A thermodynamic description of the Al–Be system: Modeling and experiment

The Al–Be system is investigated via three steps. In the first step, all of the experimentally measured phase diagram and thermodynamic data available in the literature are critically reviewed. On the basis of the assessed phase diagram, in the second step, eight decisive samples are prepared by arc melting of Al and Be pieces and annealing at 600 C for eight days. Water-quenched samples are analyzed using differential thermal analysis (DTA), X-ray diffraction (XRD), optical microscopy, and scanning electron microscopy (SEM) techniques. In the last step, an optimal thermodynamic data set for the Al–Be system has been obtained by considering the present experimental data and the reliable literature data. The calculated phase diagram and thermodynamic properties agree well with the accurate experimental values.     

Thermodynamic description of the Dy–Ni system

The Dy–Ni binary system has been thermodynamically assessed by means of the computer program Thermo-Calc. The Redlich–Kister polynomial was used to describe the solution phase, liquid (L). Ten compounds, Dy₃Ni, Dy₃Ni₂, DyNi, DyNi₂, DyNi₃, Dy₂Ni₇, DyNi₄, Dy₄Ni₁₇, DyNi₅ and Dy₂Ni₇, were treated as stoichiometric phases. The parameters of the Gibbs energy expressions were optimized according to all the available experimental information of both the equilibrium data and the thermodynamic results. A set of self-consistent thermodynamic parameters of the Dy–Ni system has been obtained. The calculations agree well with the respective experimental data.     

Thermodynamic assessment of the Pt–Si binary system

The Pt–Si binary system was thermodynamically assessed using the CALPHAD method based on the available experimental data from the literature. The solution phases, including Liquid, Fcc_A1 (Pt) and Diamond_A4 (Si), were treated as substitutional solution phases, of which the excess Gibbs energies were expressed with Redlich–Kister polynomial functions. Meanwhile, the intermetallic compounds, PtSi, Pt₆Si₅, Pt₂Si, Pt₁₇Si₈, Pt₅Si₂, Pt₃Si and Pt₂₅Si₇, were modeled as stoichiometric compounds. Subsequently, a set of self-consistent thermodynamic parameters formulating the Gibbs energies of various phases were obtained and the calculated values of phase diagram and thermodynamics were found to be in reasonable agreement with experimental data.     

Thermodynamic modeling of the V–Si system supported by key experiments

The V–Si system is reassessed based on a critical literature review involving recently reported data and the present experimental data. These new data include the thermodynamic stability of V ₆Si₅ and the enthalpies of formation for the compounds calculated by first-principles method. Two alloys were prepared in the region of (Si)+V Si₂ and annealed at 1273 K for 14 days. After X-ray diffraction (XRD) and chemical analysis of these alloys were performed, the eutectic reaction (L⇔(Si)+V Si₂) temperature was determined by differential thermal analysis (DTA). Self-consistent thermodynamic parameters for the V–Si system were obtained by optimization of the selected experimental values. The calculated phase diagram and thermodynamic properties agree well with the experimental ones. Noticeable improvements have been made, compared with the previous assessments.     

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.     

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.     

Thermodynamic and ab initio investigation of the Cu–Dy system

A combined ab initio and thermodynamic study of the Cu–Dy system has been performed and a self-consistent thermodynamic database has been obtained. Density functional theory has been applied by using the VASP code in order to obtain the enthalpy of formation at 0 K of intermetallic compounds. Experimental information on the Cu–Dy phase diagram and thermodynamic properties of its alloys have been collected. Using these data, optimized parameters have been obtained by applying the CALPHAD approach. The present results reproduce the experimental data available reasonably well, although some features of the Cu–Dy system need to be further clarified.     

Experimental investigation and thermodynamic modeling of the Al–Cu–Si system

16 ternary alloys located over the entire composition range of the Al–Cu–Si system are investigated by means of XRD, SEM/EDX and DTA. The phase equilibria associated with the kappa phase of the Cu–Si system are determined in detail and the isothermal sections at 600 and 500 ^°C are experimentally constructed. No ternary phase is observed at 600 or 500 ^°C. A thorough thermodynamic modeling for this system is then conducted based on the critically reassessed literature data and the present experimental results.     

Thermodynamic description of the Pb–Yb binary system

Thermodynamic modelling of the Pb–Yb binary system was carried out with the help of the CALPHAD method. The liquid phase has been described with the association solution model with ‘ Pb₁Y b₂’ as an associated complex. The solution phases BCC_A2 and FCC_A1 were modelled with the sublattice formalism. The αPbYb_LT and βPbYb_HT Pb sub-stoichiometric intermetallic compounds, which have a homogeneity range, were treated with the formula (Pb,Y b)_0.5(Y b)_0.5 by a two-sublattice model with Pb and Yb on the first sublattice and Yb on the second one. Pb₃Y b, Pb₃Y b₅ and PbY b₂ have been treated as stoichiometric compounds. The calculations based on the thermodynamic modelling are in good agreement with the phase diagram data and experimental thermodynamic values.     

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 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.