Ternary rare earth germanium systems with Cu and Ag—A review and a contribution to their assessment

Constitutional data of the R-(Ag, Cu)-Ge systems, with R=rare earth, are summarized and discussed. Crystal structures of the phases formed in the binary boundary systems and in the ternary systems are assessed, and the phase equilibria observed in the reported ternary systems are reviewed with special attention to the isothermal sections (generally at 400 or 600 °C) of the phase diagrams. Some regularities observed in the trends of the constitutional properties of the ternary R-(Ag, Cu)-Ge alloys are briefly described.     

Ternary rare earth germanium systems with Cu and Ag—A review and a contribution to their assessment

Constitutional data of the R-(Ag, Cu)-Ge systems, with R=rare earth, are summarized and discussed. Crystal structures of the phases formed in the binary boundary systems and in the ternary systems are assessed, and the phase equilibria observed in the reported ternary systems are reviewed with special attention to the isothermal sections (generally at 400 or 600 °C) of the phase diagrams. Some regularities observed in the trends of the constitutional properties of the ternary R-(Ag, Cu)-Ge alloys are briefly described.     

Structure and stability of Laves phases part II—structure type variations in binary and ternary systems

In Part I, various models for the prediction of the occurrence and stability of Laves phases have been discussed. In the present Part II paper, an overview is given on the various types of manifestation of Laves phases in intermetallic alloy systems with emphasis on transition metal systems. Temperature- and composition-dependent as well as stress-induced phase transformations between the cubic C15 and the hexagonal C14 and C36 structural polytypes of Laves phases were observed in various binary and ternary systems. The phase fields of the different polytypes are generally separated by small two-phase fields. Some general rules for the occurrence of the different Laves phase polytypes are derived from a study of the results of experimental phase diagram investigations of various binary and ternary systems. The solubilities and site occupancies of ternary additions in the different Laves phase polytypes and the mutual miscibility of different binary Laves phases are discussed. The need for careful experimental investigations of phase equilibria is demonstrated. Existing models discussed in the preceding Part I paper are shown to fail to predict the structure and stability of the presented Laves phases in many cases.     

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.     

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.     

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 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.     

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.     

High Entropy Alloys,Miscibility Gaps and the Rose Geometry

Recent review articles on high entropy alloys (HEAs) provide little information about miscibility gaps in multicomponent systems, especially about how to respond with alloying should they be found. Also, there is a lack of information about how miscibility gaps might appear on calculated or measured multicomponent phase diagrams. In this work concepts concerning miscibility gaps that form in binary and ternary systems are reviewed. Then the work is extended to alloys with more components including HEAs. The previous work predicts that there are significant differences between binary systems and those with three or more components. For example, miscibility gaps do not form in binary systems that have a negative heat of mixing, but they do form in ternary systems. Also, ternary systems with a positive heat of mixing can have their stability temperature lowered by adding ternary components that add positive heats of mixing. The morphology and topology of multicomponent/multiphase miscibility gaps differ from typical phase diagrams, as well. For example, one type of miscibility gap is said to have the rose geometry, because of its floral design. Normally only 2-phase miscibility gaps can form in binary and ternary systems. However using the Graph Method it is suggested that 3-phase miscibility gaps might form in HEA systems, even while trying to avoid them. A conclusion of this investigation is that with additional computational and experimental work it may be possible to expand the boundaries of where HEAs can be found.     

A thermodynamic reassessment of the Al-As-Ga system

The Al-As-Ga system is one of the most important III-V mixed crystal systems because of its advantages as a heterostructure. There are more phase equilibria data available for this system over a wider range of temperatures and compositions, than for any other III-V ternary system. In this paper, the experimental phase diagram data of the Al-As-Ga ternary system have been assessed comprehensively and critically. Especially, the most recent experiments are considered. The interaction parameters of the liquid phase and the semiconductor compound are provided. With the assessed thermodynamic parameters, the pseudobinary AlAs-GaAs phase diagram, the Al-As-Ga ternary isothermal sections, and the solidus isoconcentration curves were calculated and compared with the related experimental data.     

A thermodynamic reassessment of the Al-As-Ga system

The Al-As-Ga system is one of the most important III-V mixed crystal systems because of its advantages as a heterostructure. There are more phase equilibria data available for this system over a wider range of temperatures and compositions, than for any other III-V ternary system. In this paper, the experimental phase diagram data of the Al-As-Ga ternary system have been assessed comprehensively and critically. Especially, the most recent experiments are considered. The interaction parameters of the liquid phase and the semiconductor compound are provided. With the assessed thermodynamic parameters, the pseudobinary AlAs-GaAs phase diagram, the Al-As-Ga ternary isothermal sections, and the solidus isoconcentration curves were calculated and compared with the related experimental data.     

TEM study of structural and microstructural characteristics of a precipitate phase in Ni-rich Ni–Ti–Hf and Ni–Ti–Zr shape memory alloys

The precipitates formed after suitable thermal treatments in seven Ni-rich Ni–Ti–Hf and Ni–Ti–Zr high-temperature shape memory alloys have been investigated by conventional and high-resolution transmission electron microscopy. In both ternary systems, the precipitate coarsening kinetics become faster as the Ni and ternary element contents (Hf or Zr) of the bulk alloy are increased, in agreement with the precipitate composition measured by energy-dispersive X-ray microanalysis. The precipitate structure has been found to be the same in both Hf- and Zr-containing ternary alloys, and determined to be a superstructure of the B2 austenite phase, which arises from a recombination of the Hf/Zr and Ti atoms in their sublattice. Two different structural models for the precipitate phase were optimized using density functional theory methods. These calculations indicate that the energetics of the structure are not very sensitive to the atomic configuration of the Ti–Hf/Zr planes, thus significant configurational disorder due to entropic effects can be envisaged at high temperatures. The precipitates are fully coherent with the austenite B2 matrix; however, upon martensitic transformation, they lose some coherency with the B19′ matrix as a result of the transformation shear process in the surrounding matrix. The strain accommodation around the particles is much easier in the Ni–Ti–Zr-containing alloys than in the Ni–Ti–Hf system, which correlates well with the lower transformation strain and stiffness predicted for the Ni–Ti–Zr alloys. The B19′ martensite twinning modes observed in the studied Ni-rich ternary alloys are not changed by the new precipitated phase, being equivalent to those previously reported in Ni-poor ternary alloys.     

Thermodynamic investigation of Fe-Ti-Y ternary system

An extensive investigation on the Fe-Ti-Y system was performed via experimental measurement and thermodynamic calculation. The Fe-Ti-Y ternary couples at 1 273 K were prepared with a desire to provide accurate phase relationships needed for the refinement of this ternary phase diagram. And a tentative isothermal section of Fe-Ti-Y at 1 273 K was built based on the experimental information. In the thermodynamic modeling, the thermodynamic parameters for the Ti-Y binary system and the ternary phase in the Fe-Ti-Y system were evaluated. Those for the Fe-Ti and Fe-Y systems from literature were slightly modified for the compatibility. The isothermal sections of Fe-Ti-Y ternary system at 873 K and 1 273 K were calculated. The ternary compound Fe11TiY and Fe2(Ti, Y) solid solution formed from Fe2Ti and Fe2Y are detected, which is in good agreement with the literature information.     

Thermodynamic modeling and phase equilibria calculations of the quaternary Al-Ga-In-Sb Sastem

Quasi sub-subregular solution model with additional ternary parameters, used by Sharma et al. to model the thermodynamic properties of the liquid phases in the ternary Al-Ga-Sb, Al-In-Sb, and GaIn-Sb systems, has been extended to predict the thermodynamic properties of the liquid phase in the quaternary Al-Ga-In-Sb system. The (AlGaln)Sb compound phase in the quaternary Al-Ga-In-Sb system is considered a quasi-regular solution of AlSb, GaSb, and InSb compounds. Phase equilibria in the quaternary Al-Ga-In-Sb system are then calculated and compared with the limited experimental data available in the literature. The ternary Al-Ga-In phase diagram, required for the quaternary calculations, has also been modeled and calculated.