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.     

Experimental investigation of Polythermal Ternary Mo-Ga-As phase equilibria

The ternary Mo-Ga-As phase equilibria have been analyzed using X-ray diffraction, metallography and SEM/EDX, and also DTA. The experimental challenges resulting from low thermal stabilities of Ga-rich phases, steep increase of liquidus temperatures, and especially the high As-vapor pressure are pointed out. These difficulties could be resolved mostly by the summarized interpretation of interrelated data and seven isothermal sections in the range 1300 to 600 °C have been developed. Aternary phase τ (Mo₃₁Ga₆₁As₈) was detected and also the five following nonvariant equilibria L + M0₂AS₃ ? M0₅AS₄ + GaAs (1167 °C), L + Mo₅As₄ ? Mo₃Ga + GaAs (912 °C), L + Mo₃Ga + GaAs ? τ (883 °C), L + Mo₃Ga ? “MoGa₅” + τ (825 °C), and L + τ ? “MoGa₅” + GaAs (820 °C). The consistency of all data is confirmed by the development of a complete liquidus surface of the ternary system and the reaction scheme. These are also used to discuss the intersections of condensed phase and gas phase equilibria and the pressure dependence. The experimental study is finally compared to an approximate thermodynamic calculation, and the dominating GaAs-Mo₅As₄-Mo₃Ga solid state equilibrium is confirmed. The phase diagram is also applied to the thermochemical stability of Mo metallizations on GaAs.     

Phase relationships and stability of the μ and ζ phases in the ag-a1-x (x = zn,ga, ge) systems

Details of phase relationships in three ternary systems, Ag-Al-X (X = Zn, Ga, Ge), near the Ag-rich corner at 400 °C are presented. Metallography, XRD, scanning electron microscopy, and X-ray spectroscopy have been used to establish the respective isothermal sections at 400 °C. In each case, the μ phase and the ζ phase of the Ag-Al binary system extend into the ternary system and terminate at a three-phase region involving the Ag-rich primary solid solution (α₁ phase) in the Ag-Al-Zn and Ag-Al-Ga systems and the Ge-rich primary solid solution (α₂ phase) in the Ag-Al-Ge ternary system. The stability ranges of the μ and ζ, phases follow approximately constant electron concentration lines. The solid solubilities of Zn, Ga, and Ge in the μ phase are relatively small compared with those in the ζ, phase (up to 18 at.%). No ternary phase appears to exist in the Ag-rich portions studied in the three ternary systems.     

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.     

Experimental Study of Phase Equilibria in the System Cu-Al-Sn

Phase equilibria in the Cu-rich corner of the ternary system Cu-Al-Sn have been re-investigated. Final equilibrium microstructures of 20 ternary alloy compositions near Cu₃Al were used to refine the ternary phase diagram. The microstructures were characterized using optical microscopy (OM), x-ray diffraction (XRD), electron probe microanalysis and transmission electron microscopy. Isothermal sections at 853, 845, 833, 818, 808, 803 and 773 K have been composed. Vertical sections have been drawn at 2 and 3 at% Sn, showing β₁ as a stable phase. Three-phase fields (α + β + β₁) and (β + β₁ + γ₁) result from β → α + β₁ eutectoid and β + γ₁ → β₁ peritectoid reactions forming metastable β₁ in the binary Cu-Al. With the lowering of temperature from 853 to 818 K, these three-phase fields are shifted to lower Sn concentrations, with simultaneous shrinkage and shifting of (β + β₁) two-phase field. The three-phase field (α + β + γ₁) resulting from the binary reaction β → α + γ₁ shifts to higher Sn contents, with associated shrinkage of the β field, with decreasing temperature. With further reduction of temperature, a new ternary invariant reaction β + β₁ → α + γ₁ is observed at ~813 K. The β disappears completely at 803 K, giving rise to the three-phase field (α + β₁ + γ₁). Some general guidelines on the role of ternary additions (M) on the stability of the ordered β₁ phase are obtained by comparing the results of this study with data in the literature on other systems in the systems group Cu-Al-M.     

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.     

Phase equilibria in the Ga- In- Ni system at 600 °C

Phase equilibria are established in the Ga-In-Ni system at 600 °C using X-ray powder diffraction (XRD) and electron probe microanalysis (EPMA). The system is characterized by a notable absence of ternary solubility among the constituent binary phases. The only exception is the phase Ni₂ln₃, which dissolves a maximum of 12.7 at% Ga. Two ternary phases exist in the compositional vicinity of γ TVi₁₃Ga₉ and Ni₅Ga₃, both of which contain approximately 10 at.% In. These phases are considered to be superlattice structures derived from that of the binary, high-temperature phase γNi₃Ga₂, which possesses a partially filled NiAs (B8₁) structure. The phase diagram isotherm determined in the present investigation was also compared with an isotherm calculated using experimental thermodynamic data for the constituent binary phases, which are available in the literature. The calculated and experimental isotherms agree well.     

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 Calculation of Phase Equilibria in the C-Mo-Zr System

The C-Mo-Zr system was assessed by means of the CALPHAD approach. All of the phase equilibria available from the literature were critically reviewed. The liquid was modeled as substitutional solution phase, while the carbides including fcc-(Mo,Zr)C_1?x, bcc-(Mo), bcc-(Zr), hcp-Mo₂C, hcp-(Zr) and η-MoC were described by using corresponding sublattice models. The laves-Mo₂Zr and shp-MoC phases were considered as binary compounds with no solubility for the third component. The existence of ternary phase was not reported in this system. The modeling of C-Mo-Zr ternary system covers the entire composition and temperature ranges, and a set of self-consistent thermodynamic parameters for the C-Mo-Zr system was systematically optimized. Comprehensive comparisons between the calculated and reported phase diagram data show that the reliable information is satisfactorily accounted for by the present modeling. The liquidus projection and reaction scheme of the C-Mo-Zr system were also generated based on the present thermodynamic assessment.     

A revised thermodynamic description of the Co-W-C system

A thermodynamic reassessment of the Co-W-C system is presented. New information on the liquid (L)+face-centered cubic (fcc)+graphite+WC and L+fcc+WC+M₆C equilibria has recently been published. Because these equilibria are very important for extrapolation to higher-order systems, the ternary system has been revised. A revision of the Co-W system also has been performed.     

Phase equilibria of the constituent ternaries of the Mg-Al-Ca-Sr system

Thermodynamic modeling of the Al-Ca-Sr, Mg-Ca-Sr, Mg-Al-Ca and Mg-Al-Sr systems was conducted using the modified quasichemical model. A self-consistent database has been established for these systems. Mg-Al-Ca and Mg-Al-Sr ternary systems were studied experimentally through microstructure characterization, phase identification, and thermal analysis and thermodynamic modeling based on these experimental findings. It has been observed that the intermetallic compounds in the Mg-Ca, Mg-Sr, Al-Ca, and Al-Sr binary systems dissolve the third component in the respective ternary phase diagrams. In addition, two ternary compounds, Mg₅₆Al₄₀Sr₄ and Mg₂Al₄Ca₃, have been reported.