Experimental investigation of phase equilibria in the Ti-Fe-Cr ternary system

Phase equilibria in ternary Ti-Fe-Cr system at 873 and 1173 K were investigated in this work. Based on the phase constitutions and phase compositions in 32 samples prepared using the equilibrated alloys, the isothermal sections of the Ti-Fe-Cr ternary system were established. For this system, there were six three-phase regions at both 873 and 1173 K, the phase relations at the studied two temperatures are almost the same. Thereinto, two tentative three-phase regions of βCr₂Ti + β(Ti) + (Fe, Cr)₂Ti and βCr₂Ti + β(Ti) + αCr₂Ti were deduced near the Ti-Cr side at 1173 K. The (Fe, Cr)₂Ti phase has a large solubility of Cr, up to 59.1 at% at 873 K and 59.5 at% at 1173 K. Moreover, at 873 and 1173 K, the homogeneity ranges of the nearly linear ternary compounds τ₁ were measured to be 49.9–72.1 at% Fe and 52.7–77.2 at% Fe, respectively, and the solubility of Cr in (Fe, Cr)Ti were 9.0 at% and 10.6 at%.     

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.     

Experimental study and thermodynamic modelling of the B-Fe-Mn ternary system

This work is focused on an experimental study of phase equilibria in the B-Fe-Mn ternary system combined with a CALPHAD theoretical analysis with the aim of creating a reliable theoretical thermodynamic dataset for calculation of the phase diagram of the ternary system. Boron is modelled as an interstitial element in all solid solutions of Fe and Mn. In the experimental study, B-Mn-Fe alloys were prepared and heat-treated at 873 K for 90 days/2160 h and at 1223 K for 60 days/1440 h. Following heat treatment, the phase equilibria and composition of the coexisting phases were determined using scanning electron microscopy and X-ray diffraction analysis. The experimental results obtained, together with experimental results collected from the literature, were used in the optimization of the thermodynamic parameters by using the CALPHAD method. The result of this work is an optimized thermodynamic dataset for the B-Fe-Mn ternary system allowing the phase diagram and thermodynamic properties to be calculated.     

Measurement and thermodynamic model study on equilibrium solubility in the aqueous system of magnesium chloride and magnesium bromide

Solubilities of the ternary system MgCl₂–MgBr₂–H₂O at T=(288.15, 308.15, 323.15 and 333.15) K were investigated, and the crystallization behaviour of solid solution Mg(Cl,Br)₂·6H₂O was established. Combining our experimental results with other experimental data available in the literature at T=(298.15 and 313.15) K, the pure electrolyte solution parameters for binary systems, the T-variation mixing parameters θ_Cl,Br and ψ_Mg,Cl,Br and the equilibrium constants equations of the solid solution were obtained. Based on Pitzer model and Harvie–Weare solubility approach, the solubility modelling approach achieved a very good agreement with chloride and bromide salts equilibrium solubility data. Temperature-dependent equation in the system provides reasonable mineral solubility at T=(288.15–333.15)  K. This model expands the solubility calculation in the systems containing solid solution by evaluating chloride–bromide mixing solution parameters. Limitations of the mixed solution models due to data insufficiencies are discussed.     

Thermodynamic modelling of the Cr-Nb-Sn system

The Cr-Nb-Sn system has been studied experimentally, by first principles calculation and finally modeled with the Calphad method. The experimental study has been carried out on the Cr-Sn binary system to determine the solubility of Sn in the A2 (Cr) solid solution, but also in the Cr-Nb-Sn ternary system in order to determine phase equilibria of the isothermal section at 800 °C and 1100 °C. Besides, the formation enthalpies of all the ordered configurations of the C15 and A15 phases and the stoichiometric Nb₆Sn₅ and NbSn₂ phases have been calculated using the Density Functional Theory (DFT). The mixing enthalpies of the A2 binary solid solutions have been estimated using the Special Quasirandom Structures (SQS). All these new experimental and calculated data have been taken into account for a new thermodynamic assessment of the three binary and the ternary systems.     

Investigation of phase equilibria in the Ti-Co-Zr ternary system

Isothermal sections of the Ti-Co-Zr ternary system at 1073 K and 1173 K were determined using Ti-Co-Zr diffusion triples and equilibrated alloys with optical microscopy (OM), X-ray diffraction (XRD), scanning electron microscope (SEM) and electron probe micro-analysis (EPMA) techniques. A unknown ternary phase with composition of ～Ti_31.3Co_37.9Zr_30.8 was observed to be stable at both 1073 K and 1173 K. Two continuous solid solutions Co₂(Ti, Zr) and Co(Ti, Zr) were formed between the binary intermediate compounds Co₂Ti (c) and Co₂Zr (c) as well as between the CoTi and CoZr intermediate compounds, respectively. The solubility of Zr in the CoTi₂ phase was nearly 55.0 at% at both 1073 K and 1173 K, and the Co₁₁Zr₂ phase was proved to be non-existent at 1073 K and 1173 K. Liquid phase was observed at 1173 K and exists with a wide range in the Ti-Zr-rich part.     

Phase equilibria in the Ge-Mn-Ti ternary system at 973 K, 1073 K and 1173 K

Phase relationships in the Ge-Mn-Ti ternary system have been studied through alloy samples approach. Assisted with Electron Probe Microanalysis (EPMA) and X-ray diffraction (XRD) techniques, isothermal sections at 973 K, 1073 K and 1173 K of this system were constructed and existence of 2 ternary phases, i.e. GeMnTi and Ge₂MnTi, were confirmed. In addition, remarkable ternary solubilities in some binary compounds were detected, e.g. Ge in Mn₂Ti and Mn in Ge₅Ti₆ can be up to 15 at% and 50 at% at 1173 K, respectively. Furthermore, the substitution of Ti by Mn atoms in Ge₅Ti₆ was confirmed with Rietveld refinement results of solid solutions, Ge₅(Mn_0.30Ti_0.70)₆ and Ge₅(Mn_0.67Ti_0.33)₆.     

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.     

Measurement of phase equilibria in Ti-Co-Pt ternary system

Phase equilibria in the Ti-Co-Pt ternary system were measured through diffusion triple and alloy sampling. Based on the results from Electron Probe Microanalysis (EPMA) and X-ray diffraction (XRD) techniques, the isothermal sections of the Ti-Co-Pt system were constructed, which consist of 16 and 13 three-phased regions at 973 and 1173 K, respectively. A new ternary phase τ was detected, which contains 23.6–29.9 at% Pt at 973 K and 27.4–40.1 at% Pt at 1173 K. Furthermore, an invariant reaction between 973 and 1173 K was deduced, i.e. τ + Ti₄Pt₃ ↔ Ti₃Pt + TiPt. By the way, the solubilities of Pt mainly substituting for Co in TiCo and TiCo₃ respectively increase from 22.4 at% and 26.1 at% at 973 K to 23.8 at% and 33.1 at% at 1173 K.     

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.     

Investigation of the phase equilibria in Ti-Ni-Hf system using diffusion triples and equilibrated alloys

In present work, the phase equilibrium relations in the Ti-Ni-Hf ternary system, which are of great importance for the design of Ti-Ni based high temperature shape memory alloys, were investigated using diffusion triples and sixteen key equilibrated alloys. Based on the experimental results from electron-probe microscopy analysis (EPMA) and X-ray diffraction (XRD) techniques, two isothermal sections were constructed, which consist of 13 and 12 three-phase regions at 900 °C and 800 °C, respectively. Hf can substitute for Ti in TiNi and Ti₂Ni phases increasing from 30, 62 at% at 800 °C to 36, 64 at% at 900 °C, respectively. The Hf₇Ni₁₀ and Hf₉Ni₁₁ phases show wide ternary composition ranges, while the solubility of Ti in HfNi₅, Hf₂Ni₇, and HfNi phases are relatively limited. A new ternary phase of τ was detected for the first time, and the stoichiometry of τ phase is close to Ni:(Hf,Ti) = 11:14, with Ti substituting for Hf from ～5 at% to ～22 at%. The single-phase region of the τ phase became narrow as the decreasing of annealing temperature. Based on comparison of phase relations at 900 °C and 800 °C, it is speculated there is an invariant reaction TiNi + τ → HfNi + Ti₂Ni at between 900 °C and 800 °C.     

Measurements and calculations of solid–liquid equilibria in the quaternary system NaBr–KBr–CaBr2–H2O at 298 K

The solubilities and densities of the quaternary system NaBr–KBr–CaBr₂–H₂O were investigated by the method of isothermal solution saturation at 298 K. On the basis of the experimental data, the phase diagram, water content diagram and the density-composition diagram were plotted, respectively. In the phase diagram of quaternary system NaBr–KBr–CaBr₂–H₂O at 298 K, no complex salt or solid solution was found. There are two invariant points, five univariant curves, and four crystallization fields corresponding to NaBr, NaBr·2H₂O, KBr and CaBr₂·6H₂O. Pitzer's equations based model has been applied to calculate bromide minerals solubilities in the quaternary system NaBr–KBr–CaBr₂–H₂O at 298 K. All binary and mixing ion interaction parameters and solubility products of bromide solids are taken from previously published T-variation model for the system under study, adapted to 298 K. The predicted and experimental solubilities are in a very good agreement up to a very high total concentration of the quaternary system.     

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.     

Thermodynamics of the ZnSO4-H2SO4-H2O system

Internally consistent set of thermodynamic parameters was derived for the binary ZnSO₄–H₂O -system using the CALPHAD method. Available data on water activity, EMF measurements, solubility and heat of solution and dilution measurements was reviewed. Additional parameters for the ternary ZnSO₄–H₂SO₄–H₂O system were derived based on the available solubility and boiling point data. Solubility of zinc sulfate was predicted successfully under conditions relevant in hydrometallurgical processing of zinc, and even up to 15 mol kg⁻¹ sulfuric acid solutions. Temperature dependent Pitzer parameters for the binary and ternary systems are reported.