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.     

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.     

Experimental investigation of phase relationship in Ti–Fe-Hf ternary system

Based on diffusion triple and equilibrated alloy methods, phase relations in the Ti–Fe-Hf ternary system were investigated using the experimental data obtained through the combination of optical microscopy (OM), X-ray diffraction (XRD), scanning electron microscopy (SEM), and electron probe microanalysis (EPMA) techniques. Isothermal sections of the Ti–Fe-Hf system at both 1073 K and 1273 K were well constructed. There are three and four three-phase regions in these two sections, respectively. According to the present results, Hf can dissolve into FeTi at approximately 3.0% at both 1073 K and 1273 K. A continuous solid solution of Fe₂(Ti, Hf) forms between the binary intermediate compounds Fe₂Ti and Fe₂Hf (h). Fe₂Hf(c) and FeHf₂ show large solid solubilities. The solubility of Ti in Fe₂Hf(c) changes from 33.9% at 1073 K to 39.0% at 1273 K, while that of FeHf₂ can reach up to approximately 63.0% at 1273 K. No ternary compound exists in the Ti–Fe-Hf ternary system.     

Experimental investigation and thermodynamic calculation of the Fe–Si–Sn system

Phase equilibrium of the Fe–Si–Sn ternary system was investigated using equilibrated alloys. The samples were characterized by means of scanning electron microscopy equipped with energy dispersive X–ray spectrometry and X–ray diffraction. Isothermal sections of the Fe–Si–Sn system at 700 °C and 890 °C each consists of 5 three–phase regions. No ternary compound was found at those two temperatures. The solubility of Sn in the Fe–Si binary phases and the solubility of Si in the Fe–Sn binary phases is limited. Furthermore, thermodynamic extrapolation of the Fe–Si–Sn system was carried out. Calculated solidification path and phase relationship agreed well with experimental results.     

Experimental investigation and thermodynamic modeling of the Mg–Cu–Ca ternary system

The isothermal section in the Mg–Cu rich region of Mg–Cu–Ca ternary system at 300 °C was investigated in the present work. Two ternary compounds named as P1 and Mg_25-xCu₇₅Ca_x were observed. The solid solubility limit of the compound Mg_25-xCu₇₅Ca_x was found to be 8.29 ≤ x_Ca ≤ 15.71 with a constant value of about 75 at. % Cu at 300 °C. A narrow solid homogeneity range of the compound P1 was found to be Mg₁₉Cu₄₀Ca₄₁ to Mg₂₁Cu₄₂Ca₃₇ (in at. %). The maximum solid solubility of Ca in the terminal compound MgCu₂ (C15) was determined to be 10.20 at. % at 300 °C. The maximum ternary solid solubility of binary terminal compounds Mg₂Ca, Mg₂Cu, Cu₅Ca and CuCa were determined to be less than 2 at. %. For the more, thermodynamic modeling of the Cu–Ca binary and Mg–Cu–Ca ternary systems have been carried out by calculation of phase diagram (CALPHAD) method. The liquid solution was described using the modified quasi-chemical model (MQM). The compound energy formalism (CEF) was used for the solid phases. A self-consistent thermodynamic database of the Mg–Cu–Ca ternary system have been constructed in the present work.     

Experimental investigation and thermodynamic modeling of the Mo–Co–B ternary system

Among the ternary borides, the Mo–Co–B system is of great interest because of its excellent hardness, toughness, and stability performance. Eight samples with 60 at.% Co were designed to investigate the isothermal section of Mo–Co–B system at 1073 K in the Co-rich portion. Scanning electron microscopy, energy-dispersion spectroscopy, electron probe microanalysis, differential scanning calorimetry, and X-ray diffraction were used to investigate the phase equilibria of the samples. The formation enthalpies of the ternary borides were obtained by first-principles calculations to serve as key information for thermodynamic assessment. By coupling the reviewed experimental data from the literature, the presently determined phase equilibria, and the calculated formation enthalpies of the compounds, the thermodynamic parameters for the Mo–Co–B ternary system were optimized and used to calculate the isothermal sections, vertical section, and liquidus projection of the system. Comprehensive comparisons showed that the calculated results are in reasonable agreement with the reported phase diagram and thermodynamic data.     

Experimental investigation and thermodynamic assessment of the Zn–Cu–Sr ternary system

Zn–Cu–Sr alloys play a crucial role in the development of biodegradable implant materials based on zinc. The current study aimed to investigate the phase equilibria of the Zn–Cu–Sr ternary system in the Cu–Zn-rich region, through experimental analysis. For this purpose, fifteen and fourteen samples were respectively prepared and equilibrated at 350 and 400 °C, to determine the isothermal sections. The equilibrated alloys were then subjected to various analytical techniques such as scanning electron microscopy (SEM) equipped with energy dispersive spectrometry analysis (EDS), electron probe microanalysis (EPMA), and powder X-ray diffraction analysis (XRD). The analysis revealed the presence of five three-phase equilibria and ten two-phase equilibria in the two isothermal sections. Differential scanning calorimetry (DSC) was used to investigate the phase transformation temperature with constant values of 8 at. % Sr and 30 at. % Cu. The obtained experimental results were used to perform a thermodynamic assessment of the Zn–Cu–Sr system especial in Zn-rich region using the calculation of phase diagrams (CALPHAD) method. The modified quasi-chemical model (MQM) was used to model the liquid solution, while the compound energy formalism (CEF) was used to represent Gibbs free energies of the solid phases. The present obtained thermodynamic parameters were found to accurately reproduce the experimentally measured phase relationships in the Zn–Cu–Sr ternary system.     

Phase diagram of Ag–Pb–Sn system

The Ag–Pb–Sn ternary system is an important material system for both electronic packaging and thermoelectric applications. However, there is no experimental phase equilibria information of the ternary system. Ag–Pb–Sn alloys are prepared and their phase equilibria at various temperatures were determined. The focus was on the 500, 350, and 200 °C isothermal sections. Additional information was also obtained for 400, and 300 °C. Several samples were studied by DSC studies. No ternary compounds were found in the ternary system. The Ag–Sn binary compounds, Ag₃Sn(ε) and Ag₄Sn(ζ) at 350 °C and Ag₄Sn(ζ) at 500 °C, exhibit very small Pb solubility. The thermodynamic assessment of the ternary Ag–Pb–Sn system was carried out using the above mentioned experimental data.     

Calphad-type assessment of the Sb–Sn–Zn ternary system

The ternary Sb–Sn–Zn phase diagram was investigated experimentally by scanning electron microscopy (SEM) and differential thermal analysis (DTA) of long-term annealed samples. The overall composition of each sample was measured by energy-dispersive X-ray spectroscopy (EDX). The experimental results, together with additional available literature data, were used to perform a CALPHAD-type thermodynamic assessment of this ternary system. Two calculated isothermal sections (250 and 350 °C), an isopleth (x(Sn)=17.57%) and the Zn activity in liquid ternary Sb–Sn–Zn alloys at 550 °C for the composition ratio Sn/Sb=1/3 and at 650 °C for the ratio Sn/Sb=9 are presented with experimental points superimposed. The liquidus projection for the ternary Sb–Sn–Zn system is also presented. The agreement between calculated and experimental results is reasonable.     

Experimental investigation and thermodynamic assessment of the Mn–Zr system

The Mn–Zr binary system has been investigated via experimental measurements and thermodynamic calculations. In order to investigate phase equilibria in the Mn–Zr system, five alloys were prepared by arc melting under vacuum. All alloys were examined by means of X-ray diffraction, scanning electron microscopy and electron probe microanalysis after annealing at 650 °C for 70 days or 950 °C for 30 days. The homogeneity range of ZrMn₂ was determined to be from 25.0 to 33.2 at.% Zr at 950 °C and from 26.7 to 34.3 at.% Zr at 650 °C. The solubility of Mn in (αZr) was 1.6 at.% Mn, while that of Zr in (αMn) was 0.2 at.% Zr at 650 °C. The invariant reaction temperatures of liquid → ZrMn₂ + (βZr) and (βZr) → ZrMn₂ + (αZr) were determined to be 1131 and 785 °C, respectively. A thermodynamic assessment of the Mn–Zr system was conducted by taking into account the present experimental results and reliable literature data. The calculated results using the presently obtained parameters can well reproduce the experimental data.