Thermodynamic reassessment of the novel solid-state thermal energy storage materials: Ternary polyalcohol and amine system pentaglycerine-tris(hydroxymethyl)-amino-methane-neopentylglycol (PG-TRIS-NPG)

Organic polyalcohol and amine globular molecular crystals such as PG, TRIS, and NPG are considered as the most promising potential candidates for solid-state thermal energy storage in the orientationally disordered high temperature phases. In this study, we first propose a new PG-TRIS-NPG phase diagram based on experimental data of the three sub-binary systems NPG-PG, PG-TRIS, and NPG-TRIS with CALPHAD methodology. The NPG-PG binary phase diagram was optimized using sub-regular models that showed complete miscibility in the entire compositional range of high temperature γ′ (FCC) phase region, and an invariant equilibrium point at 299.5 K. The NPG-TRIS binary system was also calculated using sub-regular model, from sub-ambient to well above the melting temperatures, and determined three invariant equilibria at 311.1 K, 391.8 K, and 410.6 K, respectively. These calculated binary phase diagrams are in good agreement with the experimental data. The PG-TRIS-NPG ternary system has also been calculated and qualitatively analyzed using the CALPHAD method and Thermo-Calc software. A set of self-consistent thermodynamic parameters formulating the Gibbs energies of various phase in the PG-TIRS-NPG ternary system are obtained in the present work. Thermodynamic properties such as several isotherms, isopleths, and liquidus projections are calculated by using present datasets as shown in this work in which the solid ternary compound (TRIS_0.5NPG_0.5)_XPG_1−X (0.1≤x≤0.9), (TRIS_0.5PG_0.5)_XNPG_1−X (0.1≤x≤0.9), and (PG_0.5NPG_0.5)_XTRIS_1−X (0.1≤x≤0.9) with various solid-solid phase transitions at different temperatures could apply to applications in the solid-state thermal energy storage.     

Thermodynamic assessment of the cesium–oxygen system by coupling density functional theory and CALPHAD approaches

The thermodynamic properties of cesium oxides were calculated by combining ab initio calculations at 0 K and a quasi-harmonic statistical thermodynamic model to determine the temperature dependency of the thermodynamic properties. In a second approach, the CALPHAD method was used to derive a model describing the Gibbs energy for all the cesium oxide compounds and the liquid phase of the cesium–oxygen system. For this approach, available experimental data in the literature was reviewed and it was concluded that only experimental thermodynamic data for Cs₂O are reliable. All these data together with the thermodynamic data calculated by combining ab initio and the statistical model were used to assess the Gibbs energy of all the phases of the cesium–oxygen system. A consistent thermodynamic model was obtained. The variation of the relative stability of the different oxides is discussed using structural and bond data for the oxides investigated by ab initio calculations. This work suggests that the melting point for Cs₂O₂ reported in the literature (863 K) is probably overestimated and should be re-measured.     

Thermodynamic modeling of the Ca(NO3)2-MNO3 (M: alkali metal) systems

This work presents a thermodynamic evaluation of the Ca(NO₃)₂-MNO₃ (M: Li, Na, K, Rb, Cs) binary systems using the CALPHAD approach. The required Gibbs energy of liquid Ca(NO₃)₂ is missing in the literature and has been successfully evaluated in the present work with a fusion enthalpy of 23849 J mol⁻¹. The substitutional solution model can thus be employed to describe the Ca(NO₃)₂-base liquid phase. All the intermediate compounds are treated to be stoichiometric and their Gibbs energies comply with the Neumann-Kopp rule. Empirical functions relating mixing enthalpies to ionic parameters are employed to predict the corresponding values of binary melts which are used as input data to assist in parameters optimization for the liquid phases. The final calculated results show good agreement with most of the experimental and predicted data.     

Thermodynamics of liquid Sn-Pb alloys determined by vapour pressure measurements

Application of Knudsen method in the studies of liquid Sn-Pb alloys, containing from 4.85 to 95.31 mol% of lead, in temperatures from 851 to 1186 K, and liquid tin and lead, in temperatures 1360 – 1442 and 934 – 1149 K, respectively, provided experimental data which made characterization of thermodynamic properties of liquid phase of Sn-Pb system possible. Parameters of the Redlich-Kister equation, describing excess Gibbs energy of liquid phase of the examined system, were determined. With application of the third law method standard enthalpies of sublimation of tin and lead were calculated.     

Thermodynamic calculation of the T0 curve and metastable phase diagrams of the Ti–M (M = Mo,V, Nb,Cr, Al) binary systems

Based on the experimental data available in the literature, the β-α′/α′′⬠ martensitic transformation and athermal ω formation of the Ti–M (M = Mo, V, Nb, Cr, Al) binary systems at low temperature are thermodynamically described. According to β-α′/α′′⬠ martensitic transformation and metastable ω phase formation temperatures, thermodynamic parameters of these systems are assessed by means of the CALPHAD (CALculation Phase Diagram) approach supported by first-principles calculations. In addition to the metastable ω phase, only solution phases, i.e. liquid, α(hcp), β(bcc) or γ(fcc) are included and their thermodynamic parameters are adopted in the literature or revised in this work. The metastable phase diagrams of the Ti–M (M = Mo, V, Nb, Cr, Al) systems with T₀(β/α) and T₀(β/ω) curves are calculated using the obtained parameters. Comparisons between the calculated results and experimental data reported in the literature show that almost all the reliable experimental information can be satisfactorily accounted for by the present modeling.     

Thermodynamic and surface properties of liquid Ge–Si alloys

In the present work, the surface tension of liquid Si and Ge has been measured by the pendant/sessile drop combined method over the temperature range of 1723–1908 K and 1233–1313 K, respectively. The new surface tension data, the molar volumes and the melting temperatures of silicon and germanium as well as the excess Gibbs energy data of the Ge–Si liquid phase are the inputs for Calphad type modelling to study the mixing behaviour in alloy melts. The energetics of mixing in liquid Ge–Si system has been analysed through the study of the concentration dependence of various thermodynamic (activity, enthalpy of mixing, Gibbs energy of mixing), surface (surface tension and surface composition) and transport (diffusivity) properties as well as the microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) in the framework of statistical mechanical theory in conjunction with the Quasi-Lattice Theory (QLT).     

Thermodynamic modeling of Fe–Ti–Bi system assisted with key experiments

Phase equilibria of Fe–Ti–Bi ternary system have been studied in this work. Firstly, by using alloy sampling, the isothermal section of Fe–Ti–Bi ternary system at 773 K was determined, where the existence of a ternary phase Bi₂FeTi₄ was confirmed. Meanwhile, formation enthalpies of the intermediate phases BiTi₂, Bi₉Ti₈ and Bi₂FeTi₄, were obtained with first-principles calculations. Based on experimental data of phase equilibria and thermodynamic properties in literatures along with the calculated formation enthalpies in this work, thermodynamic modeling of Ti–Bi binary system and Fe–Ti–Bi ternary system were carried out with the CALPHAD approach. A set of self-consistent thermodynamic parameters to describe the Gibbs energy for various phases in Fe–Ti–Bi ternary system was finally obtained, with which solidification processes of two typical Fe–Ti–Bi alloys could be reasonably explained.