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.     

The V-Zn binary system: New experimental results and thermodynamic assessment

Experimental investigation followed by thermodynamic assessment of the V-Zn system was carried out in the present study. A series of V-Zn alloys annealed at various temperatures were examined using scanning electron microscopy coupled with energy dispersive spectroscopy/wavelength dispersive X-ray spectrometer, X-ray diffraction and differential thermal analysis. It was confirmed that V Zn₁₆, with a V content of about 5.8 at.%, was indeed an equilibrium phase. DTA results indicated that the peritectic temperature for V Zn₁₆ was about 427 ^°C. Two new metastable compounds, V Zn₉ and V ₃Zn₂, with V contents of 8.5-11.3 at.% and 60 at.%, respectively, were discovered. DTA results together with SEM-EDS examinations revealed that V Zn₉ was formed at around 450 ^°C in Zn75V25 alloy with a cooling rate greater than 12 ^°C/min. The V Zn₉ phase, however, decomposed into V Zn₃ and liquid Zn when the alloy was held above 442 ^°C. The peritectic temperatures for two equilibrium phases, V ₄Zn₅ and V Zn₃, were 651 ^°C and 621 ^°C, respectively. These measurements were slightly lower than the values determined in prior studies. The onset temperature for forming V Zn₃ decreased significantly with increasing cooling rate while its exothermic peak widened during fast cooling. These phenomena indicated that both the nucleation and growth processes for V Zn₃ were kinetically challenged.In addition, the solubility of Zn in α-V was measured. It was 2.1 at.%, 2.5 at.%, 2.6 at.%, 2.9 at.% and 3.3 at.% at 450 ^°C, 600 ^°C, 670 ^°C, 800 ^°C and 1000 ^°C, respectively. Based on the results obtained in the present study and previous investigations, the V-Zn system was reassessed thermodynamically. The assessment was in good agreement with experimental results.     

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 investigation and thermodynamic calculation of Ti-Co-Hf system

Phase relationship of Ti-Co-Hf ternary system, which may contribute to the development of both new Ti-based biomaterials and Co₁₁Hf₂ based rare-earth-free magnetic materials, have been studied by using Ti-Co-Hf diffusion triple and selected equilibrated alloys. Isothermal sections of the Ti-Co-Hf ternary system at both 1173 and 1073 K were experimentally determined by means of electron probe microanalysis (EPMA), scanning electron microscope (SEM) and X-ray diffraction (XRD). Meanwhile, structure refinements of three continuous solid solutions, i.e. Co(Ti, Hf)₂, Co₂(Ti, Hf) and BCC_B2 which were formed between CoTi₂ and CoHf₂, Co₂Ti(c) and Co₂Hf as well as CoTi and CoHf, respectively, were performed by Rietveld method. The stable temperature range of Co₁₁Hf₂ was revised to be from 1310 ± 12.5–1516 K. And Ti (about 3.7 at%) partly dissolves in Co₂₃Hf₆ at 1173 K while the solubility of Hf in Co₃Ti at both 1173 and 1073 K is relatively limited. Based on the available data of binary system, thermodynamic modeling of Ti-Co-Hf ternary system was carried out, with Co(Ti, Hf)₂, Co₂(Ti, Hf) and BCC_B2 being respectively described with models, (Co, Hf)₁(Co, Ti, Hf)₂, (Co, Ti, Hf)₂(Co, Ti, Hf)₁ and (Co, Ti, Hf, VA)_0.5(Co, Ti, Hf, VA)_0.5. A set of self-consistent thermodynamic parameters, which can reasonably reproduce the measured results, has been obtained.     

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.     

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.     

Experimental study and thermodynamic calculation of the Mn-Dy and Mn-Ho binary systems

In this work, twenty-four Mn-Dy and Mn-Ho alloys were investigated experimentally using the differential thermal analysis (DTA), scanning electron microscopy (SEM) and electronic probe microanalysis (EPMA) to study phase equilibria of the Mn-Dy and Mn-Ho binary systems. The temperatures of some invariant reactions and liquidus in the Mn-Dy and Mn-Ho binary systems were determined. Based on the experimental results obtained in the present work and the critical evaluation of the experimental data reported in the literature, the Mn-Dy and Mn-Ho binary systems were calculated using the CALPHAD method. In the thermodynamic calculation, the solution phases including liquid, α(Mn), β(Mn), γ(Mn), δ(Mn), α(Dy), β(Dy), α(Ho) and β(Ho), are treated as the substitutional solution model with the Redlich-Kister formula. The intermetallic compounds, Mn₂Dy, Mn₁₂Dy, Mn₂₃Dy₆, Mn₂Ho, Mn₁₂Ho and Mn₂₃Ho₆, are modeled as the stoichiometric compounds. Self-consistent thermodynamic parameters were obtained finally to describe the Gibbs energies of various stable phases in the Mn-Dy and Mn-Ho binary systems. The calculated results reproduce well the phase equilibria and thermodynamic properties.     

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.     

Experimental investigation and thermodynamic assessment of the Fe-Pr and Fe-Nd binary systems

In this work, Fe-Pr alloys and Fe-Nd alloys were investigated experimentally by means of thermal analysis. The temperatures of the invariant reactions and liquidus in the Fe-Pr and Fe-Nd binary systems were measured. Based on the experimental results determined in this work and the critical review of the available experimental data in published literature, the Fe-Pr and Fe-Nd binary systems were re-assessed thermodynamically using the CALPHAD method. The solution phases including liquid, bcc, fcc and dhcp are modeled by the substitutional solution model and their excess Gibbs energies are expressed with the Redlich-Kister polynomial. The intermetallic compounds, Fe₁₇Pr₂, Fe₁₇Nd₂ and Fe₁₇Nd₅ are treated as intermetallic compounds. The self-consistent thermodynamic parameters obtained finally to describe the Gibbs energies of various phases in the Fe-Pr and Fe-Nd binary systems can be used to reproduce well the phase equilibria and thermodynamic data.     

First-principles calculations assisted thermodynamic assessment of the Pt–Ga–Ge ternary system

The Pt–Ga–Ge ternary system was thermodynamically assessed by the CALPHAD (CALculaton of PHAse Diagram) approach with help of first-principles calculations. Firstly, the formation enthalpies of the Pt–Ge and Pt–Ga compounds were calculated by the first-principles method. Subsequently, the Pt–Ge system was modeled and the Pt–Ga system was re-assessed. The solution phases, Liquid, Diamond_A4 (Ge) and Fcc_A1 (Pt), were modeled as substitutional solutions, of which the excess Gibbs energy was formulated with the Redlich–Kister polynomial. The binary intermetallics, Ga₇Pt₃, Ga₂Pt, Ga₃Pt₂, GaPt, Ga₃Pt₅, GaPt₂, Ge₂Pt, Ge₃Pt₂, GePt, Ge₂Pt₃ and GePt₂, were treated as stoichiometric compounds while GePt₃ was described with a two-sublattice model. Finally, based on the currently optimized Pt–Ga and Pt–Ge binary systems along with the already assessed Ga–Ge system, phase equilibria in the Pt–Ga–Ge ternary system were extrapolated. The isothermal sections at 473 K, 973 K and 1073 K of the ternary system were calculated, showing good agreement with the experimental data. In addition, the liquidus projection of the Pt–Ga–Ge ternary system was predicted using the obtained model parameters.     

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.     

A thermodynamic assessment of the nickel–lead system

Thermodynamic properties and the phase equilibria of the Ni–Pb binary system were assessed by the CALPHAD (CALculation of PHase Diagrams) method using the available literature data. The phase diagram and the excess Gibbs energy values of the solution phases, molten alloy and the fcc solid solution were modelled using the Redlich–Kister polynomials. The experimental data was fitted by a least squares method using MTDATA software tool.     

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.