Thermodynamic evaluation and optimization of the (NaCl + KCl + MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2) system

J. Chem. Thermodynamics 36 (2004) 809–828 www.elsevier.com/locate/jct

Thermodynamic evaluation and optimization of the (NaCl + KCl + MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2) system Christian Robelin *, Patrice Chartrand, Arthur D. Pelton Centre for Research in Computational Thermochemistry (CRCT), Ecole Polytechnique, C.P. 6079, Succursale ‘‘Downtown’’, Montreal, Que., Canada H3C 3A7 Received 20 October 2003; received in revised form 30 April 2004; accepted 4 May 2004 Available online 7 July 2004

Abstract A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (NaCl + KCl + MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) system, and optimized model parameters have been found. The (MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model was used for the molten salt phase, and the (MgCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) solid solution was modeled using a cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions. Finally, the (Na,K)(Mg,Ca,Mn,Fe,Co,Ni)Cl3 and the (Na,K)2 (Mg,Mn,Fe,Co,Ni)Cl4 solid solutions were modeled using the Compound Energy Formalism.
2004 Elsevier Ltd. All rights reserved. Keywords: Molten chlorides; Transition metal chlorides; Hot corrosion; Thermodynamic modeling; Thermodynamic database

1. Introduction In this article, all available thermodynamic and phase equilibrium data for binary, ternary and quaternary subsystems of the (NaCl + KCl + MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) system are critically evaluated to obtain optimized parameters of models of all condensed solution phases. These parameters form a computer database and the models are then used to predict the thermodynamic properties of the multicomponent system. The optimization of the (MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) subsystem has been presented in a previous article [1]. The liquid solution is modeled using the Modified Quasichemical Model [2,3] which takes into account short-range ordering between nearest-neighbors on a *

Corresponding author. Tel.: +1-514-340-4711x4304; fax: +1-514340-5840. E-mail address: [email protected] (C. Robelin). 0021-9614/$ - see front matter
2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2004.05.005

lattice or sublattice. This model has been used successfully to model the (LiCl + NaCl + KCl + RbCl + CsCl + MgCl2 + CaCl2 + SrCl2 + BaCl2 ) system [4–6]. Short-range ordering is treated by considering the relative numbers of second-nearest-neighbor cation–cation pairs. The parameters of the model are the Gibbs free energy changes DgAB=Cl for the following pair exchange reactions: ðA–Cl–AÞpair þ ðB–Cl–BÞpair ¼ 2ðA–Cl–BÞpair

DgAB=Cl ; ð1Þ

where A and B are two different cations. As DgAB=Cl becomes progressively more negative, reaction (1) is shifted to the right, (A–Cl–B) pairs predominate, and the solution becomes progressively more ordered. In [2,3], the model was developed in terms of nearestneighbor pairs (A–B) for species mixing on one lattice. In the present case, since the anionic sublattice is occupied only by Cl
ions, the model can be used directly to

810

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

treat cation–cation pairs on the cationic sublattice. The parameter DgAB=Cl is the parameter DgAB (or Dgmn ) of [2] (or [3]). When DgAB=Cl is small, the degree of short-range ordering is small, and the solution approximates a random (Bragg-Williams) mixture of cations on the cationic sublattice. This is the case for most of the binary subsystems of the (MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) system [1]. On the other hand, molten (alkali chloride + MCl2 ) solutions (M ¼ Mg, Ca, Mn, Fe, Co, Ni) are well known for exhibiting extensive short-range ordering. This ordering gives rise to ‘‘Vshaped’’ enthalpy of mixing and ‘‘m-shaped’’ entropy of mixing curves, as illustrated for the (KCl + MCl2 ) (figures 1 and 2) and (NaCl + MCl2 ) (figures 3 and 4) binary liquids.

The existence of short-range ordering in molten (alkali chloride + MCl2 ) solutions has previously been modeled by introducing MCl2
4 complex anions [10–12]. For example, a fully-ordered liquid solution of the composition K2 CoCl4 would be treated as consisting of Kþ and CoCl2
4 ions. The present model does not explicitly introduce complex anions. Instead, the ordering is described as a preponderance of (K–Cl–Co) secondnearest-neighbors, with the ratio of the second-nearestneighbor coordination numbers of Co2þ and Kþ equal to 2.0. Hence, in a fully-ordered solution of the composition K2 CoCl4 , every Co2þ ion is surrounded only by Kþ ions in its second coordination shell, just as in the complex ion model. Depending on how negative DgKCo=Cl is, some (K–Cl–K) and (Co–Cl–Co) pairs can

0

0

DeltaHm / (kJ·mol-1)

DeltaHm / (kJ·mol-1)

-5

-10

CaCl2

MnCl2 -5

FeCl2 MgCl2

CoCl2

-15

NiCl2

-10

-20 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0

0.1

0.2

0.3

0.4

x (MCl2)

FIGURE 1. Calculated enthalpy of mixing of the (KCl + MCl2 ) binary liquids (M ¼ Mg, Ca, Mn, Fe, Co, Ni) versus the mole fraction of MCl2 . Østvold [7]: d, CaCl2 (810 C). Kleppa and McCarty [8]: s, MgCl2 (800 C). Papatheodorou and Kleppa [9]: N, MnCl2 (810 C); O, FeCl2 (810 C);
, CoCl2 (810 C). Dotted curve: NiCl2 (810 C).

0.7

0.8

0.9

1.0

7 o

MgCl2 (800 C) Ni C -1

DeltaS m / (J·mol ·K )

FeCl2 (810 C) 5 NiC

) 10 C l2 ( 8 o

CaC

o

3 M nC

l2

C) (810

2

l M nC 2

5

ide al

CaCl2

-1

-1

o

4

Cl Fe

l2

6

ideal

o

Cl 2 Co

6 -1

0.6

FIGURE 3. Calculated enthalpy of mixing of the (NaCl + MCl2 ) binary liquids (M ¼ Mg, Ca, Mn, Fe, Co, Ni) versus the mole fraction of MCl2 at 810 C. Østvold [7]: d, CaCl2 . Kleppa and McCarty [8]: s, MgCl2 . Papatheodorou and Kleppa [9]: M, MnCl2 ; O, FeCl2 ;
, CoCl2 . Dotted curve: NiCl2 .

7

DeltaSm / (J·mol ·K )

0.5

x (MCl2)

0 C) l 2 (81

2

4 MgCl2

3 2

o

CoCl2 (810 C) 1

1

0

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (MCl2)

FIGURE 2. Calculated entropy of mixing of the (KCl + MCl2 ) binary liquids (M ¼ Mg, Ca, Mn, Fe, Co, Ni) versus the mole fraction of MCl2 .

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (MCl2)

FIGURE 4. Calculated entropy of mixing of the (NaCl + MCl2 ) binary liquids (M ¼ Mg, Ca, Mn, Fe, Co, Ni) versus the mole fraction of MCl2 at 810 C.

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

be present in the liquid at the K2 CoCl4 composition. The complex ion models [10–12] cannot evaluate this without introducing new complex anions or without postulating two types of Co ions (Co2þ and CoCl2
4 ). Both the previous paper [1] and the present article confirm that the Modified Quasichemical Model permits a quantitative optimization of all binary and ternary subsystem data and can satisfactorily be used to predict the properties of multicomponent molten salt solutions solely from the subsystem model parameters even when appreciable short-range ordering is present.

2. Thermodynamic data for the pure compounds   All thermodynamic data (H298:15 K , S298:15 K and Cp ) for the condensed pure compounds of the (MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) and (NaCl + KCl + MgCl2 + CaCl2 ) subsystems have been given previously [1,5]. All thermodynamic data for other condensed pure compounds of the (NaCl + KCl + MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) system not already present in these subsystems were optimized in the present study and are given in table 1.

3. Thermodynamic model for the liquid phase The Modified Quasichemical Model [2,3] was used for the liquid phase. The notation of the previous articles [2,3] is maintained. For example, xNaMg is the mole fraction of second-nearest-neighbor (Na–Cl–Mg) pairs.

811

The model requires a choice of the second-nearestneighbor cation–cation ‘‘coordination numbers’’ Ziii , Zjjj , Ziji and Zijj for a given binary system i; j/Cl (where i and j are two different cations). Values of Ziji and Zijj are unique to the i; j/Cl binary system, while the value of Ziii (or Zjjj ) is common to all systems involving the i (or j) cation [2,3]. The composition of maximum short-range ordering in the i; j/Cl binary system is determined by the ratio ðZijj =Ziji Þ [2,3]. For the (NaCl + KCl) binary system [5] and for the binary subsystems of the (MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) system [1], all four coordination numbers were set to 6. For the (NaCl + CaCl2 ) binary system [5], the following choice was made: Na Ca Na Ca ZNaNa ¼ ZCaCa ¼ 6; ZNaCa ¼ 4; ZNaCa ¼ 6:

ð2Þ

For all other binary systems (ACl + MCl2 ) (where A ¼ Na, K and M ¼ Mg, Ca, Mn, Fe, Co and Ni), the following choice was made: A M ¼ ZMM ¼ 6; ZAA

A ZAM ¼ 3;

M ZAM ¼ 6:

ð3Þ

M A Note that the choice of ZAM ¼ 2  ZAM ensures that the composition of maximum short-range ordering will be near the A2 MCl4 composition as was discussed in section 1. As discussed previously [3], it is necessary to designate all ternary subsystems as either ‘‘symmetric’’ or ‘‘asymmetric’’. In the present case, all ternary systems in which all three components are divalent metal chlorides MCl2 are ‘‘symmetric’’ [1]. This symmetry makes the estimation of thermodynamic properties of the ternary liquid from binary optimized parameters very similar to

TABLE 1 Thermodynamic properties of solid compounds optimized in the present study T Range/K

 a H298:15 K

 b S298:15 K

Cp

(J  mol
1 )

(J  mol
1  K
1 )

(J  mol
1  K
1 ) 393.8505 188.7576 1,478.0513 345.6967 408.3493 2  Cp (NaCl) + Cp (FeCl2 ) ¼ 174.6840 + 0.0394396T ) 107,285T
2 ) 2,075.2T
1 188.5623 + 0.0002500T 308.9534 331.2285 142.7680 2  Cp (KCl) + Cp (FeCl2 ) ¼ 162.8349 + 0.0577404T + 622,405T
2 ) 2,075.2T
1 Cp (KCl) + Cp (FeCl2 ) ¼ 122.8191 + 0.0322724T + 257,560T
2 ) 2,075.2T
1 196.6078 136.0237 137.8713

Na6 MnCl8 Na2 MnCl4 Na9 Mn11 Cl31 Na2 Mn3 Cl8 NaMn4 Cl9 Na2 FeCl4

298.15 298.15 298.15 298.15 298.15 298.15

to to to to to to

750 750 750 700 750 700

)2,952,535.8 )1,306,516.5 )9,009,743.0 )2,271,740.1 )2,339,107.0 )1,112,916.3

557.7453 266.9466 1,960.8129 505.7829 540.4794 340.8129

Na2 CoCl4 K4 MnCl6 K3 Mn2 Cl7 KMnCl3 K2 FeCl4

298.15 298.15 298.15 298.15 298.15

to to to to to

700 750 750 800 700

)1,134,484.9 )2,253,833.1 )2,299,325.8 )934,210.9 )1,221,659.6

253.4194 447.6426 514.8463 207.7632 308.9850

KFeCl3

298.15 to 700

)787,517.1

213.8733

K2 CoCl4 KCoCl3 KNiCl3

298.15 to 750 298.15 to 650 298.15 to 1000

)1,192,313.2 )756,229.1 )749,774.1

309.4526 206.7445 188.1385

a b

Enthalpy relative to the enthalpy of the elements in their stable standard states at 298.15 K. Absolute (third law) entropy.

812

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

the Kohler interpolation method [13]. Systems with one alkali chloride and two divalent metal chlorides are asymmetric, with the alkali chloride as the asymmetric component. Finally, systems with two alkali chlorides and one divalent metal chloride MCl2 are asymmetric, with MCl2 as the asymmetric component. These asymmetries make the estimation of thermodynamic properties of the ternary liquid from binary optimized parameters very similar to the Kohler-Toop interpolation method [14]. The composition variables vij , defined previously [3], then become: vNaK ¼ xNaNa =ðxNaNa : þ xNaK þ xKK Þ;

ð4Þ

vKNa ¼ xKK =ðxNaNa þ xNaK þ xKK Þ;

ð5Þ

vMi Mj ¼ xMi Mi =ðxMi Mi : þ xMi Mj þ xMj Mj Þ

ðfor all i 6¼ jÞ; ð6Þ

vNaMi ¼ vKMi ¼ xNaNa þ xNaK þ xKK vMi Na ¼ vMi K ¼

6 X 6 X

x M m Mn

ðfor all iÞ;

ðfor all iÞ;

ð7Þ ð8Þ

m¼1 n P m

where M1 ; . . . ; M6 represent the six divalent metal cations considered in this work. Note that, for any binary system i; j/Cl, equations (4–8) reduce to: vij ¼ xii ; vji ¼ xjj :

ð9Þ

The parameters DgAB=Cl of reaction (1) for each pair are expanded, through optimization with available experimental data, as empirical polynomials in vij and vji . For ternary systems, terms may be added that give the effect of the third component upon the pair-formation energies DgAB=Cl . As described previously [3], this is done by ijk introducing the empirical ternary parameters gABðCÞ=Cl in the polynomial expansions.

4. Thermodynamic model for the solid solutions The (MgCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) extensive solid solution has been modeled previously using a cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions [1]. The (NaCl + CaCl2 ) solid solution (rich in NaCl) [5], the (CaCl2 + MgCl2 ) solid solution (rich in CaCl2 ) [5] and the (NaCl + KCl) solid solution [15] have been modeled previously in the same way. The (Na,K)(Mg,Ca,Mn, Fe,Co,Ni)Cl3 and the (Na,K)2 (Mg,Mn,Fe,Co,Ni)Cl4 solid solutions were modeled using the Compound Energy Formalism as discussed in section 9. No additional solid solutions were considered in the present study. The general case of solid solutions in the complete multicomponent system will be discussed in section 9.

5. Binary mixtures of divalent metal chlorides with NaCl The (NaCl + MgCl2 ) and (NaCl + CaCl2 ) systems have been critically evaluated and optimized previously [5]. These evaluations and all optimized model parameters are used directly in the present work. The (NaCl + MgCl2 ) phase diagram contains two incongruently melting compounds (Na2 MgCl4 and NaMgCl3 ) and no solid solutions. The (NaCl + CaCl2 ) system is a simple eutectic system with solubility of CaCl2 in solid NaCl up to a maximum of approximately 20 mol%. 5.1. The (NaCl + MnCl2 ) system The phase diagram has been measured by thermal analysis [16–18] and by differential thermal analysis (DTA) [19,20]. No solid solubility was reported and the measured limiting slopes of the NaCl and MnCl2 liquidus curves at xNaCl ¼ 1 and xMnCl2 ¼ 1 respect the limiting liquidus slope equation (10), which assumes no solid solubility:
 2 RTfusionðmÞ dT ½at xm ¼ 1; ð10Þ ¼ DhfusionðmÞ dxliquidus m where DhfusionðmÞ and TfusionðmÞ are, respectively, the enthalpy and temperature of fusion of the pure salt m. The various authors do not agree on the existing intermediate compounds. The existence of Na4 MnCl6 and NaMn2 Cl5 was reported [16,17], and supported by Xray diffraction measurements [17]. Yakovleva et al. [18] reported the existence of Na2 MnCl4 , NaMnCl3 and NaMn2 Cl5 . Seifert et al. [19–21] thoroughly studied the (NaCl + MnCl2 ) system and successively reported the existence of the following intermediate compounds: • Na4 MnCl6 , Na2 MnCl4 , NaMnCl3 and NaMn2 Cl5 [19]; • Na6 MnCl8 , Na2 MnCl4 , NaMnCl3 , Na2 Mn3 Cl8 and NaMn4 Cl9 [20]; • Na6 MnCl8 , Na2 MnCl4 , Na0:82 MnCl2:82 , Na2 Mn3 Cl8 and NaMn4 Cl9 [21]. The compounds Na6 MnCl8 , Na2 MnCl4 and Na2 Mn3 Cl8 are stable at ambient temperature and their structures are known from single crystal studies [22,23]. The enthalpies of formation from solid NaCl and MnCl2 of these three compounds at T ¼ 298:15 K have been measured by solution calorimetry [20] as ()3.82 (0.35), )2.28 (0.26) and )3.51 (0.60)) kJ  mol
1 , respectively. The values calculated from the present optimization (table 1) are ()3.82, )2.28 and )3.51) kJ  mol
1 , respectively. A phase Na0:82 MnCl2:82 with the ilmenite structure is stable above 358 C according to X-ray diffraction [21]. In [24], the composition is reported to be NaMnCl3 with a hexagonal unit cell. When cooled under DTA conditions, this phase is metastable and no decomposition occurs [21]. In the present work, the il-

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

menite phase is assumed to have the stoichiometry Na9 Mn11 Cl31 . By using solution calorimetry for quenched samples of the ilmenite phase, the enthalpy of formation of (metastable) Na9 Mn11 Cl31 from solid NaCl and MnCl2 at T ¼ 298:15 K could be determined [21]. The value obtained is )7.68 kJ  mol
1 and the value calculated from the present optimization (table 1) is )7.7 kJ  mol
1 . According to DTA-heating curves, the compound NaMn4 Cl9 is stable between 396 C and 451 C [21]. Using an emf technique, Seifert [21] measured the Gibbs free energy changes for the following reactions: • 4 NaCl + Na2 MnCl4 ¼ Na6 MnCl8 (between 317 C and 517 C), • 1.33 NaCl + 0.33 Na2 Mn3 Cl8 ¼ Na2 MnCl4 (between 287 C and 347 C),

• 1.67 NaCl + 3.67 Na2 Mn3 Cl8 ¼ Na9 Mn11 Cl31 (between 357 C and 382 C), • 2 NaCl + 3 MnCl2 ¼ Na2 Mn3 Cl8 (between 307 C and 387 C), • NaCl + 4 MnCl2 ¼ NaMn4 Cl9 (between 397 C and 447 C). The results are reproduced within the experimental error limits by the present optimization. The enthalpy of mixing of the (NaCl + MnCl2 ) liquid phase has been measured at 810 C by calorimetry [9] and the activity of NaCl in the liquid has been obtained at 612 C and 812 C by an emf technique [25]. The optimized Gibbs free energy of reaction (1) is: DgNaMn=Cl =ðJ  mol
1 Þ ¼
9894:0 þ 1257:1vNaMn
ð11Þ

4233:2vMnNa :

850

850 o

o

800 801 C

800

750

801 C

750

700 650 C

650

liquid

T / (oC)

550 o

468 C o

438 C o 411 C

0.1

0.2

0.3

0.4

0.5

0.6

450 o

o

NaMn4Cl9

364 C

Na2Mn3Cl8

Na2MnCl4

Na6MnCl8

0.0

o

Na9Mn11Cl31

o

426 C

250

500

o

400

300

550

o

464 C

442 C

350

liquid 600

0.7

0.8

384 C

400

400 C

Na2FeCl4

450

677 C

650

600

500

o

700

o

T / (oC)

813

350 300 0.9

1.0

0.0

0.1

0.2

0.3

x (MnCl2)

o

378 C (0.438)

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (FeCl2)

FIGURE 5. Calculated (NaCl + MnCl2 ) phase diagram, temperature versus mole fraction of MnCl2 . s, Sandonnini and Scarpa [16]; O, Safonov et al. [17]; +, Yakovleva et al. [18]; M, Seifert and Koknat [19];
, Seifert and Flohr [20].

FIGURE 7. Calculated (NaCl + FeCl2 ) phase diagram, temperature versus mole fraction of FeCl2 . s, Ionov et al. [26];
, Galitskii et al. [27].

1.0

0.0

0.9

-0.5

C

0.6 0.5 2C 61

a (NaCl)

o

2 81

0.7

ln [gamma (FeCl2)]

0.8

o

0.4 0.3

-1.0 -1.5 -2.0 o

920 C

-2.5

o

820 C

-3.0

0.2 -3.5

0.1

-4.0

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (MnCl2)

FIGURE 6. Calculated activity of NaCl (relative to liquid standard state) in the (NaCl + MnCl2 ) liquid versus the mole fraction of MnCl2 at 612 C and 812 C. Experimental data from Østvold [25]:
, 612 C; d, 812 C.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

x (FeCl2)

FIGURE 8. Calculated activity coefficient of FeCl2 (relative to liquid standard state) in the (NaCl + FeCl2 ) liquid versus the mole fraction of FeCl2 at 820 C and 920 C. Experimental data from Kuhnl and Besenbruch [29]: s, 820 C; d, 920 C.

814

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

The calculated enthalpy and entropy of mixing of the liquid at 810 C, as well as the calculated phase diagram and activity of NaCl in the liquid at 612 C and 812 C are shown along with the measurements in figures 3–6.

of CoCl2 in the liquid (at xCoCl2 < 0:01) has been measured at 869 C by an emf technique [33]. The optimized Gibbs free energy of reaction (1) is: DgNaCo=Cl =ðJ  mol
1 Þ ¼
12600:8 þ 2998:3vNaCo
1962:2v2NaCo þ ½6525:7


5.2. The (NaCl + FeCl2 ) system

10:8942ðT =KÞv2CoNa :

850 800

o

801 C

750

o

724 C

700 liquid

650 600 550 500

Na2CoCl4

450 400 350 300

DgNaFe=Cl =ðJ  mol
1 Þ ¼
10641:4 þ 1:1037ðT =KÞþ 1017:8vNaFe þ ½
498:1
7:5767ðT =KÞvFeNa :

ð13Þ

The calculated enthalpy and entropy of mixing of the liquid at 810 C, as well as the calculated phase diagram, activity of NaCl in the liquid between 610 C and 816 C, and Henrian activity coefficient of CoCl2 in the liquid at 869 C are shown along with the measurements in figures 3,4,9,10 and 11.

T / (oC)

The phase diagram has been measured by thermal analysis [26,27]. No solid solubility was reported and the measured limiting slopes of the NaCl and FeCl2 liquidus curves agree with equation (10). The intermediate compounds Na6 FeCl8 , Na2 FeCl4 and Na2 Fe3 Cl8 have been observed in high temperature Na/FeCl2 cells at 250 C, 350 C and 350 C, respectively [28]. According to Galitskii et al. [27], Na2 FeCl4 is unstable below 374 C and melts incongruently at 400 C. No intermediate compound was reported by Ionov et al. [26]. The existence of Na6 FeCl8 [28], Na2 FeCl4 [28] and Na2 Fe3 Cl8 [23] has been confirmed by X-ray diffraction measurements. The compounds Na6 FeCl8 and Na2 Fe3 Cl8 are not considered in the present calculations owing to the unavailability of relevant thermodynamic data. The calculated temperature range of stability of Na2 FeCl4 is 378.5 C to 400 C. The enthalpy of mixing of the liquid has been measured at 810 C by calorimetry [9] and the activity of FeCl2 in the liquid (at xFeCl2 < 0:05) has been obtained at 820 C and 920 C by an emf technique [29]. The optimized Gibbs free energy of reaction (1) is:

0.0

0.1

0.2

(0.374)

o

366 C o

349 C

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (CoCl2)

ð12Þ

The calculated enthalpy and entropy of mixing of the liquid at 810 C, as well as the calculated phase diagram and activity coefficient of FeCl2 in the liquid at 820 C and 920 C are shown along with the measurements in figures 3, 4, 7 and 8.

FIGURE 9. Calculated (NaCl + CoCl2 ) phase diagram, temperature versus mole fraction of CoCl2 . s, Bol’shakov et al. [30]; d, Seifert and Thiel [31] (smoothed data).

1.0 0.9

5.3. The (NaCl + CoCl2 ) system

a (NaCl)

C

0.7

o

5 72

0.6 0.5 0.4 0.3

C

0.2

o

0 61

The phase diagram has been measured by thermal analysis [30,31]. No solid solubility was reported and the measured limiting slopes of the NaCl and CoCl2 liquidus curves agree with equation (10). The existence of an intermediate compound Na2 CoCl4 was reported by both authors. According to Bol’shakov et al. [30], this compound decomposes at about 346 C and, according to Seifert and Thiel [31], its temperature range of stability is 338 C to 366 C. The calculated temperature range of stability of Na2 CoCl4 is 349 C to 365 C. The enthalpy of mixing of the liquid has been measured at 810 C by calorimetry [9] and the activity of NaCl in the liquid has been obtained between 610 C and 816 C by an emf technique [32]. Finally, the activity

0.8

816 o C

0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (CoCl2)

FIGURE 10. Calculated activity of NaCl (relative to liquid standard state) in the (NaCl + CoCl2 ) liquid versus the mole fraction of CoCl2 between 610 C and 816 C. Experimental data from Dutt and Østvold [32]:
, 610 C; M, 710 C; O, 725 C; s, 816 C.

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

5.4. The (NaCl + NiCl2 ) system

reference). The enthalpy of mixing of solid NiCl2 with liquid NaCl has been measured at 810 C by calorimetry [36] and the activity of NiCl2 in the liquid has been obtained at 800 C [37], 884 C [33] and 900 C [37] by an emf technique. Finally, Roumieu and Pelton [38] measured the emf of the cell Ni/(NaCl + NiCl2 ) (ref.)/bAl2 O3 /(NaCl + NiCl2 )(l)/Ni between 800 C and 1000 C (the composition of the reference melt was xNiCl2 ¼ 0:1589). The optimized Gibbs free energy of reaction (1) is: DgNaNi=Cl =ðJ  mol
1 Þ ¼
9566:1
1:9917ðT =KÞþ 687:4vNaNi
6842:6vNiNa :

0

35

-1

30

-2

25

-3

DeltaHm / (kJ·mol-1)

ln [gamma (CoCl2)]

The phase diagram has been measured by thermal analysis [30] and the visual-polythermal method [34]. No solid solubility was reported and the measured limiting slope of the NaCl liquidus curve agrees with equation (10). Pure liquid NiCl2 does not exist as a stable phase at 0.1 MPa total pressure. NiCl2 -rich samples could not be studied by Bol’shakov et al. [30] owing to the high vapor pressure. No intermediate compound has been observed. The reported temperatures of the eutectic liquid are 563 C [30], 570 C [34] and 583 C [35] (no experimental data are given by Gryzlova et al. [35] and the characteristics of the eutectic may come from another

o

NaCl-CoCl2 (869 C)

-4 o

-5

[NaCl-KCl(1:1)]-CoCl2 (759 C)

815

l iC -N l C Na

ð14Þ

2

20 K

C

iC l-N

l2

15 10

o

KCl-CoCl2 (861 C)

-6

5

-7 0.00

0.01

x (CoCl2)

0.02

0

0.03

0.0

0.1

0.2

0.3

0.4

0.5

x (NiCl2)

FIGURE 11. Calculated Henrian activity coefficient of CoCl2 (relative to liquid standard state) in the (NaCl + CoCl2 ) (869 C), (KCl + CoCl2 ) (861 C) and ([NaCl + KCl(1:1)] + CoCl2 ) (759 C) liquids versus the mole fraction of CoCl2 . Experimental data from Tumidajski and Flengas [33]: d, (NaCl + CoCl2 ) (869 C); s, (KCl + CoCl2 ) (861 C); j, ([NaCl + KCl(1:1)] + CoCl2 ) (759 C).

FIGURE 13. Calculated enthalpy of mixing for ACl(liquid) + NiCl2 (solid) ¼ (liquid solution) versus the mole fraction of NiCl2 at 810 C (A ¼ Na, K). Experimental data from Papatheodorou and Kleppa [36]: d, (NaCl + NiCl2 ); s, (KCl + NiCl2 ).

1 1100 o

1050

1031 C 0.1 MPa

950

T/ (oC)

900 850 800

liquid

o

0

ln [gamma (NiCl2)]

1000

801 C

750

-1

o

C 800 o

C 900

-2

700

-3

650 600 o

550

-4

574 C

(0.302)

0.0

500 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.1

0.2

0.3

0.4

x (NiCl2)

x (NiCl2)

FIGURE 12. Calculated (NaCl + NiCl2 ) phase diagram, temperature versus mole fraction of NiCl2 .
, Bol’shakov et al. [30]; d, Fedoseev [34].

FIGURE 14. Calculated activity coefficient of NiCl2 (relative to solid standard state) in the (NaCl + NiCl2 ) liquid versus the mole fraction of NiCl2 at 800 C and 900 C. Tumidajski and Flengas [33]:
, 884 C. Hamby and Scott [37]: d, 800 C; M, 900 C.

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

Emf / mV

0 -100 -200 o

800 C

-300

90 o 0C 10 00 o C

-400 -500 0.0

0.1

0.2

0.3

0.4

0.5

0.6

x (NiCl2)

FIGURE 15. Calculated emf of the cell Ni(s)/(NaCl + NiCl2 ) (x[NiCl2 ] ¼ 0.1589)/b-alumina/(NaCl + NiCl2 )(l)/Ni(s) versus the mole fraction of NiCl2 . Experimental data from Roumieu and Pelton [38]: s, 800 C;
, 900 C; M, 1000 C.

The calculated phase diagram, enthalpy of mixing of NiCl2 (s) with NaCl(l) at 810 C, activity coefficient of NiCl2 in the liquid at 800 C and 900 C, and emf of the cell Ni/(NaCl + NiCl2 ) (xNiCl2 ¼ 0:1589)/b-Al2 O3 / (NaCl + NiCl2 )(l)/Ni between 800 C and 1000 C are shown along with the measurements in figures 12–15. The calculated 0.1 MPa total pressure isobar is also shown in figure 12. The gas phase was assumed to be ideal. The major gaseous species under these conditions are NaCl, Na2 Cl2 and NiCl2 . The thermodynamic properties of NaCl(g) were taken from Barin et al. [39] and those of Na2 Cl2 (g) and NiCl2 (g) were taken from JANAF [40]. The calculated enthalpy and entropy of mixing curves for NaCl(l) and metastable NiCl2 (l) are shown in figures 3 and 4.

6. Binary mixtures of divalent metal chlorides with KCl

800

The (KCl + MgCl2 ) and (KCl + CaCl2 ) systems have been critically evaluated and optimized previously [5]. These evaluations and all optimized model parameters are used directly in the present work. The (KCl + MgCl2 ) and (KCl + CaCl2 ) phase diagrams contain two congruently melting compounds (KMgCl3 and KCaCl3 ), two incongruently melting compounds (K2 MgCl4 and K3 Mg2 Cl7 ) and no solid solutions.

700

o

771 C o

650 C liquid

T / (oC)

600 o

494 C

500

o

449 C

o

437 C

400

β α

o

418 C

300

6.1. The (KCl + MnCl2 ) system

457 C

o

o

386 C

KMnCl3

100

intermediate compounds are K4 MnCl6 [16,17,19], K2 MnCl4 [18], K3 Mn2 Cl7 [18,19], K4 Mn3 Cl10 [42] and KMnCl3 [16–19,41]. The existence of K4 MnCl6 and KMnCl3 was confirmed by X-ray diffraction [17]. The K2 MnCl4 and K4 Mn3 Cl10 compounds are each reported in only one article, and they are not considered in the present calculations. The existence of different allotropes for KMnCl3 is reported in the literature. According to Horowitz et al. [43], the stable room temperature form, with the NH4 CdCl3 structure, is formed very slowly. A transition to a second form of KMnCl3 occurs at a temperature which can vary between 150 C and 270 C [43], probably due to kinetic effects. This new form is tetragonal with the GdFeO3 structure [42]. A transition to a cubic form of KMnCl3 occurs at 386 (2) C [42]. Only the high temperature (cubic) form of KMnCl3 is considered in the present calculations owing to the unavailability of relevant thermodynamic data for the other forms. The enthalpy of formation of KMnCl3 from solid KCl and MnCl2 at T ¼ 298:15 K has been measured by solution calorimetry [42]. The value obtained (as well as the value calculated from the present optimization) is )15.53 kJ  mol
1 . The enthalpies of formation from solid KCl and MnCl2 of K4 MnCl6 and K3 Mn2 Cl7 at T ¼ 298:15 K have also been measured by solution calorimetry [20,42]. The reported values are ()26.07 (0.34) [20] and )25.1 [42]) kJmol
1 for K4 MnCl6 and )25.28 (0.44) kJ  mol
1 [20,42] for K3 Mn2 Cl7 . The values calculated from the present optimization are ()25.10 and )25.28) kJmol
1 , respectively. Using an emf technique, Seifert and Uebach [42] measured the Gibbs free energy changes for the following reactions:

K3Mn2Cl7

200

K4MnCl6

816

200 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (MnCl2)

The phase diagram has been measured by thermal analysis [16–18], by DTA [19] and by the visual-polythermal method [41]. No solid solubility was reported and the measured limiting slopes of the KCl and MnCl2 liquidus curves agree with equation (10). The reported

FIGURE 16. Calculated (KCl + MnCl2 ) phase diagram, temperature versus mole fraction of MnCl2 (the transition at 386 C is not calculated). s, Sandonnini and Scarpa [16]; M, Safonov et al. [17]; +, Yakovleva et al. [18];
, Seifert and Koknat [19]; O, Natsvlishvili and Bergman [41].

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

• 5 KCl + K3 Mn2 Cl7 ¼ 2 K4 MnCl6 (between 365 C and 417 C), • KCl + 2 KMnCl3 ¼ K3 Mn2 Cl7 (between 387 C and 427 C), • KCl + MnCl2 ¼ KMnCl3 (between 337 C and 442 C). The results are reproduced within the experimental error limits by the present optimization. The enthalpy of mixing of the (KCl + MnCl2 ) liquid phase has been measured at 810 C by calorimetry [9] and the activity of KCl in the liquid has been obtained between 690 C and 790 C by an emf technique [25]. The optimized Gibbs free energy of reaction (1) is: DgKMn=Cl =ðJ  mol
1 Þ ¼
18597:9 þ 1:4492ðT =KÞ
ð15Þ

10985:1vMnK :

The calculated enthalpy and entropy of mixing of the liquid at 810 C, as well as the calculated phase diagram and activity of KCl in the liquid between 690 C and 790 C are shown along with the measurements in figures 1,2,16 and 17. Note that K3 Mn2 Cl7 is calculated to decompose into K4 MnCl6 and KMnCl3 at about 216 C. It was not possible to adjust the thermodynamic properties of the three intermediate compounds so as to suppress the decomposition of K3 Mn2 Cl7 . Such a eutectoid decomposition cannot be ruled out. Even though X-ray diffraction was reported on samples at room temperature [19], K3 Mn2 Cl7 may be metastable when cooled under DTA conditions like the ilmenite phase of the (NaCl + MnCl2 ) system (section 5.1). 6.2. The (KCl + FeCl2 ) system

817

KCl and FeCl2 liquidus curves agree with equation (10). The reported intermediate compounds are K2 FeCl4 and KFeCl3 . Two allotropes exist for K2 FeCl4 : the reported transition temperatures are 268 (2) C [27] and 260 (5) C [44]. Two polymorphous transitions were observed at 240 C and 322 C by Ionov et al. [26], in disagreement with the other two studies. Two allotropes also exist for KFeCl3 : the reported transition temperatures are 305 C [26], 303 (2) C [27] and 293 (5) C [44]. Only the high temperature forms of K2 FeCl4 and KFeCl3 are considered in the present calculations owing to the unavailability of relevant thermodynamic data for the low temperature forms. The enthalpy of mixing of the liquid has been measured at 810 C by calorimetry [9] and the activity of FeCl2 in the liquid has been obtained between 700 C and 920 C by an emf technique [29,45,46]. The activity data of Josiak [46] were discarded because they are inconsistent with the other activity data. The optimized Gibbs free energy of reaction (1) is: DgKFe=Cl =ðJ  mol
1 Þ ¼
19986:3 þ 6426:1vKFe
5696:0v2KFe
8098:2vFeK
3642:3v2FeK :

ð16Þ

The calculated enthalpy and entropy of mixing of the liquid at 810 C, as well as the calculated phase diagram and activity coefficient of FeCl2 in the liquid between 727 C and 920 C are shown along with the measurements in figures 1, 2, 18 and 19. 6.3. The (KCl + CoCl2 ) system

The phase diagram has been measured by thermal analysis [26,27,44] and by DTA [44]. No solid solubility was reported and the measured limiting slopes of the

The phase diagram has been measured by DTA [47]. No solid solubility was reported and the measured limiting slopes of the KCl and CoCl2 liquidus curves

1.0

800

o

771 C

0.9 o

700

0.8

600

liquid

0.6

T / (oC)

0.5 0.4

o

400

398 C

o

393 C

o

374 C o

0C 71

351 C β α

o

0.3

500

300

o

266 C

β α

0.2

0.3

K2FeCl4

0.2 200

0.1

690 oC

0.0

o

303 C

KFeCl3

a (KCl)

o

0C 79

0.7

677 C

100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (MnCl2)

FIGURE 17. Calculated activity of KCl (relative to liquid standard state) in the (KCl + MnCl2 ) liquid versus the mole fraction of MnCl2 between 690 C and 790 C. Experimental data from Østvold [25]: M, 690 C;
, 710 C; d, 790 C.

0.0

0.1

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (FeCl2)

FIGURE 18. Calculated (KCl + FeCl2 ) phase diagram, temperature versus mole fraction of FeCl2 (the transitions at 266 C and 303 C are not calculated). s, Ionov et al. [26]; M, Galitskii et al. [27];
, Pinch and Hirshon [44].

818

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

the liquid at 861 C, phase diagram and activity of KCl in the liquid at 717 C and 790 C are shown along with the measurements in figures 1, 2, 11, 20 and 21.

0 -1

-3 -4

6.4. The (KCl + NiCl2 ) system

-5 o

0C 92 o 0C 82

-6 -7

o

o

C

7 72

-8

7 77

ln [gamma (FeCl2)]

-2

C

-9 -10 -11 -12 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (FeCl2)

FIGURE 19. Calculated activity coefficient of FeCl2 (relative to liquid standard state) in the (KCl + FeCl2 ) liquid versus the mole fraction of FeCl2 between 727 C and 920 C. Kuhnl and Besenbruch [29]:
, 820 C; j, 920 C. Ernst et al. [45]: +, 727 C; M, 777 C. Josiak [46]: s, 700 C.

The phase diagram has been measured by thermal analysis [31], by the visual-polythermal method [50] and by DTA [51]. No solid solubility was reported and the measured limiting slope of the KCl liquidus curve agrees with equation (10). NiCl2 -rich samples were not studied in [31,50], probably because of the high volatility of nickel chloride. Bazhenov et al. [51] only provide a smoothed phase diagram (no experimental points) and do not indicate the range of composition of the samples studied by DTA. The reported intermediate compounds

800

o

771 C

o

724 C

o

436 C

o

T / ( C)

500 o

400

419 C

o

362 C o

346 C

200

KCoCl3

K2CoCl4

300

o

b a

100 0.0

0.1

0.2

0.3

0.4

0.5

0.6

124 C

0.7

0.8

0.9

1.0

x (CoCl2)

FIGURE 20. Calculated (KCl + CoCl2 ) phase diagram, temperature versus mole fraction of CoCl2 (the transition at 124 C is not calculated). Experimental data (d) from Seifert [47].

1.0 0.9 0.8

a (KCl)

0.7 0.6 0.5 o

0.4

C

0.3 0.2

79 0

0.1

o

C

0.0

DgKCo=Cl =ðJ  mol
1 Þ ¼
24130:9 þ 3:1470ðT =KÞþ 1928:1vKCo þ ½
2223:4
9:9458ðT =KÞvCoK :

liquid 600

717

agree with equation (10). The reported intermediate compounds are K2 CoCl4 and KCoCl3 . Two allotropes exist for KCoCl3 : the transition at 343 (3) C reported in [47,48] was an artifact [49]. A transition is reported to occur at 125 C [48] or 123 C [49]. Only the high temperature form of KCoCl3 is considered in the present calculations owing to the unavailability of relevant thermodynamic data for the low temperature form. The enthalpies of formation from solid KCl and CoCl2 of K2 CoCl4 and KCoCl3 at T ¼ 298:15 K have been measured by solution calorimetry [49]. The values obtained (which are the same as the values calculated from the present optimization) are ()6.4 and )7.0) kJ  mol
1 , respectively. Using an emf technique, Seifert et al. [49] measured the Gibbs free energy changes for the following reactions: • KCl + KCoCl3 ¼ K2 CoCl4 (between 280 C and 345 C), • KCl + CoCl2 ¼ KCoCl3 (between 280 C and 345 C). The results are reproduced within the experimental error limits by the present optimization. The enthalpy of mixing of the liquid has been measured at 810 C by calorimetry [9] and the activity of KCl in the liquid has been obtained between 709 C and 790 C by an emf technique [32]. Finally, the activity of CoCl2 in the liquid (at xCoCl2 6 0:01) has been measured at 861 C by an emf technique [33]. The optimized Gibbs free energy of reaction (1) is:

700

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (CoCl2)

ð17Þ

The calculated enthalpy and entropy of mixing of the liquid at 810 C, Henrian activity coefficient of CoCl2 in

FIGURE 21. Calculated activity of KCl (relative to liquid standard state) in the (KCl + CoCl2 ) liquid versus the mole fraction of CoCl2 at 717 C and 790 C. Experimental data from Dutt and Østvold [32]: M, 709 C;
, 717 C; d, 790 C.

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828 0

-1

ln [gamma (NiCl2)]

are K2 NiCl4 [50] and KNiCl3 [31,50,51]. X-ray diffraction studies [31,51] and emf measurements with a galvanic cell [31] allowed the existence of K2 NiCl4 to be ruled out. Three allotropes are reported for KNiCl3 : the reported transition temperatures are 480 C [50,52] and 287 C [52]. These two transitions were observed using DTA and high-temperature X-ray powder diffraction, respectively. Only the high temperature form of KNiCl3 is considered in the present calculations owing to the unavailability of relevant thermodynamic data for the other forms. The enthalpy of formation from solid KCl and NiCl2 of KNiCl3 at T ¼ 298:15 K has been measured by solution calorimetry [53]. The value obtained is )8.16 (0.67) kJ  mol
1 and the value calculated from the present optimization is )8.16 kJ  mol
1 . Using an emf technique, Seifert et al. [49] measured the Gibbs free energy change for the following reaction: • KCl + NiCl2 ¼ KNiCl3 (between 377 C and 627 C). The results are reproduced within the experimental error limits by the present optimization. The enthalpy of mixing of solid NiCl2 with liquid KCl has been measured at 810 C by calorimetry [36] and the activity of NiCl2 in the liquid has been obtained at 800 C [37], 820 C [33] and 900 C [37] by an emf technique. The optimized Gibbs free energy of reaction (1) is:

819

-2

o

800

C o

C 900

-3

-4

o

820 C

-5 -6 0.0

0.1

0.2

0.3

0.4

x (NiCl2)

FIGURE 23. Calculated activity coefficient of NiCl2 (relative to solid standard state) in the (KCl + NiCl2 ) liquid versus the mole fraction of NiCl2 between 800 C and 900 C. Tumidajski and Flengas [33]:
, 820 C. Hamby and Scott [37]: d, 800 C; M, 900 C.

species under these conditions are KCl, K2 Cl2 and NiCl2 . The thermodynamic properties of KCl(g) were taken from Barin et al. [54] and those of K2 Cl2 (g) and NiCl2 (g) were taken from JANAF [40]. The calculated enthalpy and entropy of mixing curves for KCl(l) and metastable NiCl2 (l) are shown in figures 1 and 2.

DgKNi=Cl =ðJ  mol
1 Þ ¼
19246:8 þ ½1215:7
0:7364ðT =KÞvKNi
14578:6vNiK : ð18Þ The calculated enthalpy of mixing of NiCl2 (s) with KCl(l) at 810 C, as well as the calculated phase diagram and activity coefficient of NiCl2 in the liquid between 800 C and 900 C are shown along with the measurements in figures 13, 22 and 23. The calculated 0.1 MPa total pressure isobar is also shown in figure 22. The gas phase was assumed to be ideal. The major gaseous 1100

o

1031 C 1000 0.1 MPa 900

T / (oC)

800 771oC

liquid

700

The (NaCl + KCl) binary system as well as the (NaCl + KCl + MgCl2 ) and (NaCl + KCl + CaCl2 ) ternary systems have been critically evaluated and optimized previously [5]. These evaluations and all optimized model parameters are used directly in the present work. NaCl and KCl are completely miscible in the solid state at temperatures above 505 C. Below this consolute temperature, a solid miscibility gap is observed. MgCl2 is insoluble in the (NaCl + KCl) solid solution but CaCl2 is soluble in this solution at high NaCl contents. The compounds NaMgCl3 and KMgCl3 are mutually soluble as are Na2 MgCl4 and K2 MgCl4 . 7.1. The (NaCl + KCl + MnCl2 ) system

o

653 C

600

7. Ternary systems (NaCl + KCl + MCl2 ) with M ¼ Mg, Ca, Mn, Fe, Co and Ni

o

514 C

o

480 C

KNiCl3

500 400

o

287 C

300 200 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x (NiCl2)

FIGURE 22. Calculated (KCl + NiCl2 ) phase diagram, temperature versus mole fraction of NiCl2 (the transitions at 287 C and 480 C are not calculated). d, Seifert and Thiel [31];
, Belyaev et al. [50]; M, Bazhenov et al. [51] (smoothed data).

The calculated liquidus projection of the (NaCl + KCl + MnCl2 ) system is shown in figure 24. The (NaCl + KCl), the (Na,K)MnCl3 and the (Na,K)2 MnCl4 solid solutions were considered for the calculations (see section 9). The calculated compositions and temperatures of the ternary invariant points are listed in table 2. A small ternary excess parameter was included for the liquid phase: 001 gNaKðMnÞ=Cl =ðJ  mol
1 Þ ¼
2929:0:

ð19Þ

820

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828 900

MnCl 2 o (650 C)

800 625

700

T / (oC)

NaMn4Cl9

575 525 o

475 450

457 C

Na2Mn3Cl8 o Na9Mn11Cl31/464 C

425

o

KCl o

425

408

450

Na2MnCl4

475

300 D + E + F

C+D+F

liquid + B

A+E+F

C+E+F

B+C+F

0.0

5 67 77

60

40

0.1

0.2

0.3

0.4

B + F + NaCl-KCl(ss)

20

mol %

0.5

0.6

0.7

0.8

0.9

1.0

x (NaCl)

Na6MnCl8

5 72

675

(771 C)

liquid + B + NaCl-KCl(ss)

200

525 575 625

80

liquid + B + F

400

426 C o 442 Co 468 C

425

72 5

liquid + A + F liquid + F

o

450

K4MnCl6

liquid + A

500

438 C

K3Mn2Cl7

liquid + NaCl-KCl(ss)

600

o

o

KMnCl3 (494 C)

437 C o 418 C o 449 C

liquid

5

FIGURE 25. Calculated section of the (NaCl + KCl + MnCl2 ) phase diagram at constant molar ratio KCl/(KCl + MnCl2 ) of 0.35, temperature versus mole fraction of NaCl. Notations: A, MnCl2 ; B, Na6 MnCl8 ; C, Na2 MnCl4 ; D, Na9 Mn11 Cl31 ; E, Na2 Mn3 Cl8 ; F, KMnCl3 . Experimental data (d) from Safonov et al. [17].

NaCl o

(801 C)

FIGURE 24. Calculated liquidus projection of the (NaCl + KCl + MnCl2 ) system.

850

Six sections of the ternary system were measured by thermal analysis [17]. Five of these calculated sections are shown along with the experimental points in figures 25–29. In order to best reproduce the low temperature thermal arrests measured by Safonov et al. [17] for the (KMnCl3 + NaCl) section (figure 26) and the section at constant 50 mol% MnCl2 (figure 29), no solubility of Naþ in KMnCl3 and no solubility of Kþ in Na2 MnCl4 were assumed. The excess Gibbs free energies for the (NaMnCl3 + KMnCl3 ) and (Na2 MnCl4 + K2 MnCl4 ) binary subsystems of the (Na,K)(Mg,Ca,Mn,Fe,Co, Ni)Cl3 and (Na,K)2 (Mg,Mn,Fe,Co,Ni)Cl4 multicomponent solid solutions were then set to (see section 9): gE =ðJ  mol
1 Þ ¼ 100;000xNaMnCl3 xKMnCl3 ;

ð20Þ

gE =ðJ  mol
1 Þ ¼ 100;000xNa2 MnCl4 xK2 MnCl4 ;

ð21Þ

800 750

T / (oC)

700 650

liquid

600 550 liquid + NaCl-KCl(ss)

500

liquid + KMnCl3

450 liquid + KMnCl3 + NaCl-KCl(ss)

400 KMnCl3 + Na6MnCl8 + NaCl-KCl(ss)

350 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

FIGURE 26. Calculated (KMnCl3 + NaCl) section of the (NaCl + KCl + MnCl2 ) phase diagram, temperature versus mole fraction of NaCl. Experimental data (d) from Safonov et al. [17].

where the large arbitrary parameter of 100 kJ  mol
1 assures that the mutual solubility is negligible. Furthermore, it is assumed that there are no other solid

solutions (apart from the binary (NaCl + KCl) solution) in this system. In general, the calculated liquidus curves in figures 25–29 agree with the measurements. Where

TABLE 2 Calculated ternary invariant points of the liquidus projection of the (NaCl + KCl + MnCl2 ) system Invariant reaction

xNaCl a

xKCl a

xMnCl2 a

Temperature/C

Liquid + (KCl + NaCl)(ss) ¼ (NaCl + KCl)(ss) + K4 MnCl6 Liquid ¼ (NaCl + KCl)(ss) + K4 MnCl6 + K3 Mn2 Cl7 Liquid + KMnCl3 ¼ (NaCl + KCl)(ss) + K3 Mn2 Cl7 Liquid ¼ KMnCl3 + (NaCl + KCl)(ss):saddle point Liquid + (NaCl + KCl)(ss) ¼ KMnCl3 + Na6 MnCl8 Liquid + Na6 MnCl8 ¼ KMnCl3 + Na2 MnCl4 Liquid ¼ Na2 MnCl4 + KMnCl3 + Na9 Mn11 Cl31 Liquid + Na2 Mn3 Cl8 ¼ KMnCl3 + Na9 Mn11 Cl31 Liquid + NaMn4 Cl9 + Na9 Mn11 Cl31 ¼ Na2 Mn3 Cl8 Liquid + NaMn4 Cl9 ¼ KMnCl3 + Na2 Mn3 Cl8 Liquid + MnCl2 ¼ KMnCl3 + NaMn4 Cl9

0.139 0.135 0.166 0.266 0.333 0.360 0.345 0.320 0.371 0.283 0.275

0.578 0.566 0.509 0.369 0.274 0.219 0.188 0.193 0.117 0.203 0.207

0.283 0.299 0.325 0.365 0.393 0.421 0.467 0.487 0.512 0.514 0.518

395 381 388 408 400 389 382 385 411 390 392

a

Invariant liquid composition (mole fractions).

1.0

x (NaCl)

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

821

550

850 800 750

liquid

500

700 liquid + E liquid

600

T / (oC)

T / (oC)

650 liquid + NaCl-KCl(ss)

550

450

300

liquid + D + E

liquid + E + F C+D+F

liquid + G liquid + NaCl-KCl(ss) + G

400 350

liquid + D liquid + F

400

liquid + NaCl-KCl(ss) + F

500

450

liquid + G + H NaCl-KCl(ss) + G + H

0.0

0.1

0.2

0.3

350

NaCl-KCl(ss) + G NaCl-KCl(ss) + F + G NaCl-KCl(ss) + F

0.4

0.5

0.6

0.7

liquid + D + F

liquid + C + D C+E+F

300 0.8

0.9

1.0

0.0

0.1

0.2

0.3

0.4

0.5

x (NaCl)

x (NaCl)

FIGURE 27. Calculated section of the (NaCl + KCl + MnCl2 ) phase diagram at constant molar ratio KCl/(KCl + MnCl2 ) of 0.65, temperature versus mole fraction of NaCl. Notations: F, KMnCl3 ; G, K3 Mn2 Cl7 ; H, K4 MnCl6 . Experimental data (d) from Safonov et al. [17].

FIGURE 29. Calculated section of the (NaCl + KCl + MnCl2 ) phase diagram at constant 50 mol% MnCl2 , temperature versus mole fraction of NaCl. Notations: C, Na2 MnCl4 ; D, Na9 Mn11 Cl31 ; E, Na2 Mn3 Cl8 ; F, KMnCl3 . Experimental data (d) from Safonov et al. [17].

FeCl 2 o

700

(677 C)

650 650

600

liquid

600

T / (oC)

550

liquid + NaCl-KCl(ss)

550 liquid + NaCl-KCl(ss) + G

500 450

500

liquid + NaCl-KCl(ss) liquid + F

liquid + NaCl-KCl(ss) + H

400 G + NaCl-KCl(ss)

350 F + G + NaCl-KCl(ss)

NaCl-KCl(ss) + G + H NaCl-KCl(ss) + H

300 0.1

0.2

0.3

o

378 C

NaCl-KCl(ss)

450 500

Na2FeCl4

+ KCl-NaCl(ss)

350

400

55 0

60

0.5 70 0

x (NaCl)

agreement is not good, the limiting slope of the reported liquidus at a composition limit (x ¼ 0 or x ¼ 1) of the diagram is inconsistent with equation (10). That the reported liquidus in figure 25 is incorrect is evident from comparison with figures 26 and 27. This may be due to supercooling effects [17], which may also be responsible for the other discrepancies between the calculations and the measured points. The sixth section measured by Safonov et al. [17] was between the compositions (35 mol% KCl + 65 mol% MnCl2 ) and (50 mol% NaCl + 50 mol% MnCl2 ). Agreement between the calculations and the measured points was poor for this section, the calculated liquidus lying about 40 C above the measured points. The liquidus projection proposed by Safonov et al. from their measurements looks quite similar to the calculated projection (figure 24). These authors assumed

375 o

319

351 C

K2FeCl4

NaCl o

(801 C)

o

(374 C)

500

0

700

0 75

FIGURE 28. Calculated section of the (NaCl + KCl + MnCl2 ) phase diagram at constant 50 mol% KCl, temperature versus mole fraction of NaCl. Notations: F, KMnCl3 ; G, K3 Mn2 Cl7 ; H, K4 MnCl6 . Experimental data (d) from Safonov et al. [17].

o

KFeCl3 (398 C)

353

+H

0.4

333

o

393 C

0 65

0.0

450 400 350 3 50 309

+ KCl-NaCl(ss)

80

60

40

mol %

20

0 75

KCl o

(771 C)

FIGURE 30. Calculated liquidus projection of the (NaCl + KCl + FeCl2 ) system (the very small field of crystallization of Na2 FeCl4 is not visible on the scale of the diagram).

the existence of the compounds K4 MnCl6 , KMnCl3 , Na4 MnCl6 and NaMn2 Cl5 . Given the obvious large amount of supercooling observed in some sections and the good agreement in other sections, it is believed that the calculations and the measurements agree within the experimental error limits.

7.2. The (NaCl + KCl + FeCl2 ) system The calculated liquidus projection of the (NaCl + KCl + FeCl2 ) system is shown in figure 30. There is no experimental evidence for solid solutions other than the binary (NaCl + KCl) solution, and none

822

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

were assumed in the calculations. Two ternary excess parameters were included for the liquid phase: 011 =ðJ  mol
1 Þ ¼ 14644:0; gNaKðFeÞ=Cl

ð22Þ

001 gNaFeðKÞ=Cl =ðJ  mol
1 Þ ¼
3347:0:

ð23Þ

The liquidus temperatures at several constant mole fractions of FeCl2 , as well as the (NaCl + KFeCl3 ) section of the phase diagram, have been measured by thermal analysis [55]. The results are compared with the calculations in figures 31 and 32. (For the sake of clarity, the liquidus curves at xFeCl2 ¼ 38, 45 and 50 mol% are not shown in figure 31). Molar ratios KCl/(NaCl + KCl) equal to 0.0 and 1.0 in figure 31 correspond to the (NaCl + FeCl2 ) and (KCl + FeCl2 ) binary systems, respectively. It can be seen that the data of Tronina et al. [55], when extrapolated to these limits, do not always

agree well with the calculated binary liquidus temperatures which were based upon data of several other authors (see figures 7 and 18). In order to best reproduce the experimental temperatures [55] of the invariant points of the (NaCl + KFeCl3 ) section (figure 32), no solid solubility of Naþ was assumed in KFeCl3 and K2 FeCl4 . By analogy with equations (20) and (21), a regular excess Gibbs free energy parameter of 100 kJ  mol
1 was used for the (NaFeCl3 + KFeCl3 ) and (Na2 FeCl4 + K2 FeCl4 ) solid solutions, thereby assuring negligible mutual solubility (see section 9). The activity of FeCl2 in the liquid phase has been measured at 820 C and 920 C by an emf technique over a limited range of composition [29]. These data are compared with the calculations in figure 33. The ternary compound NaK3 FeCl6 was reported in a Russian reference quoted by Tronina et al. [55] but was not observed by these authors. It was not considered in the present study.

800 0.1

700

T / (oC)

7.3. The (NaCl + KCl + CoCl2 ) system

0.2

The phase diagram has not been reported. The activity of CoCl2 (at xCoCl2 < 0:01), measured at 759 C by an emf technique [33] in an equimolar (NaCl + KCl) melt, is compared with the calculations in figure 11. No ternary model parameters were used for the liquid and it was assumed that there are no solid solutions other than the binary (NaCl + KCl) solution.

0.3

600

0.6

500 0.4 400

7.4. The (NaCl + KCl + NiCl2 ) system

300 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

xKCl / (xNaCl+xKCl)

FIGURE 31. Calculated liquidus temperatures of (NaCl + KCl + FeCl2 ) mixtures versus the molar ratio xKCl /(xNaCl + xKCl ) at constant mole fractions of FeCl2 of 0.1, 0.2, 0.3, 0.4 and 0.6. Experimental data from Tronina et al. [55]: s, 0.1; d, 0.2;
, 0.3; M, 0.4; ., 0.6.

The phase diagram has not been reported. The activity of NiCl2 , measured at 700 C [37], 762 C [33] and 800 C [37] by an emf technique in an equimolar 0

-1

ln [gamma (FeCl2)]

800

700 liquid

T / (oC)

600 liquid + NaCl-KCl(ss)

500

-2 o

-3

0.768 (920 oC) 0.768 (820 C)

-4

0.232 (920oC) 0.232 (820 C)

o

liquid + KFeCl3 o

398 C

liquid + NaCl-KCl(ss) + KFeCl3

400

o

333 C

-6

o

309 C

300

0.00

NaCl-KCl(ss) + KFeCl3 + FeCl2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.05

0.10

x (FeCl2)

200 0.0

-5

0.8

0.9

1.0

x (KFeCl3)

FIGURE 32. Calculated (NaCl + KFeCl3 ) section of the (NaCl + KCl + FeCl2 ) phase diagram, temperature versus mole fraction of KFeCl3 . Experimental data (d) from Tronina et al. [55].

FIGURE 33. Calculated activity coefficient of FeCl2 (relative to liquid standard state) in the (NaCl + KCl + FeCl2 ) liquid versus the mole fraction of FeCl2 at constant molar ratio NaCl/(NaCl + KCl) of 0.232 and 0.768, at 820 C and 920 C. Experimental data from Kuhnl and Besenbruch [29]: j, 0.232 (820 C); d, 0.768 (820 C);
, 0.232 (920 C); s, 0.768 (920 C).

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828

823

0.0

1

ln [gamma (FeCl2)]

ln [gamma (NiCl2)]

0 o

0C 70

-1

o

0C 80

-2

-0.5 o

C 820

o

C 920

-1.0

-3

-1.5

-4 0.0

0.1

0.2

0.3

0.0

0.4

0.1

FIGURE 34. Calculated activity coefficient of NiCl2 (relative to solid standard state) in the (NaCl + KCl + NiCl2 ) liquid versus the mole fraction of NiCl2 at constant molar ratio NaCl/(NaCl + KCl) of 0.5, at 700 C and 800 C. Tumidajski and Flengas [33]:
, 762 C. Hamby and Scott [37]: d, 700 C; M, 800 C.

0.2

x (FeCl2)

x (NiCl2)

FIGURE 35. Calculated activity coefficient of FeCl2 (relative to liquid standard state) in the (NaCl + MgCl2 + FeCl2 ) liquid versus the mole fraction of FeCl2 at constant molar ratio NaCl/(NaCl + MgCl2 ) of 0.5, at 820 C and 920 C. Experimental data from Kuhnl and Besenbruch [29]: s, 820 C; M, 920 C.

8.3. The (KCl + CaCl2 + FeCl2 ) system (NaCl + KCl) melt, is compared with the calculations in figure 34. No ternary model parameters were used for the liquid and it was assumed that there are no solid solutions other than the binary (NaCl + KCl) solution.

8. Other ternary and quaternary systems

001 =ðJ  mol
1 Þ ¼
6276:0: gCaFeðKÞ=Cl

Limited data are available for six other ternary and two quaternary subsystems. The solid solutions introduced for the calculations were mentioned in section 4.

ð25Þ

8.4. The (NaCl + CoCl2 + NiCl2 ) system The calculated liquidus projection of the (NaCl + CoCl2 + NiCl2 ) system is shown in figure 37. CoCl2 and NiCl2 exhibit limited mutual solid solubility

8.2. The (NaCl + CaCl2 + FeCl2 ) system The phase diagram has not been reported. The Henrian activity coefficient (at infinite dilution) of FeCl2 has been measured at 820 C and 920 C by an emf technique [56] in an equimolar (NaCl + CaCl2 ) melt. The experimental values are RT lnðcFeCl2 Þ ¼ )10,934 and )15,367 J  mol
1 , respectively. This gives a partial excess entropy of FeCl2 equal to 44.33 J  mol
1  K
1 , which is very large and unlikely to be correct. With no ternary model parameters, the calculated values are RT lnðcFeCl2 Þ ¼
9,780 and )9,692 J  mol
1 , respectively.

0.5

o

C 777 o C 7 62

-1 o

C 920

-2

o

C 820

7C 72

C o

o

7 77

o

-3

C

ð24Þ

0

62 7

The phase diagram has not been reported. The activity of FeCl2 , measured at 820 C and 920 C by an emf technique [29] in an equimolar (NaCl + MgCl2 ) melt, is compared with the calculations in figure 35. A small ternary excess parameter was included for the liquid phase:

ln [gamma (FeCl2)]

8.1. The (NaCl + MgCl2 + FeCl2 ) system

001 gNaFeðMgÞ=Cl =ðJ  mol
1 Þ ¼
3766:0:

The phase diagram has not been reported. The activity of FeCl2 , measured by an emf technique [45,56] for two different CaCl2 /(KCl + CaCl2 ) molar ratios, is compared with the calculations in figure 36. A small ternary excess parameter was included for the liquid phase:

-4

0.2

o

7C 72

-5 0.0

0.1

0.2

0.3

0.4

0.5

x (FeCl2)

FIGURE 36. Calculated activity coefficient of FeCl2 (relative to liquid standard state) in the (KCl + CaCl2 + FeCl2 ) liquid versus the mole fraction of FeCl2 at constant molar ratio CaCl2 /(KCl + CaCl2 ) of 0.2 and 0.5. Ernst et al. [45]: d, 0.2 (627 C); j, 0.2 (727 C); M, 0.2 (777 C); +, 0.5 (627 C);
, 0.5 (727 C); O, 0.5 (777 C). Kuhnl et al. [56]: N, 0.5 (820 C); , 0.5 (920 C).

824

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828 800

NaCl o

(801 C)

liquid

liquid + NiCl2-CoCl2(ss)

T / (oC)

750

20

80

700

700 60

40

650 600

550

600

liquid + NiCl2-CoCl2(ss) + CoCl2-NiCl2(ss)

500 o

574 C

500 o

0 5050 5 00 6 0 65 0 70

liquid + NaCl + NiCl2-CoCl2(ss)

60

40

366 C

400 NaCl + NiCl2-CoCl2(ss) + CoCl2-NiCl2(ss)

20

0 85

718 C

80

60

40

0.2

0.3

0.4

0.5

0.6

MPa

20

NiCl2

mass %

(724 C)

0.1

w (NiCl2)

950

0.1

CoCl 2 o

0.0

900

800

o

300

80

0 75

FIGURE 37. Calculated liquidus projection of the (NaCl + CoCl2 + NiCl2 ) system.

FIGURE 39. Calculated section of the (NaCl + CoCl2 + NiCl2 ) phase diagram at constant NaCl mass fraction of 0.35, temperature versus mass fraction of NiCl2 . Experimental data (d) from Bol’shakov et al. [57].

800

(maximum 10 mol% on either side). The calculated ternary invariant point is virtually coincident with the binary eutectic point of the (NaCl + CoCl2 ) system. A ternary excess parameter was introduced for the liquid phase: ð26Þ

700 liquid + NaCl

T / (oC)

011 gNaCoðNiÞ=Cl =ðJ  mol
1 Þ ¼ 11506:0:

liquid

600

500

Six sections of the ternary system were measured by thermal analysis [57]. The data points and calculations are compared in figures 38–43. Agreement is within the experimental error limits.

liquid + NaCl + NiCl2-CoCl2(ss) 400 NaCl + NiCl2-CoCl2(ss) + CoCl2-NiCl2(ss) 300 0.0

8.5. The (KCl + CoCl2 + NiCl2 ) system The phase diagram has not been reported. The activity of NiCl2 , measured by an emf technique [58] for three different KCl mole fractions, is compared with the

0.1

0.2

w (NiCl2)

FIGURE 40. Calculated section of the (NaCl + CoCl2 + NiCl2 ) phase diagram at constant NaCl mass fraction of 0.73, temperature versus mass fraction of NiCl2 . Experimental data (d) from Bol’shakov et al. [57].

900

900

liquid 800

800 liquid 700

liquid + NiCl2-CoCl2(ss)

T / (oC)

T / (oC)

700

600

liquid liquid + NaCl

+ NiCl2-CoCl2(ss)

600

liquid

500

+ NiCl2-CoCl2(ss)

liquid + NaCl

+ CoCl2-NiCl2(ss)

+ NiCl2-CoCl2(ss)

400

500 liquid + NiCl2-CoCl2(ss)

liquid + NaCl + NiCl2-CoCl2(ss)

400 + CoCl2-NiCl2(ss)

NaCl + NiCl2-CoCl2(ss) + CoCl2-NiCl2(ss)

300 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

w (NiCl2)

FIGURE 38. Calculated section of the (NaCl + CoCl2 + NiCl2 ) phase diagram at constant NaCl mass fraction of 0.24, temperature versus mass fraction of NiCl2 . Experimental data (d) from Bol’shakov et al. [57].

NaCl + NiCl2-CoCl2(ss) + CoCl2-NiCl2(ss)

300 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

w (NaCl)

FIGURE 41. Calculated section of the (NaCl + CoCl2 + NiCl2 ) phase diagram at constant mass ratio NiCl2 /(CoCl2 + NiCl2 ) of 0.25, temperature versus mass fraction of NaCl. Experimental data (d) from Bol’shakov et al. [57].

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828 900

2

800

1

ln [gamma (NiCl2)]

liquid

T / (oC)

700 liquid

liquid + NaCl

+ NiCl2-CoCl2(ss)

600

500 liquid + NiCl2-CoCl2(ss)

825

o

0.5 (692 C)

0 -1 o

0.75 (647 C)

-2 -3

liquid + NaCl + NiCl2-CoCl2(ss)

400 + CoCl2-NiCl2(ss)

o

-4

0.9 (797 C)

NaCl + NiCl2-CoCl2(ss) + CoCl2-NiCl2(ss)

300 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-5

1.0

0.0

w (NaCl)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

xNiCl2 / (xCoCl2+xNiCl2)

FIGURE 42. Calculated section of the (NaCl + CoCl2 + NiCl2 ) phase diagram at constant mass ratio NiCl2 /(CoCl2 + NiCl2 ) of 0.50, temperature versus mass fraction of NaCl. Experimental data (d) from Bol’shakov et al. [57].

FIGURE 44. Calculated activity coefficient of NiCl2 (relative to solid standard state) in the (KCl + CoCl2 + NiCl2 ) liquid versus the molar ratio x(NiCl2 )/[x(CoCl2 ) + x(NiCl2 )] at constant mole fractions of KCl of 0.5, 0.75 and 0.9. Experimental data from Tumidajski and Pickles [58]: M, 0.5 (692 C);
, 0.75 (647 C); d, 0.9 (797 C).

900

to erroneous activities reported by Jindal [59]. The data points shown in figure 45 were calculated after correcting the sign of the reported emf. Since there are very few data available for the (MgCl2 + NiCl2 ) binary system [1], the data in figure 45 were reproduced by introducing a small binary model parameter:

800 liquid

T / (oC)

700 liquid 600

liquid + NaCl

+ NiCl2-CoCl2(ss)

500

DgMgNi=Cl =ðJ  mol
1 Þ ¼
1500:

liquid + NaCl + NiCl2-CoCl2(ss)

ð27Þ

400

8.7. The (NaCl + MgCl2 + CaCl2 + MnCl2 ) system

NaCl + NiCl2-CoCl2(ss) + CoCl2-NiCl2(ss) 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

w (NaCl)

FIGURE 43. Calculated section of the (NaCl + CoCl2 + NiCl2 ) phase diagram at constant mass ratio NiCl2 /(CoCl2 + NiCl2 ) of 0.75, temperature versus mass fraction of NaCl. Experimental data () from Bol’shakov et al. [57].

calculations in figure 44. Molar ratios NiCl2 / (CoCl2 + NiCl2 ) equal to 0.0 and 1.0 in figure 44 correspond to the (KCl + CoCl2 ) and (KCl + NiCl2 ) binary systems, respectively. It can be seen that the data obtained by Tumidajski and Pickles [58] for the (KCl + NiCl2 ) system do not always agree well with the calculated activities which were based upon several other data sources (see figure 23). 8.6. The (KCl + MgCl2 + NiCl2 ) and (NaCl + KCl + MgCl2 + NiCl2 ) systems The phase diagram has not been reported. The activity of NiCl2 (at xNiCl2 < 0:04) was measured at 475 C by an emf technique [59] in melts of constant molar ratio KCl/MgCl2 ¼ 67.5/32.5, and also in quaternary melts at constant molar ratio NaCl/KCl/MgCl2 ¼ 30/20/50. The sign of the emf values was reported incorrectly, leading

Two sections of the phase diagram have been measured by thermal analysis [60]. The calculated sections 4

3

ln [gamma (NiCl2)]

300

2

1

0 0.00

0.01

0.02

0.03

0.04

x (NiCl2)

FIGURE 45. Calculated activity coefficient of NiCl2 (relative to solid standard state) versus the mole fraction of NiCl2 at 475 C in ternary (KCl + MgCl2 + NiCl2 ) melts at constant molar ratio KCl/ MgCl2 ¼ 67.5/32.5, and in quaternary (NaCl + KCl + MgCl2 + NiCl2 ) melts at constant molar ratio NaCl/KCl/MgCl2 ¼ 30/20/50. Experimental data from Jindal [59]: d, KCl/MgCl2 ¼ 67.5/32.5; s, NaCl/ KCl/MgCl2 ¼ 30/20/50.

826

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828 850

liquid

750

T / (oC)

liquid + A

650

liquid + C

liquid + A + B

550 liquid + C + E

450 A+B+D

C+E

B+C+E

B+D+E

350 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

w (NaCl)

FIGURE 46. Calculated section of the (NaCl + MgCl2 + CaCl2 + MnCl2 ) phase diagram at constant mass ratio MgCl2 /CaCl2 / MnCl2 ¼ 60/30/10, temperature versus mass fraction of NaCl. Notations: A, (MgCl2 + MnCl2 )(ss); B, (CaCl2 + MgCl2 )(ss); C, (NaCl + CaCl2 )(ss); D, Na(Mg,Ca,Mn)Cl3 (ss); E, Na2 (Mg,Mn)Cl4 (ss). Experimental data (d) from Il’ichev and Vladimirova [60].

850

T / (oC)

750

liquid

liquid + A

650

liquid + C

550

liquid + A + B + D liquid + C + E

liquid +A+B

450

A+B+D

350 0.0

0.1

0.2

B+D+E

0.3

0.4

C+E

B+C+E

0.5

0.6

0.7

0.8

0.9

1.0

w (NaCl)

FIGURE 47. Calculated section of the (NaCl + MgCl2 + CaCl2 + MnCl2 ) phase diagram at constant mass ratio MgCl2 /CaCl2 / MnCl2 ¼ 1/1/1, temperature versus mass fraction of NaCl. Notations: A, (MgCl2 + MnCl2 )(ss); B, (CaCl2 + MgCl2 )(ss); C, (NaCl + CaCl2 ) (ss); D, Na(Mg,Ca,Mn)Cl3 (ss); E, Na2 (Mg,Mn)Cl4 (ss). Experimental data (d) from Il’ichev and Vladimirova [60].

are shown along with the measurements in figures 46 and 47. No additional model parameters for the liquid were introduced and the solid solutions introduced for the calculations were mentioned in section 4. These include the Na(Mg,Ca,Mn)Cl3 and the Na2 (Mg,Mn)Cl4 solid solutions for which the optimized model parameters are discussed in section 9.

9. Multicomponent system (NaCl + KCl + MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) For the liquid phase of the 8-component system, the model described in section 3 was used. For all ternary subsystems evaluated in the present study and previ-

ously [1] no, or only small, ternary excess model parameters were required to reproduce the available data. Hence, the assumption that ternary excess parameters can be neglected for all ternary subsystems for which data are lacking is expected to result in accurate predictions of the thermodynamic properties of the multicomponent liquid phase. As well as the solid solution phases discussed in section 4, it is also necessary to consider the (Na,K)(Mg,Ca,Mn,Fe,Co,Ni)Cl3 perovskite solid solution and the (Na,K)2 (Mg,Mn,Fe,Co,Ni)Cl4 solid solution. For example, extensive (Na,K)MgCl3 and (Na,K)2 MgCl4 solid solutions are observed and have been modeled [5]. Although there are no data for these solutions in the general case, the close similarity in radius of all M2þ cations (except Ca2þ ) suggests that mutual solid solubility should occur. These solutions are modeled using the Compound Energy Formalism [61] as described in detail in section VIII of [5]. The K3 Mg2 Cl7 [5] and K3 Mn2 Cl7 (section 6.1) solid compounds are assumed to be mutually insoluble. The model parameters required for the (Na,K)(Mg,Ca,Mn,Fe,Co,Ni)Cl3 and the (Na,K)2 (Mg,Mn,Fe,Co,Ni)Cl4 solid solutions are the Gibbs free en  ergies gAMCl and gA (A ¼ Na, K and M ¼ Mg, Ca, 3 2 MCl4 Mn, Fe, Co and Ni) of all pure end-member compounds, including metastable (or hypothetical) compounds, and the excess Gibbs free energy of mixing parameters for all binary subsystems. For the perovskite compounds, optimized values of   gKMCl for M ¼ Mg, Ca, Mn, Fe, Co, Ni and gNaMgCl 3 3 are available from the present and previous [5] studies.  gNaCaCl for metastable NaCaCl3 has already been esti3 mated [5]. From our experience, compounds AMCl3 and A2 MCl4 are rarely far from being stable. That is, their Gibbs free energies are just slightly more positive than is required for them to be stable. Consequently, the Gibbs free energies of the metastable perovskites NaMCl3 (M ¼ Mn, Fe, Co, Ni) were estimated by starting with a Gibbs free energy of formation from the pure chlorides (NaCl + MCl2 ¼ NaMCl3 ) equal to zero, subtracting constant increments of 1 kJ  mol
1 from this Gibbs free energy until the compound just appears as a stable phase in the (NaCl + MCl2 ) phase diagram, and then adding back an arbitrary increment of 2 kJ  mol
1 . The Gibbs free energies obtained in this way are given in table 3. In the case of KMnCl3 , KFeCl3 , KCoCl3 and KNiCl3 , several allotropes are reported but only the high temperature form was considered in the present work owing to the unavailability of relevant thermodynamic and crystallographic data for the low temperature forms. For the (NaMgCl3 + KMgCl3 ) and (NaCaCl3 + KCaCl3 ) binary systems, the excess Gibbs free energy of mixing gE has already been estimated [5]. For the (NaMnCl3 + KMnCl3 ) and (NaFeCl3 + KFeCl3 ) binary systems, a regular excess Gibbs free energy parameter of

C. Robelin et al. / J. Chem. Thermodynamics 36 (2004) 809–828 TABLE 3 Gibbs free energies of metastable solid compounds assessed in the present study g /(J  mol
1 ) NaMnCl3 NaFeCl3 NaCoCl3 NaNiCl3 Na2 NiCl4 K2 MnCl4 K2 NiCl4

  gNaCl þ gMnCl
1000 2   gNaCl þ gFeCl þ 1000 2   gNaCl þ gCoCl þ 1000 2   gNaCl þ gNiCl þ 1000 2   2  gNaCl þ gNiCl þ 1000 2   2  gKCl þ gMnCl
19000 2   2  gKCl þ gNiCl
9000 2

100 kJ  mol
1 was used in order to assure negligible mutual solubility as is consistent with the data available for the (NaCl + KCl + MnCl2 ) and (NaCl + KCl + FeCl2 ) ternary systems (sections 7.1 and 7.2). Similarly, a regular excess Gibbs free energy parameter of 100 kJ  mol
1 was used for the (NaCoCl3 + KCoCl3 ) and (NaNiCl3 + KNiCl3 ) binary systems. For the 0 0 (NaMCl3 + NaM Cl3 ) and (KMCl3 + KM Cl3 ) binary systems, gE has already been optimized [5] for M ¼ Mg, 0 M ¼ Ca. Since CaCl2 exhibits only very limited solid solubility with MCl2 (M ¼ Mn, Fe, Co, Ni) [1], it is assumed that the corresponding perovskite solutions are also virtually immiscible, and so we set: gE =ðJ  mol
1 Þ ¼ 100,000xAMCl3 xACaCl3 ;

ð28Þ

for A ¼ Na, K and M ¼ Mn, Fe, Co, Ni. In all other 0 0 cases (M, M 6¼ Ca), MCl2 and M Cl2 are completely miscible [1]. For the (NaMgCl3 + NaMnCl3 ) binary system, the excess Gibbs free energy of mixing was set to: gE =ðJ  mol
1 Þ ¼
2986:9xNaMgCl3 xNaMnCl3 ;

ð29Þ

in order to best reproduce the experimental data available for the (NaCl + MgCl2 + CaCl2 + MnCl2 ) system (section 8.7). For the (KMgCl3 + KMnCl3 ) binary system, gE was assumed to be given by an equation similar to equation (29). Finally, for all remaining binary pe0 rovskite solutions (AMCl3 + AM Cl3 ) (A ¼ Na, K), gE was set equal to the optimized [1] value of gE for the 0 corresponding (MCl2 + M Cl2 ) solid solution. For the A2 MCl4 compounds, optimized values of  gA are available from the present and previous [5] 2 MCl4 studies for K2 MgCl4 , K2 FeCl4 , K2 CoCl4 , Na2 MgCl4 , Na2 MnCl4 , Na2 FeCl4 and Na2 CoCl4 . Values for the metastable compounds Na2 NiCl4 , K2 MnCl4 and K2 NiCl4 were estimated in the same way as for the metastable perovskites as described above. The resultant Gibbs free energies are given in table 3. In the case of K2 FeCl4 , two allotropes are reported, but only the high temperature form was considered in the present work owing to the unavailability of relevant thermodynamic and crystallographic data for the low temperature form. For the (Na2 MgCl4 + K2 MgCl4 ) binary system, the ex-

827

cess Gibbs free energy of mixing has already been optimized [5]. For the (Na2 MnCl4 + K2 MnCl4 ) and (Na2 FeCl4 + K2 FeCl4 ) binary systems, a regular excess Gibbs free energy parameter of 100 kJ  mol
1 was used in order to assure negligible mutual solubility as is consistent with the experimental data available for the (NaCl + KCl + MnCl2 ) and (NaCl + KCl + FeCl2 ) ternary systems (sections 7.1 and 7.2). Similarly, a regular excess Gibbs free energy parameter of 100 kJmol
1 was used for the (Na2 CoCl4 + K2 CoCl4 ) and (Na2 NiCl4 + K2 NiCl4 ) binary systems. For the binary systems 0 0 (Na2 MCl4 + Na2 M Cl4 ) and (K2 MCl4 + K2 M Cl4 ) (M, 0 M ¼ Mg, Mn, Fe, Co, Ni), gE was assumed to be equal to the optimized [1] value of gE for the corresponding 0 (MCl2 + M Cl2 ) solid solution. 10. Conclusions In this and the previous article [1], a complete critical evaluation of all available phase diagram and thermodynamic data for all condensed phases of the (NaCl + KCl + MgCl2 + CaCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) system has been made, and optimized model parameters have been found. All data are reproduced within experimental error limits. For the binary systems (MCl2 + NiCl2 ) (M ¼ Mg, Ca, Mn, Fe, Co), only approximate optimizations could be made owing to the scarcity (and sometimes discrepancy) of available data [1]. The Modified Quasichemical Model [2,3] was used for the liquid phase, while the (MgCl2 + MnCl2 + FeCl2 + CoCl2 + NiCl2 ) solid solution was modeled using a simple cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions [1]. The Compound Energy Formalism [61] was used for the (Na,K)(Mg,Ca,Mn,Fe,Co,Ni)Cl3 perovskite phase and the (Na,K)2 (Mg,Mn,Fe,Co,Ni)Cl4 solid solution. From the optimized parameters of the binary and ternary subsystems, it is possible, from the quasichemical model, to predict the thermodynamic properties of the multicomponent liquid solution with good accuracy. The database of optimized parameters will soon be included in the FACT [62] database computing system and may be used, along with the other databases and Gibbs free energy minimization software, to calculate phase equilibria and all thermodynamic properties in multicomponent systems. This database can be applied to calculations involving electrolytes and will form a base for calculations in corrosion applications.

Acknowledgements This project was supported by a CRD grant from the Natural Sciences and Engineering Research Council of

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JCT 03/135