Phase equilibria in the reciprocal NaCl–KCl–NaNO3–KNO3 system

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 51 (2015) 111–124

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Phase equilibria in the reciprocal NaCl–KCl–NaNO3–KNO3 system D. Sergeev a,n, E. Yazhenskikh a, D. Kobertz a, K. Hack b, M. Müller a a b

Forschungszentrum Jülich GmbH, IEK-2, D-52425, Germany GTT-Technologies, Kaiserstraße 100, D-52134 Herzogenrath, Germany

art ic l e i nf o

a b s t r a c t

Article history: Received 15 June 2015 Received in revised form 1 September 2015 Accepted 1 September 2015

Differential thermal analysis of the various compositions in the KCl–NaNO3 and NaCl–KNO3 systems has been performed. Temperatures of phase transitions were obtained. The relative content of NaCl, KCl, NaNO3, and KNO3 compounds was determined by the use of X-ray diffraction analysis. These results together with the experimental data from literature were used for optimization of thermodynamic parameters for all available phases and compounds to obtain the Gibbs energy dataset which can be used for the calculation and prediction of the phase diagrams and other thermodynamic properties of these systems. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Phase equilibria Salt system Potassium Sodium Chloride Nitrate

1. Introduction Thermal energy storage (TES) is one of the promising issues of the energy-saving technologies. The primary principles of TES are based on the use of the sensible- and the latent-heat of materials. Salt systems as TES are used in industry and solar thermal power plants because of low price and suitable temperature range [1–3]. For the selection of suitable systems in application, it is of considerable importance to know their thermodynamic properties and phase diagrams. Systems based on NaCl, KCl, NaNO3, and KNO3 salts are at reasonable price and already widely used in industry. The phase diagrams and thermodynamic properties of the binary systems NaNO3–KNO3[4–9], NaCl–KCl [10–15], NaNO3–NaCl [16,17], and KNO3–KCl [16–20] were studied experimentally by different authors. Moreover, the liquidus projection of the reciprocal NaCl–KCl–NaNO3–KNO3 system was published in Ref. [21]. To complete this system the sections NaCl–KNO3 and KCl–NaNO3 have to be studied for optimizing the thermodynamic parameters of all available phases and compounds to generate the Gibbs energy dataset, which can be used for the calculation and prediction the phase diagrams and other thermodynamic properties of the whole system. This work is focussed on studying the sections NaCl–KNO3 and KCl–NaNO3 of the reciprocal NaCl–KCl–NaNO3–KNO3 system by n

Corresponding author. E-mail address: [email protected] (D. Sergeev).

http://dx.doi.org/10.1016/j.calphad.2015.09.002 0364-5916/& 2015 Elsevier Ltd. All rights reserved.

the use of differential thermal analysis (DTA) and X-ray diffraction (XRD) in connection with the critical assessment and optimisation of the complete salt system following the Calphad method.

2. Experimental 2.1. Instruments 2.1.1. Differential thermal analysis (DTA) DTA measurements were performed using a STA 449C Jupiter (Netzsch) with a silicon carbide oven (0–1600 °C) and a perpendicular sample holder with type S thermocouple (Pt/(Pt10Rh)). The temperature calibration was conducted using the structure and phase transitions temperatures of In (156.6 °C), Zn (419.6 °C), SiO2 (574 °C), K2CrO4 (673 °C), and Ag (961.8 °C). The experiments were carried out with a scan rate of 5 K/min and 4 cycles of heating and cooling. Single phase transitions were obtained from the extrapolated onset construction in the heating curve and for cooling from the extrapolated end temperature under consideration of the undercooling effect. The onset was used for the solidus and the end temperature for the liquidus transition. All the values were determined with Proteus Analysis software from Netzsch. The results showed good reproducibility from the second cycle. 2.1.2. X-ray diffractometer (XRD) A Bruker D4 Endeavour diffractometer (Bruker AXS GmbH) with Cu-Kα radiation (40 kV, 40 mA) and a NaI scintillation

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Table 1 Sample information. Chemical name

NaCl KCl NaNO3 KNO3

a b c

Source

Alfa (AESAR) Alfa (AESAR) SigmaAldrich SigmaAldrich

Puritya

Melting temperatureb (°C)

Transition temperatureb (°C)

Heatingc

Coolingc

Onset

Peak

99.99%, ultra dry 99.99%, ultra dry 99.995%

805

803

–

–

773

771

–

–

301

303

–

273

99.999%

331

335

127

134

On metal basis. The standard uncertainty (u) is u(T) ¼ 3 °C. Based on the onset of peak.

counter detector was used for the XRD analysis. The phase identification was deduced from the inorganic crystal structure database (ICSD, FIZ Karlsruhe) with the software HighScore Plus 3.0 (PANanalytical B.V.). Rietveld refinement was performed using TOPAS 4.2 software (Bruker AXS GmbH). 2.2. Samples The specifications of the compounds used for the preparation of mixtures are described in Table 1. Melting and structure transition temperatures of pure compounds were determined by the authors using DTA (Table 1, Fig. 1). in closed glass ampoules. These values show that undercooling effects on the cooling curves do nearly not see. This conclusion was used for determination of liquidus temperatures of the studied mixtures. All mixtures were prepared in a glass ampoule under purified argon inside of a glove box. The sample was heated carefully under vacuum to remove any residual moisture and then the glass ampoule was sealed. To achieve homogeneity prior to examination, the mixtures in the ampoules were sequentially melted and crystallized 3 times at a rate of 5 K/min.

important points of this system. The pure NaNO3 has one structural transition at 273 °C (Table 1, Fig. 1). Therefore, it was difficult to distinguish and separate the peaks of melting point and structure changing for the compositions 5KCl–95NaNO3, 6KCl–94NaNO3, and 7.5KCl–92.5NaNO3 (Fig. 2a). To solve this problem, additional measurements with a low heating rate of 1 K/ min were carried out. However, the signal was in this case lower and it still did not allow separating the temperature transitions. For the mixtures 10KCl–90NaNO3 and 15KCl–85NaNO3 the crystallization peak could only be seen on the cooling curves (Fig. 2a). It allowed finding out the eutectic composition 7.5KCl–92.5NaNO3 which exhibits the lowest temperature of crystallization, i.e. at 275 °C (Fig. 2a). Along with these peaks there was a small one at 110 °C (Table 2, column 3), which is also seen for other compositions (Fig. 2b). The DTA-curves of 20KCl–80NaNO3, 30KCl–70NaNO3, 35KCl–65NaNO3, and 25KCl–75NaNO3, 40KCl–60NaNO3 mixtures outline transitions related to the eutectoid transformation. It has a temperature of 209 °C and the composition 35KCl–65NaNO3 (Table 2, column 2). In addition, a small deviation from the base-line was seen in the region of 130– 200 °C (Fig. 2b, in circles) for heating and cooling curves. This line is labelled in Table 2 as column 4. Fig. 3a shows the changes of two transition signals in the concentration range of 50:50 compositions (Table 2, columns 1–3). The peak temperature of the first transition is 110 °C (onset 100 °C) for the 42.5KCl–57.5NaNO3 to 50KCl–50NaNO3 compositions and is changed to 120 °C (onset 110 °C) for 55KCl–45NaNO3 (Table 2, column 3). The second transition has a maximum onset at 242 °C for the heating and cooling curves of the 55KCl–45NaNO3 composition. This temperature is constant for compositions with higher KCl concentration (Table 2, columns 1 and 2). For KCl concentrations lower than 55 mol%, the onset is continuously changing to lower temperature and ends in two transitions with an onset at 205 °C for the first peak. Fig. 3b illustrates peaks of the liquidus line for mixtures with KCl higher than 50 mol% (Table 2). The transition temperatures were taken from the so-called end-set determination that represents the beginning of crystallization on the cooling curves. An additional peak (in circles) was observed (Table 2, column 5). All transition temperatures related to the various compositions are tabulated in Table 2.

3. Experimental results 3.1. Differential thermal analysis 3.1.1. KCl–NaNO3 The 24 compositions of KCl–NaNO3 system were synthesized in closed glass ampoules and studied by DTA. Figs. 2 and 3 show the main DTA-curves on heating and cooling, which characterize all

3.1.2. NaCl–KNO3 Nineteen compositions in the NaCl–KNO3 system were studied by DTA in closed glass ampoules in the same way as described before for the KCl–NaNO3 system. Fig. 4 shows the DTA-curves of some compositions from 5% to 40% NaCl in the temperature range 200–400 °C. In the range of NaCl concentrations below 40 mol% more than two transitions have been observed. Three transitions

Fig. 1. Heating (red/upper) and cooling (blue/lower) DTA-curves of KNO3, NaNO3, KCl, and NaCl compounds. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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113

Fig. 2. Heating (red/upper) and cooling (blue/lower) DTA-curves for various compositions in the KCl–NaNO3 system, part 1. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

are clearly resolved in heating and cooling curves of the 5NaCl–95KNO3 and 10NaCl–90KNO3 mixtures which are listed in Table 3 named as “Liquidus” (taken from cooling curves), temperatures in column 1 and 2 (Table 3) taken from heating curves. In column 3 (Table 3) values of small changes for 5NaCl–95KNO3 and 7.5NaCl–92.5KNO3 mixtures are given, which were identified

with detailed analysis, but which have to be treated with care. For 15NaCl–85KNO3 and 17.5NaCl–82.5KNO3 one more peak at 271 and 261 °C occurred on cooling respectively (Table 3, column 4). As from 30NaCl–70KNO3 system this peak remained for other compositions as well as by heating (Table 3, column 1). In addition small peaks are visible in the cooling curves for

Fig. 3. Heating (red/upper) and cooling (blue/lower) DTA-curves for various compositions in the KCl–NaNO3 system, part 2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Table 2 Variable temperatures in the system KCl–NaNO3. Mol% KCl

5 6 7.5 8.5 10 15 20 25 30 35 37.5 40 42.5 45 47.5 50 52.5 55 57.5 60 65 70 80 90

Table 3 Variable temperatures in the system NaCl–KNO3.

Columna (°C)

Mol% NaCl

1

2

3

4

5

6

283 283 275 278 300 362 398 434 446 462 475 463 482 493 483 496 484 486 495 497 537 574 656 703

– – – – – – – – – – – – – – – 370 435 – – 470 427 393 315 –

– – – – 274 261 249 234 216 209 214 220 230 240 244 244 244 244 244 244 244 243 240 243

N/V N/V 210 208 215 209 210 207 209 208 208 205 207 203 233 239 241 244 242 244 241 243 239 243

– – – – – – – 190 180 160 150 140 – – – – – – – – – – – –

108 111 108 110 114 113 111 108 111 111 110 109 110 113 116 118 119 120 120 121 117 118 N/V N/V

5 7.5 10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35 40 50 60 70 80 90

a

The standard uncertainty (u) is u(T) ¼3 °C.

32.5NaCl–68.5KNO3 and 35NaCl–65KNO3 (Fig. 4-b, in circles). The same results were found for 50NaCl–50KNO3, 60NaCl–40KNO3, 70NaCl–30KNO3 systems (Table 3, column 5). Fig. 5 shows DTA-curves in the temperature range 50–150 °C of

1

2

3

4

5

6

7

8

314 305 288 284 285 285 315 311 326 351 355 361 373 401 482 549 623 678 747

290b 291b – – – – – – – – – – – – – – – – –

– – – 278 271 261 254 256 243 240 243 242 243 243 242 241 237 238 236

242 244 244 246 247 249 248 247 249 248 250 249 250 250 247 245 239 239 237

264 264 264 266 266 264 – – – – – – – – – – – – –

– – – – – – – – – – – 264 335 – 379 365 350 N/V N/V

131 128 127 126 126 126 123 124 124 124 124 124 124 124 – – – – –

115 113 115 114 114 115 115 115 115 115 117 118 117 116 115 114 104 109 117

Note: N/V – not visible; Columns: 1 – liquidus line, 2–5 – transitions between solid and liquid phases, 6 – immiscibility of chloride solid solution, 7, 8 – solid–solid transitions of nitrates. a b

Note: N/V – not visible; Columns: 1 – liquidus line, 2 – immiscibility of chloride solid solution, 3, 4 – transitions between solid and liquid phases, 5, 6 – solid–solid transitions of nitrates.

Columna (°C)

The standard uncertainty (u) is u(T) ¼ 3 °C. These values can be mistaken.

some compositions from 5% to 70% NaCl. In this region pure KNO3 has a structural change at 134 °C (Table 1). The heating curve of 5NaCl–95KNO3 shows only one peak (Table 3, column 6), but on cooling there are two peaks with undercooling effect. As from 10NaCl–90KNO3 this peak splits into two at 127 °C and 115 °C. The values of the second peak are given in column 7 (Table 3). It occurred beginning with 20NaCl–80KNO3 and ending at

Fig. 4. Heating (red/above) and cooling (blue/under) DTA-curves in various compositions in the NaCl–KNO3 system, part 1. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

D. Sergeev et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 51 (2015) 111–124

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Fig. 5. Heating (red/upper) and cooling (blue/lower) DTA-curves in various compositions in the NaCl–KNO3 system, part 2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

90NaCl–10KNO3. 3.2. XRD analysis The reciprocal system has four compounds with sections of two compounds with different cations, but same anion (NaCl, KCl), (NaNO3, KNO3) and two with the same cation, but different anion (NaCl, NaNO3), (KCl, KNO3). Both quasi-binary subsystems along the diagonals of this reciprocal system react cross-wise by ion substitution according to the reciprocal reaction NaClþ KNO3 ¼NaNO3 þKCl. In order to determine the content of the compounds NaCl, KCl, NaNO3, KNO3 in both the NaCl–KNO3 and KCl–NaNO3 system, XRD analysis of some mixtures has been carried out. The X-ray diffraction patterns in Figs. 6 and 7 of the 20–80, 40–60, 60–40, 80– 20 compositions of KCl–NaNO3 and NaCl–KNO3 respectively allowed the estimation of the relative content of NaCl, KCl, NaNO3, and KNO3 compounds (Table 4). It should be noted that this estimation has an uncertainty of about 20%, but it gives a qualitative orientation of the content of compounds in the systems. This analysis showed that in the KCl–NaNO3 system with the content of KCl from 0% to 50%, KCl was completely substituted by NaCl and KNO3. In the range of KCl content from 50 to 100%, NaNO3 disappeared resulting in a residue of NaCl, KCl, and KNO3 compounds. One can say that the quasi-binary system KCl–NaNO3 can be represented by the two quasi-ternary systems NaCl–NaNO3–KNO3 and NaCl–KCl–KNO3. In the case of the NaCl–KNO3 system, the NaCl and KNO3 compounds were quite stable, but small amounts of KCl and NaNO3 was also formed for each composition (Table 4). 4. Models and optimization of thermodynamic parameters The experimental information on the thermodynamic properties of the present salt system (phase diagrams, phase transitions

etc.) can be evaluated and used for the generation of thermodynamic datasets for all available phases and compounds. The database consists of the optimised thermodynamic (Gibbs energy) parameters for all phases using suitable thermodynamic models for each phase. The dataset is used for the calculation of the thermodynamic properties and for predictions of phase equilibria in the unknown regions of temperature and composition of the multicomponent system. The phase diagrams and thermodynamic data of the given salt systems have been critically assessed previously in [7,22,23]. The modified quasi-chemical model for short-range ordering in the molten salt phase [24] was used. These thermodynamic data are summarized in the commercial database FT-Salt in the FactSage package [25]. In the present work the given salt system is re-evaluated because of the new experimental data on the sections NaCl–KNO3 and KCl–NaNO3. The modified associate model [26] has been applied successfully for the description of complex oxide liquids (slags) [27]. In the present work this approach is also applied for the complex salt liquid phase. Firstly, the common-ion binary salt systems in the framework of the complete system (Na, K)(Cl, NO3) are considered in terms of assessment of all thermodynamic parameters. As a next step, the complete reciprocal system is thermodynamically assessed taking into account the present experimental information along with the data available from literature. The present work is considered as a starting point of further studies incorporating additional component salts. The Gibbs energy of the liquid phase (salt) is represented by the modified associate species model. The pure liquid salts are considered as solution components. In order to describe the mixing properties of the solution the interactions between solution species were introduced. The molar Gibbs energy of the solution is a three-term expression with contributions of the reference part, the ideal and the excess part as:

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Fig. 6. X-ray diffraction patterns of various compositions in the KCl–NaNO3 system after DTA measurements.

Gm =

∑ xi Gi° + RT ∑ xi ln xi + ∑ ∑ xi xj ∑ L ij(v) (xi − xj )v i
v=0

(1)

where x i 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. L ij(v) is temperature dependant in the same way according to:

L ij(v) = A + B⋅T + C⋅T ⋅ ln T

(2)

The solid solubilities for alkali chlorides and alkali nitrates for high and low temperature modifications have been treated with a

sublattice model. According to the sublattice model, the solid solutions are expressed as (Na1 þ , K1 þ )1(Cl1  )1 and (Na1 þ , K1 þ )1 1þ ( NO1− )1(Cl1  )1, 3 )1 with the following phase components: (Na 1þ )1( NO1− (K1 þ )1(Cl1  )1, (Na1 þ )1( NO1− 3 )1 and (K 3 )1. As an example, the total Gibbs energy of the chloride phase is expressed as:

G = yNa+1 yCl−1 oGNaCl + y K +1 yCl−1 oGKCl + RT (yNa+1 ln yNa+1 + y K +1 ln y K +1 ) + Gex

(3)

The excess Gibbs energy owing to interaction between Na and K on the first sublattice, with Cl or NO3 on the second is given by the following expression:

D. Sergeev et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 51 (2015) 111–124

117

Fig. 7. X-ray diffraction patterns of various compositions in the NaCl–KNO3 system after DTA measurement. n

Gex = yNa1 + ⋅y K1 +

(v ) ∑ LNa 1 +, K1 +(yNa1 +

v=0

− y K1 + )v

(4)

where yi is the site fraction of the site constituent i on the first sublattice, and L i(,vj ) is a function of temperature. In the present assessment, the L i(,vj ) terms have been used in the usual reduced form as Eq. (2) and υ takes on the values of 0, 1 and 2. The assessment on each binary system was performed using all available experimental information on the phase diagram as well as mixing properties. The following parameters have been optimised: G0 of the binary solid solution species and of the compound K2ClNO3, the interaction parameters L i(,vj ) between binary species in the liquid and solid solutions. The introduction of non-ideal interactions

between the solid solution components in the framework of the multi-sublattice model was required, in order to obtain correct representations of the solubility regions. Under these conditions acceptable descriptions of the solid solutions could be obtained. The optimisation of the chosen solution parameters based on the available experimental data was performed using the optimiser module OptiSage included in the FactSage [28] software.

5. Results of optimisation The available experimental data on the binary and reciprocal systems from literature and from the present work have been

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Table 4 Experimental and calculated relative content of phases in the NaCl–KNO3 and KCl–NaNO3 systems at 25 °C. Mixture (mol%)

Phases (mol%) NaCl Exp

20KCl–80NaNO3 40KCl–60NaNO3 60KCl–40NaNO3 80KCl–20NaNO3 20NaCl–80KNO3 40NaCl–60KNO3 60NaCl–40KNO3 80NaCl–20KNO3 a

a

12 30 36 22 11 29 40 71

KCl Calc

Exp

20 40 40 20 19 39 60 80

– – 18 53 4 2 2 2

KNO3

NaNO3 a

a

Calc

Exp

Calc

Expa

Calc

– – 20 60 0.8 0.6 0.4 0.1

68 26 – – 8 2 4 –

60 19 – – – – – –

20 44 46 25 77 67 54 27

20 41 40 20 80 60 40 20

The relative standard uncertainty (ur) is 20%.

critically evaluated to obtain optimised parameters of all solution phases. The resulting complete Gibbs energy dataset is presented in Tables 5 and 6. ° and Cp) for the condensed ° , S298 All thermodynamic data ( H298 pure salts is given in Table 5 along with the corresponding references. The melting temperatures of sodium and potassium chlor° ides are taken from the present DTA results (Table 1), while H298 ° and S298 values and the solid-liquid transition enthalpies are

from the Barin compilation [29]. The heat capacity expressions of pure chlorides over the temperature range 298.15–2500 K have been taken from [29,30] and from the SGTE Pure substances database (SGPS). The structure of NaNO3 and KNO3 are reviewed in detail in Refs. [31–33]. The compound NaNO3 crystallizes at room temperature in the trigonal R 3̅ c space group. This phase NaNO3(s1) has a calcite ordered structure. On heating, the crystal undergoes a second order λ-like transition near to 273 °C into a structure of average trigonal R 3̅ m space group. The λ-transition is accompanied by orientation disordering of the nitrated groups and it is reversible [32,34]. The high-temperature modification is characterised by disordered calcite structure, it melts at 303 °C according the present measurements. Potassium nitrate KNO3 has three stable modifications under atmospheric pressure. At room temperature it has the orthorhombic Pmnc space group. This phase, referred to KNO3(s1), transforms on heating via a first-order phase transition [34] to the rhombohedral R 3̅ m space group (KNO3(s2)) also with disordered calcite structure. On cooling KNO3(s2) does not re-transfer into the stable KNO3(s1) phase, but, instead, into the metastable ferroelectric phase belonging to the rhombohedreal space R3m group. The latter phase is not considered in the present work. From Raman investigations [35] it was suggested that the high temperature modifications of NaNO3 and KNO3 do not have the

Table 5 Thermodynamic properties of pure compounds. Compound

° (J/mol) H298.15

S° (J/mol K)

Ref.

T (K)

Cp (J/mol K)

Cp Ref.

NaCl(s)

 411120

72.132

[29]

298–900 900–1076 1076–2500

56.304 0.0130328  T  342570/(T2)þ 2.1875  10  5  T2 59.853  0.0194622  T  688110/(T2) þ2.51622  10  5  T2 68.45

SGPS SGPS [30]

98.355

[29]

298–900 900–1076 1076–2500

56.304 0.0130328  T  342570/(T2)þ 2.1875  10  5  T2 59.853  0.0194622  T  688110/(T2) þ2.51622  10  5  T2 68.45

SGPS SGPS [30]

82.555

[29]

298–700 700–1044 1044–2000

50.47661þ 0.005924377  T  144173.9/(T2) þ 7.496682  10  6  T2 143.5698  0.1680399  T  8217836/(T2) þ 9.965702  10  5  T2 73.59656

SGPS SGPS SGPS

107.7311

SGPS

298–700 700–1044 1044–2000

50.47661þ 0.005924377  T  144173.9/(T2) þ 7.496682  10  6  T2 143.5698  0.1680399  T  8217836/(T2) þ 9.965702  10  5  T2 73.59656

SGPS SGPS SGPS

116.315

[29]

298–546 546–576 576–3000

22.62 þ0.222  T 139.00 138.20

[37] [37] [37]

298–546 546–576 576–3000

22.62 þ0.222  T 139.00 138.20

[37] [37] [37]

298–546 546–576 576–3000

22.62 þ0.222  T 139.00 138.20

[37] [37] [37]

298–407 407–608 608–3000

37.49þ 0.191  T 255  0.569  T þ 0.00063  T2 142.7

[37] [37] [37]

298–407 407–608 608–3000

37.49þ 0.191  T 255  0.569  T þ 0.00063  T2 142.7

[37] [37] [37]

298–407 407–608 608–3000

37.49þ 0.191  T 255  0.569  T þ 0.00063  T2 142.7

[37] [37] [37]

298–634 634–1473

87.9666 þ 0.1969  T  144173.9/(T2)þ 7.496682  10  6  T2 216.3

Present work Present work

ΔHtr ¼ 28158 J/mol K at 1076 K NaCl(l)  382962

KCl(s)

 436684.1

ΔHtr ¼ 26283.9 J/mol K at 1044 K KCl(l)  410400.2

NaNO3 (s1)

 467980

ΔHtr ¼ 3620 J/mol K [37] at 546 K NaNO3 (s2)  464360

122.9432

ΔHm ¼ 14980 J/mol K [37] at 576 K NaNO3 (l)  449380 148.9434

KNO3 (s1)

 494628

ΔHtr ¼ 5050 J/mol K [37] at 407 K KNO3 (s2)  489578

133.091

[29]

145.4943

ΔHtr ¼ 10015 J/mol K [37] at 608 K KNO3 (l)  479563 161.9623

K2ClNO3(s)

 920194.68

239.6

Present work

D. Sergeev et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 51 (2015) 111–124

119

Table 6 Thermodynamic data of the liquid and solid solutions. Phase

Species 1

Species 2

Interaction parameter (Lij)

Liquid salt

NaCl(l) NaNO3(l) KCl(l) NaCl(l) NaCl(l) KCl(l) NaCl(s)

KCl(l) KNO3(l) KNO3(l) NaNO3(l) KNO3(l) NaNO3(l) KCl(s) KNO3(s2)

L(0) ¼  2186; L(1) ¼ 136 L(0) ¼  1849.316 1.648  T; L(1) ¼142.237  0.319  T L(0) ¼868 1.7  T; L(1) ¼ 0 L(0) ¼1674  2.4  T; L(1) ¼ 0 L(0) ¼  6500; L(1) ¼  1000 L(0) ¼  8200; L(1) ¼  6000 L(0) ¼15975.6 þ33.08  T  5.593  T  ln(T); L(1) ¼  1650.4 L(0) ¼13046.62  15.62  T; L(1) ¼  3366.86 þ 5.38  T

KNO3(s1) 0G(KNO3)

L(0) ¼0; L(1) ¼0

(Na,K)Cl (Na1 þ , K1 þ )(Cl1  )

NaNO3(s2) (Na,K)NO3-HT (Na1 þ , K1 þ )( NO1− 3 ) (Na,K)NO3-LT (Na1 þ , K1 þ )( NO1− 3 )

NaNO3(s1) 0G NaNO ¼ 0GNaNO3 (s1)

(K,Na)NO3-LT (Na1 þ , K1 þ )( NO1− 3 )

NaNO3(s1) 0G NaNO ¼ 0GNaNO3 (s1) þ 8464.39 KNO3(s1) 0GKNO3 ¼ 0GKNO3 (s1)

3

¼ 0GKNO3 (s1) þ 13000 L(0) ¼0; L(1) ¼0

3

Fig. 8. (a) Calculated enthalpy of mixing of the liquid phase NaCl–KCl at 810 °C (line). Experimental data from Hersh, Kleppa [1965] – [46]. (b) Calculated enthalpy of mixing of the solid solution (Na,K)Cl at 25 and 500 °C (lines). Proposed by Pelton [1985] – [14] at 500 °C. Experimental data from Barret [1954] – [47] and Lister [1958] – [48]. (c) Calculated phase diagram of the system NaCl–KCl (lines). Experimental data from Akopov [1954] – [43], Bergman [1955] – [44], Bergman [1956] – [45], Coleman [1967] – [11], Pelton [1985] – [14], Vesnin [1979] – [42], Sergeev [2015] – [15].

same structure although both crystallise in the same space group. However, the corresponding thermal measurement data [4,36] indicates complete mutual solubility between the high temperature nitrates under consideration. This point will be discussed in detail below. ° ° values for the room As mentioned above, the H298.15 and S298 temperature modification of the nitrates are taken from the Barin compilation [29]. The melting and transition temperatures are taken from the present DTA-measurements, while the heats of

transitions as well as the expressions for heat capacity are taken from the DSC-measurements of Jriri et al. [37]. The order-disorder transition s1-s2 of sodium nitrate is a second order transition [38–40] with the distinct peak on the Cp curve [37]. On the other hand, the transition heat was determined in [37] by integration of the peak of Cp near the transition temperature. Using their DSC-data, Jriri et al. [37] derived thermodynamic values of two sodium nitrate modifications by assumption that it is a first order transformation. In the present work this

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Fig. 9. (a) Calculated phase diagram of the system NaNO3–KNO3 (lines). Experimental data from Bergman [1952] – [9], Kofler [1955] – [5], Klement [1974] – [39], Kramer [1980] – [6], Greis [1985] – [4], Zamali [1994] – [36], Zhang [2003] – [8], Ping [2009] – [32], Benes [2010] – [50]. (b) Calculated enthalpy of mixing of the solid solution (Na,K)NO3_HT at 201 °C. Experimental data from Zamali [1994] – [54]. (c) Calculated enthalpy of mixing of the liquid phase NaNO3–KNO3 at 346 °C and 448 °C. Experimental data from Kleppa [1960] – [52] and [1961] – [53]. (d) Calculated partial enthalpy of mixing of liquid NaNO3 in liquid salt at T ¼450 °C. Experimental data from Aghai-Khafri [1974] – [56]. (e) Calculated partial enthalpy of mixing of liquid KNO3 in liquid salt at T ¼ 450 °C. Experimental data from Aghai-Khafri [1974] – [56]. (f) Calculated heat content (HT  H298.15) of a (0.5 mol NaNO3 þ 0.5 mol KNO3) mixture. Experimental data from Kamimoto [1981] – [55].

transition is also assumed to be first order transition. According to Robelin et al. [22] this assumption does not have influence on the liquidus behaviour, which is the primary subject in the present study. Moreover, the introduction of the second-order transition would unnecessarily increase the complexity of the thermodynamic assessment. The Gibbs energy of the compound KCl  KNO3 was generated using Neumann–Kopp’s rule based on KCl(s) and KNO3(s1) with

° ° in order to reproduce subsequent optimisation of H298.15 and S298 the corresponding phase relations. The Gibbs energy data of the liquid and solid solution components along with the optimised interaction term in the framework of the chosen model for each phase are listed in Table 6. The corresponding Gibbs energy functions of the solution species are given as well in case of their difference from those of pure substances. The results of the assessments concerning the sub-binary

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and complete reciprocal salt system are shown in Figs. 8–13. 5.1. The system NaCl–KCl The phase diagram had been investigated by thermal analysis, differential thermal analysis, cooling-curve technique and X-ray diffraction. A detailed review of available experimental information has been given in [23] and in previous assessments [14,41]. In the present assessment the selected data on the liquidus and solidus data [11,14,42–45] along with our DTA-measurements of the solid–solid immiscibility gap [15]. are used for the optimisation of the thermodynamic parameters for the liquid and the solid phases. The enthalpy of mixing of the liquid has been measured at 810 °C by direct calorimetry and given in form of equation ΔHmix = xNaCl xKCl ( − 2050 − 272xNaCl )[46], where xNaCl and xKCl are mole fractions. According to [14] the excess entropy for alkali halides are small and it can be assumed that S ex=0. The measured enthalpies of mixing for the liquid phase [46] at 810 °C is expressed (Fig. 8a) in form of Redlich–Kister equation:

ΔHmix (liq) = xNaCl xKCl ( − 2186 + 136·( xKCl − xNaCl ) )

(5)

The solid solution based on sodium and potassium chlorides is considered using the sublattice approach as sub-regular solution according to Pelton et al. [14] who has deduced the equation for the excess Gibbs energy from the measurements of the solid–solid miscibility gap and from the calorimetric measurements at 25 °C [47,48]. In the present work the interaction parameters in the solid solution were optimised in the framework with the sub-regular model in order to reproduce the solid–solid immiscibility gap and the measured mixing enthalpy. The calculated values of ΔHmix are presented in Fig. 8b compared with the experimental data at 25 °C and with that from the prediction by Pelton et al. [14] at 500 °C. The calculated phase diagram of the NaCl–KCl system using the present dataset is shown in Fig. 8c compared with selected experimental points. The minimum of liquidus at 657 °C at 48.8 mol% of NaCl is calculated. The calculated solid–solid miscibility gap lies at 515 °C at 58.7 mol% of NaCl. 5.2. The system NaNO3–KNO3 The system containing potassium and sodium nitrate can be referred to as one of the most studied systems. Many of the experimental investigations are contradictory, and a scattering of data is also observed among the liquidus, solidus and solvus temperatures as reported by Jriri et al. [49]. The phase diagram is presented in two general forms: (1) the solid–liquid equilibrium is assumed to be of the eutectic type [8,50], and (2) the solid–liquid diagram has a loop with the minimum (azeotrope) and with a complete solid solution between high-temperature forms NaNO3 and KNO3 [4,36]. The discrepancy is caused by slow kinetics of the thermal transformations of nitrates. Several thermodynamic assessments are also available in Refs. [8,16,49,50]. In the recent re-optimisation of the nitrate system [22] limited solid solutions based on the high temperatures modifications of NaNO3 and KNO3 have been implemented instead of a continuous solution. The limited solutions have been presented by Xu and Chen [34,51] using Raman studies which supposed that the hightemperature forms NaNO3 and KNO3 are not miscible although they crystallise in the same R 3¯ m space group as determined by XRD. The solid solutions in the intermediate phase appeared to be a mixture of 2 solid solutions based on AlkNO3 (s2) on the scale of a few tens to hundreds of nanometres. However, thermal effects have been observed by using of thermal analysis data by several authors [4,5,9,32,36] as shown in Fig. 9a. The present DTA results at the composition 50 mol% of NaNO3 (Fig. 9a) are referred to the

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eutectoid equilibria at 116 °C, phase transformation at 170 °C, and azeotrope at 221 °C, correspondingly. The peak at 170 °C along with data of the solid–solid transformation [4,9,36] cannot be reproduced by the dataset proposed by Robelin et al. [22]. Accordingly, in the present work this system is considered as exhibiting a continuous solid solution (Fig. 9a), which appears to fit better to the reported experimental observations from thermal analysis. Along with the phase diagram data the thermodynamic information concerning the liquid and solid phases from literature are used for the modelling of the nitrate system. The enthalpy of mixing in the liquid has been measured at 346 and 448 °C by calorimetry [52,53]. The mixing enthalpy data determined by Zamali et al. [54] have been applied for the high-temperature nitrate solid solution. Moreover, heat contents data (HT–H298) from the calorimetric measurements [55] for 50:50 mixture between T ¼300 K and T ¼717 K is available. The partial enthalpy of mixing of liquid NaNO3 in the liquid solution with 1.5% rx(NaNO3)r2.1% and also the partial enthalpy of mixing of liquid KNO3 in the liquid solution with 97%rx(NaNO3)r 99% have been measured at 450 °C by Aghai-Khafri et al. [56]. The interaction parameters of the liquid and solid phases were assessed in order to reproduce all these data. The Gibbs energies of the various solutions are given in Table 6. The calculated phase diagram of the system NaNO3–KNO3 is given in Fig. 9a along with the selected experimental data [4– 6,8,9,32,36,39,50]. In the present work, three nitrate solid solutions are introduced using the sublattice approach. The high temperature polymorphs of nitrate form a complete solubility region; the azeotrope is calculated at 221 °C. The low temperature modifications of nitrates do not have the same crystal structure, therefore two corresponding solid solutions, based on the NaNO3(s1) and KNO3(s1), respectively, are introduced. The eutectoid was calculated to be at x(NaNO3)¼ 17.5 mol% at 113 °C. The calculated mixing enthalpy of the solid solution between the high temperature modifications of nitrates (referred to (Na,K)NO3-HT) at 201 °C is shown in Fig. 9b. The minimum of the calculated mixing enthalpy of the liquid for 346 °C and 448 °C is at x(NaNO3) ¼52% and equals  463.1 J/mol K (Fig. 9c). The following figures present the calculated partial enthalpies of mixing of liquid NaNO3 (Fig. 9d). and liquid KNO3 (Fig. 9e). in the liquid salt at 450 °C and the values (HT–H298) for a composition of x(NaNO3) ¼0.5 (Fig. 9f) along with measurements. The present optimised dataset is believed to represent the best possible taking into account all available thermochemical data including the mixing properties of liquid and solid solutions. 5.3. The system NaCl–NaNO3 The system NaNO3–NaCl has been considered in the framework of the review on alkali salt systems by Sangster et al. [7]. The phase diagram has been investigated by thermal analysis [17,57], the visual-polythermal method [58], and from cooling curves as well as direct solubility measurements [17]. No solid solubility is indicated in the literature. The enthalpy of mixing of the liquid has been measured by Kleppa and Meschel [59] at 454 °C by solid– liquid mixing experiments and by dilution. The result is presented in the following expression: ΔHmix = 1674*XNaCl *XNaNO3 (J/mol). The phase diagram data and the mixing enthalpy in the liquid salt were used for the generation of the Gibbs energy of liquid phase. The resulting phase diagram is shown in Fig. 10 along with all experimental data. No solid solubility was assumed for both endmembers in the present calculation. The eutectic is calculated at 94.6 mol% of NaNO3 at 293 °C.

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Fig. 10. (a) Calculated phase diagram on the system NaNO3–NaCl. Experimental data from Perman [1922] – [57], Luzhnaja [1935] – [58], Nyankovskaya [1952] – [21], Ko [1963] – [17]. (b) Calculated enthalpy of mixing of the liquid phase NaNO3–NaCl at 454 °C. Experimental data from Kleppa [1963] – [59].

Fig. 11. (a) Calculated phase diagram of the system KNO3–KCl. Experimental data from Jänecke [1928] – [60], Bergman [1947] – [18], Nyankovskaya [1952] – [21], Ko [1963] – [17], Kefer [1969] – [19], Zhang [1982] – [20]. (b) Calculated enthalpy of mixing of the liquid phase KNO3–KCl at 454 °C. Experimental data from Kleppa [1963] – [59].

Fig. 12. (a) Experimental and calculated data of the diagonal vertical section KCl–NaNO3 of the reciprocal NaCl–KCl–NaNO3–KNO3 system. Scanned data from Nyankovskaya [1952] – [21]. (b) Experimental and calculated data of the diagonal vertical section NaCl–KNO3 of the reciprocal NaCl–KCl–NaNO3–KNO3 system. Scanned data from Nyankovskaya [1952] – [21].

5.4. The system KCl–KNO3 In the system KCl–KNO3 the cooling curves method [17,18,60] as well as thermal analysis [19] have been used in order to define

the liquidus line. Only the data in [19,20] extend over the whole concentration range, all others are confined to the interval 50–100 mol% KNO3. Similar to the previous system with sodium, no solid solubility has been found. The mixing enthalpy of the liquid

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Fig. 13. Proposed (Fig. 13a) by Nyankovskaya [21] and calculated (Fig. 13b) phase diagram of the reciprocal system NaCl–KCl–NaNO3–KNO3.

measured at 454 °C [59] was adopted for the optimisation in form of the following equation: ΔHmix = 868*XKCl *XKNO3 (J/mol). The data of Kefer [19] included the compound KCl  KNO3 with a stability range 258–361 °C. Using the given data the phase diagram (Fig. 11a). and excess enthalpy in the liquid salt (Fig. 11b). are calculated. The eutectic point at 92 mol% of KNO3 at 310 °C was calculated as the best compromise to reproduce the experimental information. The solubility based on KNO3 mentioned in the work [18] was not considered. The peritectic point lies at 85% of KNO3 at 361 °C that agrees with the experimental results.

The complete reciprocal salt system is given in Fig. 13. The work published by Nyankovskaya [21] does not contain the exact experimental points, therefore these data can be used for only rough comparison with our experimental and calculated data. In general, the phase relations are reproduced well including the fields of primary crystallisation and a peritectic point, which is to be found at T ¼276 °C as shown in Fig. 13b.

6. Conclusions 5.5. The reciprocal system (Na1 þ , K1 þ )( Cl1  , NO1− 3 ) By extending our dataset to the complete reciprocal system we are able to calculate the pseudo-binary sections between the different salts and the complete reciprocal system with all isotherms and univariant lines. In order to represent the experimental phase equilibria on the diagonal isopleths (Tables 2 and 3). cross interaction parameters between Alk1NO3 and Alk2Cl were added in the liquid phase (Table 6). On the diagonal sections good agreement between the present experimental data and the calculated results is reached (Fig. 12a, 12b). Moreover, the relative content of the phases were calculated and compared with the XRD measurements (Table 4). The agreement with the experimental data is good taking into account the accuracy of quantitative composition calculations from the XRD data and the fact, that the low temperature nitrate phase was modelled with certain assumption on their stability ranges. The diagram KCl–NaNO3 (Fig. 12a). in the concentration range from 55 to 75 mol% of NaNO3 exhibits a boundary between a twophase field (above, chloride (Na,K)Cl and (Na,K)NO3-HT) and a three-phase field (below, chloride phase (Na,K)Cl; (Na,K)NO3-HT and (Na,K)NO3-LT), which resembles the phase equilibria in the NaNO3–KNO3 system regarding the boundary between the continuous solid solution based on the high temperature modifications of nitrates and the corresponding two-phase region. It should be noted that this behaviour would be difficult represented without the line between this continuous solubility and two-phase region as it is shown in literature [4,9,36] and confirmed by our DTA data (Fig. 9a).

The reciprocal KCl–NaNO3 and NaCl–KNO3 systems have been studied by the use of differential thermal analysis and X-ray diffraction analysis. The phase diagrams of both pseudo-binary sections have been proposed. The relative content of the compounds NaCl, KCl, NaNO3, and KNO3 has been determined by use of XRD. The experimental information obtained has been used for the optimization of the thermodynamic parameters of all available phases. A self-consistent thermodynamic dataset for the salt system NaCl–KCl–NaNO3–KNO3 has been generated to reproduce all available experimental information on the corresponding binary salt sub-systems along with the present measured data on the phase relations of the pseudo-binary sections KCl–NaNO3 and NaCl–KNO3. The liquid salt has been described using the modified associate species model. The nitrate and chloride solid solutions have been treated with a two-sublattice approach. Good agreement between experimental and calculated data regarding the phase equilibria and the thermodynamic properties has been achieved. The new thermodynamic dataset is ready for application in designing salt compositions for thermal energy storage.

Acknowledgements The authors would like to thank the Alexander von Humboldt Foundation for supporting this research. Mr. M. Ziegner (Forschungszentrum Jülich GmbH) is gratefully acknowledged for his assistance in carrying out the XRD analysis.

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Appendix A. Supplementary information Supplementary data associated with this article can be found in the online version at.http://dx.doi.org/10.1016/j.calphad.2015.09. 002.

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