M. Toguri, Thermodynamics of the Cu–S, Fe–S and Cu–Fe–S systems, Can. Metall. Q 15 (4) (1976) 305–318. [22] M. Hillert, L.I. Staffanson, Regular solution model for stoichiometric phases and ionic melts, Acta Chem. Scand. 24 (10) (1970) 3618–3626. [23] B. Sundman, J. Ågren, Regular solution model for phases with several components and sublattices, suitable for computer applications, J. Phys. Chem. Solids 42 (4) (1981) 297–301. [24] B. Sundman, unpublished work, 1992. [25] B.J. Skinner, F.D. Luce, Solid solutions of the type (Ca, Mg, Mn, Fe)S and their use as geothermometers for the enstatite chondrites, Amer. Mineral. 56 (7–8) (1971) 1267–1294. [26] D.J. Chakrabarti, D.E. Laughlin, The Cu–S (copper–sulfur) system, Bull. Alloy. Phase Diagr. 4 (3) (1983) 254–271. [27] M. Venkatraman, J.P. Neumann, Binary Alloy Phase Diagrams, 2nd ed., in: T.B. Massalski (Ed.), ASM International Metals Park, OH, 1990, p. 1322. [28] R. Vogel, R. Reinbach, The system iron-chromium-chreomium sulphide-iron sulphide, Arch. Eisenhü ttenwes. 11 (9) (1938) 457–462. [29] F. Jellinek, The structures of the chromium sulphides, Acta Crystallogr. 10 (1957) 620–628. [30] A. El Goresy, G. Kullerud, Phase relations in the system chromium-ironsulfur, in: P.M.D. Millman (Ed.), Proceedings of the Symposium on Meterorite Research, Reidel Publ. Co., Dordrecht, The Netherlands, 1969, pp. 638–656. [31] T.J.A. Popma, C.F. van Bruggen, Structural and magnetic phase transitions of chromium sulfides Cr1  xS with 0r x r0.12, J. Inorg. Nucl. Chem. 31 (1) (1969) 73–80. [32] H. Rau, The chromimum-sulphur system between 873 K and 1364 K, J. LessCommon Met. 55 (2) (1977) 205–211. [33] N.R. Griffing, G.W. Healy, Effect of chromium on the activity of sulfur in liquid iron, Trans. Metall. Soc. AIME 218 (1960) 849–854. [34] Y.A. Chang, J.P. Neumann, U.V. Choudary, Phase Diagrams and Thermodynamic Properties of Ternary Copper-sulfur-metal Systems, INCRA Monograph VII, International Copper Research Association, New York 1979, pp. 53–57. [35] D.J. Young, W.W. Smeltzer, J.S. Kirkaldy, Nonstoichiometry and thermodynamics of chromium sulfides, J. Electrochem. Soc. 120 (9) (1973) 1221–1224. [36] A.D. Pelton, M. Blander, Thermodynamic analyses of ordered liquid solutions by a modified quasichemical approach-application to silicate slags, Metall. Trans. B 17 (4) (1986) 805–815. [37] K.C. Mills, Thermodynamic Data for Inorganic Sulphides, Selenides and Tellurides, Nat. Phys. Lab., Teddington, UK 1974, pp. 292–301 (845 p.). [38] K.T. Jacob, D. Bhodeswara Rao, H.G. Nelson, Phase relations in the Fe–Ni–Cr–S system and the sulfidation of an austenitic stainless steel, Technical Memorandum, NASA TM-78465, 1977, N78-17147. [39] L.B. Pankratz, A.D. Mah, S.W. Watson, Thermodynamic Properties of Sulfides, BUMINES-B-689, 1987, p. 87. [40] T.A. Stolyarova, Thermochemistry of chromium sulfides, Geokhimiya 11 (2003) 1240–1242 (in Russian), Geochem. Int. 41 (11) (2003) 1134. [41] S.A. Degterov, A.D. Pelton, Thermodynamic modeling of lead distribution among matte, slag, and liquid copper, Metall. Mater. Trans. B 30B (6) (1999) 1033–1044. [42] S.A. Decterov, Y. Dessureault, A.D. Pelton, Thermodynamic modeling of zinc distribution among matte, slag and liquid copper, Can. Metall. Q. 39 (1) (2000) 43–54. [43] R. Schuhmann, O.W. Moles, Sulfur activities in liquid Cu-sulfide, Trans. AIME 3 (1951) 235–241 (Trans.191). [44] G. Sick, K. Schwerdtfeger, A contribution to the thermodynamics of hightemperature digenite Cu2-yS, Metall. Trans. B 15 (4) (1984) 736–739. [45] H.N. Lander, W.A. Krivsky, Thermodynamic Equilibrium Studies in the System Copper-Iron-Sulfur, M.I.T., United States 1951, p. 122. [46] W.A. Krivsky, Thermodynamics of the Copper-iron-sulfur System at Matte Smelting Temperatures (Ph.D. Thesis), M.I.T., MA, U.S.A, 1954. [47] D. Smith, Ph.D. Thesis, M.I.T., MA, U.S.A., 1952. [48] F. Johannssen, H. Vollmer, The system copper-copper sulfide, Z. Erzbergbau Metallhuettenwes. 13 (1960) 313–322. [49] R.S. Sharma, Y.A. Chang, A thermodynamic analysis of Cu–S system, Metall. Trans. B 11B (4) (1980) 575–583. [50] H. Rau, Homogeneity range of cubic high temperature cuprous sulfide (digenite), J. Phys. Chem. Solids 35 (10) (1974) 1415–1424. [51] W.R. Cook, Jr., Phase Changes in Cu2S as a Function of Temperature, Natl. Bur. Stds. (U.S.A.) Spec. Publ. 364, 703–712 (1972); Ph.D. thesis, Case Western Reserve University, Cleveland, OH; Gould Labs Univ. Microfilm Order No. 7227 (1971). [52] R.W. Potter II, H.T. Evans Jr., Definitive X-ray powder data for covellite, anilite, djurleite and chalcocite, J. Res. US Geol. Survey, 4, (1976) 205–212. [53] O. Kubaschewski, Phase Diagrams of Binary Iron Alloys, in: H. Okamoto (Ed.), ASM International, 1993, pp. 364–366. [54] M. Hillert, L.-I. Staffanson, Analysis of the phase equilibria in the Fe-FeS system, Metal. Trans. B 6B (1) (1975) 37–41. [55] K. Oikawa, H. Mitsui, H. Ohtani, K. Ishida, Thermodynamic calculations of phase equilibria in the Fe–Cr–S system, ISIJ Int. 40 (2) (2000) 182–190. [56] A. Fernandez Guillermet, M. Hillert, B. Jansson, B. Sundman, An assessment of the Fe-S system using a twi-sublattice model for the liquid phase, Metall. Trans. B 12B (4) (1981) 745–754. [57] R. Loebe, E. Becker, The system iron-iron sulfide, Z. Anorg. Chem. 77 (1912)

15

301–319. [58] H. Nakazawa, N. Morimoto, Phase relations and superstructures of pyrrhotite, Fe1  xS, Mater. Res. Bull. 6 (1971) 345–358. [59] K. Friedrich, Note on the melting diagram of the system FeS–Fe, Metallurgie 7 (1910) 301–319. [60] K. Miyazaki, The equilibrium diagram of the iron and iron sulphide system, Sci. Rep. Tohoku Imp. Univ. Ser. I 17 (1928) 877–882. [61] F. GrØnvold, H. Haraldsen, On the phase relations of synthetic and natural pyrrhotites (Fe1-xS), Acta Chem. Scand. 6 (1952) 1452–1469. [62] G.H. Moh, G. Kullerud, Phase Relations at Low Temperatures: The Fe-S System, Carnegie Inst, Washington Yearbk 1964, pp. 207–208. [63] E. Jensen, Pyrrhotite: melting relations and composition, Am. J. Sci. 240 (1942) 695–699. [64] W. Burgmann, G. Urbain, M.G. Frohberg, Contribution to the study of the system Fe-S in the region of iron sulfide (pyrrhotite), Mem. Sci. Rev. Met. 65 (1968) 567–578. [65] R.G. Arnold, Pyrrhotite-Pyrite Equilibrium Relations between 325 and 745 °C (Ph.D Dissertation), Princeton University, United States, 1958. [66] M. Nagamori, Technical note: compositions and free energies of ag2s and fes saturated with metal, Can. Metall. Q. 9 (1970) 531–533. [67] R. Vogel, W. Hotop, Das Zustandsschaubild Eisen-Eisensulfid-MangansulfidMangan, Arch. Eisenhü ttenwes. 11 (1) (1937) 41–54. [68] A.T. Dinsdale, SGTE data for pure elements, Calphad 15 (1991) 317–425. [69] V.Ya Dashevsky, V.I. Kashin, Solubility and activity of S in Mn and its alloys, Izv. Akad. Nauk. SSSR Metal. 5 (1973) 85–88 (in Rusiian). [70] C.T. Anderson, The heat capacities at low temperatures of manganese sulfide, ferrous sulfide and calcium sulfide, J. Am. Chem. Soc. 53 (1931) 476–483. [71] D.R. Huffman, R.L. Wild, Specific heat of MnS through the neel temperature, Phys. Rev. 148 (2) (1966) 526–527. [72] J.P. Coughlin, High-temperature heat contents of manganous sulfide, ferrous sulfide and pyrite, J. Am. Chem. Soc. 72 (1950) 5445–5447. [73] W. Lehmann, Alkaline earth sulfide phosphors activated by copper, silver, and gold, J. Electrochem. Soc. 117 (11) (1970) 1389–1393. [74] P.L. Robinson, W.E. Scott, The polysulphides of barium and calcium, J. Chem. Soc. (1931) 693–709. [75] D. Lindberg, P. Chartrand, Thermodynamic evaluation and optimization of the (Ca þC þ OþS) system, J. Chem. Thermodyn. 41 (10) (2009) 1111–1124. [76] A.A. Nayeb-Hashemi, J.B. Clark, in: Binary Alloy Phase Diagrams, 2nd ed., vol. 3, T.B. Massalski (editor-in-chief), Materials Information Society, Materials Park, Ohio, 1990. [77] W. Primak, H. Kaufman, R. Ward, X-Ray diffraction studies of systems involved in the preparation of alkaline earth sulfide and selenide phosphors, J. Am. Chem. Soc. 70 (6) (1948) 2043–2046. [78] C.-H. Leung, L.-H. van Vlack, Solubility limits in binary (Ca,Mn) chalcogenides, J. Am. Ceram. Soc. 62 (11–12) (1979) 613–616. [79] R. Kiessling, C. Westman, The MnS–CaS system and its metallurgical significance, J. Iron Steel Inst. Lond. 208 (7) (1970) 699–700. [80] R.A. Fogel, Diopside in Equilibrated Enstatite Chondrites: EET90102-The First Diopside Bearing EL6 Chondrite, Abstracts of the Lunar and Planetary Science Conference XXVI, 26, 1995, pp. 411–412. [81] Y. Lei, T. Yoshikawa, C.Q. Jia, K. Morita, Thermodynamic properties of the MnS–CuS0.5 binary system, ISIJ Int. 52 (7) (2012) 1206–1210. [82] O.V. Andreev, N.V. Sikerina, A.V. Solov'eva, Phase diagrams for the Cu2S-AIIS (AII ¼Mg, Ca, Sr, Ba), Russ. J. Inorg. Chem. (Zh. Neorg. Khim.) 50 (10) (2005) 1586–1590. [83] A.V. Solov’ewa, Phase Equilibria in the Systems AIIS – FeS, AIIS-FeS-Ln2S3, AIIS-Cu2S-Ln2S3 (AII¼Mg, Ca, Sr, Ba; Ln¼ La-Lu) (Ph.D. Thesis), Tjumen, Russia, 2012. [84] R. Vogel, T. Heumann, Das system eisen-eisensulfid-kalziumsulfid, Arch. Eisenhü ttenwes. 15 (4) (1941) 195–199. [85] T. Heumann, Die löslichkeit von eisensulfid in kalziumsulfid bei der euteklischen temperatur, Arch. Eisenhü ttenwes. 15 (12) (1942) 557–558. [86] Y.-B. Kang, Critical evaluations and thermodynamic optimizations oft the Mn–S and the Fe–Mn–S systems, Calphad 34 (2) (2010) 232–244. [87] H. Ohtani, K. Oikawa, K. Ishida, Optimization of the Fe-rich Fe–Mn–S ternary phase diagram, High. Temp. Mater. Process. 19 (3–4) (2000) 197–210. [88] S.P. Farrell, M.E. Fleet, I.E. Stekhin, A. Kravtsova, A.V. Soldatov, X. Liu, Evolution of local electronic structure in alabandite and niningerite solid solutions [Mn,Fe)S, (Mg,Mn)S, (Mg,Fe)S] using sulfur K- and L-edge XANES spectroscopy, Am. Mineral. 87 (10) (2002) 1321–1332. [89] I.E. Stekhin, A.V. Soldatov, S.P. Farrel, M.E. Fleet, Electronic structure investigation of Mg1-xFexS solid solution: X-ray absorption study, J. Synchrotron Radiat. 8 (2) (2001) 238–239. [90] A.N. Kravtsova, I.E. Stekhin, A.V. Soldatov, X. Liu, M.E. Fleet, Electronic structure of MS (M¼ Ca,Mg,Fe,Mn): X-ray absorption analysis, Phys. Rev. B: Condens. Matter Phys. 69 (13) (2004) 134109/1-134109/12. [91] V.V. Kurash, G.A. Kulikov, E.S. Makarov, Isomorphism of magnesium and iron in the niningerite (magnesium sulfide)-troilite (iron(II) sulfide) system, Geokhimiya 8 (1973) 1266–1267. [92] M.D. Osborne, M.E. Fleet, Moessbauer investigation of niningerite solid solutions magnesium iron sulfide ((Mg,Fe)S, Phys. Chem. Miner. 10 (6) (1984) 245–249. [93] C.A. McCammon, I. Jackson, A.E. Ringwood, J.D. Cashion, The binary systems iron sulfide (FeS)-magnesium sulfide and iron sulfide (FeS)-manganese sulfide (MnS): Moessbauer spectroscopy of the B1 solid solutions and highpressure phase equilibria, Phys. Chem. Miner. 11 (4) (1984) 182–193. [94] O.V. Andreev, A.V. Solov’eva, T.M. Burkhanova, MgS–FeS phase diagram, Russ. J. Inorg. Chem. (Zh. Neorg. Khimii.) 51 (11) (2006) 1826–1828. [95] M. Fischer, K. Schwerdtfeger, Thermodynamics of the system iron-manganese-sulfur: Part 1. Activities in iron sulfide-manganese sulfide solid

Please cite this article as: T. Jantzen, et al., Evaluation of thermodynamic data and phase equilibria in the system Ca–Cr–Cu–Fe–Mg–Mn– S part I: Binary and quasi-binary subsystems, Calphad (2016), http://dx.doi.org/10.1016/j.calphad.2016.04.011i

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solutions in the temperature range 1100 to 1400 °C, Metall. Trans. B 8 (3) (1977) 467–470. [96] G. Roehl, About sulfide inclusions in iron and steel: a contribution to the theory of desulphurization of irons, Stahl Eisen 33 (14) (1913) 565–567. [97] Z. Shibata, The equilibrium diagram of the iron sulfide-manganese sulfide system, Tech. Rep. Tohoku Imp. Univ. 7 (1928) 279–287. [98] H.C. Chao, L.H. van Vlack, F. Oberin, L. Thomassen, Hardness of inclusion sulfides, ASM Trans. Q 57 (4) (1964) 885–891.

[99] G.S. Mann, L.H. Van Vlack, Iron(II) sulfide-manganese(II) sulfide phase relations in the presence of excess iron, Metall. Trans. B 7B (3) (1976) 469–475. [100] M. Fischer, K. Schwerdtfeger, Thermodynamics of the system iron-manganese-sulfur. Part III: Equilibria involving solid and liquid phases in the temperature range 1100 to 1300 °C, Metall. Trans. B 9B (4) (1978) 635–641. [101] Y. Ito, N. Yonezawa, K. Matsubara, The composition of eutectic conjugation in iron-manganese-sulfur system, Trans. Iron Steel Inst. Jpn. 20 (1) (1980) 19–25 (Translated from Tetsu to Hagane, 65(3) (1979) 391–398).

Please cite this article as: T. Jantzen, et al., Evaluation of thermodynamic data and phase equilibria in the system Ca–Cr–Cu–Fe–Mg–Mn– S part I: Binary and quasi-binary subsystems, Calphad (2016), http://dx.doi.org/10.1016/j.calphad.2016.04.011i