Thermodynamic investigation on the Al2O3–BaO binary system

The Al₂O₃–BaO binary system has been studied using the CALPHAD technique in this paper. The modeling of Al₂O₃ in the liquid phase is modified from the traditional formula with the liquid phase represented by the ionic two-sublattice model as (Al³⁺, Ba²⁺)_P (AlO₂¹⁻, O²⁻)_Q. Based on the measured phase equilibrium data and experimental thermodynamic properties, a set of thermodynamic functions has been optimized using an interactive computer-assisted analysis. A comparison between the calculated results and experimental data is presented.     

Critical thermodynamic evaluation and optimization of the MnO–SiO2–“ TiO2 ”–“ Ti2O3 ” system

A complete review, critical evaluation, and thermodynamic optimization of phase equilibrium and thermodynamic properties of the MnO–SiO₂–“ TiO₂”–“ Ti₂O₃” systems at 1 bar pressure are presented. The molten oxide phase was described by the Modified Quasichemical Model. The Gibbs energies of the manganosite, spinel, pyrophanite and pseudobrookite and rutile solid solutions were taken from the previous study. A set of optimized model parameters for the molten oxide phase was obtained which reproduces all available reliable thermodynamic and phase equilibrium data within experimental error limits from 25 ^°C to above the liquidus temperatures over the entire range of compositions and oxygen partial pressure in the range of pO₂ from 10⁻²⁰ bar to 10⁻⁷ bar. Complex phase relationships in these systems have been elucidated, and discrepancies among the data have been resolved. The database of model parameters can be used along with software for Gibbs energy minimization in order to calculate any phase diagram section or thermodynamic properties.     

Thermodynamic re-assessment of the Al–Ir system

The thermodynamic assessment of the Al–Ir binary system was performed using the CALPHAD technique. The B2-AlIr phase was described, using the two sublattice model with the formula (Al,Ir,V a)_1/2(Al,Ir,V a)_1/2, while Al₉Ir₂, Al₃Ir, Al₁₃Ir₄, Al₄₅Ir₁₃, Al₂₈Ir₉, and Al_2.7Ir compounds were treated as stoichiometric compounds. The fcc-based phases (L1₀-AlIr, L1₂-Al₃Ir, L1₂-AlIr₃ and A1) were described using the four sublattice model with the formula, (Al,Ir)_1/4(Al,Ir)_1/4(Al,Ir)_1/4(Al,Ir)_1/4. From ab initio calculations (VASP) the formation enthalpies of the stable/metastable intermetallic phases involved in the Al–Ir system were estimated. The thermodynamic quantities, such as the phase equilibria, invariant reactions, and formation enthalpies of the intermetallic phases, were calculated using the obtained parameter set, and agree well with experimental data.     

Phase change materials in the ternary system NH4Cl+CaCl2+H2O

Solubility isotherms of the ternary system (NH₄Cl+CaCl₂+H₂O) were elaborately determined at T= (273.15 and 298.15) K by using the isothermal method. In the equilibrium phase diagram, there are two solubility branches corresponding to the solid phases CaCl₂⋅6H₂O and NH₄Cl. Invariant point compositions are 36.32 wt% CaCl₂ and 3.4 wt% NH₄Cl at 273.15 K, and 45.86 wt% CaCl₂ and 5.22 wt% NH₄Cl at 298.15 K. A Pitzer-Simonson-Clegg thermodynamic model was applied to represent the thermodynamic properties of this ternary system and to construct a partial phase diagram of the ternary system at temperatures between (273.15 and 323.15) K. It was found in the predicted solubility phase diagram that the double salt 2NH₄Cl⋅CaCl₂⋅3H₂O, found by other authors at (323.1 and 348.1) K, will disappear at temperatures below 298.15 K. Besides, it was found that there are two peritectic points in the ternary system with peritectic temperatures at 299.65 K and 298.15 K, and the former peritectic point falls just on the line between the composition points of NH₄Cl and CaCl₂⋅6H₂O. According to phase rule, a solution made of this point will begin to crystallize at 299.65 K and end at 298 K and therefore can be acted as a “pseudo eutectic” phase change material (PCM). A heat storing and releasing experiment of 50 grams of the PCM was carried out, obtaining a satisfying result.     

Critical thermodynamic evaluation and optimization of the MnO–“ TiO2 ”–“ Ti2O3 ” system

A complete review, critical evaluation, and thermodynamic optimization of the phase equilibrium and thermodynamic properties of the MnO–“ TiO₂”–“ Ti₂O₃” systems at 1 bar pressure are presented. The molten oxide phase was described by the Modified Quasichemical Model. The Gibbs energy of spinel, pyrophanite and pseudobrookite solid solutions were modeled using the Compound Energy Formalism, and rutile solid solution was treated as a simple Henrian solution. Manganosite solid solution was assumed to dissolve both Ti⁴⁺ and Ti³⁺. A set of optimized model parameters for all phases was obtained which reproduces all available reliable thermodynamic and phase equilibrium data within experimental error limits from 25 ^°C to above the liquidus temperatures over the entire composition ranges and in the range of pO₂ from 10⁻²⁰ to 10⁻⁷ bar. Complex phase relationships in these systems have been elucidated, and discrepancies among the data have been resolved. The database of model parameters can be used along with software for Gibbs energy minimization in order to calculate any phase diagram section or thermodynamic properties.     

Critical evaluation and thermodynamic modeling of the Fe–V–O (FeO–Fe2O3–VO–V2O3–VO2–V2O5) system

Critical evaluation and optimization of the Fe–V–O ternary oxide system was carried out based on all the available phase equilibria and thermodynamic property data at 1 atm total pressure. The Fe₃O₄–FeV₂O₄ spinel solid solution was described within the framework of Compound Energy Formalism considering the cation distribution between tetrahedral and octahedral sites. The wüstite phase, corundum phase, and VO₂ solid solution were described using a simple random mixing model. The Modified Quasichemical Model was used to describe liquid oxide solution in consideration of all multivalence states of Fe and V (Fe²⁺, Fe³⁺, V²⁺, V³⁺, V⁴⁺ and V⁵⁺). The variation of phase equilibria depending on the oxygen partial pressures and thermodynamic data in the system were well reproduced in the present study.     

Liquid–solid equilibria in quinary system Na,Mg/Cl,SO4,NO3–H2O at 298.15 K

In order to develop the nitrate deposits found close to Lop Nur in the Xinjiang region in China, the solubilities of the system Na⁺,Mg²⁺/Cl⁻,SO₄²⁻, NO₃⁻–H₂O and its subsystems, the quaternary systems Na⁺,Mg²⁺/SO₄²⁻,NO₃⁻–H₂O and Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O, were studied at 298.15 K. The phase diagrams were plotted according to the solubilities achieved. In the equilibrium phase diagram of Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O, there are two invariant points, five univariant curves and four regions of crystallization: Mg(NO₃)₂6H₂O,MgCl₂6H₂O,MgSO₄7H₂O and MgSO₄(1–6)H₂O. In the equilibrium phase diagram of Na⁺,Mg²⁺/SO₄²⁻, NO₃⁻–H₂O, there are five invariant points, eleven univariant curves and seven regions of crystallization: Na₂SO₄,Na₂SO₄10H₂O,NaNO₃,MgSO₄Na₂SO₄4H₂O,NaNO₃Na₂SO₄2H₂O,Mg(NO₃)₂6H₂O and MgSO₄7H₂O. In the equilibrium phase diagram of the Na⁺, Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O system, there are six invariant points, and ten regions of crystallization: NaCl, NaNO₃,Na₂SO₄,Na₂SO₄10H₂O,MgSO₄Na₂SO₄4H₂O, NaNO₃Na₂SO₄2H₂O,MgCl₂6H₂O,Mg(NO₃)₂6H₂O, MgSO₄(1–6)H₂O and MgSO₄7H₂O.     

Phase diagrams and thermochemical modeling of salt lake brine systems. III. Li2SO4+H2O,Na2SO4+H2O,K2SO4+H2O,MgSO4+H2O and CaSO4+H2O systems

This paper is part of a series of studies on the development of a multi-temperature thermodynamically consistent model for salt lake brine systems. Under the comprehensive thermodynamic framework proposed in our previous study, the thermodynamic and phase equilibria properties of the sulfate binary systems (i.e., Li₂SO₄ + H₂O, Na₂SO₄ + H₂O, K₂SO₄ + H₂O, MgSO₄ + H₂O and CaSO₄ + H₂O) were simulated using the Pitzer-Simonson-Clegg (PSC) model. Various type of thermodynamic properties (i.e., water activity, osmotic coefficient, mean ionic activity coefficient, enthalpy of dilution and solution, relative apparent molar enthalpy, heat capacity of aqueous phase and solid phases) were collected and fitted to the model equations. The thermodynamic properties of these systems can be well reproduced or predicted using the obtained model parameters. Comparisons with the experimental or model values in literature indicate that the model parameters determined in this study can describe all of the thermodynamic and phase equilibria properties of these binary sulfate systems from infinite dilution to saturation and freezing point temperature to approx. 500 K.     

Thermodynamic description of the Co–Ni–Ta system

The temperatures of two invariant reactions λ₃ → fcc(Co) + Co₃Ta and λ₃ → Co₃Ta + λ₂ in the Co–Ta system were identified to be 1320 and 1303 K, respectively, by Differential thermal analysis (DTA). The Co–Ta, Ni–Ta and Co–Ni–Ta systems were optimized using the CALculation of PHAse Diagram (CALPHAD) method based on the present experimental results and literature data. Three Laves phases λ₁, λ₂ and λ₃ were described using a two-sublattice model (Co,Ni,Ta)_0.6667(Co,Ni,Ta)_0.3333, and compound (Co,Ni)Ta was modeled as (Co,Ni,Ta)₁Ta₄(Co,Ni,Ta)₂(Co,Ni,Ta)₆ by a four-sublattice model. A set of reliable and self-consistent thermodynamic parameters was obtained, which can be used for a variety of thermodynamic calculations and database establishment of the Co–Ni-based superalloys.     

A thermodynamic assessment of Ni–Sb system

The Ni–Sb system was critically assessed by means of the CALculation of PHAse Diagram (CALPHAD) technique. The solution phases, Liq and (αNi), were modelled as the substitutional solutions with the Redlich–Kister equation. The intermediate phases, (γNiSb) and (βNi₃Sb), with homogeneity ranges were described respectively using three-sublattices (Sb)_1/3(Ni%,V a)_1/3(V a%,Ni)_1/3 and (Sb)_1/4(Ni%,V a)_1/2(Ni%,V a)_1/4 based on their structure features. Corresponding to the phase (βNi₃Sb), the two low-temperature phases of (δNi₃Sb) and (θNi₅Sb₂) with narrow homogeneity ranges were modelled as two-sublattice, (Ni)_3/4(Sb,Ni)_1/4 and (Ni)_5/7(Sb,Ni)_2/7. The intermetallic compound ζNiSb₂ with no homogeneity ranges was treated as stoichiometric compound. The phase ε$\epsilon$Sb was considered as pure Sb for the solubility of Ni in ε$\epsilon$Sb is very low. A set of self-consistent thermodynamic parameters of the Ni–Sb system was obtained. The optimized phase diagram and thermodynamic properties were presented and compared with experimental data.     

Phase diagrams and thermochemical modeling of salt lake brine systems. II. NaCl+H2O,KCl+H2O,MgCl2+H2O and CaCl2+H2O systems

This study is part of a series of studies on the development of a multi-temperature thermodynamically consistent model for salt lake brine systems. Under the comprehensive thermodynamic framework proposed in our previous study, the thermodynamic properties of the binary systems (i.e., NaCl+H₂O, KCl+H₂O, MgCl₂+H₂O and CaCl₂+H₂O) are simulated by the Pitzer–Simonson–Clegg (PSC) model. Various thermodynamic properties (i.e., water activity, osmotic coefficient, mean ionic activity coefficient, enthalpy of dilution and solution, relative apparent molar enthalpy, heat capacity of aqueous phase and solid phases) are collected and fitted to the model equations. The thermodynamic properties of these systems are reproduced or predicted by the obtained model parameters. Comparison to the experimental or model values in the literature suggests that the model parameters determined in this study can describe all of the thermodynamic and phase equilibria properties over wide temperature and concentration ranges. This modeling study of binary systems provides a solid basis for property predictions of salt lake brines under complicated conditions.     

Combined ab initio/CALPHAD modeling of fcc-based phase-equilibria in the Ir–Nb system

A preliminary thermodynamic assessment of the Ir–Nb system, one of the key binary systems of the Ir-based refractory superalloys, has been performed by combining ab initio calculations and the CALPHAD (CALculation of PHAse Diagrams) technique. The ground-state formation enthalpies have been calculated by the full-potential linearized augmented plane wave method. The free energies at finite temperatures have been estimated using the cluster variation method, where the effective cluster interaction energies have been extracted from the formation enthalpies by the cluster expansion method. The liquid and A1 phases are modeled as substitutional solutions. The L1₀ and L1₂ phases are described using the four-sublattice model with the formula (Ir,Nb)_1/4(Ir,Nb)_1/4(Ir,Nb)_1/4(Ir,Nb)_1/4, while other solid phases are not considered in the present assessment. The obtained parameter set reproduces well the characteristic features of the experimental phase diagram and thermodynamic quantities.     

Solubility prediction for the nonelectrolyte urea–hydrogen peroxide–water system and thermodynamic solubility product calculation for CO(NH2)2 ⋅ H2O2 using the modified Pitzer model

The Pitzer interaction model, which has been applied successfully to the thermodynamic simulation of electrolyte solutions and electrolyte–nonelectrolyte solutions, was extended to nonelectrolyte–nonelectrolyte solution system. In the present work, the modified Pitzer model was used for calculation and correlation of the ternary CO(NH₂)₂–H₂O₂–H₂O system at 283.15 K. The value of the Pitzer interaction parameters for the ternary system and the thermodynamic solubility product of CO(NH₂)₂⋅H₂O₂ were determined using a least-square optimization procedure with coupling activity coefficient and solubility data. The predicted isothermal solubilities agree well with the result obtained from the experiment. The results indicated that the modified Pitzer model could be successfully used to predict the component solubility of the nonelectrolyte–nonelectrolyte system.     

Solubility prediction for the HCl–MgCl2–H2O system at 40 C and solubility equilibrium constant calculation for HCl ⋅ MgCl2 ⋅ 7H2O at 40 C

The component solubilities of the HCl–MgCl₂–H₂O system at 40 ^°C were calculated by using Pitzer’s ion-interaction model and the solubility equilibrium constant of HCl⋅MgCl₂⋅7H₂O at 40 ^°C was evaluated according to the solubility data for the HCl–MgCl₂–H₂O system at −19.8, 0, 20, 25 and 50 ^°C. This study can provide the parameters necessary for solubility prediction for the HCl–LiCl–MgCl₂–H₂O system at 40 ^°C and supply a theoretical basis for the manufacturing process which was proposed by Gao and employed to extract MgCl₂⋅6H₂O from salt lake brine.     

Modeling of thermodynamic properties of ABr-PrBr3 (A=Li-Cs ) systems

The thermodynamic properties of ABr-PrBr₃(A=Li-Cs) systems were assessed by the CALPHAD method. The liquid phase in the systems was described by the non-stoichiometric associate model. The entropies of mixing in the liquid were evaluated from experimental liquidus and enthalpy of mixing data. For the pseudobinary compounds A₃PrBr₆,APr₂Br₇, and A₂PrBr₅ (A=K,Rb) and Cs₃PrBr₆ and CsPr₂Br₇, the dependences of Gibbs energies of formation on temperature were calculated. The anomalies of sequences of thermodynamic properties in RbBr-PrBr₃ were observed and discussed. The nature of the liquid phase and precision of calculations of the Rb₂PrBr₅(s) compound were discussed.     

Experimental investigation and thermodynamic modeling of the Ni–Ti–V system

The liquidus surface projection and isothermal section at 1273 K of the Ni–Ti–V system were established using X-ray diffraction (XRD), scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS), electron probe micro-analyzer (EPMA) and differential thermal analysis (DTA) techniques. Six primary solidification regions and four invariant reactions were deduced in the liquidus surface projection, and six three-phase regions were derived in the isothermal section at 1273 K. No ternary compound was observed. According to the experimental results in the present work and literatures, the Ni–Ti–V system was modeled by means of the CALPHAD (CALculation of PHAse Diagram) method. Two-sublattice model (Ni,Ti)₁₀(Ni,Ti)₂₀ for binary σ phase was used, and the thermodynamic parameters of the σ and NiV₃ phases in the Ni–V system was reassessed. Solution phases (liquid, fcc, bcc and hcp) were modeled with the substitutional solution model in the Ni–Ti–V system. The compounds, Ni₃Ti, NiTi₂, Ni₃V and σ, were treated as (Ni,Ti,V)_m(Ni,Ti,V)_n, and B2 were treated as (Ni,Ti,V)_0.5(Ni,Ti,V) _0.5Va₃. A set of self-consistent thermodynamic parameters of individual phases was obtained.