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.     

Elastic and thermodynamic properties of the Ni–B system studied by first-principles calculations and experimental measurements

The elastic and thermodynamic properties of NiB, Ni₂B, Ni₃B, orthorhombic Ni₄B₃(O–Ni₄B₃), monoclinic Ni₄B₃(M–Ni₄B₃), and Ni₂₃B₆, are calculated via first-principles method for the Ni–B system. The ground state energies, the full sets of elastic constants and the associated macroscopic elastic parameters of these Ni–B alloys are computed for the first time. Taking contributions from lattice vibrations and thermally excited electrons into account, thermodynamic properties at finite temperatures are then predicted. In addition, we measure the molar heat capacity at constant pressure for NiB and compare the results with the theoretical predictions. Various calculations demonstrate that the first-principles calculation can be used to clarify the diverse experimental data, and provide reliable thermodynamic data.     

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

Phase relationship of the Fe–Si–Bi ternary system was established by optical microscope, scanning electron microscope in combination with energy dispersive spectroscopy and X–ray diffraction. Isothermal sections of the Fe–Si–Bi system at 973 and 1173 K consist of 3 and 4 three–phase equilibrium regions, respectively. The liquid phase is in equilibrium with all the Fe–Si phases. No ternary compound is found and Bi is almost insoluble in the Fe–Si phases. Combining the reliable thermodynamic data from literature with the current experimental work, phase relationship of the Fe–Si–Bi system have been thermodynamically extrapolated. The calculated results are in good agreement with the experimental results.     

Experimental study and thermodynamic assessment of the Cu–Ni–Ti system

The Cu–Ni–Ti ternary system has been systematically investigated combining experimental measurements with thermodynamic modeling. With selected equilibrated alloys, the equilibrium phase relations in the Cu–Ni–Ti system at 850 °C were obtained by means of SEM/EDS (Scanning Electron Microscopy/Energy Dispersive Spectrum), EPMA (Electron Probe Micro-Analysis) and XRD (X-ray Diffractometry). Phase transformation temperatures were measured by DSC (Differential Scanning Calorimetry) analysis in order to construct various vertical sections in the Cu–Ni–Ti system. The liquidus projection of the ternary system was determined by the identifying primary crystallization phases in the as-cast alloys and from the liquidus temperatures obtained from the DSC analyses. Based on the available data of the binary systems Cu–Ni, Cu–Ti, Ni–Ti and the ternary system Cu–Ni–Ti from the literature and the present work, thermodynamic modeling of the Cu–Ni–Ti ternary system was performed using the CALculation of PHAse Diagram (CALPHAD) approach. A new set of self-consistent thermodynamic parameters for the Cu–Ni–Ti ternary system was obtained with an overall good agreement between experimental and calculated results.     

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 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 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.     

Refinement of the thermodynamic modeling of the Nb–Ni system

The Nb–Ni system is reassessed on the basis of a critical literature review involving recent experimental data. These newly published experimental data include the phase relation associated with the NbNi₈ phase, phase transition temperatures resulting from selected alloys, all invariant reaction temperatures, and enthalpies of mixing of liquid, as well as the crystallographic data on the μ$\mu$ (Nb₇Ni₆) phase. A consistent thermodynamic data set for the Nb–Ni system is obtained by optimization of the selected experimental values. The calculated phase diagram, crystallographic properties and thermodynamic properties agree reasonably with the experimental data. Noticeable improvements have been made, compared with the previous thermodynamic optimizations.     

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.     

A thermodynamic assessment of Ni–Sb system

The Ni–Sb system was critically assessed by means of the CALculation of PHAse Diagram (CALPHAD) technique. The solution phases, Liq and (αNi), were modelled as the substitutional solutions with the Redlich–Kister equation. The intermediate phases, (γNiSb) and (βNi₃Sb), with homogeneity ranges were described respectively using three-sublattices (Sb)_1/3(Ni%,V a)_1/3(V a%,Ni)_1/3 and (Sb)_1/4(Ni%,V a)_1/2(Ni%,V a)_1/4 based on their structure features. Corresponding to the phase (βNi₃Sb), the two low-temperature phases of (δNi₃Sb) and (θNi₅Sb₂) with narrow homogeneity ranges were modelled as two-sublattice, (Ni)_3/4(Sb,Ni)_1/4 and (Ni)_5/7(Sb,Ni)_2/7. The intermetallic compound ζNiSb₂ with no homogeneity ranges was treated as stoichiometric compound. The phase ε$\epsilon$Sb was considered as pure Sb for the solubility of Ni in ε$\epsilon$Sb is very low. A set of self-consistent thermodynamic parameters of the Ni–Sb system was obtained. The optimized phase diagram and thermodynamic properties were presented and compared with experimental data.