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 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.     

A thermodynamic modeling of the Cu–Pd system

The phase equilibria and thermodynamic properties of the Cu–Pd system are optimized using the CALPHAD (CALculation of PHAse Diagram) technique. In the present work, the liquid and face-centered cubic (fcc) solution phases are modeled with the substitutional solution model. A two-sublattice model (Cu,Pd)_0.75(Cu,Pd)_0.25 is applied to describe the ordered Cu₃Pd phase, the one-dimensional long-period superlattice (1D-LPS) and two-dimensional long-period superlattice (2D-LPS) structures, in order to cope with the order–disorder transition between three intermetallic compounds (Cu₃Pd, 1D-LPS and 2D-LPS) and fcc solution (A1) in the Cu–Pd system. A two-sublattice model (Cu, Pd)(Cu, Pd) is used to describe the homogeneity range of CuPd phase. A set of self-consistent thermodynamic parameters is obtained and the calculated phase diagram and thermodynamic properties are presented and compared with the experimental data.     

Thermodynamic modeling of the Mo–Ni system

Thermodynamic stability of the MoNi₂ and MoNi₈ compounds has been discussed in detail, and decision about their inclusion in thermodynamic assessment of the Mo–Ni system has been made. Enthalpies of formation of all Mo–Ni intermetallic compounds have been determined with the help of DFT calculations whereas enthalpies of mixing in the solid solutions are estimated using special quasi-random structures. Experimental phase equilibria information gathered in our recent partial investigation of the Mo–Ni system has been incorporated and thermodynamic reassessment of the Mo–Ni system has been performed with the help of the CALPHAD method. The calculated Mo–Ni phase diagram showed good agreement with selected experimental information.     

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.     

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.     

Experimental measurements and thermodynamic modeling of the Ce–Co–Fe ternary system

The experimental determinations of the isothermal section at 823 K and the supplementary measurements of the liquidus projection of the Ce-Co-Fe ternary system were presented in the present study. In the Ce-Co-Fe ternary system, in consideration of the temperature dependent solubilities of the linear phases such as Ce₂(Co,Fe)₁₇ and Ce(Co,Fe)₂, as well as the specific locations of the univariant lines between each two primary solidification surfaces, it is necessary to study more than one isothermal section and some particular as-cast alloys to construct the phase equilibria in the temperature-composition space of the Ce-Co-Fe system. The samples for determining the liquidus projection were prepared by arc-melting method under high purity argon atmosphere in a water-cooled copper hearth, and then those for measuring the isothermal section at 823 K were isothermally treated and quenched in ice water. The microstructures and the phase compositions of samples were measured by means of scanning electron microscopy (SEM), X-ray diffraction (XRD) and electron probe micro-analyzer (EPMA). Some primary solidification regions and univariant lines of the Ce-Co-Fe ternary system were complementally determined, and the reasonability of the liquidus projection reported in previous literature was further confirmed. The phase equilibrium relations at 823 K were determined, including two-phase and three-phase equilibria. No ternary compounds were discovered in the present study. Based on the experimental results of both the previous literature reports (the reported liquidus projection and isothermal sections at 723 and 1173 K) and the present experimental study, the Ce-Co-Fe ternary system was thermodynamically assessed using the CALPHAD method. The isothermal sections, the vertical sections and the liquidus projection were calculated using the present optimized thermodynamic parameters, and a reasonable agreement between the calculated results and the experimental data was obtained.     

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.