Thermodynamic description of the Mg–Eu binary system

Thermodynamic assessment of the Mg–Eu binary system has been carried out by combining first-principles calculations and Miedema’s theory with CALPHAD method. Firstly, the mixing enthalpy of the liquid alloys was calculated by using Miedema’s theory, and formation enthalpies of the intermetallic compounds were calculated by using the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). Subsequently, the liquid phase was described employing a simple substitutional model, of which the excess Gibbs energy was formulated with a Redlich-Kister expression. And the solubility of Eu in HCP_(Mg) and Mg in BCC_(Eu) were neglected. While the intermetallic compounds Mg₁₇Eu₂, Mg₅Eu, Mg₄Eu, Mg₂Eu and MgEu, were treated as stoichiometric compounds. Consequently, a set of self-consistent thermodynamic parameters for all stable phases in the Mg–Eu binary system were obtained, which can reproduce most of the thermodynamic and phase boundary 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 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.     

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.     

A thermodynamic assessment of the Co–Sn system

A critical evaluation and thermodynamic modeling of the phase diagram and thermodynamic properties have been presented for the Co–Sn system. More attention has been paid to reproduce the thermodynamic properties of the liquid Co–Sn, including the appreciable temperature dependence in the mixing enthalpy and the sign-variable activity with composition observed by experiments. A four-sublattice model has been used to describe the ordering phenomenon between $\beta {\mathrm{Co}}_3{\mathrm{Sn}}_2$ and $\alpha {\mathrm{Co}}_3{\mathrm{Sn}}_2$.     

A thermodynamic assessment of the Nd–C system

The Nd–C binary system has been assessed based on the experimental investigation, thermodynamic calculations and the literature survey. The intermediate compounds Nd₂C₃ and βNdC₂ (high-temperature form of NdC₂ phase) were considered to be the non-stoichiometric phases whereas the αNdC₂ (low-temperature form of NdC₂ phase) was treated as the stoichiometric phase. Contents of carbon in the Nd–C_sat samples in Nd–Nd₂C₃ range were measured in the present study. The phase diagram of Nd–C system and enthalpies of formation of Nd₂C₃ and NdC₂ carbides have been modeled using the FactSage software.     

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 of phase equilibria in the Mg–Gd–Er system

Phase relations of the Mg-Gd-Er system at the Mg-rich corner were investigated experimentally through alloy sampling approach. Isothermal sections at 673 K and 773 K were determined according to electron probe microanalysis (EPMA) and X-ray diffraction (XRD) results. No ternary compounds were detected at the investigation temperatures. MgEr and MgGd can form a continuous solid solution. Five three-phased fields were measured and deduced in both isothermal sections at 673 K and 773 K.