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.     

Experimental phase diagram study of the TiAl-rich part of the Ti–Al–Ni ternary system

Phase equilibria of the TiAl-rich part of the Ti–Al–Ni ternary system have been studied experimentally by scanning electron microscopy and electron probe micro-analysis of heat-treated alloys. Partial isothermal sections involving the liquid, β-Ti, α-Ti, α₂-Ti₃Al, γ-TiAl and τ₃-Al₃NiTi₂ phases were constructed between 1623 and 1273 K. Eight three-phase regions of the L + β + α, L + α + γ, L + β + γ, β + α + γ, L + β + τ₃, β + γ + τ₃, β + α₂ + τ₃ and α₂ + γ + τ₃ were derived. Extrapolations of these tie-triangles indicate the occurrence of three transition-type reactions; L + α = β + γ at around 1593 K, L + γ = β + τ₃ at around 1553 K, and β + γ = α + τ₃ at around 1393 K. The Ni solid solubility in the α and α₂ phase is extremely low, less than 1 at.% in all studied temperature ranges.     

Experimental investigation of phase relationship in Ti–Fe-Hf ternary system

Based on diffusion triple and equilibrated alloy methods, phase relations in the Ti–Fe-Hf ternary system were investigated using the experimental data obtained through the combination of optical microscopy (OM), X-ray diffraction (XRD), scanning electron microscopy (SEM), and electron probe microanalysis (EPMA) techniques. Isothermal sections of the Ti–Fe-Hf system at both 1073 K and 1273 K were well constructed. There are three and four three-phase regions in these two sections, respectively. According to the present results, Hf can dissolve into FeTi at approximately 3.0% at both 1073 K and 1273 K. A continuous solid solution of Fe₂(Ti, Hf) forms between the binary intermediate compounds Fe₂Ti and Fe₂Hf (h). Fe₂Hf(c) and FeHf₂ show large solid solubilities. The solubility of Ti in Fe₂Hf(c) changes from 33.9% at 1073 K to 39.0% at 1273 K, while that of FeHf₂ can reach up to approximately 63.0% at 1273 K. No ternary compound exists in the Ti–Fe-Hf ternary system.     

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 study of the phase relationships in the SiO2–SrO–Al2O3 system

The phase relationships in silica rich area in the SiO₂–SrO–Al₂O₃ system were determined experimentally at 1723 K (1450 °C), 1823 K (1550 °C) and 1873 K (1600 °C) using quenching technique. Phases of the quenched samples were examined and identified using light optical microscopy (LOM), scanning electron microscope (SEM) and energy dispersive x-ray spectroscopy (EDS). X-ray Diffraction (XRD) was used to confirm the presence of solid phases. Based on the experimental results, the liquidus projections in the silica rich area for the studied temperatures were constructed.     

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 on phase relationships in the Si-rich portion of the Nb–Si–W ternary system

This paper describes the experimental study on liquidus projection and the isothermal section at 1873 K of the Nb–Si–W ternary system in the Si-rich portion. The microstructures and solidification paths of the as-cast alloys were analysed. The constituent phases and their equilibrium compositions of the as-cast+heat-treated alloys were determined. The microstructure observation, the phase identification and the composition measurement were performed using scanning electron microscopy (SEM), X-ray diffraction (XRD) and electron probe microanalysis (EPMA), respectively. No ternary compound was found. For the liquidus projection in the investigated Si-rich portion, there exist four primary solidification regions, Diamond–Si, β(Nb,W)₅Si₃, Nb(W)Si₂ and W(Nb)Si₂, and two eutectic invariant reactions, L→β(Nb,W)₅Si₃+W(Nb)Si₂+Nb(W)Si₂ and L→W(Nb)Si₂+Nb(W)Si₂+Diamond–Si. The type of the latter invariant reaction was determined with the help of the thermodynamic assessment of the system. Together with literature reported investigations for the Nb–W-rich portion, the whole liquidus projection of the Nb–Si–W ternary system was constructed. For the isothermal section at 1873 K in the investigated Si-rich portion, there are three three-phase regions, liquid+Nb(W)Si₂+W(Nb)Si₂, Nb(W)Si₂+αNb(W)₅Si₃+β(Nb,W)₅Si₃ and Nb(W)Si₂+W(Nb)Si₂+β(Nb,W)₅Si₃, and seven two-phase regions, liquid+Nb(W)Si₂, Nb(W)Si₂+αNb(W)₅Si₃, αNb(W)₅Si₃+β(Nb,W)₅Si₃, Nb(W)Si₂+β(Nb,W)₅Si₃, liquid+W(Nb)Si₂, Nb(W)Si₂+W(Nb)Si₂ and W(Nb)Si₂+β(Nb,W)₅Si₃.     

Ordering in ternary BCC alloys applied to the Al–Fe–Mn system

TWIP (TWinning Induced Plasticity) steels are attracting a lot of attention due to their combination of strength and ductility. In a previous work [1] (B. Lindahl, M. Selleby, Calphad 43 (2013) 86–93) a thermodynamic assessment of the Al–Fe–Mn system, which forms the basis of TWIP steels, was presented. The previous assessment treated the A2/B2 order-disorder transformation in the bcc phase using a two-sublattice model. In the present work a four-sublattice model has been used in order to also be able to describe the transition into the ordered D0₃ compound that occurs at lower temperatures. pair interaction energies for the Fe–Mn system are evaluated which prove crucial to the extrapolations into the Al–Fe–Mn system. Along with this various aspects of modeling chemical ordering using the Calphad approach are discussed. Equations for determining the ternary compound energies from binary pair interactions energies are presented and equations for determining the parameter values from the ordered parameters are derived.     

Measurement and thermodynamic assessment of the phase equilibria in the Mg–Hg–Ga ternary system

Phase relations in the Mg–Hg–Ga ternary system have been experimentally and thermodynamically studied. At first, the isothermal sections of the Mg–Hg–Ga system in the Mg-rich region at 673 K and 473 K were investigated by using powder X-ray diffraction (XRD) and scanning electron microscope (SEM) with X-ray energy dispersive spectroscope (EDS). A ternary compound Mg₂₁Ga₅Hg₃ of tetragonal structure was detected and its homogeneity was determined. Then, based on the experimental literature, a thermodynamic assessment of the Mg–Hg–Ga ternary system was carried out by the CALPHAD approach. Consequently, a self-consistent set of thermodynamic parameters describing this system was obtained, which leads to a good fit between the calculated and experimental data.     

Experimental investigation of phase equilibrium in the Al–Nb–Hf ternary system at 600 °C and 400 °C

The phase equilibria in the Al–Nb–Hf ternary system at 600 °C and 400 °C were experimentally investigated by X-ray diffraction (XRD), scanning electron microscope (SEM) and electron probe microanalysis (EPMA/WDS). In each isothermal sections, 13 three-phase regions were measured. And their phase region boundaries were precisely determined. Among the actually measured binary compounds, only Al₃Nb, AlNb₂ and AlNb₃ have a large range of solid solubility. In addition, two stable ternary compounds τ1-Al₁₁Nb₄Hf₅ and τ2-Al₂NbHf₂, which had certain solid solubility, were newly discovered. On the basis of the experimental results and reasonable inference, the isothermal sections of ternary system at 600 °C and 400 °C were constructed.     

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.     

Experimental investigation and thermodynamic modeling of the Mo–Co–B ternary system

Among the ternary borides, the Mo–Co–B system is of great interest because of its excellent hardness, toughness, and stability performance. Eight samples with 60 at.% Co were designed to investigate the isothermal section of Mo–Co–B system at 1073 K in the Co-rich portion. Scanning electron microscopy, energy-dispersion spectroscopy, electron probe microanalysis, differential scanning calorimetry, and X-ray diffraction were used to investigate the phase equilibria of the samples. The formation enthalpies of the ternary borides were obtained by first-principles calculations to serve as key information for thermodynamic assessment. By coupling the reviewed experimental data from the literature, the presently determined phase equilibria, and the calculated formation enthalpies of the compounds, the thermodynamic parameters for the Mo–Co–B ternary system were optimized and used to calculate the isothermal sections, vertical section, and liquidus projection of the system. Comprehensive comparisons showed that the calculated results are in reasonable agreement with the reported phase diagram and thermodynamic 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.