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Thermodynamics of the Ca(NO3)2 – NaNO3 system
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 67 (2019) 101688
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Thermodynamics of the Ca(NO3)2 – NaNO3 system D. Sergeev a, *, B.H. Reis b, I. Dreger a, M. to Baben b, K. Hack b, M. Müller a a b
Forschungszentrum Jülich GmbH, IEK-2, D-52425, Germany GTT-Technologies, Kaiserstraße 103, D-52134, Herzogenrath, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Phase change materials Calcium and sodium nitrates Enthalpy increment
Thermodynamic properties of the quasi binary Ca(NO3)2–NaNO3 system are of interest with respect to thermal energy storage. In the present work the phase diagram as well as thermodynamic properties of the near eutectic mixture 45 mol% Ca(NO3)2 – 55 mol% (NaNO3)2 were determined experimentally and applied in the assessment of a new Gibbs energy dataset for thermochemical calculations. The enthalpy of fusion of the 45 mol% Ca(NO3)2 – 55 mol% (NaNO3)2 mixture is determined to be 24.7 � 0.5 kJ/mol. The melting and crystallization enthalpy have good reproducibility, which makes it possible to use this mixture as a phase change material at temperature 225 � C. The assessed dataset describes liquid phase properties using a subregular solution model in the RedlichKister formalism with high accuracy. Therefore it can be used for the prediction of thermodynamic properties of different compositions in the whole Ca(NO3)2–NaNO3 system and be included in databases for calculation of multicomponent systems including other components.
1. Introduction
2. Experimental
Nitrate salts of Na, K, and Ca are of interest for use as thermal energy storage materials [1–9]. Therefore thermodynamic properties of binary, ternary, and multicomponent systems with these components are important for further improvement of energy storage technology. Thermochemical assessments of several binary systems Ca(NO3)2 MNO3 (M: alkali metal) were carried out by Li et al. [7], but all opti mization parameters were obtained by using non-reliable thermody namic functions of Ca(NO3)2. A detailed discussion of the data problems was given in our previous paper [10]. Comparison of the enthalpy increment obtained by Li et al. [7]. with experimental data of Dancy et al. [11]. shows large deviation (34%) of the enthalpy of fusion of the near eutectic mixture 0.46Ca(NO3)2 – 0.54(NaNO3)2. In the present paper we report extensive new experimental data for the Ca(NO3)2 – NaNO3 sys tem and show an improvement of the dataset of this system by using the new thermodynamic functions of Ca(NO3)2 [10]. Additionally, we show that the extrapolation of the heat capacity of the pure liquid salts below their melting point is crucial for an accurate description of the heat capacity of near-eutectic liquid solutions - which is the most important property of salt mixtures used in sensible heat storage. Together with the new data on the latent heat of fusion, this work is an important step towards a consistent database for nitrate salts mixtures used e.g. in solar thermal storage applications [12].
2.1. Samples Pure Ca(NO3)2 was prepared from Ca(NO3)2⋅4H2O (Sigma-Aldrich, 99.995%), which was dried at 150 � C in a vacuum furnace for 24 h. TG analysis of the prepared sample shows no weight loss at low tempera tures (25 – 400 � C). Above 450 � C decomposition of Ca(NO3)2 was observed. The total weight loss due to this reaction was 66.35% and it is reasonable to assume that the remaining 33.65% of the mass is CaO, which is in a good agreement with the molar fraction of CaO in Ca(NO3)2 (34.18%). For additional information about the XRD analysis and the high temperature behavior of Ca(NO3)2 is given in Ref. [10]. The pure NaNO3 (Sigma-Aldrich, 99.995%) was used for the prepa ration of the mixtures of the Ca(NO3)2-NaNO3 system. All handling of the samples was carried out in a glove box under purified argon. The mixtures were sealed in glass ampoules under vacuum and used for DTA measurements. 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. After the heat treatment the mixtures were prepared in a glove box for use in DSC.
* Corresponding author. E-mail address: [email protected] (D. Sergeev). https://doi.org/10.1016/j.calphad.2019.101688 Received 18 June 2019; Received in revised form 1 October 2019; Accepted 20 October 2019 Available online 29 October 2019 0364-5916/© 2019 Elsevier Ltd. All rights reserved.
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2.2. Instruments
Optimization of the interaction parameters for the liquid solution has been obtained with the subroutines from the ChemApp [18] library coupled with the Nomad optimization algorithm [19,20]. Detailed in formation on the Gibbs energy modelling of the phases as well as the optimization procedures is given in the following sections.
2.2.1. Differential scanning calorimetry (DSC) Two differential scanning calorimeters were used for the determi nation of thermodynamic properties. The main parameters of these de vices are given in Table 1. Before starting the measurements the working volume of the DSC was evacuated and filled with He to obtain a dry atmosphere and to improve the heat transfer conditions. The experiments were carried out with different sample masses (Table 1). The ratio method with sapphire (α-Al2O3, NIST Standard Reference Material SRM720, purity 99.95%, metals basis) [13] as a reference was � applied for the determination of the heat capacity (Cp , J∙mol 1∙K 1) according to the following equation: �
CpðsÞ ¼
mr DSCs ⋅ ms DSCr
DSCb � ⋅C ; DSCb pðrÞ
3.1. Pure compounds The Gibbs energy function (GðTÞ) of pure compounds (i) is, by way of the Gibbs-Helmholtz equation, defined in terms of their enthalpy (HðTÞ) and entropy (SðTÞ), which in turn are functions of the heat capacity (CP ) and the respective absolute entities Δf Ho298ðiÞ and So298 ðiÞ as follows: GðTÞðiÞ ¼ HðTÞðiÞ
(1)
Z HðTÞðiÞ ¼ Δf H o298ðiÞ þ
where m – mass of the substance (g), DSC – signal of thermopile (μV). Baseline and reference measurements were performed for each measured sample separately. For determination of the enthalpy of fusion by slow heating rate (0.5 K/min) thermal analysis (SHRTA) [14] the sensitivity constant of the mHTC 96 was calibrated with the reference material 50% mol NaNO3 – 50% mol KNO3 (Ttr ¼ 223 � C, ΔfusH ¼ 9.46 kJ/mol [15]) under similar conditions, as for the proper samples.
Z SðTÞðiÞ ¼ So298ðiÞ þ
Table 1 Parameters of the differential scanning calorimeters. Company Temperature range Thermocouple Oven Heating rate Atmosphere Crucibles Sample weight
Netzsch � � 25 C–1600 C Type S Pt-Rh 15 K/min He, 10 ml/min Open Pt crucibles with lids 20–50 mg
Setaram � � 25 C–1400 C Type S - HFDSC Graphite 4 K/min He, 5 ml/min Open Pt crucibles with lids 400–500 mg
�
T
CPðiÞ 298
(3)
TdT
(4)
3.1.2. Properties of liquids During the progress of this work, it has become evident that the heat capacities of pure liquids below the melting temperature would have a significant impact on the correlation with the experimental results for the CP of the liquid solution near the eutectic composition, as discussed in section 4.2. It is then important that the heat capacities of supercooled liquids maintain a liquid-like tendency when extrapolated below each salt’s melting temperature. The liquid-like tendency is one that follows the expected behavior from the known range where liquid is stable, without necessarily assuming the value of CPðsolidÞ right below the melting temperature. However, it is also important to consider the limitations of the pure components of the system. Each salt needs to have consistent thermodynamic description of all properties at all tempera tures as well. For this reason, careful consideration has been given to the extrapolation of CPðliquidÞ to low temperatures. The extrapolation of CPðliquidÞ has had a lot of attention since the publication of Kauzmann’s work [24] on the behavior of supercooled liquids and glass transitions. Much of the attention came from the problem exposed as the “entropy paradox”, later also known as “Kauz mann’s paradox”. The problem comes from the realization that if a liquid is supercooled without crystallization, the entropy of the liquid will decrease faster than that of the kinetically inhibited solid due to the liquid’s higher heat capacity. Therefore, below a certain temperature, the liquid phase will achieve an entropy value lower than that of the solid. This is a paradox considering that a solid is significantly higher ordered than a liquid. Kauzmann postulates that his apparent paradox would be solved if one assumes that a liquid-glass transition occurs after a certain degree of supercooling. Indeed, this approach has been considered by Schnurre et al. [25] in a very critical modelling of the
The binary Ca(NO3)2-NaNO3 system is considered due to its impor tance for heat storage applications by using phase change materials, specifically materials that exhibit solid-solid or solid-liquid phase tran sitions. Therefore, the focus of this thermodynamic assessment has been placed on the condensed phases. It should be noted that the decompo sition of Ca(NO3)2 to CaO and NOx cannot be correctly calculated, which the authors plan to study in the future. Thus the system is reduced to three solid stoichiometric compounds, Ca(NO3)2 (S), NaNO3 (S1) and NaNO3 (S2), plus the liquid phase with full miscibility between Ca (NO3)2 and NaNO3 [14–19,22]. In order to model the liquid solution, properties of the liquid end-members are also necessary. The Gibbs energy modelling of the pure compounds and the liquid solution follows the Calphad approach [16] using FactSage 7.2 [17].
mHTC 96
CPðiÞ dT 298
3.1.1. Heat capacity of solids In Table 3, a third degree polynomial with two temperature ranges has been used to reproduce the results obtained for the heat capacity of solid Ca(NO3)2 by the modified segmented regression (SR) model [10], which is not directly available in FactSage. The least squares fit gave a minimum R2 of 0.9999 in all temperature ranges. Above the melting temperature (Tm ), a constant extrapolation is assumed. In the case of NaNO3, the reported heat capacity above 549 K [22] is already constant, so there is no change at the melting temperature of 579 K. The lower temperature of 130 K is necessary to take into account the effects of glass transition below room temperature (see section 3.1.3). However, ex trapolations down to 0 K are not of interest for this work.
3. Thermodynamic modelling
DSC 404C
T
Table 2 and Table 3 summarize the thermodynamic properties of the pure compounds applied in this assessment.
2.2.2. Differential thermal analysis (DTA) DTA measurements were performed using a STA 449C Jupiter (Netzsch) with a silicon carbide oven (0 � C – 1600 � C) and a perpen dicular sample holder (type S thermocouple (Pt/(Pt10Rh))). The tem perature calibration was performed using the phase transition temperatures of In (156.6 � C), Sn (231.9 � C), Bi (271.4 � C), Zn (419.5 � C), Al (660.3 � C) and Ag (961.8 � C). The resulting accuracy of transition temperature measurements is �3 � C. The experiments were carried out with a scan rate of 5 K/min and 3 cycles of heating and cooling. The results showed good reproducibility from the second cycle onwards.
Instrument
(2)
T⋅SðTÞðiÞ
2
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Table 2 Thermodynamic properties of pure compounds. ΔHo298 (J/mol)
Compound NaNO3 (S1) NaNO3 (S2) NaNO3 (L) Ca(NO3)2 (S) Ca(NO3)2 (L)
467980 464360 454778 936798 929600
Ref.
So298 (J/mol K)
Ref.
Ttransition (K)
ΔHtransition (J/mol)
Ref.
[21] [21] ** SGPS **
116.315 122.943 134.08 190.5 190.5
[21] [21] ** [10] **
549(S1→S2) 579(S2→L)
3620 14980
[22] [22]
823.15(S→L)
33400
[10]
** This work.
model [28], which has proven applicability for complex oxide and salt liquids [29]. In the current binary system, the pure liquid salts constitute the solution components without any additional associate. The practice adopted by Ref. [28] is maintained here, where the stoichiometry of the end-members is chosen in order to obtain two non-oxygen atoms per formula unit, allowing equal weighting with regard to each species ideal entropic contribution. As a result, NaNO3 remains unchanged and Ca (NO3)2 becomes (Ca(NO3)2):1.5, meaning that each atom stoichiometry is divided by 1.5. Interaction parameters between the species are introduced for description of the non-ideal mixing properties of the so lution. The molar Gibbs energy is then defined as the sum of the refer ence, the ideal and the excess contributions as:
Table 3 Heat capacities of pure compounds. Compound
T Interval (K)
CP (J/mol K)
Ref.
NaNO3 (S1)
130–549 549–3000 130–549 549–3000 130–226 226(Tg)–3000 130–298.15
22.62 þ 0.222 T 139.00 22.62 þ 0.222 T 139.00 22.62 þ 0.222 T 138.20 3.75341 þ 1.17463 T – 3.46450⋅10 3⋅T2 þ4.01602⋅10 6⋅T3 93.5551 þ 0.198423 T – 9.56265⋅10 5⋅T2 þ2.95246⋅10 8⋅T3 208.561 3.75341 þ 1.17463 T – 3.46450⋅10 3⋅T2 þ4.01602⋅10 6⋅T3 93.5551 þ 0.198423 T – 9.56265⋅10 5⋅T2 þ2.95246⋅10 8⋅T3 246
[22] [22] [22] [22]
NaNO3 (S2) NaNO3 (L) Ca(NO3)2 (S)
298.15–823.15
Ca(NO3)2 (L)
823.15(Tm)–3000 130–298.15 298.15–426.65 426.65(TK)-3000
a b
a
[22] [10] b
[10] b
Gm ¼
X X X X X ðvÞ xi Goi þ RT xi lnxi þ xi xj Lij xi i
a a
xj
�v
(5)
v¼0;1
where xi is the molar fraction of species i, Goi is the molar Gibbs energy of
the pure liquid components, and Lij , with v ¼ 0; 1, represents the ðvÞ
a
interaction parameters between species i and j, as defined by the
Redlich-Kister polynomial. Lij is temperature dependent, according to: ðvÞ
[10]
ðvÞ
This work. Adapted from source.
Lij ¼ A þ B⋅T
(6)
Because no intermediate associate species is introduced in this particular binary system and because the interaction parameters are only two, L0ij and L1ij , the modified associate species model is simplified and assumes the same formalism as a subregular substitutional solution model [16]. The coefficients A and B are optimized considering experimental data for phase equilibria (this work and [30–35]), mixing enthalpies between liquid NaNO3 and solid Ca(NO3)2 at 623 K [36], as well as the enthalpy of fusion of the 0.45Ca(NO3)2-0.55(NaNO3)2 mixture (this work). The results are shown in Table 4.
glass-liquid phase for SiO2. Their work relies on enough experimental information to describe with good accuracy the heat capacity of the liquid-glass phase. As a result, the heat capacity of the glass phase shows a remarkable correlation with the heat capacity of cristobalite, the solid structure of silica stable at the glass-transition temperature (Tg). The present work also assumes a liquid-glass transition for the description of the heat capacity of pure liquids. BelowTg , the solid heat capacity is used as an approximated value for the glass regime. In the case of NaNO3, Tg is taken from Ref. [26]. Tg of liquid Ca(NO3)2, on the other hand, is unknown. Therefore, an estimation is made from the temperature at which the liquid and the solid entropies become the same if the liquid CP is extrapolated as constant below the melting point. This can be called the Kauzmann temperature (TK ) [27] or the “ideal glass transition temperature” (T0 ) [26]. This work will use the first termi m nology, i.e. (TK ). The constant extrapolation of CP TðliquidÞ below the
4. Results and discussion 4.1. Phase equilibria of the Ca(NO3)2-NaNO3 system The phase diagram of the Ca(NO3)2-NaNO3 system has been studied experimentally many times [30–35], but in most of these works only the liquidus line was considered. We repeated these measurements ac cording to our methodology described in section 2.2.2. The main advantage of this methodology is the usage of closed glass ampoules, which allows to avoid the decomposition reaction of Ca(NO3)2 and the influence of moisture on the samples. The results are shown in Fig. 2 and in Table 5. The measurements suggest that the eutectic point lies at a compo sition near 55 mol% (NaNO3)2 and at 225 � C (498 K). The calculation with the thermodynamic dataset results in the same temperature and a slightly smaller concentration of 54.3% (NaNO3)2 for the eutectic. Noticeably, the eutectic temperature 211 � C (484 K) reported by Lay bourn [34] is far too low in comparison with the other experimental data and, even though it was considered during the optimization of the liquid excess parameters, the need to comply with the liquidus data at the same time has obviously set the limit for the final eutectic temperature. The
melting point is used since direct CP measurements of the supercooled liquid state of the pure salts are not available. As shown in section 4.3 this assumption is corroborated by measurements of the liquid CP of the eutectic mixture. Tables 2 and 3 present the resulting properties of the pure liquids with these considerations, while Fig. 1 shows the final shape of the heat capacity curves for NaNO3 and Ca(NO3)2. With these considerations, the liquid properties of pure compounds are thermodynamically self-consistent, comply with the available liter ature and provide more reliable data for the liquid solution model, which is crucial for an accurate description of the liquid salt at the eutectic temperature. 3.2. Liquid solution and optimization of parameters The liquid solution is modelled with the modified associate species 3
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Fig. 1. Heat capacity of solid and liquid-glass states for NaNO3 (a) and Ca(NO3)2 (b). Data according to Table 3.
solid-solid transition of NaNO3 was measured at 278 � C (551 K) for the mixtures at 90 mol% (NaNO3)2 and 95 mol% (NaNO3)2, which compares very well with the temperature of 276 � C (549 K) accepted for the pure compound, see Table 2, as reported by Jriri [22]. The liquidus line and eutectic composition are overall also in good agreement with the pre vious studies [30–35].
Table 4
Coefficients of the liquid solution interaction parameters Lij . ðvÞ
v
Species i
Species j
A
B
0 1
NaNO3 NaNO3
(Ca(NO3)2):1.5 (Ca(NO3)2):1.5
3943.78 59.98
2.792 3.391
4.2. Thermodynamic properties of the eutectic mixture To provide better evidence for the assessment of the Ca(NO3)2NaNO3 system, the assumed eutectic 45 mol% Ca(NO3)2 – 55 mol% (NaNO3)2 mixture was chosen for further experimental determination of heat capacity and fusion enthalpy. The heat capacity of the eutectic 45Ca(NO3)2 – 55(NaNO3)21 mixture was measured in the temperature range from 50 � C to 450 � C. Two DSC
Fig. 2. Phase diagram of the Ca(NO3)2-NaNO3 system. Table 5 Experimental values of phase transition temperatures (K) in the Ca(NO3)2(NaNO3)2 system. 2(NaNO3), mol%
Liquidus line
0 20 30 40 45 50 55 60 70 80 90 95 100
823 733 656 600 571 507 538 557 564 571 579
Eutectic line 495 497 499 498 498 499 498 498 498 497 494
Solid transition
Fig. 3. Experimental values of heat capacity for solid and liquid phases of the 45Ca(NO3)2 – 55(NaNO3)2 mixture measured by two DSC devices, linear approximation of experimental data, calculated values in this work and calcu lated results from Li et al. [7].
551 551 550
1 For all calculations was used molar mass M ¼ 167.27 g/mol of the 45Ca (NO3)2 – 55(NaNO3)2 mixture.
4
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devices (described in section 2.2.1) were used. Four samples were measured with DSC 404C (15 K/min) and two samples with mHTC 96 (4 K/min). The values obtained are shown in Fig. 3. It can be seen that different heating rates have an influence on the width of the phase transition range, but the heat capacity of the solid and liquid phases are reproducible and show good agreement with each other. The deviations of experimental data are not higher than 5%, which is good agreement for two different devices. The coefficients obtained from the heat ca pacity, as measured, are given in Table 6. Comparing the measured heat capacity with the thermodynamic evaluation by Li et al. [7] (Fig. 3), differences in the order of 17 J/(K∙mol) (7%) can be observed for the liquid region, i.e. above 310 � C (583 K). This is due to their modelling approach, which assumes that heat capacities of pure liquid end-members are equal to the heat capacities of the respective solid salts below their melting point [7]. Respecting the new experimental results reported here, we model the liquid end-members with constant heat capacities below the melting temperature down to the glass transition or Kauzmann temperature. The consistency of this modelling is explained in section 3.1.2. As a result, the calculation from our dataset has an excellent agreement with the measured CP also for the liquid region above 310 � C (583K), with a maximum difference of 4 J/(K∙mol) (1%). Integration of the peak area of the phase transition range gives the value of the enthalpy of fusion. It is 21.7 kJ/mol from DSC 404C (15 K/ min) and 24.9 kJ/mol from mHTC 96 (4 K/min). This discrepancy can be due to the construction of the sample holder of the DSC 404C, which contains only two thermocouples and does not allow to measure the phase transition enthalpy accurately. Therefore the value measured by mHTC 96, which has a Calvet-type thermocouple, is more reliable. To prove this value a slow heat rate thermal analysis (SHRTA) [14] was used. Two samples were studied in the temperature range from 190 � C to 250 � C with heating and cooling rate 0.5 K/min (3 cycles for each sample). An example of the DSC-curves is shown on Fig. 4. It shows that the heating curves are reproducible with the melting point at 225 � C (498 K). The cooling curves were not reproducible due to kinetic effects during crystallization (Fig. 4). The results of these measurements are summarized in Table 7. The fusion enthalpy determined as 24.7 kJ/mol is in good agreement with the value obtained from the heat capacity measurements (24.9 kJ/ mol using mHTC 96, 4 K/min), which confirms a good agreement be tween the sensitivity constant determined based on the enthalpy of fusion of the 50NaNO3–50KNO3 mixture and on the heat capacity of sapphire. The fusion enthalpy obtained by Dancy et al. [11] with drop calorimetry is lower (Table 7). Fig. 5 shows the comparison of the � � enthalpy increment (H T – H 298.15) calculated based on the heat ca pacity from this work and experimental values of Dancy et al. [11]. It can be seen, that Dancy’s values for the solid phase (up to 225 � C) are higher � � than in this work (the difference at 225 � C is 3.49 kJ/mol). H T – H 298.15 of the liquid phase is in a good agreement with our results taking into account the statistical deviation of Dancy’s values. Therefore, the dif ference of the enthalpy of fusion can be due to the deviation of Dancy’s values of the enthalpy increment in the solid phase. The calculated values of the enthalpy increment based on our dataset are shown in Fig. 5 in comparison with our experimental results. The agreement is very good at all temperatures. In comparison with the
Fig. 4. Heating and cooling curves of the slow heating rate (0.5 K/min) thermal analysis with HFDSC sample holder (Setaram) for 45Ca(NO3)2 – 55 (NaNO3)2 mixture.
literature, our experiments exhibit a lower scatter. For the liquid region the calculated data by Li et al. [7] are higher, since their assessment only took the scattered data from Dancy et al. [11] into account. The co efficients obtained from the enthalpy increments are given in Table 8. 4.3. Heat of solution in the Ca(NO3)2-NaNO3 system Kleppa and Hersh [36] measured the heat of solution (ΔHS;L solution ) obtained from solid Ca(NO3)2 and liquid NaNO3 mixtures at 350 � C (623 K) with a micro-calorimeter. Our calculated data is compared with
their results in Fig. 6. The calculated results reproduce well ΔHS;L solution reported in Ref. [36], with an average deviation of only 0.26 kJ/mol. As in the original article, one can also extrapolate the enthalpy of fusion of the metastable solid Ca(NO3)2 at 350 � C, from the final point of the line at 1 molar fraction of Ca(NO3)2 in Fig. 6. Here, the extrapolation gives exactly the same result as the one obtained by Kleppa and Hersh [36], i. e. 23.8 kJ/mol. As discussed in Ref. [10], however, it is unreasonable to assume this value as the real enthalpy of fusion of Ca(NO3)2 because its melting temperature lies around 200 � C above the temperature used in the experiment (350 � C), which was not considered by Li et al. [7]. Wang et al. [23] optimized the Gibbs energy of fusion (Δfus G) as a function of temperature for Ca(NO3)2. As a consequence, one obtains a corresponding optimized fusion enthalpy as a function of temperature. The value at 350 � C has been plotted in Fig. 6 (red circle) and it is much lower (more than 9 kJ/mol) than the one calculated by this work (solid line) at 1 molar fraction of Ca(NO3)2. This demonstrates that the prop erties of Ca(NO3)2 considered in the present work result in a different heat of fusion than the one optimized by Wang et al.. Although Wang et al. use a valid approach for the optimization of Δfus GðTÞ with a second-degree polynomial, this is done together with the optimization of another three parameters for the excess properties of the Ca(NO3)2-N aNO3 system and the data used for the minimization only includes phase equilibria. For this reason, the degrees of freedom for the fitting of the parameters by Wang et al. are too many and their final Δfus GðTÞ is thus not reliable. Since the present work critically reassesses the properties of solid and liquid Ca(NO3)2 individually, the calculated fusion enthalpy and Δfus GðTÞ of Ca(NO3)2 is independent of other parameters and is therefore more reliable. Had the present work not assumed reasonable standard properties
Table 6 � Coefficients of the linear equation of heat capacity (J∙mol 1∙K 1) C p ¼ A þ B∙T � a and standard uncertainty (�ΔC p) for the 45Ca(NO3)2 – 55(NaNO3)2 mixture taken from DSC measurements. Temperature range/K 298 – 498 498 – 750
A 57.609 260
�ΔC p,1 J∙mol
B 3.315∙10 –
�
1
1
K
1
5 5
Note. a Calculated according to the t-statistic with 95% confidence interval 5
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Table 7 Enthalpy of fusion of 45Ca(NO3)2 – 55(NaNO3)2 obtained with the slow heating rate (0.5 K/min) thermal analysis, calculated and literature data. Cycles 1st heating 2nd heating 3rd heating 1st cooling 2nd cooling 3rd cooling
Sample I (449.7 mg)
Sample II (452.4 mg)
24.3 23.9 24.6 24.3 24.5 23.9
Average a
25.3 25.1 25.3 24.5 25.2 25.2
24.7 � 0.5
Calculated in this work
Ref. [11]
25.3
21.9b
Note. a Standard uncertainty. b for 46Ca(NO3)2-54(NaNO3)2 mixture.
Fig. 6. Heat of solution between solid Ca(NO3)2 and liquid NaNO3 at 350 � C (623 K) calculated by this work (solid line) in comparison with the experi mental (triangle) and extrapolated (square) data from Kleppa and Hersh [36], and calculated data (circle) from Wang et al., 2015.
Fig. 5. Enthalpy increment of the 45Ca(NO3)2 – 55(NaNO3)2 mixture obtained from DSC and SHRTA results in comparison with literature data: Li_2017 - [7]; Dancy_1980 - [11].
capacities and the enthalpy of fusion allow calculation of the enthalpy increment. The new experimental data enables significant improvement of the thermodynamic assessment of the binary Ca(NO3)2-NaNO3 system. Indeed, a new thermodynamic dataset is successfully derived including the new experimental data and following the Calphad method. All calculated results agree well with the measurements, considering only two interaction parameters in the subregular liquid solution model. Such an important achievement is a consequence of the critical assumptions made for pure compounds as well. As a result, thermodynamic model ling of all the phases in the binary Ca(NO3)2-NaNO3 system is available in a fully self-consistent dataset, which can be used for prediction of thermodynamic properties within its entire composition and tempera ture range. The resulting dataset also serves as a well founded base for extension into multicomponent systems. The melting temperature of the inferred eutectic mixture 45%Ca (NO3)2 – 55%(NaNO3)2 is close to the “solar salt” 50NaNO3-50KNO3 (Tm ¼ 223 � C, ΔtrH496 ¼ 101.7 J/g [15], CPliq ¼ 1.49 J/(K∙g) [37]), but the enthalpy of fusion is considerably higher (ΔtrH498 ¼ 147.7 J/g). In the liquid state, the eutectic mixture provides a specific heat of 1.44 J/(K∙g). This mixture can be interesting for application from the economic point of view. It can be considered as potential phase change material as well as a sensible heat storage material.
Table 8 � � Coefficients of equation H T – H 298.15 ¼ A þ B∙T þ C∙T2 (kJ∙mol 1) for the enthalpy increment of the 45Ca(NO3)2 – 55(NaNO3)2 mixture determined from DSC and SHRTA results. Temperature range/K 298 – 498 498 – 750
A
B 27.028 65.545
3.035∙10 0.26
C 2
2.04∙10 –
4
for pure Ca(NO3)2, see Tables 2 and 3, it would not be possible to reproduce Kleppa and Hersh’s experimental data together with all thermodynamic properties of the Ca(NO3)2-NaNO3 system reported above. 5. Conclusions Eleven mixtures of the Ca(NO3)2–NaNO3 system were studied in closed glass containers by DTA for the determination of phase transition temperatures. The results obtained confirm previous values [30,33–35] about the eutectic composition near 45%Ca(NO3)2 – 55%(NaNO3)2 and the eutectic temperature at 225 � C (498 K). This eutectic mixture was studied by DSC. The heat capacity of the solid and liquid phases was determined with good agreement by using two different DSC devices, which confirms the reliability of our experimental approach. The enthalpy of fusion of this mixture was measured with the slow heating rate (0.5 K/min) thermal analysis. The combination of the heat
Data availability The raw and processed data required to reproduce these findings are available to download from [supplementary material].
6
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Acknowledgements
[15] M. Kamimoto, Thermodynamic properties of 50 mole% NaNO3 50% KNO3 (HTS2), Thermochim. Acta 49 (1981) 319–331. [16] H. Lukas, S.G. Fries, B. Sundman, Computational Thermodynamics: the Calphad Method, Cambridge university press, 2007. [17] C.W. Bale, E. B� elisle, P. Chartrand, S.A. Decterov, G. Eriksson, A.E. Gheribi, K. Hack, I.H. Jung, Y.B. Kang, J. Melançon, A.D. Pelton, S. Petersen, C. Robelin, J. Sangster, P. Spencer, M.A. Van Ende, FactSage thermochemical software and databases, Calphad 54 (2016) 35–53, 2010–2016. [18] S. Petersen, K. Hack, The thermochemistry library ChemApp and its applications, Int. J. Mater. Res. 98 (2007) 935–945. [19] S. Le Digabel, Algorithm 909: NOMAD: nonlinear optimization with the MADS algorithm, ACM Trans. Math Software 37 (2011) 1–15. [20] C. Audet, S. Le Digabel, C. Tribes, V. Rochon Montplaisir, The NOMAD Project, 2019. https://www.gerad.ca/nomad. [21] I. Barin, Thermochemical Data of Pure Substances, III Ed., VCH, Verlagsgesellschaft mbH. D-69451 Weinheim (Federal Republic of Germany), 1995. [22] T. Jriri, J. Rogez, C. Bergman, J.C. Mathieu, Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions, Thermochim. Acta 266 (1995) 147–161. [23] J. Wang, M. Lai, H. Han, Z. Ding, S. Liu, D. Zeng, Thermodynamic modeling and experimental verification of eutectic point in the LiNO3–KNO3–Ca(NO3)2 ternary system, J. Therm. Anal. Calorim. 119 (2015) 1259–1266. [24] W. Kauzmann, The nature of the glassy state and the behavior of liquids at low temperatures, Chem. Rev. 43 (1948) 219–256. [25] S.M. Schnurre, J. Gr€ obner, R. Schmid-Fetzer, Thermodynamics and phase stability in the Si–O system, J. Non-Cryst. Solids 336 (2004) 1–25. [26] C.A. Angell, D.B. Helphrey, Corresponding states and the glass transition for alkali metal nitrates, J. Phys. Chem. 75 (1971) 2306–2312. � ak, Aspects of the non-crystalline state, Phys. Chem. Glasses [27] C.A. Queiroz, J. Sest� Eur. J. Glass Sci. Technol. B 51 (2010) 165–172. [28] T.M. Besmann, K.E. Spear, Thermodynamic modelling of oxide glasses, J. Am. Ceram. Soc. 85 (2002) 2887–2894. [29] Yazhenskikh, E. Yazhenskikh, K. Hack, M. Müller, Critical thermodynamic evaluation of oxide systems relevant to fuel ashes and slags. Part 1: alkali oxide–silica systems, Calphad (New York. Print) 30 (2006) 270–276. [30] P.I. Protsenko, A.G. Bergman, Ternary system of fused nitrates of calcium, potassium, and sodium, Zh. Obshch. Khim. 20 (1950) 1365–1375. [31] P.I. Protsenko, Z.I. Belova, Binary systems of calcium nitrate with the nitrates of the first and second group, Russ. J. Inorg. Chem. 2 (1957) 2617–2620. [32] I.I. Il’yasov, T.I. Dunaeva, Y.G. Litvinov, Li, Cs,Ca//NO3 and Na,Cs,Ca//NO3 systems, Russ. J. Inorg. Chem. 21 (1976) 2298–2301. [33] E. Janecke, The quaternary system of the nitrates of Na-K-Ca-Mg and the systems of its components, Z. Elektrochem. Angew. Phys. Chem. 48 (1942) 453–467. [34] K. Laybourn, W.M. Madgin, D. Freeman, 36. Liquidus and solidus studies. Part IV, J. Chem. Soc. (1934) 139–146. [35] A. Lehrman, D. Breslow, The liquidus surface of the system sodium, lithium and calcium nitrates, J. Am. Chem. Soc. 60 (1938) 873–876. [36] O.J. Kleppa, L.S. Hersh, Thermochemistry of binary fused nitrates, Discuss. Faraday Soc. 32 (1961) 99–106. [37] M. Kawakami, K. Suzuki, S. Yokoyama, T. Takenaka, Heat Capacity Measurement of Molten NaNO3-NaNO2-KNO3 by Drop Calorimetry, in: VII International Conference on Molten Slags Fluxes and Salts, The South African Institute of Mining and Metallurgy, 2004.
This work was supported by the Federal Ministry for Economic Af fairs and Energy on the basis of a decision by the German Bundestag within the project PCM-Screening (FKZ 03ET1441). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.calphad.2019.101688. References [1] Q. Peng, X. Yang, J. Ding, X. Wei, J. Yang, Design of new molten salt thermal energy storage material for solar thermal power plant, Appl. Energy 112 (2013) 682–689. [2] M.M. Kenisarin, High-temperature phase change materials for thermal energy storage, Renew. Sustain. Energy Rev. 14 (2010) 955–970. [3] B. C� ardenas, N. Le� on, High temperature latent heat thermal energy storage: phase change materials, design considerations and performance enhancement techniques, Renew. Sustain. Energy Rev. 27 (2013) 724–737. [4] B. Zalba, J.M. Marı ́n, L.F. Cabeza, H. Mehling, Review on thermal energy storage with phase change: materials, heat transfer analysis and applications, Appl. Therm. Eng. 23 (2003) 251–283. [5] T. Bauer, D. Laing, R. Tamme, Overview of PCMs for concentrated solar power in the temperature range 200 to 350 � C, Adv. Sci. Technol. 74 (2010) 272–277. [6] R. Tamme, T. Bauer, J. Buschle, D. Laing, H. Müller-Steinhagen, W.-D. Steinmann, Latent heat storage above 120� C for applications in the industrial process heat sector and solar power generation, Int. J. Energy Res. 32 (2008) 264–271. [7] X. Li, K. Wang, M. Shen, Z. Wu, L. Xie, Thermodynamic modeling of the Ca(NO3)2MNO3 (M: alkali metal) systems, Calphad 59 (2017) 90–98. [8] C.Y. Zhao, Y. Ji, Z. Xu, Investigation of the Ca(NO3)2–NaNO3 mixture for latent heat storage, Sol. Energy Mater. Sol. Cells 140 (2015) 281–288. [9] Z. Jiang, G. Leng, F. Ye, Z. Ge, C. Liu, L. Wang, Y. Huang, Y. Ding, Form-stable LiNO3–NaNO3–KNO3–Ca(NO3)2/calcium silicate composite phase change material (PCM) for mid-low temperature thermal energy storage, Energy Convers. Manag. 106 (2015) 165–172. [10] D. Sergeev, B.H. Reis, M. Ziegner, I. Roslyakova, M. to Baben, K. Hack, M. Müller, Comprehensive analysis of thermodynamic properties of calcium nitrate, J. Chem. Thermodyn. 134 (2019) 187–194. [11] E.A. Dancy, P. Nguyen-Duy, Calorimetric determination of the thermodynamic properties of the binary eutectics in the NaNO3⋅Ca(NO3)2 and KNO3⋅Ca(NO3)2 systems, Thermochim. Acta 42 (1980) 59–63. [12] V.A. S€ otz, A. Bonk, J. Forstner, T. Bauer, Molten salt chemistry in nitrate salt storage systems: linking experiments and modeling, Energy Procedia 155 (2018) 503–513. [13] D.A.I. Ditmars, S. Ishihara, S.S. Chang, G. Bernstein, E.D. West, Enthalpy and heatcapacity standard reference material: synthetic sapphire (α-Al2O3) from 10 to 2250 K, J. Res. Natl. Bur. Stand. 82 (1982) 159–163. [14] D. Sergeev, E. Yazhenskikh, N. Talukder, D. Kobertz, K. Hack, M. Müller, Thermodynamics of the reciprocal NaCl–KCl–NaNO3–KNO3 system, Calphad 53 (2016) 97–104.
7
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Thermodynamics of the Ca(NO3)2 – NaNO3 system D. Sergeev a, *, B.H. Reis b, I. Dreger a, M. to Baben b, K. Hack b, M. Müller a a b
Forschungszentrum Jülich GmbH, IEK-2, D-52425, Germany GTT-Technologies, Kaiserstraße 103, D-52134, Herzogenrath, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Phase change materials Calcium and sodium nitrates Enthalpy increment
Thermodynamic properties of the quasi binary Ca(NO3)2–NaNO3 system are of interest with respect to thermal energy storage. In the present work the phase diagram as well as thermodynamic properties of the near eutectic mixture 45 mol% Ca(NO3)2 – 55 mol% (NaNO3)2 were determined experimentally and applied in the assessment of a new Gibbs energy dataset for thermochemical calculations. The enthalpy of fusion of the 45 mol% Ca(NO3)2 – 55 mol% (NaNO3)2 mixture is determined to be 24.7 � 0.5 kJ/mol. The melting and crystallization enthalpy have good reproducibility, which makes it possible to use this mixture as a phase change material at temperature 225 � C. The assessed dataset describes liquid phase properties using a subregular solution model in the RedlichKister formalism with high accuracy. Therefore it can be used for the prediction of thermodynamic properties of different compositions in the whole Ca(NO3)2–NaNO3 system and be included in databases for calculation of multicomponent systems including other components.
1. Introduction
2. Experimental
Nitrate salts of Na, K, and Ca are of interest for use as thermal energy storage materials [1–9]. Therefore thermodynamic properties of binary, ternary, and multicomponent systems with these components are important for further improvement of energy storage technology. Thermochemical assessments of several binary systems Ca(NO3)2 MNO3 (M: alkali metal) were carried out by Li et al. [7], but all opti mization parameters were obtained by using non-reliable thermody namic functions of Ca(NO3)2. A detailed discussion of the data problems was given in our previous paper [10]. Comparison of the enthalpy increment obtained by Li et al. [7]. with experimental data of Dancy et al. [11]. shows large deviation (34%) of the enthalpy of fusion of the near eutectic mixture 0.46Ca(NO3)2 – 0.54(NaNO3)2. In the present paper we report extensive new experimental data for the Ca(NO3)2 – NaNO3 sys tem and show an improvement of the dataset of this system by using the new thermodynamic functions of Ca(NO3)2 [10]. Additionally, we show that the extrapolation of the heat capacity of the pure liquid salts below their melting point is crucial for an accurate description of the heat capacity of near-eutectic liquid solutions - which is the most important property of salt mixtures used in sensible heat storage. Together with the new data on the latent heat of fusion, this work is an important step towards a consistent database for nitrate salts mixtures used e.g. in solar thermal storage applications [12].
2.1. Samples Pure Ca(NO3)2 was prepared from Ca(NO3)2⋅4H2O (Sigma-Aldrich, 99.995%), which was dried at 150 � C in a vacuum furnace for 24 h. TG analysis of the prepared sample shows no weight loss at low tempera tures (25 – 400 � C). Above 450 � C decomposition of Ca(NO3)2 was observed. The total weight loss due to this reaction was 66.35% and it is reasonable to assume that the remaining 33.65% of the mass is CaO, which is in a good agreement with the molar fraction of CaO in Ca(NO3)2 (34.18%). For additional information about the XRD analysis and the high temperature behavior of Ca(NO3)2 is given in Ref. [10]. The pure NaNO3 (Sigma-Aldrich, 99.995%) was used for the prepa ration of the mixtures of the Ca(NO3)2-NaNO3 system. All handling of the samples was carried out in a glove box under purified argon. The mixtures were sealed in glass ampoules under vacuum and used for DTA measurements. 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. After the heat treatment the mixtures were prepared in a glove box for use in DSC.
* Corresponding author. E-mail address: [email protected] (D. Sergeev). https://doi.org/10.1016/j.calphad.2019.101688 Received 18 June 2019; Received in revised form 1 October 2019; Accepted 20 October 2019 Available online 29 October 2019 0364-5916/© 2019 Elsevier Ltd. All rights reserved.
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2.2. Instruments
Optimization of the interaction parameters for the liquid solution has been obtained with the subroutines from the ChemApp [18] library coupled with the Nomad optimization algorithm [19,20]. Detailed in formation on the Gibbs energy modelling of the phases as well as the optimization procedures is given in the following sections.
2.2.1. Differential scanning calorimetry (DSC) Two differential scanning calorimeters were used for the determi nation of thermodynamic properties. The main parameters of these de vices are given in Table 1. Before starting the measurements the working volume of the DSC was evacuated and filled with He to obtain a dry atmosphere and to improve the heat transfer conditions. The experiments were carried out with different sample masses (Table 1). The ratio method with sapphire (α-Al2O3, NIST Standard Reference Material SRM720, purity 99.95%, metals basis) [13] as a reference was � applied for the determination of the heat capacity (Cp , J∙mol 1∙K 1) according to the following equation: �
CpðsÞ ¼
mr DSCs ⋅ ms DSCr
DSCb � ⋅C ; DSCb pðrÞ
3.1. Pure compounds The Gibbs energy function (GðTÞ) of pure compounds (i) is, by way of the Gibbs-Helmholtz equation, defined in terms of their enthalpy (HðTÞ) and entropy (SðTÞ), which in turn are functions of the heat capacity (CP ) and the respective absolute entities Δf Ho298ðiÞ and So298 ðiÞ as follows: GðTÞðiÞ ¼ HðTÞðiÞ
(1)
Z HðTÞðiÞ ¼ Δf H o298ðiÞ þ
where m – mass of the substance (g), DSC – signal of thermopile (μV). Baseline and reference measurements were performed for each measured sample separately. For determination of the enthalpy of fusion by slow heating rate (0.5 K/min) thermal analysis (SHRTA) [14] the sensitivity constant of the mHTC 96 was calibrated with the reference material 50% mol NaNO3 – 50% mol KNO3 (Ttr ¼ 223 � C, ΔfusH ¼ 9.46 kJ/mol [15]) under similar conditions, as for the proper samples.
Z SðTÞðiÞ ¼ So298ðiÞ þ
Table 1 Parameters of the differential scanning calorimeters. Company Temperature range Thermocouple Oven Heating rate Atmosphere Crucibles Sample weight
Netzsch � � 25 C–1600 C Type S Pt-Rh 15 K/min He, 10 ml/min Open Pt crucibles with lids 20–50 mg
Setaram � � 25 C–1400 C Type S - HFDSC Graphite 4 K/min He, 5 ml/min Open Pt crucibles with lids 400–500 mg
�
T
CPðiÞ 298
(3)
TdT
(4)
3.1.2. Properties of liquids During the progress of this work, it has become evident that the heat capacities of pure liquids below the melting temperature would have a significant impact on the correlation with the experimental results for the CP of the liquid solution near the eutectic composition, as discussed in section 4.2. It is then important that the heat capacities of supercooled liquids maintain a liquid-like tendency when extrapolated below each salt’s melting temperature. The liquid-like tendency is one that follows the expected behavior from the known range where liquid is stable, without necessarily assuming the value of CPðsolidÞ right below the melting temperature. However, it is also important to consider the limitations of the pure components of the system. Each salt needs to have consistent thermodynamic description of all properties at all tempera tures as well. For this reason, careful consideration has been given to the extrapolation of CPðliquidÞ to low temperatures. The extrapolation of CPðliquidÞ has had a lot of attention since the publication of Kauzmann’s work [24] on the behavior of supercooled liquids and glass transitions. Much of the attention came from the problem exposed as the “entropy paradox”, later also known as “Kauz mann’s paradox”. The problem comes from the realization that if a liquid is supercooled without crystallization, the entropy of the liquid will decrease faster than that of the kinetically inhibited solid due to the liquid’s higher heat capacity. Therefore, below a certain temperature, the liquid phase will achieve an entropy value lower than that of the solid. This is a paradox considering that a solid is significantly higher ordered than a liquid. Kauzmann postulates that his apparent paradox would be solved if one assumes that a liquid-glass transition occurs after a certain degree of supercooling. Indeed, this approach has been considered by Schnurre et al. [25] in a very critical modelling of the
The binary Ca(NO3)2-NaNO3 system is considered due to its impor tance for heat storage applications by using phase change materials, specifically materials that exhibit solid-solid or solid-liquid phase tran sitions. Therefore, the focus of this thermodynamic assessment has been placed on the condensed phases. It should be noted that the decompo sition of Ca(NO3)2 to CaO and NOx cannot be correctly calculated, which the authors plan to study in the future. Thus the system is reduced to three solid stoichiometric compounds, Ca(NO3)2 (S), NaNO3 (S1) and NaNO3 (S2), plus the liquid phase with full miscibility between Ca (NO3)2 and NaNO3 [14–19,22]. In order to model the liquid solution, properties of the liquid end-members are also necessary. The Gibbs energy modelling of the pure compounds and the liquid solution follows the Calphad approach [16] using FactSage 7.2 [17].
mHTC 96
CPðiÞ dT 298
3.1.1. Heat capacity of solids In Table 3, a third degree polynomial with two temperature ranges has been used to reproduce the results obtained for the heat capacity of solid Ca(NO3)2 by the modified segmented regression (SR) model [10], which is not directly available in FactSage. The least squares fit gave a minimum R2 of 0.9999 in all temperature ranges. Above the melting temperature (Tm ), a constant extrapolation is assumed. In the case of NaNO3, the reported heat capacity above 549 K [22] is already constant, so there is no change at the melting temperature of 579 K. The lower temperature of 130 K is necessary to take into account the effects of glass transition below room temperature (see section 3.1.3). However, ex trapolations down to 0 K are not of interest for this work.
3. Thermodynamic modelling
DSC 404C
T
Table 2 and Table 3 summarize the thermodynamic properties of the pure compounds applied in this assessment.
2.2.2. Differential thermal analysis (DTA) DTA measurements were performed using a STA 449C Jupiter (Netzsch) with a silicon carbide oven (0 � C – 1600 � C) and a perpen dicular sample holder (type S thermocouple (Pt/(Pt10Rh))). The tem perature calibration was performed using the phase transition temperatures of In (156.6 � C), Sn (231.9 � C), Bi (271.4 � C), Zn (419.5 � C), Al (660.3 � C) and Ag (961.8 � C). The resulting accuracy of transition temperature measurements is �3 � C. The experiments were carried out with a scan rate of 5 K/min and 3 cycles of heating and cooling. The results showed good reproducibility from the second cycle onwards.
Instrument
(2)
T⋅SðTÞðiÞ
2
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Table 2 Thermodynamic properties of pure compounds. ΔHo298 (J/mol)
Compound NaNO3 (S1) NaNO3 (S2) NaNO3 (L) Ca(NO3)2 (S) Ca(NO3)2 (L)
467980 464360 454778 936798 929600
Ref.
So298 (J/mol K)
Ref.
Ttransition (K)
ΔHtransition (J/mol)
Ref.
[21] [21] ** SGPS **
116.315 122.943 134.08 190.5 190.5
[21] [21] ** [10] **
549(S1→S2) 579(S2→L)
3620 14980
[22] [22]
823.15(S→L)
33400
[10]
** This work.
model [28], which has proven applicability for complex oxide and salt liquids [29]. In the current binary system, the pure liquid salts constitute the solution components without any additional associate. The practice adopted by Ref. [28] is maintained here, where the stoichiometry of the end-members is chosen in order to obtain two non-oxygen atoms per formula unit, allowing equal weighting with regard to each species ideal entropic contribution. As a result, NaNO3 remains unchanged and Ca (NO3)2 becomes (Ca(NO3)2):1.5, meaning that each atom stoichiometry is divided by 1.5. Interaction parameters between the species are introduced for description of the non-ideal mixing properties of the so lution. The molar Gibbs energy is then defined as the sum of the refer ence, the ideal and the excess contributions as:
Table 3 Heat capacities of pure compounds. Compound
T Interval (K)
CP (J/mol K)
Ref.
NaNO3 (S1)
130–549 549–3000 130–549 549–3000 130–226 226(Tg)–3000 130–298.15
22.62 þ 0.222 T 139.00 22.62 þ 0.222 T 139.00 22.62 þ 0.222 T 138.20 3.75341 þ 1.17463 T – 3.46450⋅10 3⋅T2 þ4.01602⋅10 6⋅T3 93.5551 þ 0.198423 T – 9.56265⋅10 5⋅T2 þ2.95246⋅10 8⋅T3 208.561 3.75341 þ 1.17463 T – 3.46450⋅10 3⋅T2 þ4.01602⋅10 6⋅T3 93.5551 þ 0.198423 T – 9.56265⋅10 5⋅T2 þ2.95246⋅10 8⋅T3 246
[22] [22] [22] [22]
NaNO3 (S2) NaNO3 (L) Ca(NO3)2 (S)
298.15–823.15
Ca(NO3)2 (L)
823.15(Tm)–3000 130–298.15 298.15–426.65 426.65(TK)-3000
a b
a
[22] [10] b
[10] b
Gm ¼
X X X X X ðvÞ xi Goi þ RT xi lnxi þ xi xj Lij xi i
a a
xj
�v
(5)
v¼0;1
where xi is the molar fraction of species i, Goi is the molar Gibbs energy of
the pure liquid components, and Lij , with v ¼ 0; 1, represents the ðvÞ
a
interaction parameters between species i and j, as defined by the
Redlich-Kister polynomial. Lij is temperature dependent, according to: ðvÞ
[10]
ðvÞ
This work. Adapted from source.
Lij ¼ A þ B⋅T
(6)
Because no intermediate associate species is introduced in this particular binary system and because the interaction parameters are only two, L0ij and L1ij , the modified associate species model is simplified and assumes the same formalism as a subregular substitutional solution model [16]. The coefficients A and B are optimized considering experimental data for phase equilibria (this work and [30–35]), mixing enthalpies between liquid NaNO3 and solid Ca(NO3)2 at 623 K [36], as well as the enthalpy of fusion of the 0.45Ca(NO3)2-0.55(NaNO3)2 mixture (this work). The results are shown in Table 4.
glass-liquid phase for SiO2. Their work relies on enough experimental information to describe with good accuracy the heat capacity of the liquid-glass phase. As a result, the heat capacity of the glass phase shows a remarkable correlation with the heat capacity of cristobalite, the solid structure of silica stable at the glass-transition temperature (Tg). The present work also assumes a liquid-glass transition for the description of the heat capacity of pure liquids. BelowTg , the solid heat capacity is used as an approximated value for the glass regime. In the case of NaNO3, Tg is taken from Ref. [26]. Tg of liquid Ca(NO3)2, on the other hand, is unknown. Therefore, an estimation is made from the temperature at which the liquid and the solid entropies become the same if the liquid CP is extrapolated as constant below the melting point. This can be called the Kauzmann temperature (TK ) [27] or the “ideal glass transition temperature” (T0 ) [26]. This work will use the first termi m nology, i.e. (TK ). The constant extrapolation of CP TðliquidÞ below the
4. Results and discussion 4.1. Phase equilibria of the Ca(NO3)2-NaNO3 system The phase diagram of the Ca(NO3)2-NaNO3 system has been studied experimentally many times [30–35], but in most of these works only the liquidus line was considered. We repeated these measurements ac cording to our methodology described in section 2.2.2. The main advantage of this methodology is the usage of closed glass ampoules, which allows to avoid the decomposition reaction of Ca(NO3)2 and the influence of moisture on the samples. The results are shown in Fig. 2 and in Table 5. The measurements suggest that the eutectic point lies at a compo sition near 55 mol% (NaNO3)2 and at 225 � C (498 K). The calculation with the thermodynamic dataset results in the same temperature and a slightly smaller concentration of 54.3% (NaNO3)2 for the eutectic. Noticeably, the eutectic temperature 211 � C (484 K) reported by Lay bourn [34] is far too low in comparison with the other experimental data and, even though it was considered during the optimization of the liquid excess parameters, the need to comply with the liquidus data at the same time has obviously set the limit for the final eutectic temperature. The
melting point is used since direct CP measurements of the supercooled liquid state of the pure salts are not available. As shown in section 4.3 this assumption is corroborated by measurements of the liquid CP of the eutectic mixture. Tables 2 and 3 present the resulting properties of the pure liquids with these considerations, while Fig. 1 shows the final shape of the heat capacity curves for NaNO3 and Ca(NO3)2. With these considerations, the liquid properties of pure compounds are thermodynamically self-consistent, comply with the available liter ature and provide more reliable data for the liquid solution model, which is crucial for an accurate description of the liquid salt at the eutectic temperature. 3.2. Liquid solution and optimization of parameters The liquid solution is modelled with the modified associate species 3
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Fig. 1. Heat capacity of solid and liquid-glass states for NaNO3 (a) and Ca(NO3)2 (b). Data according to Table 3.
solid-solid transition of NaNO3 was measured at 278 � C (551 K) for the mixtures at 90 mol% (NaNO3)2 and 95 mol% (NaNO3)2, which compares very well with the temperature of 276 � C (549 K) accepted for the pure compound, see Table 2, as reported by Jriri [22]. The liquidus line and eutectic composition are overall also in good agreement with the pre vious studies [30–35].
Table 4
Coefficients of the liquid solution interaction parameters Lij . ðvÞ
v
Species i
Species j
A
B
0 1
NaNO3 NaNO3
(Ca(NO3)2):1.5 (Ca(NO3)2):1.5
3943.78 59.98
2.792 3.391
4.2. Thermodynamic properties of the eutectic mixture To provide better evidence for the assessment of the Ca(NO3)2NaNO3 system, the assumed eutectic 45 mol% Ca(NO3)2 – 55 mol% (NaNO3)2 mixture was chosen for further experimental determination of heat capacity and fusion enthalpy. The heat capacity of the eutectic 45Ca(NO3)2 – 55(NaNO3)21 mixture was measured in the temperature range from 50 � C to 450 � C. Two DSC
Fig. 2. Phase diagram of the Ca(NO3)2-NaNO3 system. Table 5 Experimental values of phase transition temperatures (K) in the Ca(NO3)2(NaNO3)2 system. 2(NaNO3), mol%
Liquidus line
0 20 30 40 45 50 55 60 70 80 90 95 100
823 733 656 600 571 507 538 557 564 571 579
Eutectic line 495 497 499 498 498 499 498 498 498 497 494
Solid transition
Fig. 3. Experimental values of heat capacity for solid and liquid phases of the 45Ca(NO3)2 – 55(NaNO3)2 mixture measured by two DSC devices, linear approximation of experimental data, calculated values in this work and calcu lated results from Li et al. [7].
551 551 550
1 For all calculations was used molar mass M ¼ 167.27 g/mol of the 45Ca (NO3)2 – 55(NaNO3)2 mixture.
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devices (described in section 2.2.1) were used. Four samples were measured with DSC 404C (15 K/min) and two samples with mHTC 96 (4 K/min). The values obtained are shown in Fig. 3. It can be seen that different heating rates have an influence on the width of the phase transition range, but the heat capacity of the solid and liquid phases are reproducible and show good agreement with each other. The deviations of experimental data are not higher than 5%, which is good agreement for two different devices. The coefficients obtained from the heat ca pacity, as measured, are given in Table 6. Comparing the measured heat capacity with the thermodynamic evaluation by Li et al. [7] (Fig. 3), differences in the order of 17 J/(K∙mol) (7%) can be observed for the liquid region, i.e. above 310 � C (583 K). This is due to their modelling approach, which assumes that heat capacities of pure liquid end-members are equal to the heat capacities of the respective solid salts below their melting point [7]. Respecting the new experimental results reported here, we model the liquid end-members with constant heat capacities below the melting temperature down to the glass transition or Kauzmann temperature. The consistency of this modelling is explained in section 3.1.2. As a result, the calculation from our dataset has an excellent agreement with the measured CP also for the liquid region above 310 � C (583K), with a maximum difference of 4 J/(K∙mol) (1%). Integration of the peak area of the phase transition range gives the value of the enthalpy of fusion. It is 21.7 kJ/mol from DSC 404C (15 K/ min) and 24.9 kJ/mol from mHTC 96 (4 K/min). This discrepancy can be due to the construction of the sample holder of the DSC 404C, which contains only two thermocouples and does not allow to measure the phase transition enthalpy accurately. Therefore the value measured by mHTC 96, which has a Calvet-type thermocouple, is more reliable. To prove this value a slow heat rate thermal analysis (SHRTA) [14] was used. Two samples were studied in the temperature range from 190 � C to 250 � C with heating and cooling rate 0.5 K/min (3 cycles for each sample). An example of the DSC-curves is shown on Fig. 4. It shows that the heating curves are reproducible with the melting point at 225 � C (498 K). The cooling curves were not reproducible due to kinetic effects during crystallization (Fig. 4). The results of these measurements are summarized in Table 7. The fusion enthalpy determined as 24.7 kJ/mol is in good agreement with the value obtained from the heat capacity measurements (24.9 kJ/ mol using mHTC 96, 4 K/min), which confirms a good agreement be tween the sensitivity constant determined based on the enthalpy of fusion of the 50NaNO3–50KNO3 mixture and on the heat capacity of sapphire. The fusion enthalpy obtained by Dancy et al. [11] with drop calorimetry is lower (Table 7). Fig. 5 shows the comparison of the � � enthalpy increment (H T – H 298.15) calculated based on the heat ca pacity from this work and experimental values of Dancy et al. [11]. It can be seen, that Dancy’s values for the solid phase (up to 225 � C) are higher � � than in this work (the difference at 225 � C is 3.49 kJ/mol). H T – H 298.15 of the liquid phase is in a good agreement with our results taking into account the statistical deviation of Dancy’s values. Therefore, the dif ference of the enthalpy of fusion can be due to the deviation of Dancy’s values of the enthalpy increment in the solid phase. The calculated values of the enthalpy increment based on our dataset are shown in Fig. 5 in comparison with our experimental results. The agreement is very good at all temperatures. In comparison with the
Fig. 4. Heating and cooling curves of the slow heating rate (0.5 K/min) thermal analysis with HFDSC sample holder (Setaram) for 45Ca(NO3)2 – 55 (NaNO3)2 mixture.
literature, our experiments exhibit a lower scatter. For the liquid region the calculated data by Li et al. [7] are higher, since their assessment only took the scattered data from Dancy et al. [11] into account. The co efficients obtained from the enthalpy increments are given in Table 8. 4.3. Heat of solution in the Ca(NO3)2-NaNO3 system Kleppa and Hersh [36] measured the heat of solution (ΔHS;L solution ) obtained from solid Ca(NO3)2 and liquid NaNO3 mixtures at 350 � C (623 K) with a micro-calorimeter. Our calculated data is compared with
their results in Fig. 6. The calculated results reproduce well ΔHS;L solution reported in Ref. [36], with an average deviation of only 0.26 kJ/mol. As in the original article, one can also extrapolate the enthalpy of fusion of the metastable solid Ca(NO3)2 at 350 � C, from the final point of the line at 1 molar fraction of Ca(NO3)2 in Fig. 6. Here, the extrapolation gives exactly the same result as the one obtained by Kleppa and Hersh [36], i. e. 23.8 kJ/mol. As discussed in Ref. [10], however, it is unreasonable to assume this value as the real enthalpy of fusion of Ca(NO3)2 because its melting temperature lies around 200 � C above the temperature used in the experiment (350 � C), which was not considered by Li et al. [7]. Wang et al. [23] optimized the Gibbs energy of fusion (Δfus G) as a function of temperature for Ca(NO3)2. As a consequence, one obtains a corresponding optimized fusion enthalpy as a function of temperature. The value at 350 � C has been plotted in Fig. 6 (red circle) and it is much lower (more than 9 kJ/mol) than the one calculated by this work (solid line) at 1 molar fraction of Ca(NO3)2. This demonstrates that the prop erties of Ca(NO3)2 considered in the present work result in a different heat of fusion than the one optimized by Wang et al.. Although Wang et al. use a valid approach for the optimization of Δfus GðTÞ with a second-degree polynomial, this is done together with the optimization of another three parameters for the excess properties of the Ca(NO3)2-N aNO3 system and the data used for the minimization only includes phase equilibria. For this reason, the degrees of freedom for the fitting of the parameters by Wang et al. are too many and their final Δfus GðTÞ is thus not reliable. Since the present work critically reassesses the properties of solid and liquid Ca(NO3)2 individually, the calculated fusion enthalpy and Δfus GðTÞ of Ca(NO3)2 is independent of other parameters and is therefore more reliable. Had the present work not assumed reasonable standard properties
Table 6 � Coefficients of the linear equation of heat capacity (J∙mol 1∙K 1) C p ¼ A þ B∙T � a and standard uncertainty (�ΔC p) for the 45Ca(NO3)2 – 55(NaNO3)2 mixture taken from DSC measurements. Temperature range/K 298 – 498 498 – 750
A 57.609 260
�ΔC p,1 J∙mol
B 3.315∙10 –
�
1
1
K
1
5 5
Note. a Calculated according to the t-statistic with 95% confidence interval 5
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Table 7 Enthalpy of fusion of 45Ca(NO3)2 – 55(NaNO3)2 obtained with the slow heating rate (0.5 K/min) thermal analysis, calculated and literature data. Cycles 1st heating 2nd heating 3rd heating 1st cooling 2nd cooling 3rd cooling
Sample I (449.7 mg)
Sample II (452.4 mg)
24.3 23.9 24.6 24.3 24.5 23.9
Average a
25.3 25.1 25.3 24.5 25.2 25.2
24.7 � 0.5
Calculated in this work
Ref. [11]
25.3
21.9b
Note. a Standard uncertainty. b for 46Ca(NO3)2-54(NaNO3)2 mixture.
Fig. 6. Heat of solution between solid Ca(NO3)2 and liquid NaNO3 at 350 � C (623 K) calculated by this work (solid line) in comparison with the experi mental (triangle) and extrapolated (square) data from Kleppa and Hersh [36], and calculated data (circle) from Wang et al., 2015.
Fig. 5. Enthalpy increment of the 45Ca(NO3)2 – 55(NaNO3)2 mixture obtained from DSC and SHRTA results in comparison with literature data: Li_2017 - [7]; Dancy_1980 - [11].
capacities and the enthalpy of fusion allow calculation of the enthalpy increment. The new experimental data enables significant improvement of the thermodynamic assessment of the binary Ca(NO3)2-NaNO3 system. Indeed, a new thermodynamic dataset is successfully derived including the new experimental data and following the Calphad method. All calculated results agree well with the measurements, considering only two interaction parameters in the subregular liquid solution model. Such an important achievement is a consequence of the critical assumptions made for pure compounds as well. As a result, thermodynamic model ling of all the phases in the binary Ca(NO3)2-NaNO3 system is available in a fully self-consistent dataset, which can be used for prediction of thermodynamic properties within its entire composition and tempera ture range. The resulting dataset also serves as a well founded base for extension into multicomponent systems. The melting temperature of the inferred eutectic mixture 45%Ca (NO3)2 – 55%(NaNO3)2 is close to the “solar salt” 50NaNO3-50KNO3 (Tm ¼ 223 � C, ΔtrH496 ¼ 101.7 J/g [15], CPliq ¼ 1.49 J/(K∙g) [37]), but the enthalpy of fusion is considerably higher (ΔtrH498 ¼ 147.7 J/g). In the liquid state, the eutectic mixture provides a specific heat of 1.44 J/(K∙g). This mixture can be interesting for application from the economic point of view. It can be considered as potential phase change material as well as a sensible heat storage material.
Table 8 � � Coefficients of equation H T – H 298.15 ¼ A þ B∙T þ C∙T2 (kJ∙mol 1) for the enthalpy increment of the 45Ca(NO3)2 – 55(NaNO3)2 mixture determined from DSC and SHRTA results. Temperature range/K 298 – 498 498 – 750
A
B 27.028 65.545
3.035∙10 0.26
C 2
2.04∙10 –
4
for pure Ca(NO3)2, see Tables 2 and 3, it would not be possible to reproduce Kleppa and Hersh’s experimental data together with all thermodynamic properties of the Ca(NO3)2-NaNO3 system reported above. 5. Conclusions Eleven mixtures of the Ca(NO3)2–NaNO3 system were studied in closed glass containers by DTA for the determination of phase transition temperatures. The results obtained confirm previous values [30,33–35] about the eutectic composition near 45%Ca(NO3)2 – 55%(NaNO3)2 and the eutectic temperature at 225 � C (498 K). This eutectic mixture was studied by DSC. The heat capacity of the solid and liquid phases was determined with good agreement by using two different DSC devices, which confirms the reliability of our experimental approach. The enthalpy of fusion of this mixture was measured with the slow heating rate (0.5 K/min) thermal analysis. The combination of the heat
Data availability The raw and processed data required to reproduce these findings are available to download from [supplementary material].
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Acknowledgements
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