The isothermal section of the La–Si–Mg system at 500 C

The isothermal section of the La–Si–Mg system at 500 ^°C was constructed in the whole concentration range by means of the SEM-EDXS and XRPD characterization of about forty alloys prepared by induction melting and then annealed. Phase equilibria are characterized by the following ternary phases: τ₁-La_2+xSi₂Mg_1−x (0≤x≤0.35,tP10-Mo₂FeB₂), τ₂-LaSi₂Mg₂ (tP5-CeSi₂Mg₂), τ₃-LaSi₂Mg (structure still unknown) and τ₄-La₆SiMg₂₃ (cF120-Zr₆SiZn₂₃). The high temperature binary phase LaMg₂ (cF24-MgCu₂) has been found to be stabilized at 500 ^°C probably by a small amount of Si. Phases in binary subsystems do not generally form extended ternary solid solutions except for (La_1−xMg_x)₃Si₂ (0≤x≤0.167,tP10-U₃Si₂). Crystal structures of phases τ₁-La_2+xSi₂Mg_1−x and (La_1−xMg_x)₃Si₂ are correlated, the former being a substitution derivative of the latter.     

Phase equilibria of the Mg–Sn-Nd ternary system at 400 °C

The phase equilibria of the Mg–Sn-Nd ternary at 400 °C were investigated by X-ray powder diffraction (XRD), scanning electron microscope equipped with an energy dispersive spectrometer (SEM-EDS). Seven stable ternary compounds and one eutectoid decomposed structure (A₁) were observed in the section. The crystal structure for the phases: τ₁ (MgSnNd, I4/mmm, tI12) and τ₂ (MgSn₂Nd, I42 m, tI32) were confirmed. τ₃ (Mg₇₅Sn_3.5Nd_21.5) is the iso-structure of Mg₂₃SnLa₆ (Zn₂₃SiZr₆ prototype, cF120 Pearson's code) and τ₄ (Mg₄₀₊₃Sn_26.7-3Nd_33.3) has the same structure and homogeneity range of Mg_4-xSn_2+xLa₃(0.12 < x ≤ 0.4) (Cu₄Si₂Zr₃ prototype, hP9 Pearson's code). The crystal structure of τ₅ (Mg₄₄Sn₃₄Nd₂₂), τ₆ (Mg₄₀Sn₃₆Nd₂₄) and τ₇ (Mg₁₆₊₃Sn₄₅Nd_39-3) are not determined. Two binary compounds Nd₃Sn and Nd₂Sn₃, which were not included in the Nd–Sn binary phase diagram, were detected in this work. All detected Nd–Sn binary compounds show different amounts of Mg solubility, among which NdSn₃ and Nd₅Sn₄ dissolve up to 10 and 6.8 at.% Mg and the rest Nd–Sn binary phases contain 1–3 at.% Mg. The MgNd phase dissolves up to 6.0 at. % Sn.     

Experimental phase diagram study of the TiAl-rich part of the Ti–Al–Ni ternary system

Phase equilibria of the TiAl-rich part of the Ti–Al–Ni ternary system have been studied experimentally by scanning electron microscopy and electron probe micro-analysis of heat-treated alloys. Partial isothermal sections involving the liquid, β-Ti, α-Ti, α₂-Ti₃Al, γ-TiAl and τ₃-Al₃NiTi₂ phases were constructed between 1623 and 1273 K. Eight three-phase regions of the L + β + α, L + α + γ, L + β + γ, β + α + γ, L + β + τ₃, β + γ + τ₃, β + α₂ + τ₃ and α₂ + γ + τ₃ were derived. Extrapolations of these tie-triangles indicate the occurrence of three transition-type reactions; L + α = β + γ at around 1593 K, L + γ = β + τ₃ at around 1553 K, and β + γ = α + τ₃ at around 1393 K. The Ni solid solubility in the α and α₂ phase is extremely low, less than 1 at.% in all studied temperature ranges.     

Phase equilibria in the Au–In–Sn ternary system

Phase equilibria of the Au–In–Sn system have been investigated by Differential Scanning Calorimetry (DSC), metallographic examination, Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDS) measurements. The 130 ^°C isothermal section of the phase diagram was studied. The ternary diagram shows six three-phase fields, and one ternary Au₄In₃Sn₃ phase, which melts incongruently at 382 ^°C and shows a homogeneity range between 21 and about 30 at.% In, at constant Au/Sn ratio.     

Phase-equilibria investigation of the Dy-Mo-Si ternary system at 1173 K (900 °C)

The phase equilibria of the Dy-Mo-Si ternary system at 1173 K (900 °C) was experimentally determined in the entire concentration range by using x-ray powder diffraction (XRPD), scanning electron microscope equipped with energy dispersive spectrometer (SEM-EDS), and differential scanning calorimetry (DSC). The results show that there are 13 single-phase regions, 24 two-phase regions, and 12 three-phase regions in the studied isothermal section. Nine binary compounds, i.e., α-MoSi₂, Mo₅Si₃, Mo₃Si, α-DySi₂, β-DySi_1.67, Dy₃Si₄, DySi, Dy₅Si₄, and Dy₅Si₃ and one ternary compound Dy₂Mo₃Si₄ were confirmed to exist at this temperature. The highest solubilities of Dy in Mo₃Si and Mo in β-DySi_1.67 are both determined to be less than 1 at.%. While the solubilities of Dy in (Mo), Mo₅Si₃, and α-MoSi₂ and Mo in (α-Dy), α-DySi₂, Dy₃Si₄, DySi, Dy₅Si₄, and Dy₅Si₃ and Si in (α-Dy) and (Mo) are about 1–6.8 at.%. Combining both DSC analysis and XRPD results, it is concluded that the polymorphic transformation of α-DySi₂↔β-DySi₂ does not occur in the range of 573 K (300 °C) to 1323 K (1050 °C). DySi₂ phase exists as α-DySi₂ within the temperature range. β-DySi₂ is a metastable phase that exists in higher temperatures.     

Critical assessment of the Ag–Bi–Sn ternary system

A history of system assessments was given, and all the experimental works on its thermodynamics and constitution were mentioned, as well. A dataset for preliminary optimization was constructed, all existing phases of ternary system were listed and appropriate thermodynamic models were chosen. Optimization was carried out in the subsequent steps, and ternary thermodynamic parameters of all the phases under accord were determined. Equilibrium calculations resulted in phase boundary coordinates, invariant reaction parameters and thermodynamic function values; a Scheil reaction scheme was constructed, as well. Calculated quantities were then compared to the existing experimental data displaying the excellent agreement. Suggestion on the choice of alloy compositions was given as for solder material.     

Measurement of the phase equilibria in the Al–Zr–Y system at 673 and 823 K

Phase equilibria of the Al–Zr–Y ternary system at 673 and 823 K were investigated by using 14 equilibrated alloys, and the two isothermal sections were then established. The phase relations were almost the same at both isothermal sections. There were fourteen ternary-phase regions. Meanwhile, the solubilities of the third element in the binary compounds at both temperatures were discussed. The solid solubilities of Y in all observed Al–Zr binary compounds (i.e., Al₃Zr, Al₂Zr, Al₃Zr₂, AlZr, Al₃Zr₄, Al₂Zr₃, AlZr₂ and AlZr₃) were measured, and the solubilities of Y in Al₃Zr₄ phase reached to 11.9 at% at 823 K. In addition, there were solubilities of Zr in all observed Al–Y binary compounds (i.e., α-Al₃Y, Al₂Y, AlY, AlY₂ and Al₂Y₃), and the solubility of Zr in AlY₂ phase could reach to 13.3 at% at 673 K. The phase equilibria of the Al–Zr–Y ternary system determined by the present work have provided new phase diagram data for a future thermodynamic assessment of this system.     

Surface tension calculation of the Sn–Ga–In ternary alloy

Surface tensions of the Sn–Ga–In ternary alloy are calculated from the surface tensions of the Sn–Ga, Ga–In and In–Sn sub-binary systems by using geometric models (the Kohler model and the Toop model), and a general solution model (the Chou model). The calculated results are in excellent agreement with the experimental data (except for the Kohler model), assuming an experimental accuracy of ±2.5%. At the same time, the surface tensions of the Sn–Ga–In ternary alloy at 773 K and their sub-binary systems are predicted on the basis of Butler’s equation, in combination with thermodynamic data, and different model parameters β$\beta$ equal to the ratio of the coordination number in the surface phase to that in the bulk phase. Different values of β$\beta$ have almost no influence on the surface tensions. The predicted results agree with the experimental data. Therefore, the resulting iso-surface tension curves for the Sn–Ga–In ternary alloy at 773 K, especially those calculated by using the Toop model, are reasonable.     

The study of the Pb–Se–Te phase diagram: Part 2 – The thermodynamic assessment of the Se–Te and Pb–Se–Te systems

Pb–Se–Te ternary system is of significant importance for thermoelectric applications. In spite of this, no systematic experimental or theoretical study of its phase diagram has been carried out up to now. The CALPHAD type theoretical assessment was done in the scope of this work for the Se–Te and Pb–Se–Te systems based on our own experimental work and the experimental results from literature. It was found out that the reassessment of the existing Se–Te phase diagram assessments is necessary because of some discrepancies between the experimental results and calculations for this system. This new dataset was consequently used for the new assessment of the Pb–Se–Te system and very good agreement was reached with existing experimental data.     

Thermodynamic modeling of the Ta–Mo–C ternary system

The Ta–Mo–C system was assessed by means of the CALPHAD approach. All of the phase diagram and thermodynamic information available from the literature were critically reviewed. The liquid was modeled as substitutional solution phase, while the carbides including fcc-(Mo,Ta)C_1-x, bcc-(Mo,Ta), hcp-(Mo,Ta)₂C and η-MoC were described by using corresponding sublattice models. The ζ-Ta₄C_3-x was considered as a linear compound with carbon content fixed, while shp-MoC was treated to be a binary stoichiometric phase. There was no ternary compound reported in this system. The modeling of Ta–Mo–C ternary system covers the entire composition and temperature ranges, and a set of self-consistent thermodynamic parameters for the Ta–Mo–C system was systematically optimized. Comprehensive comparisons between the calculated and reported phase diagram and thermodynamic data show that the reliable information is satisfactorily accounted for by the present modeling. The liquidus projection and reaction scheme of the Ta–Mo–C system were also generated by using the present thermodynamic parameters.     

Experimental investigation and thermodynamic modeling of the Mg–Sn–Sr ternary system

The isothermal sections of the Mg–Sn–Sr ternary system in the Mg-rich region at 415 and 350 °C have been determined using the scanning electron microscopy (SEM) equipped with energy dispersive X-Ray spectrometry (EDS). The existence of the MgSnSr ternary compound was confirmed in these two isothermal sections. Two new compounds, named Mg₅Sn₃Sr and Mg₂₅Sn₂₄Sr_14, were found in the present work based on the SEM/EDS results. Thermodynamic optimization of the Sn–Sr binary and Mg–Sn–Sr ternary systems were carried out using the CALPHAD (CALculation of PHAse Diagrams) technique. The Modified quasi-chemical model (MQM) was used for the liquid solution which exhibits a high degree of short-range ordering behavior. The solid phases were described with the Compound energy formalism (CEF). Finally, a self-consistent thermodynamic databases for the Mg–Sn–Sr ternary system has been constructed in the present work, which can be an efficient and convenient guidance to investigate and develop the Mg-based alloys.     

Measurement and thermodynamic assessment of the phase equilibria in the Mg–Hg–Ga ternary system

Phase relations in the Mg–Hg–Ga ternary system have been experimentally and thermodynamically studied. At first, the isothermal sections of the Mg–Hg–Ga system in the Mg-rich region at 673 K and 473 K were investigated by using powder X-ray diffraction (XRD) and scanning electron microscope (SEM) with X-ray energy dispersive spectroscope (EDS). A ternary compound Mg₂₁Ga₅Hg₃ of tetragonal structure was detected and its homogeneity was determined. Then, based on the experimental literature, a thermodynamic assessment of the Mg–Hg–Ga ternary system was carried out by the CALPHAD approach. Consequently, a self-consistent set of thermodynamic parameters describing this system was obtained, which leads to a good fit between the calculated and experimental data.     

Phase diagrams for liquid–liquid and liquid–solid equilibrium of the ternary poly ethylene glycol di-methyl ether 2000 + tri-sodium phosphate + water system at different temperatures and ambient pressure

Complete phase diagrams for the poly ethylene glycol di-methyl ether 2000 (PEGDME₂₀₀₀)+Na₃PO₄+H₂O system at T$T$ = (298.15, 308.15 and 318.15) K were determined. Liquid–liquid equilibria (LLE) for the aqueous PEGDME₂₀₀₀+Na₃PO₄ system were determined experimentally at T$T$ = (298.15, 308.15, 313.15 and 318.15) K. The effects of temperature on the binodals and tie-lines of the investigated aqueous two-phase system (ATPS) were also studied. Furthermore, the modified local composition segment-based NRTL and Wilson models and also osmotic virial equation were used for the correlation and prediction of the liquid–liquid phase behavior of the studied system.