Thermodynamic optimization and calculation of the ErCl3–MCl (M=Li,Na,K,Rb,Cs ) systems

In this paper, the binary phase diagrams of the ErCl₃–MCl (M = Li, Na, K, Rb, Cs) systems were studied by the CALPHAD (CALculation of PHAse Diagram) approach. The modified quasi-chemical model in the pair-approximation for short-range ordering was used to describe the Gibbs energies of the liquid phase in the systems. From measured phase diagram data and experimental thermochemical properties, a series of thermodynamic functions has been optimized based on computer-assisted analysis. A discussion of thermodynamic functions for strong interaction binary systems was undertaken. The results showed that the calculated phase diagrams and optimized thermodynamic parameters are self-consistent.     

Thermodynamic assessment of TbCl3–MCl (M=Na,K, Rb,Cs) binary systems

The phase diagrams of TbCl₃–MCl (M=Na, K, Rb, Cs) binary systems were reassessed by CALPHAD method. The liquid phase has been described by the associate model with main 3Na⁺+TbCl₆³⁻ associate. The Gibbs energies of formation of solid compounds were calculated and compared with previous data. The entropy of mixing of the liquid phase has been used for the interpretation of structure of this phase.     

Phase equilibria in LaBr3-TlBr pseudobinary system. Thermodynamic assessment of LaBr3-MBr (M = Li,Na, K,Rb, Cs,Tl) pseudobinary systems

The phase equilibria in the lanthanum(III) bromide-thallium bromide pseudobinary system was established by means of differential scanning calorimetry (DSC). The DSC investigations were performed on samples with different compositions in the whole mole fraction x(LaBr₃) range. This system includes one intermediate compound Tl₂LaBr₅. It melts congruently at 829 K. The compositions of TlBr-Tl₂LaBr₅ and Tl₂LaBr₅-LaBr₃ eutectics, corresponding to LaBr₃ mole fraction x = 0.088 (T = 687 K) and x = 0.491 (T = 788 K) respectively, was found from Tammann's plot. The LaBr₃-TlBr pseudobinary system was also optimized by CALPHAD method using the available experimental data. Experimental and calculated data concerning LaBr₃-TlBr system were compared with data for LaBr₃-MBr (M = Li-Cs) systems, which have also been optimized by CALPHAD method. The thermodynamic properties of the liquid phase in the systems were modelled using the Associated Solution Model with {3 M⁺ + LaBr₆³⁻} (M = Li-Cs, Tl) associate. The dependencies of mixing enthalpy and mixing entropy on mole fraction x(LaBr₃) were estimated for all investigated systems. The dependencies of formation Gibbs energy on temperature and temperature range of existence of intermediate compounds have been calculated and discussed. The CALPHAD optimization indicates that the participation of the associate in the liquid phase in the LaBr₃-MBr (M = K⋯Cs, Tl) systems increases with the increase of the ionic radius of the monovalent metal.     

Thermodynamic assessment of the Bi-alkali metal (Li,Na, K,Rb) systems using the modified quasichemical model for the liquid phase

Bi-alkali metal (Li, Na, K, Rb) binary systems have been systematically assessed based on the available phase diagrams and thermodynamic data. The modified quasichemical model, which takes short-range ordering into account, is used to describe the liquid phase. All intermetallic phases are treated as stoichiometric compounds. A set of self-consistent model parameters is obtained and the experimental data are reproduced well within experimental error limits. The enthalpy of mixing, entropy of mixing, and activity of element are calculated, showing the liquid phase exhibits maximum short-range ordering at 75 at% X (X=Li, Na, K, Rb). Some systematic variations and regularities are presented, indicating the enthalpy and entropy of mixing for the liquid phase at the maximum short-range ordering along with the enthalpy of formation and melting temperature of intermediate compound BiX₃ change with the atomic radius of alkali metals regularly.     

Ab initio calculation of the BCC Fe–Al–Mo (Iron–Aluminum–Molybdenum) phase diagram: Implications for the nature of the phase

The metastable phase diagram of the BCC-based ordering equilibria in the Fe–Al–Mo system has been calculated via a truncated cluster expansion, through the combination of Full-Potential-Linear augmented Plane Wave (FP-LAPW) electronic structure calculations and of Cluster Variation Method (CVM) thermodynamic calculations in the irregular tetrahedron approximation. Four isothermal sections at 1750 K, 2000 K, 2250 K and 2500 K are calculated and correlated with recently published experimental data on the system. The results confirm that the critical temperature for the order–disorder equilibrium between Fe₃Al–D0₃ and FeAl–B2 is increased by Mo additions, while the critical temperature for the FeAl–B2/A2 equilibrium is kept approximately invariant with increasing Mo contents. The stabilization of the Al-rich A2 phase in equilibrium with overstoichiometric B2–(Fe,Mo)Al is also consistent with the attribution of the A2 structure to the τ₂ phase, stable at high temperatures in overstoichiometric B2–FeAl.     

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.     

Calculation and optimization of LaBr3–MBr (Li–Cs) phase diagrams by CALPHAD method

Phase diagram of LaBr₃–MBr (M=Li–Cs) pseudo-binary systems were reassessed by CALPHAD method with Associate Model and Redlich–Kister Model. In addition the LaBr₃–LiBr system was optimized through the application of the Quasichemical Model, and LaBr₃–RbBr system was optimized by Partially Ionic Two-sublattice Model. Optimized thermodynamic properties were compared with the data previously calculated by Quasichemical Model and Partially Ionic Two-sublattice Model as well as with experimental data. The influence of the used models for calculated thermodynamic properties has been discussed.     

Critical thermodynamic evaluation of oxide systems relevant to fuel ashes and slags. Part 3: Silica–alumina system

The Al₂O₃–SiO₂ system was reassessed using the associate species model for the liquid and the sublattice and associate species model for the mullite. The available phase diagram data were collected and evaluated for the purpose of improving the solution database. The new data for the liquid phase and mullite are compatible with data for the pure stoichiometric component oxides from the FACT Pure Substance database. The phase equilibria re-calculated using the improved solution data are in good agreement with experimental data. This work continues the studies concerning the thermodynamic assessment of oxide systems relevant to ashes and slags.     

Thermodynamic evaluation and optimization of Al–Gd, Al–Tb, Al–Dy, Al–Ho and Al–Er systems using a Modified Quasichemical Model for the liquid

The Al–Gd, Al–Tb, Al–Dy, Al–Ho and Al–Er (Al–heavy rare earths) binary systems have been systematically assessed and optimized based on the available experimental data and ab-initio data using the FactSage thermodynamic software. A systematic technique (reduced melting temperature proposed by Gschneidner) was used for estimating the Al–Tb phase diagram due to lack of experimental data. Optimized model parameters of the Gibbs energies for all phases which reproduced all the reliable experimental data to satisfaction have been obtained. The optimization procedure was biased by putting a strong emphasis on the observed trends in the thermodynamic properties of Al–RE phases. The Modified Quasichemical Model, which takes short-range ordering into account, is used for the liquid phase and the Compound Energy Formalism is used for the solid solutions in the binary systems. It is shown that the Modified Quasichemical Model used for the liquid alloys permits one to obtain entropies of mixing that are more reliable than that based on the Bragg–Williams random mixing model which does not take short-range ordering into account.     

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.     

Solidification structure of CaO–SiO2–MgO–Al2O3 (–CaF2) systems and computational phase equilibria: Crystallization of MgAl2O4 spinel

The solidification behaviour of the CaO–SiO₂–Al₂O₃–CaF₂–10% MgO system, which is similar to the inclusion compositions in the stainless steel and the crystallization of spinel have been investigated using XRD, SEM-EDS, and an image analyser. The solidification mode and the phase equilibria were computed by employing thermochemical software. The liquidus temperature of the oxides containing 5% CaF₂ increases with increasing alumina content from 10% to 30%, while the solidus temperature has little dependence on alumina content. The size of spinel crystals in the final microstructure increases on increasing the content of alumina, resulting from that the oxides spending more time at higher temperatures below the liquidus temperature, where crystal growth is generally faster than nucleation, during slow cooling. The liquidus temperature of the oxides containing 30% Al₂O₃ is scarcely varied, while the solidus temperature decreases by increasing the content of CaF₂ to 10%. The size of spinel crystals decreases as the content of CaF₂ increases, resulting from the fact that the oxides could spend more time at relatively lower temperatures, where nucleation is faster than growth, during the cooling process.     

Modelling and calculation of the phase diagrams of the LiF–NaF–RbF–LaF3 system

Four ternary phase diagrams of the quaternary system LiF–NaF–RbF–LaF₃ were calculated from the data of LiF–NaF, LiF–RbF, LiF–LaF₃, NaF–RbF, NaF–LaF₃ and RbF–LaF₃ binary phase diagrams using the Kohler symmetric and Kohler–Toop asymmetric approximation. Excess Gibbs parameters of all six mentioned binaries were optimized using the experimental results taken from the literature. For the LiF–RbF system our own data were used. In all cases very good agreement between the experimental data and our optimized values was achieved. Excess Gibbs functions for the liquid phases were obtained using the modified quasi-chemical method based on quadruplet interactions and the excess Gibbs function for the solid solution was calculated by a sublattice model. The quaternary eutectic was determined and a set of pseudo-ternary systems with fixed ratio of LaF₃ was calculated in order to find the optimal composition for a molten salt fuel.     

Calculation of phase diagrams of the reciprocal quaternary systems Li, Na, K/CO3, SO4; Li, Na/CO3, SO4, OH; Li, K/CO3, SO4, OH and Na, K/CO3, SO4, OH

Phase diagrams of the quaternary reciprocal salt systems Li, Na, K/CO₃, SO₄; Li, Na/CO₃, SO₄, OH; Li, K/CO₃, SO₄, OH; and Na, K/CO₃, SO₄, OH (the last three up to 10 mol % hydroxide) were calculated from the optimised thermodynamic properties of their sub-systems via the Conformal Ionic Solution Theory by means of a computer program designed for the purpose.