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 reassessment of the Fe–Si–Zn system

Based on the critical evaluation of the experimental data available in the literature, the isothermal section of the Fe–Si–Zn system at 873 K was measured using a combination of X-ray analysis and scanning electron microscopy with energy-dispersive X-ray analysis. No ternary phase is observed at 873 K. A thermodynamic modeling for the Fe–Si–Zn system was then conducted by considering the reliable experimental data from the literature and the present work. All the calculated phase equilibria agree well with the experimental ones. It is noteworthy that a stable liquid miscibility gap appears in the computed ternary phase diagrams although it is metastable in the three boundary binaries.     

Experimental investigation and thermodynamic calculation of the Mg–Mn–Ni system

Based on the critical review of the ternary Mg–Mn–Ni system, 12 alloys were prepared using a powder metallurgy method in a glove box. The isothermal section of the Mg–Mn–Ni system at 400 °C was determined. Ternary compound τ (Mg₃MnNi₂) was confirmed in the present work. In order to obtain the phase transition temperatures, differential scanning calorimetry (DSC) was applied to the selected alloys using sealed Ta crucibles. The invariant reaction temperatures for two invariant reactions in the Mg-rich corner were measured. Considering the experimental data from present work and literature, the Mg–Mn–Ni system was optimized and a set of thermodynamic parameters was obtained. Calculated results fit well with the experimental data.     

Experimental investigation and thermodynamic calculation of the phase equilibria in the Fe–Ni–V system

The phase equilibria in the Fe–Ni–V ternary system were investigated by means of electron probe microanalysis (EPMA) and X-ray diffraction (XRD). Three isothermal sections of the Fe–Ni–V ternary system at 1000 °C, 1100 °C and 1200 °C were established. On the basis of the obtained experimental data, the phase equilibria in the Fe–Ni–V system were thermodynamically assessed using (CALculation of PHAse Diagrams) CALPHAD method, and a consistent set of thermodynamic parameters leading to reasonable agreement between the calculated results and experimental data was obtained.     

Experimental study and thermodynamic calculation of the Y–Co–Fe system

In this work, the phase equilibria of the Y–Co–Fe ternary system were studied experimentally by scanning electron microscope (SEM) with energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD). The phase transition temperatures and phase formation of Y–Co–Fe alloys were examined by differential thermal analysis (DTA) and SEM-EDS. No ternary intermetallic compounds were detected. The continuous solid solution phases Y₂(Co, Fe)₁₇, Y(Co, Fe)₃ and Y(Co, Fe)₂ were formed from the respective Y–Co and Y–Fe binary intermetallic compounds. The solubility of Fe in YCo₅ and Y₂Co₇ and the solubility of Co in Y₆Fe₂₃ were determined. Based on the experimental results determined in this work and reported in the literature, the thermodynamic calculation of the Y–Co–Fe ternary system was performed using the CALPHAD method in combination with the previous assessments of three Y–Co, Y–Fe and Co–Fe binary systems. The liquidus projection, isothermal sections and vertical sections of this ternary system were calculated. The good agreement between the calculated results and the experimental results was achieved. A set of self-consistent thermodynamic parameters for describing various phases in the Y–Co–Fe ternary systems was obtained finally, which would provide a good basis for the development of the thermodynamic database of multi-component Y–Co–Fe based alloy systems.     

Experimental investigation and thermodynamic modeling of the Cr–Zr–Si system

The phase equilibria of the Cr–Zr–Si ternary system were studied combined with the key experiments and thermodynamic assessment. Thirty-five ternary alloys were prepared to determine the isothermal sections at 900 and 1000 °C by means of X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDS). Five ternary compounds, i.e., τ₁ (CrSi₂Zr), τ₂ (Cr₄Si₅Zr₂), τ₃ (Cr₄Si₇Zr₄), τ₄ (CrSiZr) and τ₅ (Cr₃SiZr₂), were confirmed. The solubilities of the third element in binary compounds were determined. Based on the experimental phase equilibria data available in the present work and the literature, as well as the thermodynamic parameters of constitutive binary systems, the Cr–Zr–Si system was evaluated by using the CALPHAD (CALculation of PHAse Diagram) method. A set of self-consistent thermodynamic parameters was obtained. Three isothermal sections and liquidus projection were calculated and the reaction scheme was constructed. The calculated results are in agreement with the experimental data.     

Experimental investigation and thermodynamic description of the Fe–Mo–Zr system

The phase relations at 1273 K and liquidus surface projection of the Fe–Mo–Zr system were investigated by means of electron probe micro-analyzer (EPMA), scanning electron microscopy coupled with energy dispersive spectroscopy (SEM-EDS) and X-ray diffraction (XRD) methods. The composition range of C14 Laves phase was determined at 1273 K. The maximum solubility of Mo in C15–Fe₂Zr, Mo in Fe₂₃Zr₆, Fe in C15–Mo₂Zr and Zr in μ phase is about 4.8, 0.6, 17.7 and 4.6 at.% at 1273 K, respectively. The isothermal section at 1273 K of the Fe–Mo–Zr system on the whole composition ranges was constructed using 30 annealed alloys. In the liquidus surface projection, the primary solidification phase regions of bcc(Fe), C15–Fe₂Zr, C14, μ, R, σ, bcc(Zr), C15–Mo₂Zr and bcc(Mo) were experimentally confirmed using 31 as-cast alloys. Based on the experimental data in literature and the present work, the Fe–Mo–Zr system was optimized using CALPHAD method, and a set of self-consistent reliable thermodynamic parameters was obtained.     

Experimental investigation and thermodynamic modeling of the Fe−Si−Zr system

The Fe−Si−Zr alloys have attracted considerable interests in recent decades. It is important to study this ternary phase diagram for experimental design. In this paper, the Fe−Si−Zr ternary system is investigated by combining the experiments and thermodynamic calculations. Liquidus surface projection of the Fe−Si−Zr system is characterised using X-ray powder diffraction (XRD), scanning electron microscopy (SEM) with energy dispersive spectrometer (EDS) and differential thermal analysis (DTA). The liquidus projection of this ternary system is constructed by identifying primary crystallization phases and invariant reaction temperatures in the as-cast alloys. Eleven different primary solidification regions are observed. Based on the experimental results of this work and the data from the previous work in the literature, the thermodynamic calculation of the Fe−Si−Zr system is performed using CALPHAD (CALculation of PHAse Diagrams) technique. A set of self-consistent thermodynamic parameters of the Fe−Si−Zr system is obtained. The calculated results are in good agreement with the experimental data. This study provides a set of reliable thermodynamic parameters to the Fe-based thermodynamic database, and a cost-effective tool to design experiments and manufacturing processes.     

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.     

Experimental investigation and thermodynamic description of the Ni–Ti–W system

The liquidus surface projection and isothermal sections at 1173 and 1373 K of the Ni–Ti–W system were constructed on the basis of microstructure and phase constituents of as-cast and annealed alloys, which were obtained by means of scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS), X–ray diffraction (XRD). Six primary solidification regions were determined in the liquidus surface projection. Five and six three-phase regions were derived in the isothermal sections at 1173 and 1373 K, respectively. No new ternary compounds were found. Based on the present experimental data, the Ni–Ti–W system was optimized using CALPHAD (CALculation of PHase Diagram) method. The solution phases, liquid, fcc, bcc, and hcp, were treated as substitutional solution. Two compounds Ni₃Ti and NiTi₂ were treated as (Ni,Ti,W)_m(Ni,Ti,W)_n, and Ni₄W was treated as (Ni,Ti)₄W₁ by a two-sublattice model. NiTi with B2 crystal structure was treated as the ordered phase of bcc solution, and model was (Ni,Ti,W)_0.5(Ni,Ti,W)_0.5(Va)₃. A set of self-consistent thermodynamic parameters was obtained.     

Experimental investigation and thermodynamic modeling of the Ni–Ti–V system

The liquidus surface projection and isothermal section at 1273 K of the Ni–Ti–V system were established using X-ray diffraction (XRD), scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS), electron probe micro-analyzer (EPMA) and differential thermal analysis (DTA) techniques. Six primary solidification regions and four invariant reactions were deduced in the liquidus surface projection, and six three-phase regions were derived in the isothermal section at 1273 K. No ternary compound was observed. According to the experimental results in the present work and literatures, the Ni–Ti–V system was modeled by means of the CALPHAD (CALculation of PHAse Diagram) method. Two-sublattice model (Ni,Ti)₁₀(Ni,Ti)₂₀ for binary σ phase was used, and the thermodynamic parameters of the σ and NiV₃ phases in the Ni–V system was reassessed. Solution phases (liquid, fcc, bcc and hcp) were modeled with the substitutional solution model in the Ni–Ti–V system. The compounds, Ni₃Ti, NiTi₂, Ni₃V and σ, were treated as (Ni,Ti,V)_m(Ni,Ti,V)_n, and B2 were treated as (Ni,Ti,V)_0.5(Ni,Ti,V) _0.5Va₃. A set of self-consistent thermodynamic parameters of individual phases was obtained.     

Experimental investigation and thermodynamic modeling of the Cu–Mn–Ni system

The phase equilibria of the ternary Cu–Mn–Ni system in the region above 40 at.% Mn at 600 ^°C were investigated by means of optical microscopy, X-ray diffraction, scanning electron microscopy with energy dispersive X-ray spectroscopy and electron probe microanalysis. The isothermal section of the Cu–Mn–Ni system at 600 ^°C consists of 4 two-phase regions (cbcc_A12 +fcc_A1, cub_A13 +fcc_A1, cbcc_A12 + cub_A13, L₁₀$L{1}_0$ +fcc_A1) and 1 three-phase region (cbcc_A12 +cub_A13 +fcc_A1). The disordered fcc_A1 phase exhibits a large continuous solution between γ$\gamma$(Cu,Ni) and γ$\gamma$(Mn). The L₁₀$L{1}_0$ phase only equilibrates with fcc_A1 phase, and the solubility of Cu in L₁₀$L{1}_0$ phase is up to 16 at.%. A thermodynamic modeling for this system was performed by considering reliable literature data and incorporating the current experimental results. A self-consistent set of thermodynamic parameters was obtained, and the calculated results show a general agreement with the experimental data.     

Experimental study and thermodynamic remodeling of the Bi–Cu–Ni system

Phase equilibria in the Bi–Cu–Ni ternary system have been studied using differential thermal analysis (DTA) as well as by using the calculation of the phase diagram (CALPHAD) method. Literature experimental phase equilibria data and DTA results from this study were used for thermodynamic modeling of the Bi–Cu–Ni ternary system. Isothermal sections at 300, 400, and 500 °C, vertical sections from bismuth corner with molar ratio Cu:Ni=1/3, 1/1 and 3/1 and vertical section at 40 at.% Cu were calculated and compared with corresponding experimental results. Reasonable agreement between the calculated and experimental data was observed in all cases.