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Based on the experimental phase equilibria and thermodynamic data, a critical evaluation and thermodynamic assessment of the PbO–V2O5 system has been performed. The liquid phase is described by the modified quasichemical model, which takes short-range ordering in liquid solution into account. All intermediate phases are treated as stoichiometric compounds. A set of self-consistent thermodynamic functions for all phases in the PbO–V2O5 system is obtained. The available phase equilibria and thermodynamic data are reproduced well within experimental error limits.

The V–O system has been critically evaluated and thermodynamically assessed based on the available phase diagram and thermodynamic data using the CALPHAD method. The liquid phase over the whole composition range from metallic liquid to oxide melt is described by the modified quasichemical model with five species: VII, VIII, VIV, VV and O, which takes short-range ordering in liquid solution into account. All solid solutions are modeled considering respective crystal structures. A set of self-consistent thermodynamic parameters of the V–O system is obtained and the available experimental data are reproduced well within experimental error limits. Especially for the VOx solid solution, the site fractions of vacancies in both vanadium and oxygen sublattices are reproduced well using the present model and parameters.

Based on the critical evaluation of available phase diagram, thermodynamic, and crystal structure data, the ternary Ti-C-O system is thermodynamically assessed using the Calculation of Phase Diagram method. Both binary Ti-C and Ti-O systems are reassessed to obtain the successful description of ternary Ti-C-O system for the first time. The liquid phase is described by the modified quasichemical model, which takes short-range ordering in liquid solution into account. All solid solutions are described using compound energy formalism. In particular, a completed solid solution between TiC x and TiO y with the excess solubilities of Ti, C, and O is accurately described with the (Ti, Va)1(C, O, Va)1 solution structure. The thermodynamic models with a set of optimized self-consistent model parameters can reproduce available reliable experimental data within experimental error limits. The results are also applied to the thermodynamic analysis of complex carbothermic TiO2 reduction process.

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.

Thermodynamic assessment of the In-Ni-Sb ternary system has been performed using the CALPHAD technique. The phases ζ(Ni2In) and ζ(NiSb) with the same B8-type structure in the subbinary systems are modified using the same three-sublattice model: (Ni,Va)1/3(Ni,Va)1/3(Ni,X)1/3 (X = In, Sb), in order to give the continuous solid solution phase ζ in the In-Ni-Sb ternary system a better description. This modification is also made to the Gibbs free energy expression of the InSb phase. The parameters of the thermodynamic descriptions of the In-Ni-Sb ternary system are optimized on the basis of the three modified subbinary systems. A set of self-consistent thermodynamic parameters of the In-Ni-Sb system is obtained according to five isothermal sections and three vertical sections. Most of the experimental data can be satisfactorily reproduced by the present parameters. The liquidus projection and the invariant reactions are also presented. By simply considering the standards of melting temperature and thermodynamic stability, part of the ζ-phase is more suitable as a contact material to InSb semiconductor.

The binary phase diagrams of the YCl3–ACl (A=Li, Na, K, Rb, Cs) systems were studied using the CALPHAD technique and nonlinear mathematical method. The new modified quasi-chemical model in the pair-approximation for short-range ordering was applied to describe the Gibbs energies of the liquid phase in these systems. And the paper created the Artificial Neural Networks (ANN) model to study the interaction coefficients of two ending compounds composing the binary systems which are important for thermodynamic study of multi-elements system. Based on measured phase equilibrium data, a set of thermodynamic functions has been optimized and calculated. The effects of ionic radius, electronegativity and mole fraction of YCl3 on interaction coefficients were investigated in more detail.

The knowledge of phase diagram and thermodynamic properties of the Si-Ta and Si-W systems is of technical importance for metallic contacts between Ta, W, and SiC in electrical and electronic devices. The phase diagram and thermodynamic properties of the Si-Ta and Si-W systems were assessed using the CALPHAD approach with available experimental data. The intermetallic compounds of the two systems were modeled as stoichiometric ones. A set of self-consistent thermodynamic parameters were obtained and the calculated phase equilibria were found to be in reasonable agreement with most experimental data. The calculated enthalpies of formation of the silicides in the Si-Ta and Si-W systems were compared with the reported values. The enthalpies of mixing of liquid at 2000 K in similar Si-transition metal systems were used for comparison in order to judge the rationality of the calculations. The assessed thermodynamic descriptions of the Si-Ta and Si-W binary systems will serve as part of the thermodynamic database for the Si-C-M (M: Ta and W) alloys.

According to measured experimental phase diagram data and thermodynamic data, the HoCl3-MCl (M = Na, K, Rb, Cs) phase diagrams were determined by the CALPHAD technique. The Gibbs energies of liquid phases in these systems have been optimized and calculated by the modified quasi-chemical model in the pair-approximation for short-range ordering. A series of thermodynamic functions have been optimized and calculated on the basis of an interactive computer-assisted analysis. The results show that the thermodynamic properties and phase diagrams are self-consistent. The optimized results for the systems are discussed.

YbCl3-MCl (M = Na, K, Rb, Cs) systems were optimized and calculated using the CALPHAD (CALculation of PHAse Diagram) technique. The modified quasi-chemical model in the pair-approximation for short-range ordering was used to describe the Gibbs energies of liquid phase in the systems. On the basis of the measured phase diagram data and experimental thermodynamic properties, a series of thermodynamic functions were optimized and calculated through an interactive computer-assisted analysis. Furthermore, some reasonable discussions on the thermodynamic parameters for these strong interaction binary systems were carried out. The results showed that the optimized parameters and experimental data are thermodynamically self-consistent.

The activities of Sn of liquid Ag–Bi–Sn alloys for three cross-sections with the constant molar ratios of Ag:Bi = 2:1, 1:1, and 1:2 are measured at 627 and 727 ∘ C by an electromotive force (emf) method with a liquid electrolyte. The previous thermodynamic descriptions of the Ag–Bi–Sn ternary system are modified by considering the literature data and our own experimental results. The thermodynamic interaction parameters of the Bi–Sn binary and the Ag–Bi–Sn ternary liquid phase are optimized using the emf and calorimetric data from the present work. Based on the self-consistent optimized thermodynamic parameters the phase diagram and thermodynamic properties of the Ag–Bi–Sn ternary system are calculated and compared with the experimental data. The agreement between the calculated results and the experimental data has been significantly improved.

The Al2O3-SrO 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+, Sr2+) P ( $${\hbox{AlO}_{2}^{1-}}$$ , 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. The calculated results are compared with experimental data. A comparison between this system and similar systems is also given.

In this article, following a brief introduction concerning experimental measurements of surface and interfacial tensions, methods for calculating surface tension and surface segregation for binary, ternary, and multicomponent high-temperature melts based on Bulter's original treatment [1] and on available physical properties and thermodynamic data, especially excess Gibbs free energies of bulk phase and surface phase versus temperature obtained from thermodynamic databases using the calculation of phase diagram (CALPHAD) approach, with special attention to the model parameter, have been described. In addition, the geometric models can be extended to predict surface tensions of multicom-ponent systems from those of sub-binary systems. For illustration, some calculated examples, including Pb-free soldering systems and phase-diagram evaluation of binary alloys in nanoparticle systems are given. On the basis of surface tensions of high-temperature melts, interfacial tensions between liquid alloy and molten slag as well as molten slag and molten matter can be calculated using the Girifalco-Good equation [2]. Modifications are suggested in the Nishizawa's model [3] for estimation of interfacial tension in liquid metal (A)/ceramics (MX) systems so that the calculations can be carried out based on the sublattice model and thermodynamic data, without deliberately differentiating the phase of MX at high temperature. Finally, the derivation of an approximate expression for predicting interfacial tension between the high-temperature multi- component melts, employing Becker's model [4] in conjunction with Bulter's equation and interfacial tension data of the simple systems is described, and some examples concerning pyrometallurgical systems are given for better understanding.

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.

An optimization of the binary GdCl 3 –ACl (A=Na,K,Rb,Cs) systems has been carried out using the CALPHAD technique. The new modified quasi-chemical model in the pair-approximation for short-range ordering was used to describe the Gibbs energies of the liquid phase in these systems. Based on the measured phase equilibrium data and experimental thermochemical properties, the GdCl 3 –ACl phase diagrams were optimized and calculated. A set of thermodynamic functions has been optimized based on an interactive computer-assisted analysis. The calculations based on the obtained descriptions show good agreement with experimental phase diagrams and thermodynamic values.

By using the CALPHAD technique, an optimization of the binary YbCl3-AECl2 (AE=Mg, Ca, Sr, Ba) systems was carried out. From measured phase equilibrium data and experimental integral properties, the YbCl3-AECl2 phase diagrams were optimized and calculated. A set of thermodynamic functions was optimized based on an interactive computer-assisted analysis. The calculated phase diagrams and thermodynamic data are self-consistent.

The Gibbs energy of the liquid phases in the SmCl 3 –MCl (M=Na, K, Rb, Cs) systems is described by a modified quasi-chemical model. Based on measured phase equilibrium data and experimental thermochemical properties of these binary systems, a set of thermodynamic functions has been optimized by using the CALPHAD technique. The calculations based on the obtained descriptions show good agreement with experimental phase diagrams and thermodynamic values.

By using the CALPHAD technique, an optimization of the binary EuCl3–MCl (M = Na, K, Rb, Cs) systems has been carried out. To describe the Gibbs energies of liquid phases in these systems the new modified quasi-chemical model was used in the pair-approximation for short-range ordering. From the measured phase equilibrium data and the experimental thermo-chemical properties, the EuCl3–MCl phase diagrams were optimized and calculated. A set of thermodynamic functions has been optimized based on an interactive computer-assisted analysis. The calculated phase diagrams and thermodynamic data are self-consistent.

Phase diagram and thermodynamic properties of the Ni-Ga system are assessed based on the CALPHAD approach, using all available experimental data and applying appropriate thermodynamic models. The liquid phase and the Ni-based solid solution (Ni) are treated as disordered solutions. The thermodynamic behavior of the ordered intermetallic compounds with appreciable ranges of homogeneity, Ni3Ga and NiGa, are described by a two-sublattice model, and the order-disorder transformation between Ni3Ga and fcc-(Ni) is also explicitly considered in this work. The other five intermetallic compounds are treated as stoichiometric line compounds. The phase diagram and the thermodynamic properties calculated from the optimized model parameters are in good agreement with most of the experimental data.

By using the CALPHAD technique, an optimization of the binary CeCl 3 –AECl 2 (AE=Mg,Ca,Sr,Ba) systems has been carried out. For describing the Gibbs energies of liquid phase in these systems, the new modified quasichemical model in the pair-approximation for short-range ordering was used. From the measured phase equilibria data and experimental thermochemical properties, the CeCl 3 –AECl 2 phase diagrams were optimized and calculated. A set of thermodynamic functions has been optimized based on an interactive computer-assisted analysis. The calculated phase diagrams and thermodynamic data are self-consistent.

The phase diagram of one promising lead-free solder system---the In-Sn-Zn system was well constructed by using accurate experimental methods in conjunction with CALPHAD technique. This work is a good example to show that the CALPHAD technique is very useful for phase diagram measurements, especially for those systems with a lot of experimental difficulties. The ternary interaction parameter of the Sn-In-Zn liquid phase was also calculated based on our experimental data and thermodynamic properties from the literatures.

The phase relations in the Fe-rich region of the Nd-Fe-V system at room temperature have been investigated by means of powder X-ray diffraction. In the investigated composition region, two ternary phases: Nd(Fe1 - xVx)(12) (x = 0.125-0.167) and Nd-3(Fe1 - xVx)(29) (x = 0.064-0.091), and one pseudobinary phase: Nd-2(Fe1 - xVx)(17), (x = 0.000-0.061) were observed. Dependences of the lattice parameters on x for Nd(Fe1 - xVx)(12), Nd-3(Fe1 - xVx)(29) and Nd-2(Fe1 - xVx)(17) are presented. The preferred site occupation of V in Nd(Fe1 - xVx)(12) and Nd-2(Fe1 - xVx)(17) is deduced from the slope of a and c with V content. (C) 1999 Elsevier Science S.A. All rights reserved.

The phase diagrams and thermodynamic properties of the Cu-R (R: Ce, Pr, Nd, Sm) systems are reevaluated on the basis of all available experimental data, including the enthalpies of mixing reported recently. The Redlich-Kister polynomial with two or three terms is used to describe the excess Gibbs energies of liquid phases in the Cu-R systems. All intermediate phases are treated as stoichiometric, and their Gibbs energies of formation are optimized. Based on the optimized thermodynamic parameters, phase diagrams and thermodynamic properties of the Cu-R systems are calculated and compared with the experimental results. The optimized parameters seem to be in good agreement with the experimental data and might represent the regularity and systematic variation of these systems.

The BaB2O4-BaF2-2NaF-NaB2O4 reciprocal system has been investigated by combination of experimental measurements with theoretical calculation. The Na2B2O4-2NaF binary and Na2B2O4-BaF2 pseudo-binary phase diagrams are measured by means of DTA and X-ray diffraction. The thermodynamic functions for all sub-binary systems are derived from measured phase diagrams and thermodynamic data by CAL-PHAD technique, and the sub-binary phase diagrams are calculated according to phase equilibrium principle. Then, the thermodynamic functions for sub-binary systems are extrapolated to the BaB2O4-BaF2-2NaF-Na2B2O4 reciprocal system, and the phase diagram of the reciprocal system is calculated. The calculated phase diagrams are verified by additional experiments. (C) 1996 Academic Press, Inc.

The subsolidus phase relations of the Nd{sub 2}O{sub 3}-Pr{sub 6}O{sub 11}-CuO ternary system sintered in air at 950{degrees}C have been investigated by X-ray powder diffraction. The system can be divided into one ternary phase region and three binary phase regions. The solid solution Nd{sub 2-x}Pr{sub x}CuO{sub 4-{delta}} has been observed to exist over the composition region 0 < x < 2. The solid solution has a tetragonal structure, and its lattice parameters increase linearly with the increasing of the praseodymium content.

The subsolidus phase relations of Nd2O3-SrO-CuO ternary system sintered in air at 950-1000-degrees-C have been investigated by X-ray powder diffraction. The system can be divided into 13 three-phase regions and five two-phase regions. In this system there exist at least four compounds and their solid solutions: Nd2SrCu2O6, Nd1+xSr2-xCu2O6 (0 less-than-or-equal-to x less-than-or-equal-to 0.4), Nd2-xSrxCuOy (1.2 less-than-or-equal-to x less-than-or-equal-to 1.5) and NdxSr3-xCu5Oy (0 less-than-or-equal-to x less-than-or-equal-to 1.5). None of these compounds are superconducting above 4.2 K.

Based on the advanced thermodynamic models, the optimized thermodynamic data for these two systems were derived from experimental phase dragrams. In optimization the excess molar volume of liquid was represented by a polynomial of composition and optimized by the combination of the two experimental phase diagrams. The calculated and experimental phase diagrams were in good agreement. This indicated the present method for treatment of excess molar volume is reasonable. The calculated results showed that the application of pressure on the present system restrains the formation of short range order of atoms in the liquid at about x = 0.85mol NaIO3.

The Nd2O3CuO phase diagram was calculated by using a regular solution model. The interaction parameters were derived from reliable experimental data. The phase diagram was constructed after an approximate treatment of the decomposition of CuO at 1025 °C. The calculated results were compared with experimental data.

The phase relation in the Fe-rich region of the Gd-Fe-Ti system at 1373 K has been investigated by means of x-ray diffraction and the phase-disappearing method. In the investigated composition region, four ternary phases: GdFe11Ti, GdFe9Ti2, Gd(Fe1-xTix)(9) (x approximate to=0.062), Gd-3(Fe1-xTix)(29) (x=0.0111-0.0339), one pseudobinary phase: Gd-2(Fe1-xTix)(17) (x=0.0000-0.0511) and three binary phases: Gd6Fe23, Fe2Ti and GdFe3, are observed. Dependence of the lattice parameters on Ti content (x) in Gd-2(Fe1-xTix)(17) and Gd-3(Fe1-xTix)(29) is reported. (C) 1998 Elsevier Science S.A.

The phase diagram of the EuI{sub 2}-KI binary system was studied by differential thermal analysis (DTA) and X-ray powder diffraction (XRD). The phase diagram of the EuI{sub 2}-KI system shows the existence of one congruently melting compound, KEu{sub 2}I{sub 5}, and one incongruently melting compound, K{sub 4}EuI{sub 6}. There are two eutectic points located at 465 C, 20 mol% KI and 439 C, 60 mol% KI, respectively.

The phase diagram of Na 2 B 2 O 4 -K 2 B 2 O 4 binary system was determined by means of DTA and X-ray diffraction methods to be complete solid solution system with minimum melting point: T min =836° C , x min =0.375 mol. K 2 B 2 O 4 . The solidus was calculated from measured liquidus by generalized Kohler and Pelton method (2). The miscibility gap of soild solution was predicted thermodynamically and confirmed by high temperature X-ray diffraction experiments.

In this paper the system NaClCaCl 2 SrCl 2 and its binary systems were studied. Using a previously calculated phase diagram of the NaClCaCl 2 SrCl 2 system as a basis, accurate measurements were carried out by MDTA with high sensitivity. It is a simple eutectic system with a eutectic point at 41.9 mol % NaCl, 40.C mol % CaCl 2 , 18.1 mol % SrCl 2 , 744 K. In the liquidus surface for saturation with the CaCl 2 SrCl 2 solid solution a univariant line starts from a point 24.8 mol % NaCl, 50.1 % CaCl 2 , 25.1 mol % SrCl 2 at 823 K. The uncertainty in the liquidus temperatures is estimates to be less than ±5K, for the reason that the errors due to Supercooling and change of sample compositions were reduced by our experimental method. A new calculation of the phase diagram of the NaClCaCl 2 SrCl 2 system has been performed with a new asymmetric method. It is based upon a critical assessment of the thermodynamic properties and phase diagrams of the binary systems. The agreement between our present measured and calculated phase diagrams is within ±2.5 mol %. Their good agreement indicates that the phase diagram calculated from the binary data is relatively sensitive to the se1f-consistency between thermodynamic properties and phase diagrams of binary systems.

The enthalpy of fusion of barium inelaborate was estimated from the limiting slopes of liquidus of BaB 2 O 4 -Na 2 B 2 O 4 and BaB 2 O 4 -K 2 B 2 O 4 systems. The optimized thermodynamic data for these two systems were derived from experimental phase diagrams. In optimization, the ionic fractions and equivalent fractions were introduced for representing ideal mixing entropy and excess Gibbs free energy.