Experimental study and thermodynamic modelling of the B-Fe-Mn ternary system

This work is focused on an experimental study of phase equilibria in the B-Fe-Mn ternary system combined with a CALPHAD theoretical analysis with the aim of creating a reliable theoretical thermodynamic dataset for calculation of the phase diagram of the ternary system. Boron is modelled as an interstitial element in all solid solutions of Fe and Mn. In the experimental study, B-Mn-Fe alloys were prepared and heat-treated at 873 K for 90 days/2160 h and at 1223 K for 60 days/1440 h. Following heat treatment, the phase equilibria and composition of the coexisting phases were determined using scanning electron microscopy and X-ray diffraction analysis. The experimental results obtained, together with experimental results collected from the literature, were used in the optimization of the thermodynamic parameters by using the CALPHAD method. The result of this work is an optimized thermodynamic dataset for the B-Fe-Mn ternary system allowing the phase diagram and thermodynamic properties to be calculated.     

Experimental and thermodynamic study of the Mg-Sn-Ca-Sr quaternary system: Part I-Mg-Sn-Ca ternary system

Four key samples of the Mg-Ca-Sn ternary system in the Mg-rich region at 415 and 350 °C have been determined using the Scanning Electron Microscopy (SEM) equipped with Energy Dispersive X-Ray Spectrometry (EDS). The existence of the CaMgSn ternary compound was confirmed in these two isothermal sections. Thermodynamic optimizations of the Ca-Sn binary system and Mg-Ca-Sn ternary system were carried out using the CALPHAD (Calculation of Phase Diagrams) technique. The Modified Quasichemical Model (MQM) was used for the liquid solution which exhibits a high degree of short-range ordering behavior in the liquid solution. The solid phases are modeled with the Compound Energy Formalism (CEF). Finally, a self-consistent thermodynamic database of Mg-Ca-Sn ternary system has been constructed in the present work, which would provide an efficient and convenient way to study and develop the new Mg-Sn based alloys.     

Experimental investigation and thermodynamic calculation of the B-Fe-Mo ternary system

The phase relationship of the B-Fe-Mo ternary system has been investigated combining experimental results with thermodynamic modeling. The liquidus projection of the ternary system in the Fe-rich region was constructed by identifying primary crystallization phases in the as-cast alloys and determining liquid temperatures obtained from the DSC analyses. Eight different primary solidification regions were observed, and they are BCC, FCC, Mo₂FeB₂, Fe₂B, FeB, σ, and R, respectively. And four invariant reactions were identified in the Fe-rich region. Thermodynamic optimization of the B-Fe-Mo ternary system was performed using CALPHAD approach based on the thermodynamic models of the three constitutional binary systems and the experimental results of the ternary system. A set of self-consistent thermodynamic parameters for the B-Fe-Mo system were obtained with reasonable agreement between the experimental and calculated results.     

A thermodynamic reassessment of the Si-Sr system

The Si-Sr binary system has been thermodynamically reassessed in the present work based on the critically reviewed experimental data available in the literature, especially newly published experimental phase diagram data in the Si-rich side. The liquid phase has been modeled with both the substitutional solution model and the associate model, and two sets of self-consistent thermodynamic parameters that describe the system are thus obtained. The shortcomings of the previous assessment are removed, and a better agreement with experimental data is achieved compared with the previous assessment.     

Coupled experimental study and thermodynamic modeling of the MnO-Mn2O3-Ti2O3-TiO2 system

A coupled experimental study and thermodynamic modeling of the MnO-Mn₂O₃-Ti₂O₃-TiO₂ system at 1 bar total pressure is presented. Classical equilibration and quenching experiments followed by the phase analysis using electron probe microanalysis (EPMA) and X-ray diffraction (XRD) were employed to obtain equilibrium compositions of the liquid and solid solutions in air. The molten oxide phase was described by using the Modified Quasichemical Model which considers short-range ordering, and the Gibbs energies of the solid solutions (pseudobrookite, ilmenite and spinel) were described using the Compound Energy Formalism based on their crystal structures. A set of optimized model parameters of all phases was obtained, which reproduces all available and reliable thermodynamic data and phase diagrams within experimental error limits from 298 K (25 °C) to above the liquidus temperatures over the entire range of composition under oxygen partial pressures from metallic saturation to 1 bar. The complex phase relationships in the system have been elucidated and discrepancies among the experimental data have been resolved. The database of the model parameters can be accessed by FactSage software with the Gibbs energy minimization to calculate any phase diagrams and thermodynamic properties of the MnO-Mn₂O₃-Ti₂O₃-TiO₂ system.     

Experimental study and thermodynamic assessment of the Ag–Ti system

A thermodynamic assessment of the binary Ag–Ti system was performed based on the evaluation of the literature and the results of the present experiments. For the experimental study, special deep embedding diffusion couples were prepared and analyzed by scanning electron microscopy (SEM) and electron probe microanalysis (EPMA). The phase equilibrium relationship and the conjugate phase compositions were determined at 1023 K, 1253 K, 1373 K and 1474 K respectively. For the thermodynamic assessment, the Redlich–Kister polynomial was used to describe the solution phases, liquid (L), bcc, hcp, and fcc. The sublattice-compound energy model was employed to describe the intermediate phase, (AgTi), with a homogeneity range. The other intermediate phase, AgTi₂, without a homogeneity range was treated as the stoichiometric phase. A set of self-consistent thermodynamic parameters of the Ag–Ti system has been obtained. The calculated phase diagram was presented and compared with the experimental data.     

Thermodynamic assessment of the KCl–K2CO3–NaCl–Na2CO3 system

Phase equilibria and thermodynamic properties of the KCl–K₂CO₃–NaCl–Na₂CO₃ system were analyzed on the basis of the thermodynamic evaluation of the KCl–NaCl,KCl–K₂CO₃,NaCl–Na₂CO₃,K₂CO₃–Na₂CO₃ and KCl–K₂CO₃–NaCl–Na₂CO₃ systems. The Gibbs energies of individual phases was approximated by two-sublattice models for ionic liquids and crystals. Most of the experimental information was well described by the present set of thermodynamic parameters. The lowest monovariant eutectic temperature in the KCl–NaCl–Na₂CO₃ system is located at 573 ^°C, with a composition of X_Na2CO3=0.31,X_KCl=0.35 and X_NaCl=0.34.     

Experimental investigation and thermodynamic calculation of Ti-Hf-Mn system

The phase relationship of Ti-Hf-Mn system was studied by diffusion triple and equilibrated alloy methods. The isothermal sections at 1373, 1273 and 1173 K for this system were constructed by means of electron probe microanalysis (EPMA) and X-ray diffraction (XRD) for the first time. No ternary phase was found in the system at all these temperatures. Six, seven and seven three-phase equilibria regions have been determined at 1373, 1273 and 1174 K, respectively. In this ternary system, the intermetallic compounds TiMn₂, HfMn₂ and HfMn exhibit wide solid solution range at those three temperatures. In particular, the solution range of Ti in HfMn phase decreases with the increase of temperature, from 30.5 at% at 1173 K to 26.5 at% at 1373 K. Based on all available experimental data, the Ti-Hf-Mn system was evaluated using the CALPHAD method. The calculation results are in excellent agreement with the experimental data.     

Experimental investigation and thermodynamic description of the Cu-Cr-Zr system

The Cu-Cr-Zr ternary system was investigated via thermodynamic modeling coupled with key experiments. The isothermal section of the Cu-Cr-Zr system at 1123 K was determined by means of optical microscopy, X-ray diffraction and electron probe microanalysis, and the phase transformation temperatures were measured by differential scanning calorimetry. The Cu-Cr sub-binary system was re-assessed with a substitutional solution model for the solution phases to ensure its compatibility in multi-component system. A set of self-consistent thermodynamic parameters for the Cu-Cr-Zr systems was obtained using the CALPHAD (CALculation of PHAse Diagram) approach, and the calculated phase diagram is in a satisfactory agreement with the present experimental results and literature information. An increase of the thermodynamic stability for the CuZr and Cr₂Zr phases due to the ternary solubility is verified by calculation.     

Experimental reinvestigation and thermodynamic description of Bi-Te binary system

The Bi-Te phase diagram was determined by equilibrium alloy method, combined with electron probe microanalysis (EPMA), X-ray diffraction (XRD) and thermal analysis (DSC). The experimental result shows that there is a β-phase with a large composition range at low temperature, while Bi₂Te and Bi₄Te₃ are relatively stable in the solid-liquid region. A consistent phase diagram that covers the experimental findings has been achieved. Based on the new experimental phase diagram, coupling with the reported thermodynamic data, the thermodynamic optimization of the Bi-Te binary system was carried out with the help of CALPHAD approach. A group of reasonable thermodynamic parameters was obtained.     

A thermodynamic reassessment of the Ca–Pb system

New experimental measurements of the mixing enthalpy of the liquid phase and the enthalpies of formation of the intermetallic compounds along with the data already taken into account in previous thermodynamic assessments have been used in a reassessment of the thermodynamic parameters of the Ca–Pb system. The calculations based on the thermodynamic modelling are in good agreement with the phase diagram data and experimental thermodynamic values.     

Experimental investigation and thermodynamic assessment of the Al-Co-Ni system

The Al-Co-Ni system is essential to both Co- and Ni-based superalloys. In this study phase relationships among A1, L1₂ and B2 at 800 °C have been investigated by using equilibrated alloys. Four samples were prepared and annealed at 800 °C for 14 days. SEM-EDXS and XRD were used to analyze the annealed samples. The results indicated that two-phase L1₂+B2 and three-phase A1+L1₂+B2 regions exit.A thermodynamic reassessment of the entire Al-Co-Ni system has been made according to the CALPHAD method. Compared to the previous assessments, more recent experimental results have been considered. In the Al-Co binary system, the phase named Y-Co₄Al₁₃ has been added on the basis of the available literature. The order-disorder model has been adopted to describe the A1/L1₂ and A2/B2 phase relations, respectively. Three ternary compounds in the Al-rich region have been introduced. Three-sublattice model has been selected to describe the τ₁ phase with a considerable solubility extension. Thermodynamic interaction parameters have been optimized, considering the available experimental data. In this work several diagrams were calculated, which can fit experimental results in the whole composition range. A satisfactory agreement was obtained. As a result phase equilibria in the interested ferromagnetic shape memory alloys are calculated.     

Experimental investigation and thermodynamic assessment of phase equilibria in the Cr-Re-Ru ternary system

The phase equilibria of the Cr-Re-Ru ternary system at 1100 °C and 1200 °C have been experimentally investigated using electron probe microanalyzer and X-ray diffraction. The σ₁-Cr₂Re₃ and σ₂-Cr₂Ru phases with the same D8_b crystal structure do not form a continuous intermetallic compound phase at 1100 °C and 1200 °C in the Cr-Re-Ru ternary system confirmed by experimental results. According to the experimental results in this work, the Cr-Re-Ru ternary system has been assessed by means of the CALPHAD (CALculation of PHAse Diagrams) method. The calculated isothermal section at 1400 °C shows that the two independent phases σ₁-Cr₂Re₃ and σ₂-Cr₂Ru are replaced by the continuous intermetallic compound σ. The current established thermodynamic database of the Cr-Re-Ru ternary system may provide the essential information, and support for the thermodynamic assessment of multicomponent system and the development of Ni-based superalloys.     

A thermodynamic reassessment of the La–Sn system

Thermodynamic modelling of the La–Sn binary system was carried out with the help of the CALPHAD (CALculation of PHAse Diagram) method. The liquid phase has been described with the association solution model with a ‘ La₁Sn₁’ associated complex. The intermetallic compounds were treated as stoichiometric phases. The calculated phase diagram and the thermodynamic properties of the system are in satisfactory agreement with the majority of the experimental data.