Experimental investigation of phase equilibria in the Al–Cr–Fe system

The literature of the ternary Al–Cr–Fe system was evaluated and major open questions were identified. Transition temperatures between α-Fe,Al (A2) – FeAl (B2) and FeAl (B2) – Fe₃Al (D0₃) as well as solidus/liquidus temperatures in the Cr-rich corner were determined. The results from thermal analysis show a substantial decrease of the A2/B2 transition temperature with increasing Cr content at constant x(Al). Furthermore, a partial solidus and liquidus projection below 50 at.-% Al were created. Several partial isothermal sections have been studied with equilibrated alloys and diffusion couples. Therefore, complementary methods were used such as thermal analysis, electron microscopy, chemical analysis, X-ray powder diffraction and electron probe microanalysis. Equilibration experiments have been performed at 973 K, 1173 K, 1315 K, 1373 K and 1423 K and two partial isothermal sections at the two lowest temperatures were constructed indicating a solubility of 22 at.-% iron in the AlCr₂ phase at 973 K.     

Assessment of diffusion mobility for bcc phase of Ti–Al–Ni ternary system

The experimental diffusion coefficients of the Ti–Ni binary and Ti–Al–Ni ternary bcc phase were critically evaluated to assess the diffusion mobilities by the DICTRA-type phenomenological treatment. The calculated diffusion coefficient shows reasonable consistency with the diffusion coefficient extracted in the experiment, including the impurity and inter-diffusion coefficients in bcc Ti–Ni binary alloy and the main interdiffusion coefficient in bcc Ti–Al–Ni ternary alloy. The difference between the calculated and experimental ternary cross coefficients is within appropriate relative errors. The predicted composition profiles and diffusion paths reasonably represent the diffusion processes that occur in Ti–Ni binary and Ti–Al–Ni ternary diffusion couples, thereby validating the mobility database assessed in the present work.     

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.     

Gibbs energies of formation of Mn3C,M(Fe,Mn)3C and Mn23C6 from the ternary phase equilibria in the FeMnC system

The high temperature phase relations in the FeMnC system have been analyzed in light of the recently developed thermodynamic method by the authors to obtain the Gibbs energies of formation of Mn₂₃C₆ and Mn,C. A new thermodyn/amic treatment is outlined and applied to obtain the stability of the ternary carbide M(Fe,Mn)₃C without any a priori assumption of a solution model for the M₃C phase. The recommended Gibbs energies of formation for the Mn carbides, Mn₃C and Mn₂₃C₆ With γ-Mn (graphite) as the Standard states are:

The present method can be extended to obtain a consistent set of thermodynamic data for binary and ternary carbides from various ternary metal-metal-carbon phase relations.     

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 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 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.     

B2-disorder phase boundary calculations in Fe rich region of Fe-Si binary system with tetrahedron approximation of CVM

The phase boundary between B2 ordered and disordered phases in the Fe-rich region of the Fe-Si binary system is calculated by Cluster Variation Method (CVM). The configurational entropy is formulated within the tetrahedron approximation of CVM, and the internal energy is derived by Cluster Expansion Method (CEM) operated on a set of total energies calculated by DFT. The Debye Gruneisen model is employed to introduce the vibrational effect. The second order transition for the B2 order-disorder transition is confirmed, which is in agreement with the published phase diagram data and the results of previous CALPHAD calculations. The calculated transition temperature in the present study is higher around the stoichiometric composition and lower in the Fe-rich region compared to the experimental transition temperature. One reason for this overestimation and underestimation of the transition temperature may stem from the facts that the local atomic displacement and wide range atomic correlations are not considered in the present study. The transition temperature is also determined using Thermo-Calc software with the SSOL4 database. The transition temperature obtained by Thermo-Calc calculations accurately reproduces the experimental results. Hence, it is considered that the interaction parameters and the ordering parameters of CALPHAD free energy implicitly include the contributions of short range ordering and local atomic displacement.     

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.     

Relative stability of ordered phases in bcc Cu-Al-Zn

The relative stability of the short range ordered and different long range ordered structures in body centered cubic Cu-Al-Zn is studied by means of the Cluster Variation Method in the Irregular Tetrahedron approximation (IT-CVM). The energetic parameters (constant pair interchange energies for first and second neighbor pairs) used in our calculations have been extracted from experimental order-disorder transition temperatures. It is shown that the use of constant pair interchange energies allows accurate reproduction of the experimental transition temperatures in the binary subsystems Cu-Al and Cu-Zn. Several isothermal sections of the ternary system at temperatures between 600 and 900 K have been calculated. The two-phase field for compositions around Cu₃Al in the ternary system was determined: It was found that such region extends to around 15 at.% Zn in the pseudo-binary Cu_0.76-0.5x-Al_0.24-0.5x-Zn_x.