The ternary Gd-Li-Mg system: Phase diagram study and computational evaluation

The binary Gd-Li and the ternary Gd-Li-Mg systems were studied experimentally by thermal analysis and phase equilibration and also by thermodynamic calculations using the CALPHAD method. Ternary phase equilibria at 250 °C were studied with 55 different alloys that were annealed for 400 h and analyzed by x-ray diffractometry. A thermodynamic assessment of the binary Gd-Li system was also performed and the calculated phase diagram is presented. In the Gd-Li-Mg system, ternary solubilities of Li in GdMg (up to 5 at.% Li), GdMg₂ (up to approximately 3 at.% Li), and GdMg₃ (up to 5 at.% Li) were found at 250 °C. No ternary compound was observed. Lattice parameters for different compositions are given for these phases. Thermal analysis using a ternary key sample of composition near the invariant reaction L′=L+(βGd)+GdMg provided the data that were needed to determine a thermodynamic parameter for the ternary liquid. Thermodynamic data sets for the ternary solid solution phases were also developed. Based on the present data sets and those of the binary Gd-Mg and Li-Mg systems from the literature, the phase equilibria in the entire ternary system were calculated. Isothermal and vertical sections of the phase diagram and the projection of the liquidus surface are shown. These calculated phase diagrams are well supported by the experimental data.     

The ternary Gd-Li-Mg system: Phase diagram study and computational evaluation

The binary Gd-Li and the ternary Gd-Li-Mg systems were studied experimentally by thermal analysis and phase equilibration and also by thermodynamic calculations using the CALPHAD method. Ternary phase equilibria at 250 °C were studied with 55 different alloys that were annealed for 400 h and analyzed by x-ray diffractometry. A thermodynamic assessment of the binary Gd-Li system was also performed and the calculated phase diagram is presented. In the Gd-Li-Mg system, ternary solubilities of Li in GdMg (up to 5 at.% Li), GdMg₂ (up to approximately 3 at.% Li), and GdMg₃ (up to 5 at.% Li) were found at 250 °C. No ternary compound was observed. Lattice parameters for different compositions are given for these phases. Thermal analysis using a ternary key sample of composition near the invariant reaction L′=L+(βGd)+GdMg provided the data that were needed to determine a thermodynamic parameter for the ternary liquid. Thermodynamic data sets for the ternary solid solution phases were also developed. Based on the present data sets and those of the binary Gd-Mg and Li-Mg systems from the literature, the phase equilibria in the entire ternary system were calculated. Isothermal and vertical sections of the phase diagram and the projection of the liquidus surface are shown. These calculated phase diagrams are well supported by the experimental data.     

Thermodynamic optimization of the boron-cobalt-iron system

A thermodynamic optimization of the boron-cobalt-iron ternary system is performed based on thermodynamic models of the three constitutional binary systems and the experimental data on phase diagrams and thermodynamic properties of the ternary system. The liquid, fcc_A1, bcc_A2 and hcp_A3 solution phases are described by the substitutional solution model. The three intermediate line compounds, (Co,Fe)B, (Co,Fe)₂B and (Co,Fe)₃B, are described by the two sublattice model. A set of thermodynamic parameters are obtained. The calculated phase diagram and thermodynamic properties are in reasonable agreement with most of the experimental data.     

Mg-Zn-Si体系的相平衡计算及应用

利用Calphad方法重新评估了Mg-Si二元系的液相,并结合Mg-Zn和Zn-Si二元系热力学数据,外推得到Mg-Zn-Si三元系热力学参数;同时根据Mg2Si-MgZn2伪二元相图实验数据评估了Mg-Zn-Si系的液相三元相交互作用参数,计算相图与实验数据较一致。利用Scheil凝固模型模拟了Mg-2.33Zn-0.9Si(at%)合金的凝固过程,预测了镁合金在铸造冷却过程中的相演变信息,模拟计算结果与实验结果吻合较好     

Experimental Investigation of the Ternary Ge-Sn-In and Ge-Sn-Zn Systems

This paper presents results of experimental examinations of alloys from the ternary Ge-Sn-In and Ge-Sn-Zn systems. Differential thermal analysis, scanning electron microscopy with energy dispersive spectroscopy and x-ray diffraction were used for the experimental investigation of the prepared samples. Obtained experimental results were compared with the thermodynamically extrapolated phase diagrams of the Ge-Sn-In and Ge-Sn-Zn ternary systems based on the thermodynamic parameters for the constitutive binary systems. A good agreement is seen, which suggests that it is not necessary to introduce new thermodynamic parameters for the ternary Ge-Sn-In and Ge-Sn-Zn systems. By using the proposed thermodynamic dataset, a liquidus projection and invariant reactions have been predicted for both investigated ternary systems.     

Thermodynamic calculation of phase diagrams of the 60 common-ion ternary systems containing cations Li,Na, K,Rb, Cs and anions F,Cl, Br,I

The phase diagrams of all 60 possible common-ion ternary alkali halide systems were calculated thermodynamically. The thermodynamic properties of the ternary phases were calculated from the optimized properties of the binary subsystems, which were obtained from previously reported critical evaluations of binary data. Calculated ternary phase diagrams are compared with experimental diagrams in those 47 systems for which the latter are available. In most cases, agreement is within experimental error limits. For five systems, a small empirical correction term was added to the Gibbs energy expression in order to bring the calculated and reported diagrams into coincidence. The calculated ternary diagrams are considered to be the best evaluated diagrams that can be deduced from currently available data. A probable maximum inaccuracy was estimated for each system.     

Thermodynamic calculation of phase diagrams of the 60 common-ion ternary systems containing cations Li, Na, K, Rb, Cs and anions F, Cl, Br, I

The phase diagrams of all 60 possible common-ion ternary alkali halide systems were calculated thermodynamically. The thermodynamic properties of the ternary phases were calculated from the optimized properties of the binary subsystems, which were obtained from previously reported critical evaluations of binary data. Calculated ternary phase diagrams are compared with experimental diagrams in those 47 systems for which the latter are available. In most cases, agreement is within experimental error limits. For five systems, a small empirical correction term was added to the Gibbs energy expression in order to bring the calculated and reported diagrams into coincidence. The calculated ternary diagrams are considered to be the best evaluated diagrams that can be deduced from currently available data. A probable maximum inaccuracy was estimated for each system.     

Computational thermodynamic model for the Mg−Al−Y system

The ternary Mg−Al−Y system was thermodynamically modeled based on the optimization of the binary subsystems Mg−Al, Mg−Y, and Al−Y using the CALPHAD approach. Mg−Al data was taken from the COST507 database, whereas the other two binary systems were reoptimized in this work. The liquid phase was described by a Redlich-Kister polynomial model, and the intermediate solid solutions were described by a sublattice model. Ternary interaction parameters were introduced to enable the best representation of the experimental data while considering the occurrence of the ternary compound Al₄MgY. The constructed database is used to calculate and predict thermodynamic properties, binary phase diagrams of Al−Y and Mg−Y, and liquidus projections of the ternary Mg−Al−Y. The calculated phase diagrams and the thermodynamic properties are in good agreement with the corresponding experimental data from the literature. Sixteen ternary four-phase-equilibria invariant points were predicted in the Mg−Al−Y system: seven ternary eutectic points, eight ternary quasi peritectic points, and one ternary peritectic point. Further, fifteen three-phase-equilibria in variant points were determined: eight saddle points and seven binary eutectic points.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the Al-Mg, Al-Sr, Mg-Sr, and Al-Mg-Sr Systems

All available thermodynamic and phase diagram data were critically assessed for all phases in the Al-Mg, Al-Sr, and Mg-Sr systems at 1 bar pressure from room temperature to above the liquidus temperatures. For these systems, all reliable data were simultaneously optimized to obtain a set of model equations for the Gibbs energy of the liquid alloy and all solid phases as functions of composition and temperature. The modified quasi-chemical model was used for the liquid. The Al-Mg-Sr ternary phase diagram was calculated from the optimized thermodynamic properties of the binary systems. Since no reliable ternary data were available, three assumptions were made: no ternary terms were added to the model parameters for the thermodynamic properties of the liquid, no ternary solid solutions are present in the system, and no ternary compound is present in the system. The calculated ternary phase diagram is thus a first approximation, which can be improved by the addition of new experimental data and can be used as a base for the calculation of phase diagrams of multicomponent systems.     

Thermodynamic study of phase equilibria in the Ni-Si-B system

A thermodynamic analysis of the phase equilibria in the Ni-Si-B ternary system was conducted. A regular solution approximation based on a sublattice model was adopted to describe the Gibbs energies for the individual phases in the binary and ternary systems. A set of thermodynamic parameters for the individual phases was evaluated from literature data on phase boundaries and thermochemical properties. The optimized parameters reproduced the experimental data, for the most part, satisfactorily. However, in the calculated isothemal section at 850 °C, phase equilibria between the fcc phase and Ni₆Si₂B or Ni₃Si(β ₁) and Ni₆Si₂B were found instead of the experimentally observed equilibria between Ni₃Si(β ₁) and Ni₃B or Ni₅Si₂(γ) and Ni₃B. Further, in the primary crystal surface for the fcc phase, the calculated liquidus temperatures were higher than the reported values by approximately 80 °C. Therefore, it is considered that the fcc phase evaluated in the Ni-Si system by Lindhólm and Sundman is too stable.     

Thermodynamic study of phase equilibria in the Ni-Si-B system

A thermodynamic analysis of the phase equilibria in the Ni-Si-B ternary system was conducted. A regular solution approximation based on a sublattice model was adopted to describe the Gibbs energies for the individual phases in the binary and ternary systems. A set of thermodynamic parameters for the individual phases was evaluated from literature data on phase boundaries and thermochemical properties. The optimized parameters reproduced the experimental data, for the most part, satisfactorily. However, in the calculated isothemal section at 850 °C, phase equilibria between the fcc phase and Ni₆Si₂B or Ni₃Si(β ₁) and Ni₆Si₂B were found instead of the experimentally observed equilibria between Ni₃Si(β ₁) and Ni₃B or Ni₅Si₂(γ) and Ni₃B. Further, in the primary crystal surface for the fcc phase, the calculated liquidus temperatures were higher than the reported values by approximately 80 °C. Therefore, it is considered that the fcc phase evaluated in the Ni-Si system by Lindhólm and Sundman is too stable.     

Thermodynamic analysis of some binary phase diagrams involving liquid crystals

A computer-coupled thennodynamic/phase diagram analysis was performed on the phase diagram data of seven binary systems involving liquid crystals. These include five systems based on a homologous series of compounds and two others having 1:1 intermediate compounds. The excess Gibbs energies of the solution phases were thereby calculated, and evaluated phase diagrams were generated that are thermodynamically self-consistent. The results are discussed in the light of what is known about excess solution properties in such systems. The usefulness of the thermodynamic analysis is examined with respect to the prediction of the eutectics of ternary and higher order liquid crystal mixtures. The “Equal G Analysis” is also briefly discussed with reference to the estimation of the nonidealities of mesophase solutions.     

Thermodynamic analysis of some binary phase diagrams involving liquid crystals

A computer-coupled thennodynamic/phase diagram analysis was performed on the phase diagram data of seven binary systems involving liquid crystals. These include five systems based on a homologous series of compounds and two others having 1:1 intermediate compounds. The excess Gibbs energies of the solution phases were thereby calculated, and evaluated phase diagrams were generated that are thermodynamically self-consistent. The results are discussed in the light of what is known about excess solution properties in such systems. The usefulness of the thermodynamic analysis is examined with respect to the prediction of the eutectics of ternary and higher order liquid crystal mixtures. The “Equal G Analysis” is also briefly discussed with reference to the estimation of the nonidealities of mesophase solutions.