Edouard Koffi Kouassi

Max Wedjers Manouan

Eulogne Zoro

David Boa

Pierre Benigni

Hmida Zamali

Jacques Rogez

Dalila Hellali
email: dalilahlali@hotmail.fr

Experimental investigation and thermodynamic evaluation of the CsNO3-LiNO3-NaNO3 ternary system

Keywords: Phase diagram, DTA, XRD, Calphad, CsNO3-LiNO3-NaNO3 ternary system

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The CsNO3-LiNO3 binary system is characterized by a congruent equimolar compound Cs0.5Li0.5NO3 which appears at (334 ± 2) K. Two eutectic reactions are found at (445 ± 2) K and (435 ± 2) K, respectively. The system exhibits also a plateau at (427 ± 2) K corresponding to the polymorphic transition of CsNO3. The CsNO3-LiNO3-NaNO3 ternary system shows two ternary eutectic reactions at (408 ± 2) K and (405 ± 2) K, respectively. Combining our results with experimental data available in the literature, an optimization of the thermodynamic parameters in the ternary system is performed with the help of Calphad approach. A reasonable agreement between the calculated results and the experimental data is obtained.

Introduction

Energy storage is a key element to improve the efficiency of thermal energy utilization in various branches of the industry (construction, electronic, biomedical, textile, automotive, etc.), as it allows the decoupling between production and demand of energy. In applications with intermittent energy generation, such as solar thermal systems or waste heat recovery, an appropriate thermal storage system is essential [START_REF] Medrano | Experimental evaluation of commercial heat exchangers for use as PCM thermal storage systems[END_REF]. Among the different modes of thermal energy storage, latent heat storage (LHS) is particularly attractive due to the high energy storage density with a possible isothermal operation, lower costs and compactness [START_REF] Gil | State of the art on high temperature thermal energy storage for power generation. Part 1-Concepts, materials and modellization[END_REF][START_REF] Cabeza | Materials used as PCM in thermal energy storage in buildings: A review[END_REF][START_REF] Khare | Selection of materials for high temperature latent heat energy storage[END_REF]. LHS uses phase change materials (PCMs) as heat storage medium which absorb and release energy through phase change transitions at constant temperature [START_REF] Zalba | Review on thermal energy storage with phase change: materials, heat transfer analysis and applications[END_REF][START_REF] Farid | A review on phase change energy storage: materials and applications[END_REF][START_REF] Sharma | Latent heat storage materials and systems: a review[END_REF][START_REF] Agyenim | A review of materials, heat transfer and phase change problem formulation for latent heat thermal energy storage systems (LHTESS)[END_REF][START_REF] Oró | Review on phase change materials (PCMs) for cold thermal energy storage applications[END_REF][START_REF] Zhou | Review on thermal energy storage with phase change materials (PCMs) in building applications[END_REF][START_REF] Cárdenas | High temperature latent heat thermal energy storage: Phase change materials, design considerations and performance enhancement techniques[END_REF][START_REF] Li | Numerical study on the thermal behavior of phase change materials (PCMs) embedded in porous metal matrix[END_REF][START_REF] Pielichowska | Phase change materials for thermal energy storage[END_REF][START_REF] Li | Analysis of HTFs, PCMs and fins effects on the thermal performance of shell-tube thermal energy storage units[END_REF]. According to the working temperature, PCMs can be divided into low temperature, medium temperature and high temperature. The temperature range associated to each group can vary depending on the applications [START_REF] Gil | State of the art on high temperature thermal energy storage for power generation. Part 1-Concepts, materials and modellization[END_REF][START_REF] Pielichowska | Phase change materials for thermal energy storage[END_REF][START_REF] Hoshi | Screening of high melting point phase change materials (PCM) in solar thermal concentrating technology based on CLFR[END_REF][START_REF] Wang | A novel sebacic acid/expanded graphite composite phase change material for solar thermal medium-temperature applications[END_REF][START_REF] Zhou | Thermal characterisation of binary sodium/lithium nitrate salts for latent heat storage at medium temperatures[END_REF][START_REF] Cáceres | Encapsulated Nitrates Phase Change Material Selection for Use as Thermal Storage and Heat Transfer Materials at High Temperature in Concentrated Solar Power Plants[END_REF][START_REF] Mao | Recent investigations of Phase Change Materials use in solar thermal energy storage system[END_REF]. It has been pointed out that PCMs with a melting temperature between 393 K and 573 K are of great interest in the industrial and domestic applications of solar thermal energy (drying, cooling, distillation, etc.) [START_REF] Zhou | Thermal characterisation of binary sodium/lithium nitrate salts for latent heat storage at medium temperatures[END_REF][START_REF] Li | Development of medium-temperature composite phase change material with high thermal stability and conductivity[END_REF][START_REF] Miró | Thermal energy storage (TES) for industrial waste heat (IWH) recovery: A review[END_REF]. Because alkali nitrates seem to be potential solid-liquid PCMs in the temperature range (373-573) K [START_REF] Roget | Study of the KNO3-LiNO3 and KNO3-NaNO3-LiNO3 eutectics as phase change materials for thermal storage in a low-temperature solar power plant[END_REF], we have undertaken, for some years now, the development of multicomponent nitrate mixtures based on NaNO3 which has been found as a proper PCM with respect to its heat of fusion and corrosiveness [START_REF] Helali | Thermodynamic assessment of the ternary AgNO3-LiNO3-NaNO3 system[END_REF][START_REF] Hellali | Experimental study of phase equilibria in the (AgNO3 + LiNO3 + NaNO3) ternary system[END_REF][START_REF] Manouan | Thermodynamic modeling of the AgNO3-CsNO3-NaNO3 ternary system[END_REF]. The purpose of our studies is to access the composition of mixtures having a lower congruent melting temperature (T < 573 K) through the phase diagram study.

One of the systems that draw our attention is the AgNO3-CsNO3-LiNO3-NaNO3 quaternary system. It is worth noting that the phase diagram determination of a multicomponent system based only on experimental methods is time consuming and expensive. Therefore, the prediction work using the numerical method along with the available data of lower order systems, becomes a necessity.

Except for CsNO3-LiNO3 system, all limiting binary systems of the AgNO3-CsNO3-LiNO3-NaNO3 quaternary system have been assessed thermodynamically and the parameters describing the Gibbs energy of all binary phases are well-known [START_REF] Helali | Thermodynamic assessment of the ternary AgNO3-LiNO3-NaNO3 system[END_REF][START_REF] Hellali | Experimental study of phase equilibria in the (AgNO3 + LiNO3 + NaNO3) ternary system[END_REF][START_REF] Manouan | Thermodynamic modeling of the AgNO3-CsNO3-NaNO3 ternary system[END_REF][START_REF] Jriri | Thermodynamic analysis of the CsNO3-KNO3-NaNO3 system[END_REF]. Two of the four ternary sub-systems of the quaternary system have been already evaluated in our previous works: AgNO3-LiNO3-NaNO3 [START_REF] Helali | Thermodynamic assessment of the ternary AgNO3-LiNO3-NaNO3 system[END_REF][START_REF] Hellali | Experimental study of phase equilibria in the (AgNO3 + LiNO3 + NaNO3) ternary system[END_REF] and AgNO3-CsNO3-NaNO3 [START_REF] Manouan | Thermodynamic modeling of the AgNO3-CsNO3-NaNO3 ternary system[END_REF]. But up to now, no thermodynamic modeling of the remaining two (AgNO3-CsNO3-LiNO3 and CsNO3-LiNO3-NaNO3) is available.

As a part of the investigation of the AgNO3-CsNO3-LiNO3-NaNO3 quaternary system, the present work is devoted to the thermodynamic evaluation of the CsNO3-LiNO3-NaNO3 system. The main purpose is to provide the Gibbs free energy parameters of all the phases using Calphad method which has three keywords: critical review, modelisation and optimization. For a better understanding of phase equilibria in the CsNO3-LiNO3 and CsNO3-LiNO3-NaNO3 systems especially at low temperature (298 K < T < 350 K), an experimental investigation was undertaken using X-ray diffraction and differential thermal analysis.

Critical review of literature information

General aspects

Since the 19th-century, the thermodynamic properties especially phase change properties of pure nitrates CsNO3, LiNO3, NaNO3 and their mixtures have been reported by several authors. Most of data were reviewed, evaluated and compiled in many handbooks and publications [START_REF] Janz | Molten Salts Handbook[END_REF][START_REF] Stern | High Temperature Properties and Decomposition of Inorganic Salts Part 3, Nitrates and Nitrites[END_REF][START_REF] Janz | Physical Properties Data Compilations Relevant to Energy Storage. II. Molten Salts: Data on Single and Multi-Component Salt Systems[END_REF][START_REF] Mossarello | Création d'une banque informatisée de données cohérentes sur les propriétés thermodynamiques des mélanges de sels fondus[END_REF][START_REF] Dessureault | Evaluation critique des données thermodynamiques et des diagrammes de phases des systèmes AOH-AX, ANO3-AX, ANO3-BNO3[END_REF][START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Pankratz | Thermodynamic Properties of Carbides, Nitrides, and Other Selected Substances[END_REF][START_REF] Landolt-Börnstein | Thermodynamic properties of inorganic materials, Group IV[END_REF][START_REF] Sangster | Thermodynamics and phase diagrams of 32 binary common-ion systems of the group Li,Na,K,Rb,Cs//F[END_REF][START_REF] Shackelford | CRC -Materials Science and Engineering Handbook[END_REF][START_REF] Binnewies | Thermochemical Data of Elements and Compounds, Second, Revised and Extended Edition[END_REF][START_REF] Hellali | Contribution à l'étude thermodynamique des mélanges binaires et ternaires des nitrates d'argent, de césium, de lithium, de sodium et de rubidium[END_REF][START_REF] Monia | Heat capacities and enthalpies of fusion of lithium and rubidium nitrates: Heat capacities, enthalpies of fusion and enthalpies of formation of the intermediate compounds Ag0.5Rb0.5NO3 and Li0.5Rb0.5NO3[END_REF]. Though these databanks provide easily useful data for different applications whether practically or in simulation techniques, sometimes they need to be updated taking into account new information. In the present work, a new critical review is proposed as an actualization of previous compilations. This task is based on a thermodynamic analysis associated to statistical evaluation.

The thermodynamic analysis is focused on salt sample characteristics (purity, mass, etc.) and experimental methods (apparatus, procedures, conditions, etc.) which are the two major elements affecting measurements. Phase change properties of salts can be investigated by different experimental methods. But, the most commonly techniques used are differential scanning calorimetry (DSC) and differential thermal analysis (DTA) which are recognized as the most accurate methods [START_REF] Sharma | Latent heat storage materials and systems: a review[END_REF][START_REF] Kamimoto | The possibility of high-temperature heat capacity measurements by Differential Scanning Calorimetry[END_REF][START_REF] Sharma | Review on thermal energy storage with phase change materials and applications[END_REF][START_REF] Kuravi | Thermal energy storage technologies and systems for concentrating solar power plants[END_REF][START_REF] Soares | Review of passive PCM latent heat thermal energy storage systems towards buildings' energy efficiency[END_REF][START_REF] Kenisarin | Thermophysical properties of some organic phase change materials for latent heat storage. A review[END_REF][START_REF] Sun | Melting temperature and enthalpy variations of phase change materials (PCMs): a differential scanning calorimetry (DSC) analysis[END_REF]. However, some conditions must be fulfilled to get reliable data. For example, the phase transition process is affected by the combination of sample mass and heating rate [START_REF] Sun | Melting temperature and enthalpy variations of phase change materials (PCMs): a differential scanning calorimetry (DSC) analysis[END_REF][START_REF] Drissi | Thermal analysis by DSC of Phase Change Materials, study of the damage effect[END_REF]. It was also showed that impurities of a sample affect the value of its thermochemical properties [START_REF] Kamimoto | The possibility of high-temperature heat capacity measurements by Differential Scanning Calorimetry[END_REF][START_REF] Lomonaco | Stockage d'énergie thermique par matériaux à changements de phase adapté aux centrales solaires thermodynamiques[END_REF][START_REF] Lomonaco | Sodium nitrate thermal behavior in latent heat thermal energy storage: A study of the impact of sodium nitrite on melting temperature and enthalpy[END_REF]. In addition, a good calibration of a device can be a guarantee for accurate measurements [START_REF] Charrier | Determination of the temperature and enthalpy of the solid-solid phase transition of caesium nitrate by differential scanning calorimetry[END_REF][START_REF] Ferro | Remarks about data reliability in experimental and computational alloy thermochemistry[END_REF]. When thermal properties of salts are measured, an appropriate crucible should be considered [START_REF] Kamimoto | The possibility of high-temperature heat capacity measurements by Differential Scanning Calorimetry[END_REF][START_REF] Gomez | High-Temperature Phase Change Materials (PCM) Candidates for Thermal Energy Storage (TES) Applications[END_REF][START_REF] Zhao | Experimental analysis on crucible selection of thermal properties of nitrate salt[END_REF], and so on. Apart from experimental operations, the way the transition temperature and the latent heat are determined from DTA or DSC curves can be one of the greatest sources of error. Generally, the temperature of the thermal effect is defined as the onset temperature i.e. the intersection point of the tangent from start edge inflexion point and the baseline [START_REF] Li | Thermal property characterization of a low supercooling degree binary mixed molten salt for thermal energy storage system[END_REF]. Regarding the latent heat of transition, the challenge is the choice of an initial and final temperature marking before integrating the peak [START_REF] Coscia | Thermophysical properties of LiNO3-NaNO3-KNO3 mixtures for use in concentrated solar power[END_REF].

The statistical analysis is performed, in the present work, to define the scattering of data. For the statistical significance determination, one-way ANOVA (Analysis of Variance) is used (95% confidence level). When the ANOVA produces a statistically significant test, Duncan post-hoc test is carried out. At this stage, the uncertainty of the different measurements is a crucial parameter. Unfortunately, some of original papers do not report uncertainty. In this case, the highest value of uncertainty of different bibliographic sources is taken. All statistical analyses are made with IBM SPSS version 22 software.

Finally, it is important to notice that when data go through critical evaluation, the use of the original values is recommended in order to avoid propagation of errors. Thereby, smoothed numerical values and data from compilations (handbooks) are not taken into account.

Pure nitrates

Cesium nitrate (CsNO3)

Most of CsNO3 crystallographic data obtained prior to 1974 were compiled by Rao et al. [START_REF] Rao | Crystal Structure Transformations in Inorganic Nitrites, Nitrates, and Carbonates[END_REF]. They showed that CsNO3 exhibits, between room temperature and its melting temperature, two stable crystalline forms at normal pressure. The low temperature form (phase II) is hexagonal P31m with a = 10.87 Å and c = 7.76 Å. At high temperature, CsNO3 has a cubic structure (phase I) with a = 4.499 Å. Results of later works [START_REF] Fernandes | Infrared spectroscopic study of the phase transitions in CsNO3, RbNO3 and NH4NO3[END_REF][START_REF] Owens | Raman scattering study of the extrenal librational modes of the  3 NO ion in the high temperature phase transitions of CsNO3 and RbNO3[END_REF][START_REF] Lucas | The structure (Neutron) of phase II caesium nitrate at 298 K, CsNO3[END_REF][START_REF] Dean | Structures of phase IV rubidium nitrate, RbNO3, and phase II caesium nitrate, CsNO3[END_REF][START_REF] Chary | Structural phase transition in CsNO3: dielectric studies[END_REF][START_REF] Pohl | Caesium nitrate (II) at 296 K[END_REF][START_REF] Zhou | Structure refinement of CsNO3(II) by coupling of 14 N MAS NMR experiments with WIEN2k DFT calculations[END_REF] are in agreement with the number of crystallographic forms of CsNO3 [START_REF] Rao | Crystal Structure Transformations in Inorganic Nitrites, Nitrates, and Carbonates[END_REF]. However the cell parameters and space groups are a little bit different from those reported by Rao et al. [START_REF] Rao | Crystal Structure Transformations in Inorganic Nitrites, Nitrates, and Carbonates[END_REF].

The recent paper of Somov et al. [START_REF] Somov | Monoclinic low-temperature polymorph of cesium nitrate[END_REF] pointed out a new CsNO3 low temperature structure (monoclinic) with space group P21/c and lattice parameters : a = 4.5699 [START_REF] Oró | Review on phase change materials (PCMs) for cold thermal energy storage applications[END_REF] Å, b = 11.1871 [START_REF] Zhou | Review on thermal energy storage with phase change materials (PCMs) in building applications[END_REF] Å, c = 9.1484(18) Å, β = 131. [START_REF] Hellali | Experimental study of phase equilibria in the (AgNO3 + LiNO3 + NaNO3) ternary system[END_REF](3)°. This allotropic form, stable at room temperature, was prepared by crystallization of a mixture of water and dimethylsulfoxide C2H6OS (DMSO).

Heat capacity • Low-temperature phase: CsNO3 (II)

Low temperature heat capacity of CsNO3 has been determined by different authors [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Satoh | The free rotation of  3 NO ion in some nitrates[END_REF][START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF][START_REF] Flotow | Heat capacity from 5 to 350 K and thermodynamic properties of cesium nitrate to 725 K[END_REF][START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF]. All data are gathered in the same plot (Fig. 1a). Fig. 1b presents an enlargement in the temperature range (300 -425) K. The experimental techniques and relative uncertainties are given in brackets.

The scattering of the experimental data is within ± 3%, except for the results of Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF]. Data of these authors, obtained by DSC, are about 6% lower than those of Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF] determined by the same method. As stated above, DSC is among the more suitable methods to determine heat capacity, but accurate measurements depend on several factors. The data of Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF] are considered as more reliable because a great care was taken during their experiments to overcome most of practical challenges (calibrations, heat capacity of the empty calorimeter, sample purity and masses, oxidation and corrosion of interior of the calorimeter, etc.). Therefore, heat capacity obtained by Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] is rejected. On the other hand, one can notice that the data of Flotow et al. [START_REF] Flotow | Heat capacity from 5 to 350 K and thermodynamic properties of cesium nitrate to 725 K[END_REF] extrapolated from low temperature are consistent with those of Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF].

• High-temperature phase: CsNO3 (I)

High-temperature heat capacities of CsNO3 collected from literature data [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Satoh | The free rotation of  3 NO ion in some nitrates[END_REF][START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF][START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] are presented in Fig. 2. As it can be seen, the values of Ichikawa and Matsumoto [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF] obtained by adiabatic calorimetry, agree satisfactorily with those of Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF] determined by DSC. The results found by Mustajoki [START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF] using an adiabatic calorimetric method, are also in agreement, in the temperature range (450 -550) K, with these two sets of data [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF].

However, for T > 550 K, Mustajoki [START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF] reported higher values. For example, between 660 K and 680 K, the difference between his data and the above two sets of data is about 10%. The fact that the heat capacity increases drastically with an increase in the temperature may be attributed to a phase transition. As for CsNO3 (II), the DSC results published by Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] are the lowest data in the temperature range (430 -610) K. The heat capacity of CsNO3 (I) determined by Satoh [START_REF] Satoh | The free rotation of  3 NO ion in some nitrates[END_REF], using an ice calorimetric technique, is abnormally high compared to the other literature data. For lack of more experimental information, his data are considered inaccurate.

Based on sample characteristics and calorimeter operation, it is worthy to consider the data of Ichikawa and Matsumoto [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF] and those of Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF] as the most reliable with uncertainty of ±2%.

• Liquid phase

The heat capacities of CsNO3 liquid phase from different authors [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF][START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] are presented in Fig. 3. There is some scatter in the data. However, results obtained by Ichikawa and Matsumoto [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF] and by Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF] agree satisfactorily within experimental uncertainties. The discrepancy between the data of Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF] and those of Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] who used the same experimental technique (DSC) is of the order of 26%. Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] have the highest values in contrast to those of the solid phases. The data of Mustajoki [START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF] are about 10% lower compared to those of Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] and about 18% higher than the data of Ichikawa and Matsumoto [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF] and Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF].

For the reasons mentioned above, the data of Ichikawa and Matsumoto [START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF] and those of Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF] are considered as the most reliable with uncertainty of ±2%.

Temperature and enthalpy of phase changes (solid-solid transition, melting)

Thermochemical properties (enthalpy and temperature) of solid-solid transition and melting of CsNO3 have been reported by many authors [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Hellali | Contribution à l'étude thermodynamique des mélanges binaires et ternaires des nitrates d'argent, de césium, de lithium, de sodium et de rubidium[END_REF][START_REF] Charrier | Determination of the temperature and enthalpy of the solid-solid phase transition of caesium nitrate by differential scanning calorimetry[END_REF][START_REF] Chary | Structural phase transition in CsNO3: dielectric studies[END_REF]. The data gathered during the present work are presented in Table 1 altogether with the experimental techniques and the sample characteristics (purity and treatment before the use).

The data have been classified into four groups based on the used experimental method: (i) DSC (Differential Scanning Calorimetry); (ii) STA/DTA (Simultaneous Simple or Direct and Differential Thermal Analysis); (iii) Other calorimetry (e.g., drop calorimetry, adiabatic calorimetry, near adiabatic, and dissolution calorimetry); (iv) Chemical analysis and all other methods (e.g., electrochemical measurement, mixing method, volume discontinuity method, XRD, XPS, EMF, Raman spectroscopy).

• Solid-solid transition temperature (TII/I)

The solid-solid transition temperatures (TII/I) of CsNO3 compiled from literature lie in the (423 -434) K range [32, 38, 49, 60, 65-73, 77-79, 83-89] with a maximum uncertainty of ±2 K. The differences between values are statistically significant. Therefore, the Duncan posthoc test is carried out to see where differences between values occur. The post-hoc test leads to five homogeneous subsets. The higher value (434 K) of Gordon and Campbell [START_REF] Gordon | Differential thermal analysis of inorganic compounds. Nitrates and perchlorates of the alkali and alkaline earth groups and their subgroups[END_REF] stands alone, this means that "434 K" is significantly different from all the other temperature values.

As mentioned in their paper, many experimental factors such as heating rate, geometry of apparatus and especially the type of recording system influence the appearance of the DTA curves. DTA curves obtained by Gordon and Campbell [START_REF] Gordon | Differential thermal analysis of inorganic compounds. Nitrates and perchlorates of the alkali and alkaline earth groups and their subgroups[END_REF] are not enough accurate. So, it seems justified to cast some doubts about the reliability of this transition temperature value.

The lower value (423 K) obtained by Fermor and Kjekshus [START_REF] Fermor | On the Electrical Properties of RbNO3 and CsNO3[END_REF] using electrical measurements is questionable due to the limitations of the technique used. Indeed, this temperature determined from the curve of resistivity versus inverse of absolute temperature may be underestimated. For example, in their same work, a value of 425 K for TII/I is obtained from the curve of dielectric constant versus temperature on heating. The Duncan test without the result of Gordon and Campbell [START_REF] Gordon | Differential thermal analysis of inorganic compounds. Nitrates and perchlorates of the alkali and alkaline earth groups and their subgroups[END_REF] and that of Fermor and Kjekshus [START_REF] Fermor | On the Electrical Properties of RbNO3 and CsNO3[END_REF] leads to three homogeneous subsets. Two values are considered to be problematic: 430.35 K (Ichikawa and Matsumoto [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF], AC) and (424±1) K (Zamali and Jemal [START_REF] Zamali | Diagrammes de phases des systèmes binaires KNO3-CsNO3 et KNO3-NaNO3[END_REF], DTA). [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF] used a Pt-Rh thermocouple for the temperature measurements. This thermocouple was calibrated by a cryoscopic method for pure-grade recrystallized reagents KNO3, K2SO4, Ag2SO4 and KClO4. Although, the solid-solid transition temperature recorded for KNO3 (402.95 K) seems reliable [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Zamali | Diagrammes de phases des systèmes binaires KNO3-CsNO3 et KNO3-NaNO3[END_REF], that obtained under the same experimental conditions for RbNO3 (439.45 K, first solid-solid phase transition) is higher at least 2 K than most of published data [START_REF] Monia | Heat capacities and enthalpies of fusion of lithium and rubidium nitrates: Heat capacities, enthalpies of fusion and enthalpies of formation of the intermediate compounds Ag0.5Rb0.5NO3 and Li0.5Rb0.5NO3[END_REF]. Therefore, the solid-solid transition temperature of CsNO3 obtained by Ichikawa and Matsumoto [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF] may be considered as high.

Ichikawa and Matsumoto

The II/I phase transition temperature obtained by Zamali and Jemal [START_REF] Zamali | Diagrammes de phases des systèmes binaires KNO3-CsNO3 et KNO3-NaNO3[END_REF] is lower than all those determined with the same method (DTA). Their value which was neither confirmed in the works from the same laboratory [84-86, 88, 89] is looked as less reliable. The data of Mustajoki [START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF] similar to that of Zamali and Jemal [START_REF] Zamali | Diagrammes de phases des systèmes binaires KNO3-CsNO3 et KNO3-NaNO3[END_REF] is also considered as less reliable. The data of Chary et al. [START_REF] Chary | Structural phase transition in CsNO3: dielectric studies[END_REF] and Bakes et al. [START_REF] Bakes | Etude d'anomalies électroniques d'origine structural en sels fondus[END_REF] are ignored because of lack of information about the purity of salts used. Finally, 7 [START_REF] Chary | Structural phase transition in CsNO3: dielectric studies[END_REF][START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF][START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Gordon | Differential thermal analysis of inorganic compounds. Nitrates and perchlorates of the alkali and alkaline earth groups and their subgroups[END_REF][START_REF] Bakes | Etude d'anomalies électroniques d'origine structural en sels fondus[END_REF][START_REF] Fermor | On the Electrical Properties of RbNO3 and CsNO3[END_REF][START_REF] Zamali | Diagrammes de phases des systèmes binaires KNO3-CsNO3 et KNO3-NaNO3[END_REF] of the 24 determinations are rejected. Although two homogeneous subsets are obtained, the differences between the measurements are not statistically significant (p-value = 0.447 > 0.05). The mean value of 427.2735 K and standard deviation equal to 2.0113 K comparable to experimental uncertainty, are obtained.

The statistic analysis of solid-solid transition temperature of CsNO3, which is an example for all other statistical analyses, is repoted in Supplementary data section. and Kjekshus [START_REF] Fermor | On the Electrical Properties of RbNO3 and CsNO3[END_REF] (423 K), all other published values are acceptable within the maximum experimental uncertainty of ±2 K. However, it is important to notice that the values of Zamali and Jemal [START_REF] Zamali | Diagrammes de phases des systèmes binaires KNO3-CsNO3 et KNO3-NaNO3[END_REF] (424±1) K and Mustajoki [START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF] Considering all acceptable data, the mean value is recalculated and the recommended value for the solid-solid transition temperature of CsNO3 proposed in this work is (427±2) K.

• Melting temperature (Tm)

The compiled melting temperatures (Tm) of CsNO3 vary from 677 K to 690 K [32, 38, 65-68, 70-76, 79-81, 83-90] with an experimental uncertainty of about ±2 K. Only Owens [START_REF] Owens | Melting properties of the alkali nitrates to 10000 atmospheres[END_REF] claimed an uncertainty of ±5 K. Using volume discontinuity method, he found a melting temperature of 683 K. The temperature measurement was done with Chromel-Alumel thermocouple. For this type of thermocouple, the uncertainty does not exceed ±2.2 K [START_REF] Nakos | Uncertainty analysis of thermocouple measurements used in normal and abnormal thermal environment experiments at Sandia's radiant heat facility and lurance canyon burn site[END_REF]. So, the uncertainty obtained by Owens [START_REF] Owens | Melting properties of the alkali nitrates to 10000 atmospheres[END_REF] is considered as very high. Due to less accurate experimental method used, the melting temperature proposed by Owens [START_REF] Owens | Melting properties of the alkali nitrates to 10000 atmospheres[END_REF] is considered less reliable. The data of Bakes et al. [START_REF] Bakes | Etude d'anomalies électroniques d'origine structural en sels fondus[END_REF], Diogenov and Sarapulova [START_REF] Diogenov | 3 and Li, Na, Rb || NO3 systems, Russ[END_REF], and Shenkin [START_REF] Shenkin | Fusion diagrams for binary systems comprising alkali metal nitrates and chlorides[END_REF] are rejected because of lack of information about the purity of salts used. During the present analysis, an uncertainty of ±2 K is retained.

The 20 of the 25 determinations tested are statistically different. The post-hoc test leads to 4 homogeneous subsets.

Two values are totally incompatible: 690 K [START_REF] Kleppa | Heats of fusion of the monovalent nitrates by hightemperature reaction calorimetry[END_REF] and 677 K [START_REF] Hellali | Contribution à l'étude thermodynamique des mélanges binaires et ternaires des nitrates d'argent, de césium, de lithium, de sodium et de rubidium[END_REF][START_REF] Gordon | Differential thermal analysis of inorganic compounds. Nitrates and perchlorates of the alkali and alkaline earth groups and their subgroups[END_REF][START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF][START_REF] Sirousse-Zia | Complément à l'étude thermodynamique de sels fondus à anion polyatomique[END_REF]. The higher value (690 K) obtained by Kleppa and McCarty [74] using high-temperature reaction calorimetry can raise reasonable doubts. Indeed, the experimental method used is not accurate enough compared to DSC and ATD. For the same reason, the value of Plyuschev et al. [START_REF] Plyushchev | The diagrams of phase transformation of the binary systems obtained from rubidium and cesium nitrates with the nitrates of strontium and barium[END_REF] (687 K) is rejected.

By not considering the value of Kleppa and McCarty [START_REF] Kleppa | Heats of fusion of the monovalent nitrates by hightemperature reaction calorimetry[END_REF] and that of Plyuschev et al. [START_REF] Plyushchev | The diagrams of phase transformation of the binary systems obtained from rubidium and cesium nitrates with the nitrates of strontium and barium[END_REF], the subsets move from 4 to 2. The temperature determined by Ichikawa and Matsumoto [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF] (684.85 K) stands alone. The melting temperature obtained under the same experimental conditions for LiNO3 (529.65 K), NaNO3 (583.35 K) and KNO3 (609.45 K) [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF] are higher than most of published data [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Monia | Heat capacities and enthalpies of fusion of lithium and rubidium nitrates: Heat capacities, enthalpies of fusion and enthalpies of formation of the intermediate compounds Ag0.5Rb0.5NO3 and Li0.5Rb0.5NO3[END_REF]. Therefore, as already mentioned, the results of Ichikawa and Matsumoto [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF] seem to be systematically high. The new statistical analysis taking into account 17 of the 25 experimental results shows that the values of 683 K [START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF][START_REF] Bélaïd-Drira | Diagramme de phases et propriétés thermodynamiques du liquide du système binaire CsNO3-NaNO3[END_REF][START_REF] Secco | Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems[END_REF] and 677 K [START_REF] Hellali | Contribution à l'étude thermodynamique des mélanges binaires et ternaires des nitrates d'argent, de césium, de lithium, de sodium et de rubidium[END_REF][START_REF] Gordon | Differential thermal analysis of inorganic compounds. Nitrates and perchlorates of the alkali and alkaline earth groups and their subgroups[END_REF][START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF][START_REF] Sirousse-Zia | Complément à l'étude thermodynamique de sels fondus à anion polyatomique[END_REF] are incompatible.

The melting temperature determined by Secco and Secco (683 K) [START_REF] Secco | Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems[END_REF] using DSC method is slightly higher than all those obtained by the same technique [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Hellali | Contribution à l'étude thermodynamique des mélanges binaires et ternaires des nitrates d'argent, de césium, de lithium, de sodium et de rubidium[END_REF][START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF][START_REF] Marchidan | Heat of melting for eutectics formed in binary-systems of AgNO3 with KNO3, RbNO3, CsNO3, AgCl and AgBr[END_REF][START_REF] Abdessattar | Experimental study and thermodynamic analysis of (CsNO3-TlNO3) binary system[END_REF]. Though the method is accurate, some reasonable doubts may be exist about their value. Indeed, the melting temperature obtained under the same experimental conditions for TlNO3 (483.15 K) [START_REF] Secco | Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems[END_REF] are higher than most of published data [START_REF] Abdessattar | Experimental study and thermodynamic analysis of (CsNO3-TlNO3) binary system[END_REF] obtained by DSC method. On the other hand, Bélaïd-Drira et al. [START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF][START_REF] Bélaïd-Drira | Diagramme de phases et propriétés thermodynamiques du liquide du système binaire CsNO3-NaNO3[END_REF] obtained a slightly higher value of melting temperature of CsNO3 (683 K) than that of Abdessattar et al. ((681±1) K) [START_REF] Abdessattar | Experimental study and thermodynamic analysis of (CsNO3-TlNO3) binary system[END_REF], although they worked under similar experimental conditions. The higher value, (683±1) K, seems less reliable.

Finally, 11 of the 25 determinations were rejected [67, 70, 73-76, 84, 86-88, 90]. The differences between the results considered are not statistically significant. One homogeneous subset is obtained with the mean value of 678.4500 K and standard deviation (SD) equal to 2.0894 K comparable to experimental uncertainty.

Comparison between the mean value for the melting temperature of CsNO3 and the all experimental results is presented in Fig. 5. One can notice that the results of Bélaïd-Drira et al. [START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF][START_REF] Bélaïd-Drira | Diagramme de phases et propriétés thermodynamiques du liquide du système binaire CsNO3-NaNO3[END_REF] ((683±1) K), Secco and Secco [START_REF] Secco | Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems[END_REF] ((683±2) K) and Wacharine et al. [START_REF] Wacharine | The phase diagram of CsNO3-RbNO3[END_REF] ((682±1) K), are consistent with each other and are just above the upper limit of acceptable values. The data of Ichikawa and Matsumoto [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF] ((684.85±0.10) K), Plyuschev et al. [START_REF] Plyushchev | The diagrams of phase transformation of the binary systems obtained from rubidium and cesium nitrates with the nitrates of strontium and barium[END_REF] (687 K), Kleppa and McCarty [74] (690 K) and Shenkin [START_REF] Shenkin | Fusion diagrams for binary systems comprising alkali metal nitrates and chlorides[END_REF] Considering all acceptable data, the mean value is recalculated and the recommended value for the melting temperature of CsNO3 proposed in this work is (678±1) K.

• Solid-solid transition enthalpy (ΔII/IH°)

The values of solid-solid transition enthalpy of CsNO3 (ΔII/IH°) collected from different sources are between 1464 J mol -1 and 5020 J mol -1 [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Hellali | Contribution à l'étude thermodynamique des mélanges binaires et ternaires des nitrates d'argent, de césium, de lithium, de sodium et de rubidium[END_REF][START_REF] Charrier | Determination of the temperature and enthalpy of the solid-solid phase transition of caesium nitrate by differential scanning calorimetry[END_REF][START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF][START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF][START_REF] Bridgman | Polymorphic changes under pressure of the univalent nitrates[END_REF][START_REF] Rao | Crystal structure transformations of alkali sulphates, nitrates and related substances: thermal hysteresis in reversible transformations[END_REF][START_REF] Marchidan | Heat of melting for eutectics formed in binary-systems of AgNO3 with KNO3, RbNO3, CsNO3, AgCl and AgBr[END_REF][START_REF] Secco | Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems[END_REF][START_REF] Abdessattar | Experimental study and thermodynamic analysis of (CsNO3-TlNO3) binary system[END_REF]. The higher value found by Marchidan and Vasu [START_REF] Marchidan | Heat of melting for eutectics formed in binary-systems of AgNO3 with KNO3, RbNO3, CsNO3, AgCl and AgBr[END_REF] (5020 J mol -1 ) using DSC method seems less reliable and is not taken into account in the present analysis. Indeed, this value is about 30% higher than the mean value of all data obtained by the same experimental method.

Using DTA technique, Rao and Rao [START_REF] Rao | Crystal structure transformations of alkali sulphates, nitrates and related substances: thermal hysteresis in reversible transformations[END_REF] gave the lowest value of solid-solid transition enthalpy (1464.4 J mol -1 ) with a high uncertainty (±15%). They prepared CsNO3 from the corresponding carbonate (Cs2CO3, analytical grade), but no details were given about the process or the purity. Impurities in the salt can explain the lower value of enthalpy. In addition, no indication was given about the working atmosphere (gas used) which is important to protect salt from any pollution or contamination. Doubts about the reliability of the value may be raised. Therefore, the solid-solid enthalpy of Rao and Rao [START_REF] Rao | Crystal structure transformations of alkali sulphates, nitrates and related substances: thermal hysteresis in reversible transformations[END_REF] is rejected.

Considering a maximum uncertainty of ±5%, it is found that the differences between the remaining values (8 of the 10 determinations) are statistically significant. The post-hoc test shows 2 homogeneous subsets. The value of Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] (3800 J mol -1 ) and that of Secco and Secco [START_REF] Secco | Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems[END_REF] (3050 J mol -1 ) are questioned. Both were obtained by DSC method. The data of Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] is the highest, while the value of Secco and Secco [START_REF] Secco | Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems[END_REF] is the lowest. Their data are not considered as reliable because of some deficiencies already identified in their works. The enthalpy given by Mustajoki [START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF] similar to that of Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] is also rejected. The remaining five data [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Hellali | Contribution à l'étude thermodynamique des mélanges binaires et ternaires des nitrates d'argent, de césium, de lithium, de sodium et de rubidium[END_REF][START_REF] Charrier | Determination of the temperature and enthalpy of the solid-solid phase transition of caesium nitrate by differential scanning calorimetry[END_REF][START_REF] Bridgman | Polymorphic changes under pressure of the univalent nitrates[END_REF][START_REF] Abdessattar | Experimental study and thermodynamic analysis of (CsNO3-TlNO3) binary system[END_REF] lead to one homogeneous subset with the mean value of 3412.0000 J mol -1 and standard deviation equal to 153.8331 J mol -1 . This standard deviation corresponds to a relative uncertainty of 4.5 %.

Fig. 6 shows the comparison of the mean value with the published data. Solid-solid transition enthalpies published by Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] (3800 J mol -1 ) and, Secco and Secco [START_REF] Secco | Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems[END_REF] ((3050±5%) J mol -1 ) are close to the upper and lower limits of acceptable values, respectively. However, those mentioned by Rao and Rao [START_REF] Rao | Crystal structure transformations of alkali sulphates, nitrates and related substances: thermal hysteresis in reversible transformations[END_REF] ((1464.4 ± 15%) J mol -1 ) and, Marchidan and Vasu [START_REF] Marchidan | Heat of melting for eutectics formed in binary-systems of AgNO3 with KNO3, RbNO3, CsNO3, AgCl and AgBr[END_REF] (5020 J mol -1 ) are very far from these limits. Considering all acceptable data, the mean value is recalculated and the recommended value for the solid-solid transition enthalpy of CsNO3 proposed in this work is (3466±142) J mol -1 .

• Melting enthalpy (ΔmH°)

The published melting enthalpies of CsNO3 (ΔmH°) lie between 12100 J mol -1 and 15500 J mol -1 [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Hellali | Contribution à l'étude thermodynamique des mélanges binaires et ternaires des nitrates d'argent, de césium, de lithium, de sodium et de rubidium[END_REF][START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF][START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF][START_REF] Bakes | Etude d'anomalies électroniques d'origine structural en sels fondus[END_REF][START_REF] Kleppa | Heats of fusion of the monovalent nitrates by hightemperature reaction calorimetry[END_REF][START_REF] Trunin | Designing and investigations of salt systems for solar energy utilization[END_REF][START_REF] Secco | Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems[END_REF][START_REF] Abdessattar | Experimental study and thermodynamic analysis of (CsNO3-TlNO3) binary system[END_REF] with a maximum experimental uncertainty of ±5%.

First of all, the melting enthalpy of Bakes et al. [START_REF] Bakes | Etude d'anomalies électroniques d'origine structural en sels fondus[END_REF] is rejected because of lack of information about the purity of the salt used. The higher value (15500 J mol -1 ) obtained by Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] using DSC method, does not agree with any other value determined by the same experimental technique. This can be explained by the abnormally high value of heat capacity in the liquid phase. Accordingly, the melting enthalpy of Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] is considered unreliable. Using adiabatic calorimetry, Mustajoki [START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF] also gave a high melting enthalpy (14100 J mol -1 ) related to the high heat capacity in the liquid phase. This value is considered less reliable. Indeed, the melting enthalpy obtained by integration of apparent heat capacity curves is subject to sources of significant experimental uncertainty. Besause the original paper of Trunin [START_REF] Trunin | Designing and investigations of salt systems for solar energy utilization[END_REF] could not be acquired during the present work, his data (13838 J mol -1 ) is not taking into account.

The post-hoc test applied to the retained data [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Hellali | Contribution à l'étude thermodynamique des mélanges binaires et ternaires des nitrates d'argent, de césium, de lithium, de sodium et de rubidium[END_REF][START_REF] Kleppa | Heats of fusion of the monovalent nitrates by hightemperature reaction calorimetry[END_REF][START_REF] Secco | Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems[END_REF][START_REF] Abdessattar | Experimental study and thermodynamic analysis of (CsNO3-TlNO3) binary system[END_REF] shows that the value of Kleppa and McCarty [START_REF] Kleppa | Heats of fusion of the monovalent nitrates by hightemperature reaction calorimetry[END_REF] (13443.2 J mol -1 ) and that of Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF] (12100 J mol -1 ) obtained by reaction calorimetry and DSC method, respectively, are questioned. Based on the most accurate method, the value of Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF] is kept and that of Kleppa and McCarty [74] is rejected.

Finally, one homogeneous subset [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Hellali | Contribution à l'étude thermodynamique des mélanges binaires et ternaires des nitrates d'argent, de césium, de lithium, de sodium et de rubidium[END_REF][START_REF] Secco | Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems[END_REF][START_REF] Abdessattar | Experimental study and thermodynamic analysis of (CsNO3-TlNO3) binary system[END_REF] with the mean value of 12545.0000 J mol -1 and standard deviation equal to 652.7565 J mol -1 , is obtained. The standard deviation corresponds to a relative uncertainty of 5.2 %.

Plot of experimental melting enthalpies of CsNO3 from different sources compared

with the mean value is shown in Fig. 7. The enthalpy value obtained by Bakes et al. [START_REF] Bakes | Etude d'anomalies électroniques d'origine structural en sels fondus[END_REF] (13352 J mol -1 ) and that of Kleppa and McCarty [74] ((13443.2±179.9) J mol -1 ) are just above the upper limit of acceptable values. While, the data of Mustajoki [START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF] ((14100.08±125.52) J mol -1 ), Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] (15500 J mol -1 ) and Trunin [START_REF] Trunin | Designing and investigations of salt systems for solar energy utilization[END_REF] (13838 J mol -1 ) are far from this limit. Considering all acceptable data, the mean value is recalculated and the recommended value for the melting enthalpy of CsNO3 proposed in this work is (12545±413) J mol -1 .

Lithium nitrate (LiNO3)

According to Rao et al.'s compilation [START_REF] Rao | Crystal Structure Transformations in Inorganic Nitrites, Nitrates, and Carbonates[END_REF], LiNO3 crystallizes at 298 K and under atmospheric pressure in rhombohedral form (calcite type) c R3 with a = 4.692 Å and c = 15.22 Å. There is no evidence for a phase transition between room temperature and the melting point. However, a study of the temperature variation of the electronic spectrum showed a discontinuity in the absorption coefficient [START_REF] Rao | Crystal Structure Transformations in Inorganic Nitrites, Nitrates, and Carbonates[END_REF]. This discontinuity was attributed to orientational disorder indicating a transformation as in NaNO3 or in NH4NO3. Later, Wu et al. [START_REF] Wu | Structure of LiNO3: point charge model and sign of the 7 Li quadrupole coupling constant[END_REF] confirmed the calcite type structure of LiNO3 with a = 4.6920(3) Å and c = 15.2149(13) Å.

Heat capacity • Solid phase

The heat capacity of LiNO3 solid phase has been published by different authors [START_REF] Monia | Heat capacities and enthalpies of fusion of lithium and rubidium nitrates: Heat capacities, enthalpies of fusion and enthalpies of formation of the intermediate compounds Ag0.5Rb0.5NO3 and Li0.5Rb0.5NO3[END_REF][START_REF] Li | Thermal property characterization of a low supercooling degree binary mixed molten salt for thermal energy storage system[END_REF][START_REF] Rao | Crystal Structure Transformations in Inorganic Nitrites, Nitrates, and Carbonates[END_REF][START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF][START_REF] Takahashi | Heat capacities and latent heats of LiNO3, NaNO3, and KNO3[END_REF][START_REF] Goodwin | On the latent heat of fusion and the specific heat of salts in the solid and liquid state[END_REF][START_REF] Franzosini | Heat and entropy of fusion of lithium, sodium and potassium nitrates[END_REF][START_REF] Kamimoto | Enthalpy measurements on LiNO3 and NaNO2 by twin hightemperature calorimeter[END_REF]. Results of different measurements are plotted in Fig. 8. The experimental techniques and relative uncertainties are showed in brackets. The constant values of the heat capacity suggested in some publications [START_REF] Goodwin | On the latent heat of fusion and the specific heat of salts in the solid and liquid state[END_REF][START_REF] Franzosini | Heat and entropy of fusion of lithium, sodium and potassium nitrates[END_REF][START_REF] Kamimoto | Enthalpy measurements on LiNO3 and NaNO2 by twin hightemperature calorimeter[END_REF] are ignored. These values are either smoothed or calculated.

As it can be seen, the data of Ichikawa and Matsumoto [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF], Takahashi et al. [START_REF] Takahashi | Heat capacities and latent heats of LiNO3, NaNO3, and KNO3[END_REF], Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] agree satisfactorily within relative uncertainty of ±3%. The heat capacity values reported by Monia et al. [START_REF] Monia | Heat capacities and enthalpies of fusion of lithium and rubidium nitrates: Heat capacities, enthalpies of fusion and enthalpies of formation of the intermediate compounds Ag0.5Rb0.5NO3 and Li0.5Rb0.5NO3[END_REF] agree with those of Coscia et al. [START_REF] Coscia | Thermophysical properties of LiNO3-NaNO3-KNO3 mixtures for use in concentrated solar power[END_REF], but are lower than the other values [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF][START_REF] Takahashi | Heat capacities and latent heats of LiNO3, NaNO3, and KNO3[END_REF]. Monia et al. [START_REF] Monia | Heat capacities and enthalpies of fusion of lithium and rubidium nitrates: Heat capacities, enthalpies of fusion and enthalpies of formation of the intermediate compounds Ag0.5Rb0.5NO3 and Li0.5Rb0.5NO3[END_REF] did not found a clear reason for this discrepancy, but they noticed that it could be due to the impurities. To this, one should add the hygroscopic nature of LiNO3. In our opinion, the purity of salts employed is not the major source of the discrepancy between heat capacity values. Indeed, all investigations are based on samples with sufficient purity (> 99.0%). Therefore, it is the calorimeter operation that can be incriminated. For example, the heat capacity values determined by Monia et al. [START_REF] Monia | Heat capacities and enthalpies of fusion of lithium and rubidium nitrates: Heat capacities, enthalpies of fusion and enthalpies of formation of the intermediate compounds Ag0.5Rb0.5NO3 and Li0.5Rb0.5NO3[END_REF] for RbNO3, under the same experimental conditions, are systematically low compared to literature data. The lower values of heat capacity [START_REF] Monia | Heat capacities and enthalpies of fusion of lithium and rubidium nitrates: Heat capacities, enthalpies of fusion and enthalpies of formation of the intermediate compounds Ag0.5Rb0.5NO3 and Li0.5Rb0.5NO3[END_REF][START_REF] Coscia | Thermophysical properties of LiNO3-NaNO3-KNO3 mixtures for use in concentrated solar power[END_REF] are considered as less reliable. The data of Li et al. [START_REF] Li | Thermal property characterization of a low supercooling degree binary mixed molten salt for thermal energy storage system[END_REF] are extremely low compared to all other values.

• Liquid phase

The heat capacity of LiNO3 liquid phase has been reported several times [START_REF] Monia | Heat capacities and enthalpies of fusion of lithium and rubidium nitrates: Heat capacities, enthalpies of fusion and enthalpies of formation of the intermediate compounds Ag0.5Rb0.5NO3 and Li0.5Rb0.5NO3[END_REF][START_REF] Li | Thermal property characterization of a low supercooling degree binary mixed molten salt for thermal energy storage system[END_REF][START_REF] Coscia | Thermophysical properties of LiNO3-NaNO3-KNO3 mixtures for use in concentrated solar power[END_REF][START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF][START_REF] Takahashi | Heat capacities and latent heats of LiNO3, NaNO3, and KNO3[END_REF][START_REF] Cordaro | Thermodynamic properties of molten nitrate salts[END_REF]. The temperature dependence of the molar heat capacity, according to several authors, is presented in Fig. 9. The experimental techniques and relative uncertainties are showed in brackets.

The data of Takahashi et al. [START_REF] Takahashi | Heat capacities and latent heats of LiNO3, NaNO3, and KNO3[END_REF] and, Maeso and Largo [START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF] obtained by DSC are in fairly good agreement with the values of Ichikawa and Matsumoto [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF] obtained by adiabatic calorimetry. As for the solid phase, the heat capacity values reported by Monia et al. [START_REF] Monia | Heat capacities and enthalpies of fusion of lithium and rubidium nitrates: Heat capacities, enthalpies of fusion and enthalpies of formation of the intermediate compounds Ag0.5Rb0.5NO3 and Li0.5Rb0.5NO3[END_REF], Li et al. [START_REF] Li | Thermal property characterization of a low supercooling degree binary mixed molten salt for thermal energy storage system[END_REF] and, Coscia et al. [START_REF] Coscia | Thermophysical properties of LiNO3-NaNO3-KNO3 mixtures for use in concentrated solar power[END_REF] are low. These data are considered as unreliable.

Fig. 9 shows that the heat capacity of LiNO3 liquid phase is constant. The value proposed by some authors [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Maeso | The heat capacities of LiNO3 and CsNO3 from 350 to 700 K, Thermochim[END_REF][START_REF] Takahashi | Heat capacities and latent heats of LiNO3, NaNO3, and KNO3[END_REF] is (140±2%) J K -1 mol -1 . This value is in good agreement with that of Cordaro et al. [START_REF] Cordaro | Thermodynamic properties of molten nitrate salts[END_REF] ((142.99±1.68) J K -1 .mol -1 ) obtained by DSC method.

Temperature and enthalpy of melting

Temperature and enthalpy of melting of LiNO3 have been reported by many authors [22, 38, 39, 52-54, 67, 68, 72, 74, 75, 80, 81, 84, 90, 93-112]. The data gathered during the present work are presented in Table 2 altogether with the experimental techniques and the sample characteristics.

• Melting temperature

The published melting temperatures (Tm) of LiNO3 vary from 517.95 K to 543 K.

These data lead to a relative uncertainty of about 5% very higher than experimental uncertainties (< 1%). An absolute uncertainty of ± 2 K is accepted in the present analysis.

This value seems reasonable considering the temperature range of experimental results.

The data from Refs. [START_REF] Diogenov | 3 and Li, Na, Rb || NO3 systems, Russ[END_REF][START_REF] Shenkin | Fusion diagrams for binary systems comprising alkali metal nitrates and chlorides[END_REF][START_REF] Ruiz | Thermal decomposition of supported lithium nitrate catalysts[END_REF][START_REF] Vallet | Phase diagrams and thermodynamic properties of some molten nitrate mixtures[END_REF][START_REF] Schürmann | Kalorimetric und thermodynamik des systems LiNO3-NaNO3[END_REF][START_REF] Campbell | The systems: LiNO3-NH4NO3 and LiNO3-NH4NO3-H2O[END_REF] are rejected because of the defiency of information about purity of salt.

Mohammad et al. [START_REF] Mohammad | Premelting, Melting, and Degradation Properties of Molten Alkali Nitrates: LiNO3, NaNO3, KNO3, and Binary NaNO3-KNO3[END_REF] gave the lowest temperature (517.95 K) among all those obtained by DTA method [START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF][START_REF] Kefi | Experimental investigation and calculation of the phase diagram of the binary system (LiNO3+TlNO3)[END_REF][START_REF] Vallet | Phase diagrams and thermodynamic properties of some molten nitrate mixtures[END_REF][START_REF] Guizani | Diagramme de phases LiNO3-KNO3[END_REF][START_REF] Hichri | Système binaire AgNO3-LiNO3 : Diagramme de phases et propriétes thermodynamiques des mélanges à l'état liquide[END_REF]. This may be related to the low sensitivity of the DTA/TGA apparatus used, as mentioned in their paper. The value of Bol'shakov et al. [START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF] (531 K) is a little bit high. Their experimental method is considered less accurate. Roget et al.

[22] using DSC method obtained a value similar to that of Bol'shakov et al. [START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF]. The high value obtained by Roget et al. [START_REF] Roget | Study of the KNO3-LiNO3 and KNO3-NaNO3-LiNO3 eutectics as phase change materials for thermal storage in a low-temperature solar power plant[END_REF] may be due to the way that the melting temperature was determined from the DSC curve. Indeed, using the same DSC method and the same heating/cooling rate (2 K min -1 ), Mohammad et al. [START_REF] Mohammad | Premelting, Melting, and Degradation Properties of Molten Alkali Nitrates: LiNO3, NaNO3, KNO3, and Binary NaNO3-KNO3[END_REF] obtained 524.85 K, for the onset point, 529.95 K for the offset point, these temperatures have been determined from deviations from heat flow baselines, and 528.15 K for the melting temperature which seems to be the temperature corresponding to the peak top (temperature corresponding to the end of melting).

All these values [START_REF] Roget | Study of the KNO3-LiNO3 and KNO3-NaNO3-LiNO3 eutectics as phase change materials for thermal storage in a low-temperature solar power plant[END_REF][START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF][START_REF] Mohammad | Premelting, Melting, and Degradation Properties of Molten Alkali Nitrates: LiNO3, NaNO3, KNO3, and Binary NaNO3-KNO3[END_REF] are considered as unreliable and are disregarded. Thus, 25 of 34 determinations are analyzed statistically. The post-hoc test leads to 3 homogeneous subsets.

The value of Goodwin and Kalmus [START_REF] Goodwin | On the latent heat of fusion and the specific heat of salts in the solid and liquid state[END_REF] (523 K) and that of Li et al. [START_REF] Li | Thermal property characterization of a low supercooling degree binary mixed molten salt for thermal energy storage system[END_REF] (528.05 K) are questioned. Based on the more accurate experimental method, the value of Li et al. [START_REF] Li | Thermal property characterization of a low supercooling degree binary mixed molten salt for thermal energy storage system[END_REF] obtained by DSC is preferred. Finally, rejecting all data statistically comparable to that of Goodwin and Kalmus [START_REF] Goodwin | On the latent heat of fusion and the specific heat of salts in the solid and liquid state[END_REF] within the experimental uncertainty, one homogeneous subset formed by 20 results is obtained. The mean value of 526.5900 K with standard deviation of 1.9243 K are obtained. Considering all acceptable data, the mean value is recalculated and the recommended value for the melting temperature of LiNO3 proposed in this work is (527±2) K.

[ 2 2 ] [ 3 8 ] [ 3 9 ] [ 5 2 ] [ 5 3 ] [ 5 4 ] [ 6 7 ] [ 6 8 ] [ 7 2 ] [ 7 4 ] [ 7 5 ] [ 8 0 ] [ 8 1 ] [ 8 4 ] [ 9 0 ] [ 9 3 ] [ 9 4 ] [ 9 5 ] [ 9 6 ] [ 9 8 ] [ 9 9 ] [ 1 0 0 ] [ 1 0 0 ] [ 1 0 1 ] [ 1 0 1 ] [ 1 0 2 ] [ 1 0 3 ] [ 1 0 4 ] [ 1 0 5 ] [ 1 0 6 ] [ 1 0 7 , 1 0 8 ] [ 1 0 9 ] [ 1

• Melting enthalpy

Disregarding the very high value of Tye et al. [START_REF] Tye | Proceedings of the seventh symposium on thermophysical properties[END_REF] (36700 J mol -1 ), the melting enthalpies of LiNO3 (ΔmH°) compiled from literature lie between 23020 J mol -1 and 26924.04 J mol -1 which lead to a relative uncertainty of about 15% very higher than experimental uncertainties (< 6%). A maximum relative uncertainty of ± 5% is considered in the present evaluation.

Rejecting the data from Refs. [START_REF] Ruiz | Thermal decomposition of supported lithium nitrate catalysts[END_REF] and [START_REF] Schürmann | Kalorimetric und thermodynamik des systems LiNO3-NaNO3[END_REF] Considering all acceptable data, the mean value is recalculated and the recommended value for the melting enthalpy of LiNO3 proposed in this work is (25068±924) J mol -1 .

[ 9 9 ] [ 1 0 0 ] [ 1 0 1 ] [ 1 0 1 ] [ 1 0 5 ] [ 1 1 0 ] [ 1 1 1 ] Bibliographic references D mH°(LiNO 3) (J mol

Sodium nitrate (NaNO3)

As stated by Rao et al. [START_REF] Rao | Crystal Structure Transformations in Inorganic Nitrites, Nitrates, and Carbonates[END_REF], NaNO3 crystallizes at 298 K and under atmospheric pressure in rhombohedral c R3 with a = 5.0696 Å and c = 16.829 Å. Sodium nitrate has been found to undergo, around 548.5 K, a phase transition from phase NaNO3(II), ordered rhombohedral phase (calcite type), to NaNO3(I), a disordered rhombohedral phase. Numerous studies [START_REF] Lefebvre | Structure determination of sodium nitrate near the order-disorder phase transition[END_REF][START_REF] Poon | The excess optical birefringence and phase transition in sodium nitrate[END_REF][START_REF] Reeder | Spontaneous strain at the structural phase transition in NaNO3[END_REF][START_REF] Schmahl | X-Ray diffraction study of the orientational order/disorder transition in NaNO3: evidence for order parameter coupling[END_REF][START_REF] Payne | A neutron diffraction study of the order-disorder phase transition in sodium nitrate[END_REF][START_REF] Gonschorek | The crystal structures of NaNO3 at 100 K, 120 K, and 563 K[END_REF][START_REF] Yurtseven | Temperature dependence of the Raman intensity and the Bandwidth close to the order-disorder phase transition in NaNO3[END_REF][START_REF] Antao | The  c R3 m R3 transition in nitratine, NaNO3, and implications for calcite, CaCO3[END_REF][START_REF] Ketelaar | The atomic arrangement in solid sodium nitrate at high temperatures[END_REF] devoted to the phase transition in NaNO3 crystal, agree well with those reviewed by Rao et al. [START_REF] Rao | Crystal Structure Transformations in Inorganic Nitrites, Nitrates, and Carbonates[END_REF] and showed that the transition between low temperature form (phase-II), c R3 , and high temperature form (phase-I), m R3 , of NaNO3 is a second-order transition caused by internal rotation of the

 3
NO groups in the crystal. However, Ballirano [START_REF] Ballirano | Laboratory parallel-beam transmission X-ray powder diffraction investigation of the thermal behavior of nitratine NaNO3: spontaneous strain and structure evolution[END_REF] pointed out that no univocal indication on the c R3 (phase-II)  m R3 (phase-I) transition mechanism can be obtained, because of the relevant role played by the arbitrary assumptions required for defining the c0 dependence from temperature of the high temperature phase.

Heat capacity • Low temperature phase: NaNO3 (II)

Low temperature heat capacity of NaNO3 has been determined by different authors [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Coscia | Thermophysical properties of LiNO3-NaNO3-KNO3 mixtures for use in concentrated solar power[END_REF][START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Takahashi | Heat capacities and latent heats of LiNO3, NaNO3, and KNO3[END_REF][START_REF] Goodwin | On the latent heat of fusion and the specific heat of salts in the solid and liquid state[END_REF]. In Fig. 12, the heat capacity from literature is plotted as a function of temperature. The results obtained by Ping et al. [START_REF] Ping | Composition dependence of the solid state transitions in NaNO3/KNO3 mixtures[END_REF] and by D'Aguanno et al. [START_REF] D'aguanno | Thermostatic properties of nitrate molten salts and their solar and eutectic mixtures[END_REF] using DSC method can not be reported in the present work, because only the plot without the experimental values is available in their papers.

As it can be seen, all experimental results agree satisfactorily within experimental uncertainties, except for the data of Dikant [START_REF] Dikant | Specific heat, thermal diffusivity and thermal conductivity of Ca doped NaNO3 crystals near the transition point[END_REF] and those of Coscia et al. [START_REF] Coscia | Thermophysical properties of LiNO3-NaNO3-KNO3 mixtures for use in concentrated solar power[END_REF][START_REF] Coscia | Ternary molten salt heat transfer fluids for energy applications[END_REF] which are too high and too low, respectively.

Dikant [START_REF] Dikant | Specific heat, thermal diffusivity and thermal conductivity of Ca doped NaNO3 crystals near the transition point[END_REF] used a pulse method which is considered to be less accurate than adiabatic calorimetry and differential scanning calorimetry. Therefore, poor reliability may be attached to his determinations. No particular reason is found for low values of Coscia et al. [START_REF] Coscia | Thermophysical properties of LiNO3-NaNO3-KNO3 mixtures for use in concentrated solar power[END_REF][START_REF] Coscia | Ternary molten salt heat transfer fluids for energy applications[END_REF] using DSC technique.

It is worthy to notice that the original paper of Kubicar [131] could not be retrieved during the present work. So the data from this paper are not reported in Fig. 12. However, the following comments can be considered. Klement [START_REF] Klement | A macroscopic description for the λ transition in sodium nitrate[END_REF] noticed that Kubicar's specific heat values [131] are systematically superior to the other, reasonably coherent [START_REF] Miekk-Oja | Kalorimetrische Untersuchungen ueber Umwandlungen in NaNO3 und KNO3[END_REF][START_REF] Sokolov | Heat capacity and enthalpy of melting of sodium nitrate[END_REF][START_REF] Mustajoki | Kalorimetrische Untersuchungen mit Bezug auf die Umwandlung in NaNO3 und Dessen Sghmelzvorgang[END_REF][START_REF] Reinsborough | Specific heat of sodium nitrate and silver nitrate by medium high temperature adiabatic calorimetry[END_REF]. This is probably due to the difficulties in calibration for the pulse technique used.

• High temperature phase: NaNO3 (I)

Heat capacity data of NaNO3 (I) are available from various authors [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Coscia | Thermophysical properties of LiNO3-NaNO3-KNO3 mixtures for use in concentrated solar power[END_REF][START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Takahashi | Heat capacities and latent heats of LiNO3, NaNO3, and KNO3[END_REF][START_REF] Miekk-Oja | Kalorimetrische Untersuchungen ueber Umwandlungen in NaNO3 und KNO3[END_REF][START_REF] Sokolov | Heat capacity and enthalpy of melting of sodium nitrate[END_REF][START_REF] Mustajoki | Kalorimetrische Untersuchungen mit Bezug auf die Umwandlung in NaNO3 und Dessen Sghmelzvorgang[END_REF][START_REF] Janz | Melting and pre-melting phenomena in alkali metal nitrates[END_REF][START_REF] Reinsborough | Specific heat of sodium nitrate and silver nitrate by medium high temperature adiabatic calorimetry[END_REF][START_REF] Dikant | Specific heat, thermal diffusivity and thermal conductivity of Ca doped NaNO3 crystals near the transition point[END_REF][START_REF] Nguyen-Duy | Calorimetric determination of the thermodynamic properties of the alkali metal salts NaNO3, KNO3, Na2Cr2O7, K2Cr2O7 and their binary eutectic solutions[END_REF][START_REF] Rogers | Melting-crystallization and premelting properties of NaNO3-KNO3. Enthalpies and heat capacities[END_REF][START_REF] Carling | Heat capacity of NaNO3 and KNO3 from 350 to 800 K, Thermochim[END_REF][START_REF] Ping | Composition dependence of the solid state transitions in NaNO3/KNO3 mixtures[END_REF][START_REF] Coscia | Ternary molten salt heat transfer fluids for energy applications[END_REF][START_REF] D'aguanno | Thermostatic properties of nitrate molten salts and their solar and eutectic mixtures[END_REF]. The results gathered from literature during the present work are plotted in Fig. 13. Not taking into account the high values obtained by Dikant [START_REF] Dikant | Specific heat, thermal diffusivity and thermal conductivity of Ca doped NaNO3 crystals near the transition point[END_REF] already considered as unreliable, the discrepancy between the experimental data is found to be more than 10%. All reported data are obtained either by differential scanning calorimetry or by adiabatic calorimetry which are the most accurate methods. Accordingly, a critical review in order to get reliable data of heat capacity of NaNO3(I) is rather challenging. However, Jriri et al.'s measurements [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF] and those of Miekk-Oja [START_REF] Miekk-Oja | Kalorimetrische Untersuchungen ueber Umwandlungen in NaNO3 und KNO3[END_REF] agree within ± 3%, which is to a certain extent comparable to the experimental uncertainty in the heat capacity values. .mol -1

)

Miekk-Oja [START_REF] Miekk-Oja | Kalorimetrische Untersuchungen ueber Umwandlungen in NaNO3 und KNO3[END_REF] (AC, 1%)

Sokolov and Shmidt [START_REF] Sokolov | Heat capacity and enthalpy of melting of sodium nitrate[END_REF] (AC, 0.5%)

Mustajoki [START_REF] Mustajoki | Kalorimetrische Untersuchungen mit Bezug auf die Umwandlung in NaNO3 und Dessen Sghmelzvorgang[END_REF] (AC, <0.7%)*

Mustajoki [START_REF] Mustajoki | Kalorimetrische Untersuchungen mit Bezug auf die Umwandlung in NaNO3 und Dessen Sghmelzvorgang[END_REF] (AC, <0.7%)**

• Liquid phase

The heat capacity data of NaNO3 liquid phase are available in different bibliographic sources [32, 54, 65, 67, 93, 94, 97, 127, 129, 133-137, 139-143, 145-150]. The experimental data vs. temperature are shown in Fig. 14. Only the measurements of Asahina et al. [START_REF] Asahina | Reports of the Government Industrial Research Institute[END_REF] are not reported because we could not get their original paper. Except for the high values of Mustajoki [START_REF] Mustajoki | Kalorimetrische Untersuchungen mit Bezug auf die Umwandlung in NaNO3 und Dessen Sghmelzvorgang[END_REF], all measurements are in fairly good agreement with each other within experimental uncertainties.

From Fig. 14, it is reasonable to assume a constant heat capacity in the NaNO3 liquid phase with a mean value about 140 J K -1 mol -1 [START_REF] Douglas | Specific heats of liquid metals and liquid salts[END_REF][START_REF] Asahina | Reports of the Government Industrial Research Institute[END_REF]. However, most of data obtained by drop calorimetry are higher than this mean value: Goodwin and Kalmus [START_REF] Goodwin | On the latent heat of fusion and the specific heat of salts in the solid and liquid state[END_REF] (152.9 ± 1%) J K -1 mol -1 , Nguyen-Duy and Dancy [START_REF] Nguyen-Duy | Calorimetric determination of the thermodynamic properties of the alkali metal salts NaNO3, KNO3, Na2Cr2O7, K2Cr2O7 and their binary eutectic solutions[END_REF] ((212 ± 32) J K -1 mol -1 ) and Douglas [START_REF] Douglas | Specific heats of liquid metals and liquid salts[END_REF] (155.7 J K -1 mol -1 ). Only Janz et al. [START_REF] Janz | Melting and pre-melting phenomena in alkali metal nitrates[END_REF] (130.54 J K -1 mol -1 ), and Kawakami et al. [START_REF] Kawakami | Heat capacity measurement of molten NaNO3-NaNO2-KNO3 by drop calorimetry, VII International Conference on Molten Slags Fluxes and Salts[END_REF] ((129 ± 3) J K -1 mol -1 ) showed lower values. Compared to DSC and adiabatic calorimetry, drop calorimetry is considered as less accurate.

Temperature and enthalpy of phase changes (solid-solid transition, melting)

A wealth of experimental data exists on the thermochemical properties of NaNO3.

Bibliographic information as complete as possible are gathered in Table 3. However, very old papers published in 19th century especially temperatures of transition are disregarded. Most of these data were summarized by Menzies and Dutt [START_REF] Menzies | The liquidus surface of the ternary system composed of the nitrates of potassium, sodium and calcium[END_REF].

• Solid-solid transition temperature (TII/I)

The solid-solid transition temperature of NaNO3 from literature is detected in the range (530 -552.

(iv) Data from chemical analysis and all other methods

All considered values [114-116, 120, 122, 183, 187, 188] are in the range (548 -552.7) K,

i.e. superior to 547 K.

(v) Critical analysis of all data

From the preliminary analysis above, two groups of data are obtained: TII/I  547 K and TII/I > 547 K.

The question here is which one contains the reliable value of solid-solid transition of NaNO3? As stated in section 2.1, apart from the salt purity, experimental procedures such as atmosphere, gas flow, crucible material, calibration, heating/cooling rate and the way the transition temperature is determined from the thermal analysis curve, are the basic causes of the discrepancy in the data. In the particular case of NaNO3, Dancy [START_REF] Dancy | Molar enthalpy of solid-solid transition in NaNO3[END_REF] pointed out that the source of the discrepancies in the values of solid-solid transition temperature obtained from DSC measurements lies also in the difficulty in identifying the beginning of this transition.

Indeed, the transition is known as a gradual phase transition (λ-type) starting at about 423 K and ending at about 549 K, just below the melting point [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Takahashi | Heat capacities and latent heats of LiNO3, NaNO3, and KNO3[END_REF][START_REF] Reinsborough | Specific heat of sodium nitrate and silver nitrate by medium high temperature adiabatic calorimetry[END_REF][START_REF] Dikant | Specific heat, thermal diffusivity and thermal conductivity of Ca doped NaNO3 crystals near the transition point[END_REF][START_REF] Carling | Heat capacity of NaNO3 and KNO3 from 350 to 800 K, Thermochim[END_REF][START_REF] Ghosh | Differential Scanning Calorimetric studies of several compounds showing order-disorder[END_REF][START_REF] Brehat | Analysis of the temperature-dependent infrared active lattice modes in the ordered phase of sodium nitrate[END_REF].

On the other hand, Kawashima et al. [START_REF] Kawashima | Behaviour of the fundamental absorption edge of sodium nitrate near the lambda transition[END_REF] noticed that the λ-transition temperature (Tλ) is the most difficult point to be controlled by the thermal control system, because the heat capacity shows anomalous temperature dependence at Tλ. From these observations and paying more attention to the data obtained by chemical analysis and all other methods, it is worthy to consider the transition temperature higher than 547 K in agreement with the data from all other calorimetry methods.

Based on this assumption, 32 determinations of 42 are statistically analyzed. 3 homogeneous subsets are obtained. Disregarding, the three questionable values : 552 K [START_REF] Poon | The excess optical birefringence and phase transition in sodium nitrate[END_REF], 552.3 K [START_REF] Schmahl | X-Ray diffraction study of the orientational order/disorder transition in NaNO3: evidence for order parameter coupling[END_REF] and 552.7 K [START_REF] Antao | The  c R3 m R3 transition in nitratine, NaNO3, and implications for calcite, CaCO3[END_REF], one homogeneous subset is obtained leading to the mean value of [101] ((532.45±4.9) K, DTA), Nguyen-Duy and Dancy [START_REF] Nguyen-Duy | Calorimetric determination of the thermodynamic properties of the alkali metal salts NaNO3, KNO3, Na2Cr2O7, K2Cr2O7 and their binary eutectic solutions[END_REF] (535 K), Dancy [START_REF] Dancy | Molar enthalpy of solid-solid transition in NaNO3[END_REF] (530 K)

and Maeso [157,[START_REF] Maeso | The phase diagrams of LiNO3-NaNO3 and LiNO3-KNO3: the behaviour of liquid mixtures[END_REF] ((540.1±1) K) are far from the lower limit. Considering all acceptable data, the mean value is recalculated and the recommended value for the solid-solid transition temperature of NaNO3 proposed in this work is (549±2) K.

[ 2 2 ] [ 3 8 ] [ 7 7 ] [ 8 6 ] [ 1 0 1 ] [ 1 0 5 ] [ 1 1 5 ] [ 1 1 7 ] [ 1 1 9 ] [ 1 2 2 ] [ 1 2 8 ] [ 1 3 0 ] [ 1 3 3 ] [ 1 3 6 ] [ 1 4 4 ] [ 1 5 4 ] [ 1 5 5 ] [ 1 5 7 ] [ 1 6 2 ] [ 1 6 8 ] [ 1 7 1 ] [ 1 7 3 ] [ 1 7 6 ] [ 1 8 2 ] [ 1 8 5 ] [ 1 8 7 ] [ 1 8 9 ] [ 1

• Melting temperature (Tm)

The NaNO3 melting point found by numerous authors, lies in the range (571. [START_REF] Mustajoki | Die spezifische Wärme des Cäsiumnitrats im Temperaturintervall 50…450°C sowie Dessen Umwandlungs und Schmelzwärme[END_REF] 170-182, 184, 185, 192-196] which leads to a relative uncertainty of about 3% higher than experimental uncertainties (< 1%). So, the differences in data are statistically significant. Disregarding publications in which salt purity was not defined, 52 determinations of 63 are analyzed. The post-hoc test leads to at least 4 homogeneous subsets. As done above, data from each of experimental technique are firstly examined, before the critical analysis of all data.

(i) Data from DSC method

Melting temperature values of NaNO3 obtained by DSC method are between 574.55 K and 583 K. The post-hoc test shows that the following values stand alone: 574.55 K [START_REF] Mohammad | Premelting, Melting, and Degradation Properties of Molten Alkali Nitrates: LiNO3, NaNO3, KNO3, and Binary NaNO3-KNO3[END_REF] and 583 K [START_REF] Carling | Heat capacity of NaNO3 and KNO3 from 350 to 800 K, Thermochim[END_REF]. For the same reasons mentioned in the case of LiNO3, the lower value of Mohammad et al. [START_REF] Mohammad | Premelting, Melting, and Degradation Properties of Molten Alkali Nitrates: LiNO3, NaNO3, KNO3, and Binary NaNO3-KNO3[END_REF] is regarded as unreliable. The higher value (583 K) obtained by

Carling [START_REF] Carling | Heat capacity of NaNO3 and KNO3 from 350 to 800 K, Thermochim[END_REF] also seems less reliable. Indeed, the melting temperature of KNO3 determined by this author under the same experimental conditions is the highest value among those published except the value of Morita et al. [START_REF] Morita | Dai-2-rui: Shosen[END_REF] as showed in the compilation done by Jriri et al. [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF].

Disregarding the data of Mohammad et al. [START_REF] Mohammad | Premelting, Melting, and Degradation Properties of Molten Alkali Nitrates: LiNO3, NaNO3, KNO3, and Binary NaNO3-KNO3[END_REF] and Carling [START_REF] Carling | Heat capacity of NaNO3 and KNO3 from 350 to 800 K, Thermochim[END_REF], all data lie between 577.5 K and 581 K.

(ii) Data from DTA technique

The data obtained from DTA technique vary from 571 K to 581 K. The post-hoc test leads to 4 homogeneous subsets which can be grouped into two sets of data (571.65 -575.21) K [START_REF] Mohammad | Premelting, Melting, and Degradation Properties of Molten Alkali Nitrates: LiNO3, NaNO3, KNO3, and Binary NaNO3-KNO3[END_REF][START_REF] Sergeev | Phase equilibria in the reciprocal NaCl-KCl-NaNO3-KNO3 system[END_REF][START_REF] Zhao | Investigation of the Ca(NO3)2-NaNO3 mixture for latent heat storage, Solar Ener[END_REF] and (578 -581) K [83, 86, 170-175, 178, 179]. The data belonging to the first group are considered as less reliable. Ballirano [START_REF] Ballirano | Laboratory parallel-beam transmission X-ray powder diffraction investigation of the thermal behavior of nitratine NaNO3: spontaneous strain and structure evolution[END_REF] noticed that for kinetic reasons, melting starts at 577 K and is completed at 581 K.

(iii) Data from other calorimetric methods

The data obtained from all other calorimetry methods compiled during the present work vary from 578 K to 583.2 K. The post-hoc test leads to 3 homogeneous subsets. Two values stand alone: 578 K [START_REF] Sergeev | Thermodynamics of the reciprocal NaCl-KCl-NaNO3-KNO3 system[END_REF] and 583.2 K [START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF]. Disregarding these values, all data lie between 579.2 K and 583 K.

(iv) Data from chemical analysis and all other methods

Apart from the value of Menzies and Dutt [START_REF] Menzies | The liquidus surface of the ternary system composed of the nitrates of potassium, sodium and calcium[END_REF] (588.25 K) obtained by freezing curve, all data (578.65 K-581 K) agree satisfactorily within experimental uncertainties.

(v) Critical analysis of all data

From the preliminary analysis above, it is established that the melting temperature of NaNO3 belongs to the range (577.5 -581) K. Finally, 41 determinations of 52 are analyzed.

These 41 determinations lead to one homogeneous subset with the mean value of 579.4488 K and standard deviation of 1.909 K.

The mean value and the experimental results are compared in Fig. Considering all acceptable data, the mean value is recalculated and the recommended value for the melting temperature of NaNO3 proposed in this work is (579±2) K.

• Solid-solid transition enthalpy

Many works devoted to the solid-solid transition of NaNO3 seem to substantiate the second-order transition [START_REF] Jriri | Thermodynamic study of the condensed phases of NaNO3, KNO3 and CsNO3 and their transitions[END_REF][START_REF] Ichikawa | The heat capacity of lithium, sodium, potassium, rubidium, and caesium nitrates in the solid and liquid states[END_REF][START_REF] Takahashi | Heat capacities and latent heats of LiNO3, NaNO3, and KNO3[END_REF][START_REF] Reinsborough | Specific heat of sodium nitrate and silver nitrate by medium high temperature adiabatic calorimetry[END_REF][START_REF] Dikant | Specific heat, thermal diffusivity and thermal conductivity of Ca doped NaNO3 crystals near the transition point[END_REF][START_REF] Carling | Heat capacity of NaNO3 and KNO3 from 350 to 800 K, Thermochim[END_REF][START_REF] Ghosh | Differential Scanning Calorimetric studies of several compounds showing order-disorder[END_REF][START_REF] Kawashima | Behaviour of the fundamental absorption edge of sodium nitrate near the lambda transition[END_REF][START_REF] Brehat | Analysis of the temperature-dependent infrared active lattice modes in the ordered phase of sodium nitrate[END_REF] with enthalpy equal to zero.

However, this transition can also be considered as a sluggish first-order transition [START_REF] Rapoport | Polymorphism and melting of ammonium, thallous, and silver nitrates to 45 kbar[END_REF] with enthalpy varying between 418 J mol -1 and 4686 J mol The range of acceptable values is very small. Less than 40% of the experimental data are in agreement within the uncertainty of ±5%. Apart from the data of Schürmann and Nedeljkovic [START_REF] Schürmann | Kalorimetric und thermodynamik des systems LiNO3-NaNO3[END_REF] (4686.08 J mol -1 ) and Carling [START_REF] Carling | Heat capacity of NaNO3 and KNO3 from 350 to 800 K, Thermochim[END_REF] ((4420±130) J mol -1 ), the published first-order solid-solid transition enthalpies of NaNO3 outside the acceptable values range are distributed below the lower limit of this range. Only the value of Mustajoki [START_REF] Mustajoki | Kalorimetrische Untersuchungen mit Bezug auf die Umwandlung in NaNO3 und Dessen Sghmelzvorgang[END_REF] (3950 J mol - 1 ) is very close to the upper limit of the acceptable values. Taking into account the experimental uncertainty, this value may be considered as acceptable. Considering the data belonging to the acceptable values range, the mean value is recalculated and the recommended value for the first-order solid-solid transition enthalpy of NaNO3 proposed in this work is (3733±123) J mol -1 .

• Melting enthalpy

Bibliographic data of NaNO3 melting enthalpy, except those published in 19th century [START_REF] Regnault | Recherches sur la chaleur spécifique des corps simples et des corps composés[END_REF][START_REF] Person | Recherches sur la chaleur latente de fusion[END_REF] are between 10030 J mol -1 and 16790 J mol -1 [22, 32, 38, 47, 54, 73, 74, 93-95, 97, 101, 105, 127-130, 133, 135, 136, 141, 152-154, 157-161, 163-166, 168, 170, 177, 179-181, 197, 198] leading to a relative uncertainty more than 40%. Disregarding publications in which salt purity was not defined, 38 determinations of 44 are analyzed. The post-hoc test leads to 4 homogeneous subsets. The lower value of Martin et al. [START_REF] Martin | An experimental study of a non-eutectic mixture of KNO3 and NaNO3 with a melting range for thermal energy storage[END_REF] ((118±2) kJ kg -1 equal to (10030±170) J mol -1 ) obtained by DSC method stands alone. Reasonable doubts exist about this value. Indeed, surprisingly Martin et al. [START_REF] Martin | An experimental study of a non-eutectic mixture of KNO3 and NaNO3 with a melting range for thermal energy storage[END_REF] noticed that their value is in good agreement with the measurements of Rogers and Janz [START_REF] Rogers | Melting-crystallization and premelting properties of NaNO3-KNO3. Enthalpies and heat capacities[END_REF] with less than 10% deviation. Let us remind that the melting enthalpy obtained by Rogers and Janz [START_REF] Rogers | Melting-crystallization and premelting properties of NaNO3-KNO3. Enthalpies and heat capacities[END_REF] is (15439±1%) J mol -1 approximately equal to 181.6 kJ kg -1 .

The higher value of Cordaro et al. [START_REF] Cordaro | Thermodynamic properties of molten nitrate salts[END_REF] ((16790±260) J mol -1 ) obtained by DSC method is also regarded as unreliable.

Rejecting the values of Martin et al. [START_REF] Martin | An experimental study of a non-eutectic mixture of KNO3 and NaNO3 with a melting range for thermal energy storage[END_REF] and Cordaro et al. [START_REF] Cordaro | Thermodynamic properties of molten nitrate salts[END_REF], the post-hoc test leads to 2 homogeneous subsets. The value of Romero-Sanchez et al. [START_REF] Romero-Sanchez | Green chemistry solutions for sol-gel micro-encapsulation of phase change materials for high-temperature thermal energy storage[END_REF] (13438.5 J mol -1 ) obtained by DSC is questioned. This value is slightly lower than all other values obtained by the same experimental method. The reason can be found in the conditions used for the experiments.

Finally, 35 determinations of 38 forming one homogeneous subset lead to the mean value of 15159.9625 J mol -1 with standard deviation of 700.9186 J mol -1 . This standard deviation corresponds to a relative uncertainty of 4.623 %.

Plot of experimental melting enthalpy of NaNO3 from different sources compared with mean value is shown in Fig. 18. Only three values ((16790±260) J mol -1 [START_REF] Cordaro | Thermodynamic properties of molten nitrate salts[END_REF], (10030±170) J mol -1 [START_REF] Martin | An experimental study of a non-eutectic mixture of KNO3 and NaNO3 with a melting range for thermal energy storage[END_REF], 13438.5 J mol -1 [START_REF] Romero-Sanchez | Green chemistry solutions for sol-gel micro-encapsulation of phase change materials for high-temperature thermal energy storage[END_REF]) are truly outside the range of acceptable values. Taking into account the experimental uncertainty, the value of Roget et al. [START_REF] Roget | Study of the KNO3-LiNO3 and KNO3-NaNO3-LiNO3 eutectics as phase change materials for thermal storage in a low-temperature solar power plant[END_REF] (15980 J mol -1 ) which is slightly higher than the upper limit of acceptable values may be acceptable. Considering all acceptable data, the mean value is recalculated and the recommended value for the melting enthalpy of NaNO3 proposed in this work is (15129±365) J mol -1 .

[ 2 2 ] [ 3 2 ] [ 3 8 ] [ 4 7 ] [ 5 4 ] [ 7 3 ] [ 9 3 ] [ 9 7 ] [ 1 0 1 ] [ 1 0 1 ] [ 1 3 5 ] [ 1 3 6 ] [ 1 4 1 ] [ 1 5 2 ] [ 1 5 2 ] [ 1 5 2 ] [ 1 5 2 ] [ 1 5 2 ] [ 1 5 2 ] [ 1 5 3 ] [ 1 5 4 ] [ 1 5 7 ] [ 1 6 0 ] [ 1 6 1 ] [ 1 6 3 ] [ 1 6 4 ] [ 1 6 8 ] [ 1 7 0 [ 1 7 0 ] [ 1 7 7 ] [ 1 7 9 ] [ 1 9 7 ] [ 1

Boundary systems

CsNO3-LiNO3 system

Phase diagram

The phase diagram data of the CsNO3-LiNO3 system have been determined by several researchers. These data were critically assessed by Mossarello [START_REF] Mossarello | Création d'une banque informatisée de données cohérentes sur les propriétés thermodynamiques des mélanges de sels fondus[END_REF] and Sangster [START_REF] Sangster | Thermodynamics and phase diagrams of 32 binary common-ion systems of the group Li,Na,K,Rb,Cs//F[END_REF],

respectively. From these reviews, one can notice that the phase diagram of the system CsNO3-LiNO3 exhibits a congruently melting compound Cs0.5Li0.5NO3 which forms eutectic mixtures with the end members. However, some discrepancies exist in the values of temperature and composition of eutectics. Using simultaneously direct and differential thermal analysis, Bélaïd-Drira et al. [START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF] reinvestigated the phase diagram of the CsNO3-LiNO3 system. Their data were not included in the previous assessments [START_REF] Mossarello | Création d'une banque informatisée de données cohérentes sur les propriétés thermodynamiques des mélanges de sels fondus[END_REF][START_REF] Sangster | Thermodynamics and phase diagrams of 32 binary common-ion systems of the group Li,Na,K,Rb,Cs//F[END_REF]. Though, Bélaïd-Drira et al. [START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF] confirmed that the system has a 1:1 congruently melting compound and two eutectics, their work raised a question about the existence of the intermediate compound at ambient temperature. Indeed, by X-ray diffraction, they suggested that this compound does not exist at room temperature in contrast to the work of Bol'shakov et al. [START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF] who found that this coumpound exists at 273 K and has a polymorphic transition at 339 K. Unfortunately, Bélaïd-Drira et al. [START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF] did not present X-ray patterns as a proof. Therefore, it is necessary to readdress this issue which affects mainly the equilibria in the solid state.

The liquidus data [START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF][START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF]201] are in good agreement except for the LiNO3-rich side where Bol'shakov et al. [START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF] showed very higher values.

Thermochemical data

Only the liquid mixing enthalpies of CsNO3-LiNO3 system are available in the literature [START_REF] Kleppa | Heats of mixing in liquid alkali nitrate systems[END_REF][START_REF] Meschel | Enthalpies of mixing in ternary fused nitrates[END_REF]. From their study, Kleppa and Hersh [START_REF] Kleppa | Heats of mixing in liquid alkali nitrate systems[END_REF] proposed an analytical expression for the enthalpy of mixing. They used regular model solution with an interaction parameter λ = -12552 J mol -1 . Meschel and Kleppa [START_REF] Meschel | Enthalpies of mixing in ternary fused nitrates[END_REF] expressed also molar enthalpy of mixing of liquid LiNO3 with (undercooled) liquid CsNO3 at 623 K (Eq. 1).

   

1 0 CsNO LiNO LiNO CsNO LiNO mix X X X X X mol J H     D  (1) With Xi, mole fraction of component i (i = LiNO3, CsNO3).
Meschel and Kleppa [START_REF] Meschel | Enthalpies of mixing in ternary fused nitrates[END_REF] found at 623 K, (13640±126) J mol -1 for the enthalpy of fusion of pure CsNO3.

Though, both expressions lead to similar results, we prefer that of Meschel and Kleppa [START_REF] Meschel | Enthalpies of mixing in ternary fused nitrates[END_REF] because of the non-regular behaviour which is more realistic considering the presence of the intermediate compound Cs0.5Li0.5NO3 in the binary system. By dissolution measurements in eutectic mixture of KNO3-TlNO3-LiNO3 ternary system used as bath at 373 K, Zoro et al. [204] determined the enthalpy of formation of the Cs0.5Li0.5NO3 compound referred to the corresponding pure nitrates as -323 J mol -1 .

Phase diagrams of CsNO3-NaNO3 and LiNO3-NaNO3 systems

The phase diagrams of CsNO3-NaNO3 and LiNO3-NaNO3 systems were extensively studied. A critical analysis of the experimental data and thermodynamic evaluations were presented in the literature [START_REF] Helali | Thermodynamic assessment of the ternary AgNO3-LiNO3-NaNO3 system[END_REF][START_REF] Jriri | Thermodynamic analysis of the CsNO3-KNO3-NaNO3 system[END_REF][START_REF] Mossarello | Création d'une banque informatisée de données cohérentes sur les propriétés thermodynamiques des mélanges de sels fondus[END_REF][START_REF] Dessureault | Evaluation critique des données thermodynamiques et des diagrammes de phases des systèmes AOH-AX, ANO3-AX, ANO3-BNO3[END_REF][START_REF] Sangster | Thermodynamics and phase diagrams of 32 binary common-ion systems of the group Li,Na,K,Rb,Cs//F[END_REF]205,[START_REF] An | Thermodynamic reevaluation and experimental validation of the CsNO3-KNO3-NaNO3 system and its subsystems[END_REF]. Both systems present a simple eutectic reaction with virtually no solid solubility in either of the pure components.

The calculated liquidus, eutectic temperature ( e T ) and composition ( e X ) obtained for CsNO3-NaNO3 system are comparable [START_REF] Jriri | Thermodynamic analysis of the CsNO3-KNO3-NaNO3 system[END_REF][START_REF] Mossarello | Création d'une banque informatisée de données cohérentes sur les propriétés thermodynamiques des mélanges de sels fondus[END_REF][START_REF] Sangster | Thermodynamics and phase diagrams of 32 binary common-ion systems of the group Li,Na,K,Rb,Cs//F[END_REF]205] ( e T = 461 K -464 K; e NaNO X 3 = 0.535 -0.541). However, the calculated eutectic temperature and composition given by An et al.

Phase diagram of the CsNO3-LiNO3-NaNO3 ternary system

To the best of our knowledge, the only experimental information of phase diagram of the CsNO3-LiNO3-NaNO3 ternary system are from Diogenov and Sarapulova [START_REF] Diogenov | 3 and Li, Na, Rb || NO3 systems, Russ[END_REF]. By visualthermal method, they investigated nine vertical sections and presented their results only in graphical form. They also established the crystallization surface of the ternary system. They The NaNO3-Cs0.5Li0.5NO3 section is a quasi-binary and presents a eutectic reaction (Liq = NaNO3 + Cs0.5Li0.5NO3) at 408 K.

Using the Wilson equation, Davison and Sun [START_REF] Davison | Thermodynamic analysis of solid-liquid phase equilibria of nitrate salts[END_REF] estimated the phase equilibria of CsNO3-LiNO3-NaNO3 system. Their work presents one major weakness: the phase diagram of CsNO3-LiNO3 binary system was described as a simple eutectic one.

Experimental investigations

Using a DTA device of great sensitivity, three samples in the CsNO3-LiNO3 binary system (molar compositions of LiNO3 , 3 LiNO X = 0.25; 0.50; 0.75) were analyzed. In addition, two vertical sections in the CsNO3-LiNO3-NaNO3 ternary system were also studied:

2 . 0 3  NaNO X and 1 / 3 3  LiNO CsNO X X
. A detailed description of the apparatus has been given in a previous work [START_REF] Jriri | Contribution à l'étude thermodynamique des systèmes binaires et ternaires de nitrates alcalins[END_REF]. The DTA measuring program consists in two heating/cooling cycles.

The heating and cooling rates were in the range (0.3 -0.5) K min -1 . Temperatures were measured using Pt/Pt10%Rh thermocouples calibrated against the invariant temperatures of high pure AgNO3 (99.9 wt% purity) and KNO3 (99.999 wt% purity). The overall uncertainty of the DTA temperature measurements was estimated at ±2 K.

The existence of the equimolar Cs0.5Li0.5NO3 compound at ambient temperature was addressed using the X-ray diffraction technique. Samples (CsX, Li1-X)NO3 with X = 1 (pure CsNO3); 0 (pure LiNO3) and 0.5, were analyzed at room temperature with a Siemens D5000 X-ray powder diffractometer, equipped with a copper anticathode using the Kα ray (λ = 1.5406 Å).

Reagents and samples preparation

Pure nitrates with high purity, CsNO3 (Aldrich, 99.99%), LiNO3 (Aldrich, 99.99%) and NaNO3 (Aldrich, 99.995%) were used, for the preparation of mixtures, without further purification. All these nitrates were kept in a desiccator. Appropriate amounts of dried salts were melted several times in a platinum crucible to obtain a homogeneous substance. Then, mixtures were cooled and kept for 2 days in desiccator before analysis. For the sample (Cs0.5, Li0.5)NO3, because of the likely presence of the intermediate compound Cs0.5Li0.5NO3 at ambient temperatue, the coprecipitation method was also used.

In order to avoid any pollution of samples, all preparations were conducted in the glove box filled with argon.

Results and discussion

Phase diagram of the CsNO3-LiNO3 binary system

DTA Study

From the analysis of DTA curves, the equilibrium temperatures were determined (Table 4). Because of the pronounced tendency of supercooling, only the heating temperatures were considered. All the DTA curves show a thermal effect at about 334 K corresponding to either polymorphic transition temperature of the equimolar compound Cs0.5Li0.5NO3 [START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF] or its formation temperature [START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF]. As an example, the DTA curves obtained for the sample with 3 LiNO X = 0.5 are given in Fig. 21. Whatever the method of elaboration, the thermograms have the same shape. Such an observation is a feature of an easy crystallization of the intermediate compound. The first peak observed during the heating at a mean temperature of 335 K is associated either with the formation of the intermediate compound Cs0.5Li0.5NO3 [START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF] or its polymorphic transition [START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF]. A very weak effect (second peak) at 427.65 K appearing only in the sample obtained by repeated melting and cooling (Fig. 21a) is a signature of the II/I transition of CsNO3. The thermal effect occurring at 443 K (Figs. 21a and21b) is associated with the eutectic reaction: L = CsNO3 (I) + Cs0.5Li0.5NO3. That reveals a slight excess of CsNO3 in the two samples (Cs0.5, Li0.5)NO3 due certainly to weighing errors. The peak found at (456±2) K (Fig. 21a) or (463±2) K (Fig. 21b) corresponds to the fusion of the (Cs0.5, Li0.5)NO3 samples.

X-Ray results

The diffraction pattern at room temperature of sample (Cs0.5, Li0.5)NO3 prepared by coprecipitation is presented in Fig. 22 altogether with that of pure LiNO3 (Fig. 22a) and that of pure CsNO3 (Fig. 22b). As clearly showed in Fig. 22c, the XRD measurements revealed only the characteristic peaks of CsNO3 and LiNO3. This gives support to the presence of biphasic domain: "CsNO3 + LiNO3" which is in a very good agreement with Bélaïd-Drira et al.'s work [START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF]. Therefore, the intermediate compound Cs0.5Li0.5NO3 does not exist at room temperature and the thermal effect observed at 335 K is obviously associated with its formation (heating) or its eutectoid decomposition (cooling).

CsNO3-LiNO3-NaNO3 ternary system

As for the CsNO3-LiNO3 system, the interpretation of the thermal effects leads to the equilibrium temperatures in both vertical sections: The stable forms of the pure nitrates (CsNO3, LiNO3 and NaNO3) are considered as single components. In Calphad-type approach, the Gibbs energy of the unary system i in a

Pure components

given physical state φ is generally expressed by Eq. ( 2):

... ln ) 15 . 298 ( ) (

1 7 4 3 2 0 0            hT gT fT eT dT T cT bT a K H T G SER i i  (2) ) 15 . 298 ( 0 K H SER i
is the molar enthalpy of the component "i" in its standard reference state (SER) at 298.15 K and 10 5 Pa; T is the absolute temperature in Kelvin. The coefficients a, b, c…, are obtained from an optimization procedure.

From Eq. ( 2), the heat capacity of "i", in the state φ, can be evaluated by the following expression:

...

2 42 12 6 2 2 6 3 2 ,          hT gT fT eT dT c C i P  (3)
This expression is valid for temperatures above 298.15 K. In Calphad 2 nd generation thermodynamic databases, temperatures below 298.15 K are not considered. It has to be pointed out that, in non-magnetic materials, the heat capacity at low temperature can be expressed by the following equation [START_REF] Palumbo | Thermodynamic modeling of crystalline unary phases[END_REF]:

3 AT T C low P    (4)
where,  is termed the electronic heat capacity coefficient and A is a parameter depending on the Debye temperature θD.

The plot T C low

P / versus T 2 should therefore give a straight line. As seen above, the transition NaNO3 (II)  NaNO3 (I) is assumed to be a second-order structural transition. This kind of transition is rarely represented in current thermodynamic unary databases. As stated in Ref. [START_REF] Stølen | Chemical Thermodynamics of Materials Macroscopic and Microscopic Aspects[END_REF], the thermodynamic description of second-order transitions is a big challenge.

In the present work, as in the most evaluations [START_REF] Helali | Thermodynamic assessment of the ternary AgNO3-LiNO3-NaNO3 system[END_REF][START_REF] Manouan | Thermodynamic modeling of the AgNO3-CsNO3-NaNO3 ternary system[END_REF][START_REF] Jriri | Thermodynamic analysis of the CsNO3-KNO3-NaNO3 system[END_REF][START_REF] Sangster | Thermodynamics and phase diagrams of 32 binary common-ion systems of the group Li,Na,K,Rb,Cs//F[END_REF][START_REF] Beneš | A DSC study of the NaNO3-KNO3 system using an innovativeencapsulation technique[END_REF][START_REF] Abdessattar | Experimental investigation and calculation of the phase diagram ofthe binary system (NaNO3-TlNO3)[END_REF][START_REF] Sergeev | Phase equilibria in the reciprocal NaCl-KCl-NaNO3-KNO3 system[END_REF]205,[START_REF] Robelin | Thermodynamic evaluation and optimization of the (NaNO3 + KNO3 + Na2SO4 + K2SO4) system[END_REF][START_REF] Li | Experimental investigation and thermodynamic modeling of the NaCl-NaNO3-Na2SO4 ternary system[END_REF], the solid-solid transition in NaNO3 is considered as a first-order transition. Robelin et al. [START_REF] Robelin | Thermodynamic evaluation and optimization of the (NaNO3 + KNO3 + Na2SO4 + K2SO4) system[END_REF] noticed that, this assumption has no effect on the calculated liquidus temperatures but the calculated number of phases at equilibrium at low temperatures may be incorrect. The temperature dependence of Gibbs energy for NaNO3 given by Li et al. [START_REF] Li | Experimental investigation and thermodynamic modeling of the NaCl-NaNO3-Na2SO4 ternary system[END_REF] is considered in the present evaluation.

Liquid phase

In the present evaluation, the substitutional solution model is used to describe the liquid phase. This model yields the following expression for the molar Gibbs energy:

xs L i L i L i L i i L i L m G x X RT G X G , 0 ) ln(      (5)
Referred to the enthalpies of the components in their stable state at 298.15 K,

  xs L i L i L i i SER i L i L i i SER i L i L m G X X RT K H G X K H X G , 0 0 0 ) ln( ) 15 . 298 ( ) 15 . 298 (         (6) L i
X is the molar fraction of the component "i" in the liquid phase (L), L i G 0 is the Gibbs energy of "i" in the liquid state (L), R is the gas constant, T is the absolute temperature, xs L G , is the excess Gibbs energy of the liquid phase (L) and can be described by the following expression:

   L NaNO LiNO CsNO L CsNO L NaNO L LiNO L CsNO L j L i n L j i L j L i xs L L X X X X X X L X X G 3 3 3 3 3 3 3 , , 0 0 , ,            L NaNO LiNO CsNO L NaNO L NaNO LiNO CsNO L LiNO L X L X 3 3 3 3 3 3 3 3 , , 2 , , 1   (7)
where,

L j i L ,  ( ) , , 3 3 3 NaNO LiNO CsNO j i   and L NaNO LiNO CsNO L 3 3 3 , ,



are the binary and the ternary interaction parameters, which are proposed by the Redlich-Kister polynomial [START_REF] Redlich | Algebraic representation of thermodynamic properties and the classification of solutions[END_REF] and the Redlich-Kister-Muggianu formalism [START_REF] Muggianu | Enthalpies de formation des alliages liquides bismuth-étain-gallium à 723 K. Choix d'une représentation analytique des grandeurs d'excès intégrales et partielles de mélange[END_REF][START_REF] Hillert | Empirical methods of predicting and representing thermodynamic properties of ternary solution phases[END_REF], respectively. These parameters can be temperature dependent as follows:

... ln     T T C T B A L L L L L     (8) The coefficients L A  , L B  , L C 
, …, are constants to be optimized.

Stoichiometric phase

The intermediate phase Cs0.5Li0.5NO3 named I in this work, is a stoichiometric compound and is modeled as (CsNO3)0.5(LiNO3)0.5. Its standard Gibbs energy of formation from the pure CsNO3 (hexagonal form, Hcp) and LiNO3 (rhombohedral form, Rhombo-S)

nitrates is written as a function of temperature according to Eq. ( 9):

T T C T C C G G G G S bo r LiNO hcp CsNO I I f ln 5 . 0 5 . 0 3 2 1 hom 0 0 0 0 3 3       D  (9)
with constants C1, C2 and C3 to be assessed.

Optimization and results

Optimization is the last step in the thermodynamic assessment task. By paraphrasing Ref. [START_REF] Saunders | CALPHAD (Calculation of Phase Diagrams): a Comprehensive Guide[END_REF], optimization can be defined as a fitting process whereby the adjustable coefficients in the Gibbs energy equations are altered such that the best representation of both the experimentally measured equilibrium and thermochemical properties are obtained.

In the present work, the optimization is carried out using the Parrot module of the Thermo-Calc software [START_REF] Andersson | [END_REF]. The optimization procedure is based on generalized least squares (GLS) method which permits to assign each data a weight factor that reflects the uncertainty of measurements.

All recommended solid-solid transition and melting properties of CsNO3, LiNO3 and NaNO3 from our critical analysis summarized in Table 7 are used in the present optimization.

Pure components

The thermodynamic descriptions for the pure nitrates (stable and metastable phases) based on our present work (CsNO3 and LiNO3) and from Ref. [START_REF] Li | Experimental investigation and thermodynamic modeling of the NaCl-NaNO3-Na2SO4 ternary system[END_REF] (NaNO3) are presented in Table 8. The limits of temperature at low temperature for CsNO3 are determined from the plot T C low P / versus T 2 , low P C is the heat capacity of the low temperature CsNO3 form (see Fig. 25). The calculated heat capacities of the three pure nitrates compared with the selected experimental data are presented in Figs. [START_REF] Jriri | Thermodynamic analysis of the CsNO3-KNO3-NaNO3 system[END_REF], 27 and 28. As it can be seen, the calculated heat capacities agree well with experimental data within experimental uncertainty for CsNO3 and LiNO3.

In assumption of first-order solid-solid transition, the agreement between calculation and experimental data for NaNO3 can be considered as reasonable.

Binary systems

CsNO3-LiNO3 system

Combining our present phase diagram results and those from literature [START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF]201] with the enthalpies of mixing [START_REF] Meschel | Enthalpies of mixing in ternary fused nitrates[END_REF], the CsNO3-LiNO3 binary system has been optimized. Because of the very high liquidus temperatures on the LiNO3-rich side, the data of Bol'shakov et al. [START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF] were disregarded. During the optimization procedure, the mutual solid solubilities of CsNO3 and LiNO3 were neglected in agreement with the experimental results [START_REF] Bol'shakov | Binary systems based on alkali metal nitrates[END_REF][START_REF] Bélaïd-Drira | Diagramme de phases du système binaire CsNO3-LiNO3. Activité des constituants du liquide[END_REF]201]. In addition, we have given slightly more weight to our phase diagram data taken to be more accurate. The enthalpy of formation determined by Zoro et al. [204] was also considered.

The thermodynamic parameters for liquid phase and intemediate compound Cs0.5Li0.5NO3 (named I) are listed in Table 9.

Fig. 29 shows the calculated phase diagram and the selected experimental data. As can be seen, the calculation is in agreement with the experimental values.

Table 10 shows a comparison between the calculated and measured characteristics invariant equilibrium (temperature and composition) in the CsNO3-LiNO3 system. All invariant temperatures agree well within maximum ±4 K.

The calculated mixing enthalpy of liquid phase presented in Fig. 30 shows a good agreement with the experimental data.

CsNO3-NaNO3 and LiNO3-NaNO3 systems

Because of the new lattice stabilities of pure nitrates considered in this work, the thermodynamic parameters of Jriri et al. [START_REF] Jriri | Thermodynamic analysis of the CsNO3-KNO3-NaNO3 system[END_REF] and those of Hellali et al. [START_REF] Helali | Thermodynamic assessment of the ternary AgNO3-LiNO3-NaNO3 system[END_REF] were adjusted slightly in order to reproduce the same phase diagrams as shown in Figs. 19 and20. The new parameters are listed in Table 9.

CsNO3-LiNO3-NaNO3 ternary system

To obtain a satisfactory agreement with the phase diagram data, a ternary interaction term was necessary to represent the thermodynamic properties of the ternary liquid phase.

Only the enthalpic part to the ternary interactive parameters was evaluated. Indeed, the entropic part had no significant effect on the calculation. The ternary interactive parameters obtained from the present optimization are listed in Table 9. Diogenov and Sarapulova [START_REF] Diogenov | 3 and Li, Na, Rb || NO3 systems, Russ[END_REF] reported a temperature at 408 K, on the basis of their investigation.

As presented in Fig. 32, the calculation confirms the two eutectic reactions (E1 and E2) suggested by our experimental work at (407 ± 2) K and (405 ± 2) K, respectively. Though the temperatures of both invariant reactions are in agreement within the experimental uncertainty with those of Diogenov and Sarapulova (405 K and 403 K) [START_REF] Diogenov | 3 and Li, Na, Rb || NO3 systems, Russ[END_REF], there are differences in the compositions. Details of these invariant reactions are shown in Table 11.

The calculated monovariant lines (Fig. 33) and those obtained experimentally by Diogenov and Sarapulova [START_REF] Diogenov | 3 and Li, Na, Rb || NO3 systems, Russ[END_REF] are almost similar. However, the polymorphic transition of CsNO3 seems to be ignored in the work of Diogenov and Sarapulova [START_REF] Diogenov | 3 and Li, Na, Rb || NO3 systems, Russ[END_REF] and may be one of reasons of discrepancy in the invariant compositions. (2) section:

Conclusions

Critical assessment of the ternary CsNO3-LiNO3-NaNO3 system has been performed through an optimization procedure in which the experimental information based on our present work and those from literature were used. The first achievement of this work is the recommended thermochemical properties of CsNO3, LiNO3 and NaNO3. Then, the phase equilibria in binary CsNO3-LiNO3 and the ternary CsNO3-LiNO3-NaNO3 systems were studied using XRD and DTA techniques. Finally, a self consistent thermodynamic database of CsNO3-LiNO3-NaNO3 ternary system has been constructed, which reproduced the available data within the experimental uncertainty.

The existence of the Cs0.5Li0.5NO3 equimolar compound in CsNO3-LiNO3 system is confirmed with a eutectoid decomposition at 334.00 K. The phase diagram shows two eutectic reactions at 447.12 K and 436.10 K, respectively.

Table 1

Temperatures and enthalpies of solid-solid transition and melting of CsNO3 from literature TII/I (K) Tm (K) ΔII/IH°(J mol -1 ) ΔmH°(J mol -1 ) Method (a) Sample characteristics Ref.

2 )

 2 in the ternary CsNO3-LiNO3-NaNO3 system are investigated. X-ray diffraction (XRD) technique is also used to analyze phases in the CsNO3-LiNO3 binary system at room temperature.

Fig. 1 .

 1 Fig. 1. Temperature dependence of the molar heat capacity of CsNO3 (II) from different sources. (a) Temperature range (0 -425) K. (b) Enlargement in the temperature range (300 -425) K. Error bars represent the experimental uncertainties on Cp. C : Calorimetry ; AC : Adiabatic Calorimetry ; DSC : Differential Scanning Calorimetry ; *Data obtained on heating ; **Data obtained on cooling ; n.u. : no uncertainty mentioned.

Fig. 2 .

 2 Fig. 2. Temperature dependence of the molar heat capacity of CsNO3 (I) from different sources in the temperature range (425 -678) K. Error bars represent the experimental uncertainties on Cp. C : Calorimetry ; AC : Adiabatic Calorimetry ; DSC : Differential Scanning Calorimetry ; *Data obtained on heating ; **Data obtained on cooling ; n.u. : no uncertainty mentioned.

Fig. 3 .

 3 Fig. 3. Temperature dependence of the molar heat capacity of CsNO3 liquid phase (T > 678 K) from different sources. Error bars represent the experimental uncertainties on Cp. C: Calorimetry; AC: Adiabatic Calorimetry; DSC: Differential Scanning Calorimetry; *Data obtained on heating; **Data obtained on cooling.

Fig. 4

 4 Fig. 4 represents the mean value of solid-solid transition temperature with the experimental results collected from literature. Apart from the experimental values of Ichikawa

Fig. 4 .

 4 Fig. 4. Experimental solid-solid transition temperature of CsNO3 from different sources compared with the mean value (this work). Error bars represent experimental uncertainties. Acceptable values are inside dashed lines.

Fig. 5 .

 5 Fig. 5. Experimental melting temperature of CsNO3 from different sources compared with the mean value (this work). Error bars represent experimental uncertainties. Acceptable values are inside dashed lines.

Fig. 6 .

 6 Fig. 6. Experimental solid-solid transition enthalpy of CsNO3 from different sources compared with the mean value (this work). Error bars represent experimental uncertainties. Acceptable values are inside dashed lines.

Fig. 7 .

 7 Fig. 7. Experimental melting enthalpy of CsNO3 from different sources compared with the mean value (this work). Error bars represent experimental uncertainties. Acceptable values are inside dashed lines.

1 )Fig. 8 .

 18 Fig. 8. Temperature dependence of the molar heat capacity of LiNO3 solid phase (300 K < T < 520 K) from different sources. Error bars represent the experimental uncertainties on Cp. AC: Adiabatic Calorimetry; DSC: Differential Scanning Calorimetry; *values collected from the plot; **n.u.: no uncertainty mentioned.

1 )Fig. 9 .

 19 Fig. 9. Temperature dependence of the molar heat capacity of LiNO3 liquid phase (530 K < T < 700 K) from different sources. Error bars represent the experimental uncertainties on Cp. AC: Adiabatic Calorimetry; DSC: Differential Scanning Calorimetry; *values collected from the plot; **n.u.: no uncertainty mentioned.

Fig. 10

 10 Fig. 10 compares all the melting temperatures collected from literature with the mean value. Most of the experimental melting temperatures fall within the range of acceptable values. Very few values are outside this range. The data of Roget et al. [22] ((530.85±1) K), Bol'shakov et al. [72] (531 K) and, Diogenov and Sarapulova [75] (530 K) are just above the upper limit of acceptable values. While, the value of Goodwin and Kalmus (523 K) [94] is just below the lower limit of acceptable values. The data of Ruiz et al. [99] (520.55 K), Mohammad et al. [101] ((517.95±4.9) K, DTA) and Campbell [109] ((543±0.5) K) are far from the limits of acceptable values.

Fig. 10 .

 10 Fig. 10. Experimental melting temperature of LiNO3 from different sources compared with the mean value (this work). Error bars represent experimental uncertainties. Acceptable values are inside dashed lines.

Fig. 11 .

 11 Fig. 11. Experimental enthalpy of melting of LiNO3 from different sources compared with the mean value (this work). Error bars represent experimental uncertainties. Acceptable values are inside dashed lines.

Fig. 12 .

 12 Fig. 12. Temperature dependence of the molar heat capacity of NaNO3 (II) from different sources. (a) Temperature range (0 -550) K. (b) Enlargement in the temperature range (300 -550) K . Error bars represent the experimental uncertainties on Cp. AC : Adiabatic Calorimetry ; Pulse : Pulse method ; DSC : Differential Scanning Calorimetry ; *Data obtained on heating ; **Data obtained on cooling ; ***Values collected from the plot ; ****n.u. : no uncertainty mentioned.

Fig. 13 .

 13 Fig. 13. Temperature dependence of the molar heat capacity of NaNO3 (I) (550 K < T < 580 K) from different sources. Error bars represent the experimental uncertainties on Cp. AC : Adiabatic Calorimetry; Pulse : Pulse method; DSC : Differential Scanning Calorimetry; *Data obtained on heating ; **Data obtained on cooling ; ***Values collected from the plot ; ****n.u. : no uncertainty mentioned.

Fig. 14 .

 14 Fig. 14. Temperature dependence of the molar heat capacity of NaNO3 liquid phase (580 K < T < 800 K) from different sources. Error bars represent the experimental uncertainties on Cp. AC : Adiabatic Calorimetry ; Pulse : Pulse method ; DSC : Differential Scanning Calorimetry ; *Data obtained on heating ; **Data obtained on cooling ; ***Values collected from the plot.

  548.9993 K with standard deviation of 1.7927 K.The comparison between the mean value and experimental data collected from literature is presented in Fig.15. Most of the published values are acceptable within the admitted experimental uncertainty of ±2 K. The data of Poon and Salje[START_REF] Poon | The excess optical birefringence and phase transition in sodium nitrate[END_REF] (552 K), Schmahl and Salje[START_REF] Schmahl | X-Ray diffraction study of the orientational order/disorder transition in NaNO3: evidence for order parameter coupling[END_REF] ((552.3±0.5) K) and Antao et al.[START_REF] Antao | The  c R3 m R3 transition in nitratine, NaNO3, and implications for calcite, CaCO3[END_REF] ((552.7±0.5) K) are very close to the upper limit of acceptable values. While, the values of Roget et al.[START_REF] Roget | Study of the KNO3-LiNO3 and KNO3-NaNO3-LiNO3 eutectics as phase change materials for thermal storage in a low-temperature solar power plant[END_REF] (544.95 K), Rao and Rao[START_REF] Rao | Crystal structure transformations of alkali sulphates, nitrates and related substances: thermal hysteresis in reversible transformations[END_REF] (545 K), Beneš et al.[START_REF] Beneš | A DSC study of the NaNO3-KNO3 system using an innovativeencapsulation technique[END_REF] (545.5 K) and Benages-Vilau[START_REF] Benages-Vilau | Growth, morphology and solid state miscibility of alkali nitrates[END_REF][START_REF] Benages-Vilau | The NaNO3-KNO3 phase diagram[END_REF] (544 K), are just below the lower limit of acceptable values. Only the data of Mohammad et al.

Fig. 15 .

 15 Fig. 15. Experimental solid-solid transition temperature of NaNO3 from different sources compared with the mean value (this work). Error bars represent experimental uncertainties.Acceptable values are inside dashed lines. For clarity reasons, the number of categories between tick-mark labels is 2.

Fig. 17 .

 17 Fig. 17. Experimental solid-solid transition enthalpy of NaNO3 (first-order transition) from different sources compared with the mean value (this work). Error bars represent experimental uncertainties. Acceptable values are inside dashed lines.

Fig. 18 .

 18 Fig. 18. Experimental melting enthalpy of NaNO3 from different sources compared with the mean value (this work). Error bars represent experimental uncertainties. Acceptable values are inside dashed lines.

  Figs.19 and 20).

Fig. 19 .

 19 Fig. 19. Calculated phase diagram of CsNO3-NaNO3 system with thermodynamic parameters of Jriri et al. [26].

Fig. 20 .

 20 Fig. 20. Calculated phase diagram of LiNO3-NaNO3 system with thermodynamic parameters of Hellali et al. [23].

  identified two ternary eutectic reactions at 403 K (E1) and 405 K (E2). The equations and the molar compositions ( i E MNO X3 , M = Li, Na; i = 1, 2) corresponding to the two invariant reactions are given below: E1: Liq = LiNO3 + NaNO3 + Cs0.5Li0.5NO3;

Fig. 21 .

 21 Fig. 21. DTA curves of samples (Cs0.5, Li0.5)NO3 at 0.5 K min -1 heating rate. (a) Sample obtained by repeated melting and cooling; (b) sample obtained by coprecipitation.

Fig. 22 .

 22 Fig. 22. X-ray diffraction patterns recorded at room temperature of samples in the CsNO3-LiNO3 binary system. (a) LiNO3 and (Cs0.5, Li0.5)NO3; (b) CsNO3 and (Cs0.5, Li0.5)NO3; (c) (Cs0.5, Li0.5)NO3.

  curves in these sections are shown in Figs. 23 (sample (Cs0.15, Li0.65, Na0.2)NO3) and 24 (sample (Cs0.25, Li0.25, Na0.5)NO3). The experimental results are listed in Tables5 and 6. All tabulated temperatures are the mean repeatable values.

Fig. 23 .

 23 Fig. 23. DTA curves of sample (Cs0.15, Li0.65, Na0.2)NO3 at 0.5 K min -1 heating rate.

Fig. 24 . 4 . Thermodynamic modeling and optimization 4 . 1

 24441 Fig. 24. DTA curves of sample (Cs0.25, Li0.25, Na0.5)NO3 at 0.5 K min -1 heating rate.

Fig. 25 .

 25 Fig. 25. Heat capacity of pure CsNO3 plotted as Cp/T versus T 2 .

Fig. 26 .Fig. 27 .

 2627 Fig. 26. Calculated heat capacity of pure CsNO3 compared with experimental data. Hcp: low temperature phase of CsNO3 (CsNO3 (II)); Cubic: high temperature phase of CsNO3 (CsNO3 (I))

Fig. 28 .

 28 Fig. 28. Calculated heat capacity of pure NaNO3 from parameters of Li et al. [212] compared with experimental data. Rhombo-L: low temperature phase of NaNO3 (NaNO3 (II)); Rhombo-H: high temperature phase of NaNO3 (NaNO3 (I)).

Fig. 29 .

 29 Fig. 29. Calculated phase diagram of CsNO3-LiNO3 system compared with experimental data. Cubic: high temperature phase of CsNO3 (CsNO3 (I)); Rhombo-S: solid phase of LiNO3; Hcp: low temperature phase of CsNO3 (CsNO3 (II)); I: intermediate compound Cs0.5Li0.5NO3.

Fig. 30 .

 30 Fig. 30. Calculated enthalpy of mixing of liquid CsNO3-LiNO3 at 623 K, along with data from Meschel and Kleppa [203]. Reference states: liquid CsNO3 and LiNO3.

Figs. 31 and 32 represent the vertical sections calculated at 3

 3 Figs. 31 and 32 represent the vertical sections calculated at

Fig. 31 .

 31 Fig. 31. Calculated vertical section at

Fig. 32 .

 32 Fig. 32. Calculated vertical section at

Fig. 33 .

 33 Fig. 33. Calculated monovariant lines in the CsNO3-LiNO3-NaNO3 ternary system superimposed with data from Diogenov and Sarapulova [75]. (1) Section:

  : low temperature phase of NaNO3 (NaNO3 (II)); Hcp: low temperature phase of CsNO3 (CsNO3 (II)); I: intermediate compound Cs0.5Li0.5NO3; Cubic: high temperature phase of CsNO3 (CsNO3 (I)); Rhombo-S: solid phase of LiNO3.

  (a) LTE : Linear Thermal Expansion measurements ; CC : Cooling curve FC: Freezing curve; EMF : Electromotive force; OM : Optical measurements ; XRD : X-Ray diffraction ; IR : Infrared spectroscopy ; EM : Electrical measurements ; EC : Electrical conductivity ; DTD : Differential Transformer Dilatometry ; MC : Melting curves ; VD : Volume discontinuity; SDT/MS: Simultaneous Dynamic Thermogravimetry and Mass Spectrometry; VT : Visual-Thermal method ; MTA : Microthermal Analysis ; FPD : Freezing point depression measurements.

  because of absence of salt purity information, the 17 remaining determinations lead to 2 homogeneous subsets according to the post-hoc test. The value of Cordaro et al.[START_REF] Cordaro | Thermodynamic properties of molten nitrate salts[END_REF] (24320 J mol -1 , DSC) and that of Doucet and Franzosini and Sinistri[START_REF] Franzosini | Heat and entropy of fusion of lithium, sodium and potassium nitrates[END_REF] ((26677.18±292.88) J mol -1 , DC; (26777.6±376.6) J mol -1 , Cry), Ruiz et al.[START_REF] Ruiz | Thermal decomposition of supported lithium nitrate catalysts[END_REF] (23020 J mol -1 ) and, Doucet and Vallet[START_REF] Doucet | Etude thermodynamique des mélanges de nitrate de potassium et nitrate de lithium fondus[END_REF] (26924.04 J mol -1 ), all other published values are acceptable within the experimental uncertainty of ±5%.

	28000
	27000
	26000
	25000
	24000
	23000
	22000
	[ 2 2 ] [ 3 8 ] [ 3 9 ] [ 5 3 ] [ 5 4 ] [ 6 8 ] [ 7 4 ] [ 9 3 ] [ 9 4 ] [ 9 5 ] [ 9 5 ] [ 9 6 ] [ 9 7 ]
	Vallet [110] (26924.04 J mol -1 , freezing) are inquired. Based on the more accurate
	experimental method, the value of Cordaro et al. [97] is preferred.
	Finally, one homogeneous subset formed by 16 measurements lead to the mean value
	of 25050.4049 J mol -1 with standard deviation of 1268.1701 J mol -1 which corresponds to a
	relative uncertainty of 5.062 %.

Plot of experimental melting enthalpy values of LiNO3 from different sources compared with the mean value is shown in Fig. 11. Apart from the experimental values of

  7) K[22, 32, 38, 67, 77, 83, 86, 93, 101, 105, 114-117, 119, 120, 122, 126, 128-130, 132, 133, 135, 136, 144, 153-159, 161, 162, 164, 165, 168, 169, 171-173, 175, 176, 178, 182, 183, 185-191] which leads to a relative uncertainty of about 4% very higher than experimental uncertainties (< 1%). This means that the data differ significantly from each other. Without taking into account publications in which salt purity is not defined, 42 determinations of 52 are analyzed. The post-hoc test leads to 10 homogeneous subsets. Before the critical evaluation of all considered data, an analysis of each of the following four groups of experimental techniques is first carried out.Considering the experimental uncertainties of about ± 2 K, it appears that the transition temperatures are widely scattered from 530 K to 551 K[22, 32, 38, 93, 101, 135, 136, 153- 159, 161, 162, 164, 165, 168]. The post-hoc test leads to 7 homogeneous subsets. The lowest values are given by Dancy[START_REF] Dancy | Molar enthalpy of solid-solid transition in NaNO3[END_REF] (530 K) and Maeso[157,[START_REF] Maeso | The phase diagrams of LiNO3-NaNO3 and LiNO3-KNO3: the behaviour of liquid mixtures[END_REF] (540 K). Each of these values forms one subset. The other 5 subsets can be divided into 2 groups: TII/I  547 K and TII/I > The data obtained from DTA technique vary from 532.45 K to 549 K[77, 83, 86, 101, 144, 169, 171-173, 175, 176, 178]. The post-hoc test gives 3 homogeneous subsets. The value of Mohammad et al.[START_REF] Mohammad | Premelting, Melting, and Degradation Properties of Molten Alkali Nitrates: LiNO3, NaNO3, KNO3, and Binary NaNO3-KNO3[END_REF] (532.45 K) stands alone (one subset). The two major subsets lead to mean values of (547 ± 2) K and (548.5 ± 0.4) K, respectively.

	547 K.
	(ii) Data from DTA technique
	(iii)	Data from other calorimetric methods

(i) Data from DSC method

Without taking into account the value of Schürmann and Nedeljkovic

[START_REF] Schürmann | Kalorimetric und thermodynamik des systems LiNO3-NaNO3[END_REF]

(548 K) and that of Nguyen-Duy and Dancy

[START_REF] Nguyen-Duy | Calorimetric determination of the thermodynamic properties of the alkali metal salts NaNO3, KNO3, Na2Cr2O7, K2Cr2O7 and their binary eutectic solutions[END_REF]

(535 K) (lack of salt purity), all data lie between 548 K and 549.2 K, i.e. TII/I > 547 K.

Table 2

 2 Temperatures and enthalpies of melting of LiNO3 from literature

	Tm (K)	ΔmH°(J mol -1 )	Method (a) Sample characteristics	Ref.
	525.9	25025.22	DSC	99.8% (used without further purification)	[93]
	527.5±3	24500	DSC	Reagent grade (kept at 380 K under vacuum for 24 h)	[68]
	527.5	---	DSC	Reagent grade (recrystallized from redistilled water and	[98]
				dried in the oven at 378 K for 3 days)
	520.55	23020	DSC	Not defined	[99]
	528	25647.912	DSC	Reagent grade (dried in a separate furnace at 423 K for 24 h	[54]
				and stored over desiccant)
	---	24320±1420	DSC	Commercial source (dried in an oven at 523 K under a flow	[97]
				of nitrogen gas)
	525±1	24517±5%	DSC	99.99% (used without purification but care was taken to	[38]
				avoid moisture)
	530.85±1	24889.506±5%	DSC	> 99% (kept in an oven at 353 K)	[22]
	525±1	24500±4%	DSC	99.99% (used without further purification)	[39]
	524±1	24526±1226	DSC	99.99% (dried in a desiccators at 380 K for more than 24 h) [100]
	527	---	DSC	> 99.0% (dried at 373 K for 48 h)	[52]
	530.85±4.9 24553.90±208.35 DSC	99.99% (used without purification and deshydration)	[101]
	528.05±0.3 24972±0.5%	DSC	> 99.0% (placed in powder state in a constant temperature	[53]
				air blast oven, 393 K, for drying 24 h)
	525.75±0.1 ---	DTA	Not defined	[102]
	527.5±1	---	DTA	99.99% (kept at 380 K in an oven)	[103]
	527.5±1	---	DTA	99.99%	[84]
	526±1	---	DTA	99.99%	[104]
	526±1	---	DTA	99.99% (dried in a desiccators at 380 K for more than 24 h) [100]
	517.95±4.9 24836.76±208.35 DTA	99.99% (used without purification and deshydration)	[101]
	523	25522.4	DC	Great purity (purified by repeated crystallization)	[94]
	526	25258.81	DC	Not defined	[105]
	525	24600	DC	Pure grade (heated to about 463 K in a pyrex tube under	[96]
				vacuum)
	526.3±0.2	26677.18±292.88 DC	Reagent grade (carefully dried under vacuum at 473 K for	[95]
				few days) / Spectroscopic purity (obtained by dehydration
				of LiNO3.3H2O)
	527	24941	RC	Analytical reagent (used without purification)	[74]
	528±3	---	C	99.98%	[80]
	529.5	---	AC	Pure-grade recristallyzed (special grade)	[67]
	526.3±0.2	26777.6±376.6	Cry	Reagent grade (carefully dried under vacuum at 473 K for	[95]
				few days) / Spectroscopic purity (obtained by dehydration
				of LiNO3.3H2O)
	---	25355	DC	Not defined	[111]
	526±2	---	CC	Prepared from well washed lithium carbonate (no impurity	[106]
				was detected by ordinary analytical tests)
	524.55±0.4 ---	CC	Reagent grade (recrystallized)	[107, 108]
	543±0.5	---	PC	Not defined	[109]
	531	---	CC	Chemically pure	[72]
	526.25±0.1 26924.04	Freezing	Pure grade (deshydrated during a long time)	[110]
	530	---	VT	Not defined	[75]
	526	---	VT	> 99.5%	[90]
	527	---	Equil.	Not defined	[81]
	(a) DSC : Differential Scanning Calorimetry ; DTA : Differential Thermal Analysis ; DC : Drop calorimetry; RC :
	Reaction calorimetry ; C : calorimetry; AC : Adiabatic Calorimetry ; Cry : Cryometry ; CC : Cooling Curve ;

PC : Plato method of graduated cooling ; VT : Visual-Thermal method; Equil. : Equilibrium method.

Table 3

 3 Temperatures and enthalpies of solid-solid transition and melting of NaNO3 from literature TII/I (K) Tm (K) ΔII/IH°(J mol -1 ) ΔmH°(J mol -1 ) Method (a) Sample characteristics

	Ref.

Table 3 (

 3

		continued)
	TII/I (K)	Tm (K)	ΔII/IH°(J mol -1 ) ΔmH°(J mol -1 )	Method (a) Sample characteristics	Ref.
	548.65	---	---	---	DTA	Reagent grade	[169]
	---	579	---	14610 -14958	QDTA	Reagent grade (99.98 mole%).	[170]
						Sample placed in Ag (99.999%)
						container
	545	---	418.4±15%	---	DTA	Analytical grade (dried and stored	[77]
						in desiccator)
	(548 -549)	---	---	---	DTA	Analytical reagent grade	[144]
	±2
	548±0.25	578±0.25	---	---	DTA	Analytical grade (recrystallized	[171]
						and dried in an oven)
	549±1	579±1	---	---	DTA	99.5% (kept in an oven at 395 K)	[83]
	548.5±0.5	579±0.5	---	---	DTA	99.95%	[172]
	549±0.5	579±0.5	---	---	DTA	99.9% (dried for more than 24 h	[173]
						at 394 K in an oven)
	549±1	579±1		---	DTA	99.99% (kept in an oven at 380	[86]
						K)
	---	580	---	---	DTA	Reagent grade	[174]
	549±1	579±1	---	---	DTA	99.995% (dried for more than 24	[175]
						h at 380 K in a desiccator)
	546±3	575±3	---	---	DTA	99.995%	[176]
	---	575.21±4.8 2561.9±0.76%	14930.25±0.76%	STA	> 99%	[177]
	549±1	578±1	---	---	DTA	99.995%	[178]
	---	581	---	15045	STA	> 99%	[179]
	532.45±4.9 571.65±4.9 ---	15300±256.7	DTA	99.995% (kept at 378 K for 1 h)	[101]
	---	579.6±0.1	---	15049±33	AC	99.99%	[127]
	549.2	579.2	3950	14602±7%	AC	99.9%	[128]
	548.7	580	---	15272	AC	High purity	[130]
	548	583.2	---	---	AC	Special grade	[67]
	---	584	---	15810	AC	Not defined	[180]
	---	581	---	15439±2%	DC	Great purity (purified by repeated	[94]
						crystallization)
	---	579.2±0.1	---	15648	DC	Reagent grade (dried in an oven at	[95]
						403 K for a few hours)
	---	580	---	14937	DC	Not defined	[181]
	548.6	---	3770	---	DC	Analytical reagent grade	[126]
	549.2	580.2	728	14728	DC	reagent grade (oven-dried at 403	[129]
						K)
	548	579	4686.08	15459.88	DC	Not defined	[105]
	535	581	1590	14644	DC	Not defined	[133]
	---	581	---	---	DC	Best grade (keptat 405 K for more	[137]
						than 24 hours)
	549±2	578±2	---	---	DC	99.995%	[182]
	---	583	---	15464±134	RC	Analytical grade (without further	[74]
						purification)
	---	---	---	15523	Cry	Reagent grade (dried in an oven at	[95]
						403 K for a few hours)
	(a) DTA : Differential Thermal Analysis ; QDTA : Quantitative differential thermal Analysis ; STA :
	Simultaneous Thermal Analysis ; AC : Adiabatic calorimetry ; DC : Drop calorimetry ; RC : Reaction
	calorimetry ; Cry: cryometry.

Table 3 (

 3

		continued)
	TII/I (K)	Tm (K)	ΔII/IH°(J mol -1 ) ΔmH°(J mol -1 ) Method (a)	Sample characteristics		Ref.
	551±1	---	---	---	LTE	Commercial	salt	[183]
						(recrystallized three times)
	---	585	---	---	CC	Chemically pure		[184]
	---	578.65±0.4 ---	---	CC	Reagent grade (recrystallized	[108]
						and dried)
	---	579±0.1	---	---	CC	Not defined (dried salt)		[102]
	---	588.25±0.2 ---	---	FC	Analytical reagent (dried)		[151]
	---	581	---	15315	EMF	Not defined		[73]
	548	581	---	---	Raman diff.	Not defined		[185]
	549.1	---	---	---	Raman diff.	Not defined		[119]
	(548.74-	---	---	---	Neutron diff.	Not defined		[117]
	551.02)
	±(0.47-0.54)
	549.75	---	---	---	Absorption edge Not defined		[186]
	552	---	---	---	OM	> 99.999%		[114]
	549±3	580±3	---	---	XRD	> 99.999%		[115]
	552.3±0.5	---	---	---	XRD	> 99.999%		[116]
	552.7±0.5	---	---	---	XRD	99.999% (held at 373 K for 10
						min)

Table 8

 8

	Gibbs energy	0	G i 	( T	)		0 H	SER i	(	15 . 298	K	)	for pure nitrates
	Nitrates Phase			Symbol		T/K			Gibbs energy (J mol -1 )	Ref.
	CsNO3	CsNO3(II)	Hcp				5 -17			-20210.0+0.7T-0.01011T 2 -1.330 10 -4 T 4	This work
											17 -427		-23576.5+264.206T-55.52Tln(T)-0.076816T 2
														+42984.2003T -1 -351803.795T -2 +1267294.59T -3
											427 -3000	-50921.0+778.5T-136.545Tln(T)-3.1445 10 -4 T 2
														+1472528.05T -1
		CsNO3(I)	Cubic			5 -17			-19545.0+4.275T-0.06076T 2 -1.15 10 -4 T 4	This work
											17 -427		-22583.0+244.31T-50.9091Tln(T)-0.10102T 2
														+38829.4483T -1 -321553.964T -2 +1178960.83T -3
											427 -678		-94736.20+1398.25964T-228.16118Tln(T)
														+0.043805T 2 +4920826.52T -1
											678 -3000	-36280.0+787.55T-141.025Tln(T)+5.116 10 -4 T 2
														-1614045.65T -1
		Liquid			Liq				5 -17			-9435.0-2.175T-0.07389T 2 -1.07 10 -4 T 4	This work
											17 -427		-13260.0+275.0T-57.601Tln(T)-0.1033T 2
														+53870.3382T -1 -478775.974T -2 +1837388.34T -3
											427 -3000	-31599.30+805.058T-145.255Tln(T)
	LiNO3	Solid			Rhombo-S 298.15 -527 -18320.5096+207T-38.8286Tln(T)	This work
														-0.077378T 2
											527 -3000	-67100+925.70T-147.4028Tln(T)
														+0.0014728T 2 +3544600T -1
		Liquid			Liq				298.15 -527 -3695.00+203.35T-37.7090Tln(T)-0.156T 2	This work
														+3.7129 10 -5 T 3
											527 -3000	-25277.10+814.9266T-140.2302Tln(T)

Two ternary eutectic reactions have been found in the ternary CsNO3-LiNO3-NaNO3 system at 407.76 K and 404.63 K, respectively. Both are appropriate melting temperatures for medium temperature heat storage. The set of thermodynamic parameters obtained in this work could be used for the prediction of phase equilibria in multicomponent systems based on CsNO3, LiNO3 and NaNO3.

Table 4

Experimental results of DTA measurements (heating) in the CsNO3-LiNO3 system Composition Experimental equilibrium temperature (K)

Table 9

Thermodynamic parameters in the CsNO3-LiNO3-NaNO3 ternary system (in J.mol