Thermodynamic assessment of the Cu–Dy binary system

The Cu–Dy binary system has been thermodynamically assessed with CALPHAD approach. The solution phases including liquid, Bcc, Fcc and Hcp were treated as substitutional solution phases, of which the excess Gibbs energies were formulated with Redlich–Kister polynomial functions. The binary intermetallic compounds were treated as stoichiometric phases. A set of self-consistent thermodynamic parameters for describing various phases in this system has been obtained, which can well reproduce the corresponding experimental data.     

Thermodynamic modeling of the Ca–Ag binary system

The Ca–Ag binary system has been assessed with CALPHAD approach based on experiment information about phase diagram and thermodynamic properties. The excess Gibbs energies of the solution phases including liquid, bcc and fcc were formulated with Redlich–Kister polynomial functions. The intermetallic compounds Ca₂Ag₉, Ca₂Ag₇, CaAg₂, CaAg, Ca₅Ag₃ and Ca₃Ag were treated as stoichiometric phases. Self-consistent thermodynamic parameters have been obtained and the calculated results agree well with most literature data. Several diagrams and tables concerning the Ca–Ag system are presented.     

Thermodynamic assessment of the Ga–Sc and Ga–Tb systems

The Ga–Sc and Ga–Tb binary systems have been assessed with CALPHAD method. Liquid is treated as substitutional solution phase, of which the excess Gibbs energies are modeled by Redlich–Kister polynomial function. The binary intermetallic compounds are treated as stoichiometric phases. Thermodynamic parameters of various phases have been optimized and the calculated results are in reasonable agreement with experimental data.     

Thermodynamic Assessment of Zn-Fe-Nb Ternary System

The Nb-Zn binary system has been thermodynamically assessed using CALPHAD approach by combining available experimental data and the data from ab initio calculations of the formation enthalpies for NbZn₂, NbZn₃ and NbZn₁₅. Solution phases including Liquid, Bcc, Hcp were modeled as substitutional phases, of which the excess Gibbs energies being formulated with the Redlich-Kister polynomial function. All the binary compounds were treated as stoichiometric phases. Incorporated with the reported thermodynamic parameters of Fe-Zn and Fe-Nb binary systems, two isothermal sections at 723 and 873 K of Zn-Fe-Nb ternary system were thermodynamically optimized where one stoichiometric ternary phase (τ) and the ternary solubility in intermetallic compound (ε) were taken into consideration. Furthermore, liquidus projection was predicted accordingly.     

Thermodynamic assessments of the Cu–Th and Mo–Th systems

The thermodynamic assessments of the Cu–Th and Mo–Th binary systems were carried out by using Calculation of Phase Diagrams (CALPHAD) method on the basis of the experimental data including the thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, bcc, and fcc phases are described by the subregular solution model with the Redlich–Kister equation and those of the four intermetallic compounds Cu₆Th, Cu_3.6Th, Cu₂Th and CuTh₂ in the Cu–Th binary system were described by the sublattice model. A set of self-consistent thermodynamic parameters are obtained, and the calculated phase diagrams and thermodynamic properties are presented and compared with the experimental data from literatures. The calculated thermodynamic properties as well as phase diagrams are in good agreement with the experimental data.     

Phase equilibria on the ternary Mg–Mn–Ce system at the Mg-rich corner

Three isopleths at the Mg-rich corner of Mg–Mn–Ce ternary system were investigated via thermal analysis, SEM/EPMA and XRD. A ternary eutectic reaction was observed at 1 wt.% Mn and 23 wt.% Ce and 592 °C. A solid-solution type ternary intermetallic compound, (Mg,Mn)₁₂Ce, was observed with 0.5 at% solid solubility of Mn in the tetragonal Mg₁₂Ce. With the aid of thermodynamic modeling and experiments, a revised phase diagram for the binary Mg–Ce system and the isopleths of 0.6, 1.8 and 2.5 wt.% Mn were proposed up to 25 wt.% Ce.     

Thermodynamic modeling of the Ce–Zn and Pr–Zn systems

In order to develop the thermodynamic database of phase equilibria in the Mg–Zn–Re (Re: rare earth element) base alloys, the thermodynamic assessments of the Ce–Zn and Pr–Zn systems were carried out by using the calculation of phase diagrams (CALPHAD) method on the basis of the experimental data including thermodynamic properties and phase equilibria. Based on the available experimental data, Gibbs free energies of the solution phases (liquid, bcc, fcc, hcp and dhcp) were modeled by the subregular solution model with the Redlich–Kister formula, and those of the intermetallic compounds were described by the sublattice model. A consistent set of thermodynamic parameters has been derived for describing the Gibbs free energies of each solution phase and intermetallic compound in the Ce–Zn and Pr–Zn binary systems. An agreement between the present calculated results and experimental data is obtained.     

A thermodynamic analysis of the Al-Re system

Phase equilibria and thermodynamic data of the Al-Re system are critically reviewed. In addition to the three solution phases, liquid, fcc Al, and hcp Re, there exist six intermetallic compounds in this binary. The thermodynamic properties of the system are analyzed using thermodynamic models for the Gibbs energy of individual phases of the system. A regular solution model is used for the three substitutional solution phases, and the intermetallic phases are treated as stoichiometric compounds. The model parameters are optimized from a limited amount of experimental data. The calculated phase diagram and thermodynamic values are in accord with the available experimental values.     

Thermodynamic modeling of the Al–Cr system

By means of calculation of phase diagram (CALPHAD) technique, the Al–Cr system was critically assessed. Three solution phases (liquid, body-centered cubic, face-centered cubic) were modeled with the Redlich–Kister equation. The intermetallic compounds Al₇Cr, Al₁₁Cr₂, Al₄Cr, Al₈Cr₅, AlCr₂, which have a homogeneity range, were treated as the formulae Al₇(Al,Cr), Al₁₁(Al,Cr)₂, Al₄(Al,Cr), (Al,Cr)₈(Al,Cr)₅, (Al,Cr)(Al,Cr)₂ using two-sublattice model, respectively. A set of self-consistent thermodynamic parameters describing the Gibbs energy of each individual phase as a function of composition and temperature for the Al–Cr system was obtained.     

Phase formation in rapidly solidified R2T17 intermetallics

Rapid solidification was utilized to produce a series of light and heavy rare earth-transition metal intermetallics in the R_H–Co, R_L–Co/Fe, and Sm–Co(Fe) systems with R_H = Dy and Tb and R_L = Pr and Sm. The influence of Nb–C and Zr–C additions on phase formation in the binary and ternary alloys has also been investigated. The X-ray diffraction patterns obtained with synchrotron radiation were refined by the Rietveld method for structural phase determination and analysis. It was found that the ability to create disorder strongly depended on the rare earth element, with light rare earth systems possessing more disorder, and rapid solidification effectively suppressed the development of long-range order in these compounds. Cobalt in contrast to iron favored the formation of disordered structures. Replacement up to two out of the three of the cobalt atoms with iron in the Sm–Co–Fe system has retained the establishment of the disordered TbCu₇-variant and exhibited complete cobalt–iron solubility. Additions of Nb–C and Zr–C have also greatly influenced the order formation. The comparison of lattice parameters of the intermetallic compounds obtained by rapid solidification to the parameters of equilibrium 2–17 phases summarized in the literature revealed that formation of partially ordered and disordered structures was associated with expansion of the both a- and c-axes in Th₂Zn₁₇- and Th₂Ni₁₇-type phases for all binary compounds.     

Phase equilibria on Ni–Al interface under low oxygen pressure

Seventeen phases of the Ni–Al–O system at high temperatures were analyzed using thermodynamic calculations. An Ni–Al–O isothermal stability diagram was obtained from the thermochemical data. The diagram describes the interface equations for Ni/Al intermetallic compounds, Al/Al₂O₃, and Al₂O₃/Al_XNi_Y compounds, and their corresponding regions. Four univariant equilibria points and ten bivariant equilibria lines below 1126 K were obtained. The equations for the coexistence points and interface lines were also obtained. A three-domain diagram of Ni–Al–O phase arrangement at temperatures between 900 and 1191 K is shown. Thermodynamic calculations confirmed that the formation of nickel aluminate spinel (NiAl₂O₄) requires a threshold NiO activity (log a_NiO = −205.3/T − 0.347) and the partial pressure of oxygen (log P_O2=−24622/T+8 atm). In the Ni–Al–O system, a_NiO < 0.266 at 900 K, the compounds in the Ni/Al interface are formed in the order Al₃Ni_(s) → Al₃Ni_2(s) → AlNi_(s) → AlNi_3(s) → Al₂O_3(α). When a_NiO < 0.351 at 1911 K, the compounds in the Ni/Al interface are formed in the order AlNi_(s) → Al₂O_3(α).     

Thermodynamic analysis of alloys Ti–Al, Ti–V, Al–V and Ti–Al–V

Thermodynamic analysis of three binary Ti-based alloys: Ti–Al, Ti–V, and Al–V, as well as ternary alloy Ti–Al–V, is shown in this paper. Thermodynamic analysis involved thermodynamic determination of activities, coefficient of activities, partial and integral values for enthalpies and Gibbs energies of mixing and excess energies at four different temperatures: 2000, 2073, 2200 and 2273 K, as well as calculated phase diagrams for the investigated binary and ternary systems. The FactSage is used for all thermodynamic calculations.     

Thermodynamic modeling of the Au-Sb-Si ternary system

Thermodynamic optimization of the Au-Sb binary system was updated as well as the Si-Sb binary system was assessed thermodynamically using the CALPHAD method based on the critical review of the available experimental information from the published literature. The solution phases including liquid, fcc_A1(Au), diamond_A4(Si) and rhombohedral_A7(Sb), are modeled as substitutional solutions and their excess Gibbs energies are expressed by a Redlich-Kister polynomial. The solubility of Si in the intermetallic compound AuSb₂ is not taken into account because of the lack of experimental information. Combined with previous assessment of the Au-Si binary system, thermodynamic modeling of the Au-Sb-Si ternary system was performed to reproduce well the measured phase equilibria. The liquidus projection and several vertical sections of this ternary system were calculated, which are in reasonable agreement with the reported experimental data.     

Thermodynamic assessments of Ag–Dy and Ag–Er binary systems

Thermodynamic assessments of Ag–Dy and Ag–Er binary systems have been performed by using CALPHAD method. In order to provide necessary data for thermodynamic assessment, the formation enthalpies of Ag₂Dy, AgDy, Ag₂Er and AgEr were calculated by using projector augmented-wave (PAW) method within generalized gradient approximation (GGA) in first-principles frame. During assessments of the Ag–Dy and Ag–Er binary systems, the solution phases (liquid, fcc and hcp) were treated as substitutional solutions, of which the excess Gibbs energies were modeled by Redlich–Kister polynomial, and all intermetallic compounds were described as stoichiometric phases. Consequently, phase diagrams of these two binary systems were thermodynamically optimized and the self-consistent thermodynamic parameters of involved phases obtained.     

Formation of AB2-intermetallics by diffusion in the Au–Sb–Bi system

Binary diffusion couples, in which one single-phased product layer is growing between pure elements, were employed to study the diffusion properties of Au₂Bi- and AuSb₂-intermetallics at 230 and 330 °C. The position of the Kirkendall-marker plane inside the reaction zones revealed that in this temperature range the minority element is the faster diffuser in the Laves-phase Au₂Bi as well as in AuSb₂. The concept of integrated diffusion coefficient is used to describe the growth kinetics of the intermetallic compounds. The integrated diffusion coefficient in an intermetallic is related to the tracer diffusivities of the components and the thermodynamic stability of the phases involved in the interaction. The tracer diffusion coefficients were deduced from the interdiffusion experiments. The isothermal cross-section through the ternary phase diagram Au–Sb–Bi at 230 °C was constructed by means of the diffusion couple technique. No ternary phases are found in this system. Both intermetallic compounds Au₂Bi and AuSb₂ are in equilibrium with the (Sb,Bi)-solid solution. The solubility of Sb in the Laves-phase Au₂Bi was found to be negligible. Up to about 10.5 at.% of Bi can be dissolved in the AuSb₂-phase, the Bi-atoms substituting Sb in the cubic lattice of AuSb₂.     

Phase Equilibria of the Al-Sc-Zr Ternary System at 500 °C

Phase equilibria of the Al-Sc-Zr ternary system at 500 °C have been experimentally investigated by determining twenty-seven equilibrium alloys. X-ray diffraction and electron probe microanalysis were used to identify the phases and their compositions. The isothermal section of the Al-Sc-Zr system at 500 °C was constructed based on the experimental results and the information on the three constituent binary systems. Sixteen two-phase equilibrium regions and ten three-phase equilibrium regions were included and no ternary compounds were observed. The experimental results indicated that all the binary intermetallic compounds exhibited appreciable solubility of the third component. Besides, the continuous solid solution θ (Al(Sc, Zr)₂) forms between AlSc₂ and AlZr₂.     

Phase equilibria of the Sn–Ag–Ni ternary system and interfacial reactions at the Sn–Ag/Ni joints

There are no previous phase equilibria studies of the Sn–Ag–Ni ternary system, even though the phase equilibria information is important for the electronic industry. The isothermal section of the Sn–Ag–Ni ternary system at 240 °C has been determined in this study both by experimental examination and thermodynamic calculation. Experimental results show no existence of ternary compounds in the Sn–Ag–Ni system, and all the constituent binary compounds have very limited solubilities of the ternary elements. The binary Ni₃Sn₂ phase is very stable and is in equilibrium with most of the phases, Ag₃Sn, ζ-Ag₄Sn, Ag, Ni₃Sn₄ and Ni₃Sn phases. A preliminary thermodynamic model of the ternary system is developed based on the models of the three binary constituent systems without introducing any ternary interaction parameters. This ternary thermodynamic model is used with a commercial software Pandat to calculate the Sn–Ag–Ni 240 °C isothermal section. The phase relationships determined by calculation are consistent with those determined experimentally. Besides phase equilibria determination, the interfacial reactions between the Sn–Ag alloys with Ni substrate are investigated at 240, 300 and 400 °C, respectively. It is found that the phase formations in the Sn–3.5wt%Ag/Ni couples are very similar to those in the Sn/Ni couples.     

Thermodynamic and topological instability approaches for forecasting glass-forming ability in the ternary Al–Ni–Y system

A thermodynamic approach to predict bulk glass-forming compositions in binary metallic systems was recently proposed. In this approach, the parameter γ* = ΔH^amor/(ΔH^inter − ΔH^amor) indicates the glass-forming ability (GFA) from the standpoint of the driving force to form different competing phases, and ΔH^amor and ΔH^inter are the enthalpies for glass and intermetallic formation, respectively. Good glass-forming compositions should have a large negative enthalpy for glass formation and a very small difference for intermetallic formation, thus making the glassy phase easily reachable even under low cooling rates. The γ* parameter showed a good correlation with GFA experimental data in the Ni–Nb binary system. In this work, a simple extension of the γ* parameter is applied in the ternary Al–Ni–Y system. The calculated γ* isocontours in the ternary diagram are compared with experimental results of glass formation in that system. Despite some misfitting, the best glass formers are found quite close to the highest γ* values, leading to the conclusion that this thermodynamic approach can be extended to ternary systems, serving as a useful tool for the development of new glass-forming compositions. Finally the thermodynamic approach is compared with the topological instability criteria used to predict the thermal behavior of glassy Al alloys.