Heat Capacity of Solid Halide Eutectics and Their Enthalpy at Melting Point

: The isobaric heat capacity of solid eutectic mixtures LiCl-KCl-CsCl, LiBr-CsBr and LiBr-KBr-CsBr was investigated from room temperature up to melting point. The molar heat capacity of all mixtures under study was found to be close to the additive sum of that of pure salts. The heat accumulated up to melting temperature is directly dependent on the melting point.


Introduction
Eutectic mixtures comprising halide salts are used as phase-change materials. The melting temperatures of eutectics are much lower than those of pure salts [1]. Low temperatures have certain advantages including a low vapour pressure in molten state and low corrosion activity.
It makes halide eutectics very attractive for use in solar energy production [2][3][4][5][6] or power sources [7]. Heat capacity is very important since it indicates the amount of energy that a given system can possess under certain conditions. Heat capacity has been shown to be temperature independent in a molten state according to many studies [8][9][10][11], but in solids, the heat capacity rises with temperature. There are scarce data on the heat capacity of solid eutectic halide mixtures. FLINAK, a well-known eutectic mixture was measured in a solid state [12,13].
The aim of the present research was to investigate the heat capacity of the solid halide eutectic mixtures within temperature interval from room temperature up to melting point. The study was focused on the mixtures with melting temperatures below 600 K.

Materials and Methods
Alkali halide salts classified as "chemically pure" (99.5% of main substance) were used for mixture preparation. Lithium chloride was provided by FMC (UK), caesium salts were from Vekton, Russia. and lithium and potassium bromides were from Reachim, Russia. Chloride salts were purified by zone melting [14,15]. LiBr was purified from moisture and other admixtures through double recrystallization from anhydrous acetonitrile solution with additional treatment with molecular sieves. KBr and CsBr were purified from moisture by stepwise with vacuum drying. The detailed procedure was given in our previous work [1]. The mixtures prepared were subjected to thermal and gravimetric analysis in order to verify the melting temperature and sample mass stability. The samples were homogenous, and the melting temperature difference was within 5 degrees. The compositions of eutectic mixtures are given in Table 1. The study of heat capacity was carried out on the samples of the prepared mixtures using the STA 449C Jupiter synchronous thermal analyser (NETZSCH). The experiments were carried out under the following conditions: heating rate 10K/min; argon atmosphere; and Pt-Rh crucibles with a perforated lid. The heat capacity was determined in three stages: first stage-measurement of the base curve when the crucibles were empty; second stage-measurement with a standard sample (sapphire); and final stage-measurement with test sample. The detailed description of the experimental procedure has been described elsewhere [1]. The uncertainty of heat capacity determination was 5%.

Results and Discussion
The heat capacity of solid eutectic mixtures under investigation is given in Table 2 according to temperature. The isobaric heat capacities of solid eutectic mixtures were measured up to melting temperature.
The results for LiCl-KCl-CsCl are shown in Figure 1. The calculation of molar heat capacity according to the Neumann-Kopp rule [16,17] is also presented as Cp mixture = ∑Cp component salt.
The usage of this rule for halide salt mixtures can be justified by the similarity of the halide salts' thermodynamic properties [18]. The experimental and calculated values were in good agreement. The pure salt data were taken from the available literature [8,19]. Experimental and calculated data were used for the calculation of the enthalpy accumulated by eutectic mixture up to the melting temperature. Calculation of the integral (by the standard trapezoid method [20]) from the LSQM-line produced a value of 21.9 kJ mole -1 for LiCl-KCl-CsCl. The accuracy of the calculations was approximately ±7.5%. halide salts' thermodynamic properties [18]. The experimental and calculated values were in good agreement. The pure salt data were taken from the available literature [8,19]. Experimental and calculated data were used for the calculation of the enthalpy accumulated by eutectic mixture up to the melting temperature. Calculation of the integral (by the standard trapezoid method [20]) from the LSQM-line produced a value of 21.9 kJmole -1 for LiCl-KCl-CsCl. The accuracy of the calculations was approximately ±7.5%. Molten bromide eutectics possess certain advantages in comparison with chloride systems, primarily, due to lower temperatures. For this reason, they were also interesting subjects for study. The isobaric heat capacities of solid eutectic mixtures LiBr-KBr and LiBr-KBr-CsBr were measured up to melting point.
The heat capacities of the bromide eutectics being investigated are shown in Figures  2 and 3. The enthalpy of samples was calculated for bromide eutectics for premelting temperature. Calculation of the integral gave the value of 21.4 kJ mole -1 for LiBr-KBr-CsBr and 23.95 kJ mole -1 for LiBr-CsBr. Comparison of enthalpy and melting temperature indicated their dependency. The data for eutectic mixtures can be considered as a derivative of pure salts and, thus, they have the same dependency as that of individual salts. The results for eutectic mixtures are given in Table 3 and Figure 4. The enthalpy and melting points of chloride, bromide, and iodide salts were taken from literature [21] and are shown in Table  4 and Figure 4. -our data, line-values calculated according to the additive law based on the data available from the literature [8,19].
Molten bromide eutectics possess certain advantages in comparison with chloride systems, primarily, due to lower temperatures. For this reason, they were also interesting subjects for study. The isobaric heat capacities of solid eutectic mixtures LiBr-KBr and LiBr-KBr-CsBr were measured up to melting point.
The heat capacities of the bromide eutectics being investigated are shown in Figures 2 and 3. The enthalpy of samples was calculated for bromide eutectics for premelting temperature. Calculation of the integral gave the value of 21.4 kJ mole -1 for LiBr-KBr-CsBr and 23.95 kJ mole -1 for LiBr-CsBr. Comparison of enthalpy and melting temperature indicated their dependency. The data for eutectic mixtures can be considered as a derivative of pure salts and, thus, they have the same dependency as that of individual salts. The results for eutectic mixtures are given in Table 3 and Figure 4. The enthalpy and melting points of chloride, bromide, and iodide salts were taken from literature [21] and are shown in Table 4 and Figure 4.       The fitting was carried out by two mathematical methods: LSQM and the interval method. LSQM is well known and provides reliable fitting parameters of data under treatment, but it gives only the maximal (by modulus) bounds e max of measuring errors. Consequently, the parameters calculated by the standard least square method (LSQM) gives too broad an uncertainty interval. Under given conditions of uncertainty, interval analysis methods [22,23] give the guaranteed estimates of parameters (the information sets) which defines the area of possible values of property under investigation. The fitting line was as follows: H (T) = A × T + B, where H is the enthalpy of the solid eutectic near melting point, T is the melting temperature, and A and B are the empirical coefficients.
The results of data treatment are shown in Figures 5 and 6. Figure 5 demonstrates the information set (the possible values of coefficients A and B). According to interval analysis, the minimal coefficient B is 5.48 × 10 −2 kJ mole −1 K −1 , which relates to the maximal coefficient A equal to 23.9 KJ mole −1 . Maximal coefficient B is 6.95 × 10 −2 kJ mole −1 K −1 , which relates to 18  The results obtained demonstrated the independence of fitting results from the treatment method.
Thus, the amount of heat accumulated by solid halide eutectic mixtures up to melting point can be described by the following linear equation: The enthalpy of the melting of halide eutectics is also dependent on the melting point [24] according to the following formula: where H is enthalpy of fusion, and T m is melting point.
Thus, it is possible to calculate the amount of energy accumulated by salt or eutectic mixture before and just after melting as follows ( Figure 7): The results of estimation on the basis of the interval approach are the following: The results obtained demonstrated the independence of fitting results from the treatment method.
Thus, the amount of heat accumulated by solid halide eutectic mixtures up to melting point can be described by the following linear equation: H=62.2× Tm− 10718 Jmole -1 The enthalpy of the melting of halide eutectics is also dependent on the melting point [24] according to the following formula: This is the heat that the system possesses just after melting. This equation allows for the estimation of the amount of heat that the eutectic mixture can accumulate for heat storage. Figure 7. Enthalpy of salts and mixtures before (navy) and after melting (magenta).

Conclusions
1. The molar heat capacity of all mixtures under study was found to be close to the additive sum of that of pure salts. 2. The enthalpy of the solid eutectic mixtures closes to melting temperature was directly