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.     

A thermodynamic description of the Al–Ca–Zn ternary system

A comprehensive thermodynamic database of the Al–Ca–Zn ternary system is presented for the first time. Critical assessment of the experimental data and re-optimization of the binary Al–Zn and Al–Ca systems have been performed. The optimized model parameters of the third binary system, Ca–Zn, are taken from the previous assessment of the Mg–Ca–Zn system by the same authors. All available as well as reliable experimental data both for the thermodynamic properties and phase boundaries are reproduced within experimental error limits. In the present assessment, the modified quasichemical model in the pair approximation is used for the liquid phase and Al_FCC phase of the Al–Zn system to account for the presence of the short-range ordering properly. Two ternary compounds reported by most of the research works are considered in the present calculation. The liquidus projections and vertical sections of the ternary systems are also calculated, and the invariant reaction points are predicted using the constructed database.     

The thermodynamic analysis of Guinier–Preston zones in aged supersaturated Al–Cu alloys

Being the structural cause of hardening, Guinier–Preston (GP) zones in many alloys still attract much interest. The expression of energy for GP zones in the Al–Cu alloy is established by combining the essential Gibbs energy with the interfacial energy and the strain energy. Based on the equilibrium between GP zones and the surrounding matrix, a quantitative analysis on the sizes, concentrations, aging temperatures and their relationships can be predicted. The size and the concentration of GP zones calculated with defined composition and aging temperature accord with the experimental results well.     

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 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.     

Thermodynamic description of the Cu–Ag–Zr system

Based on the CALPHAD method, the Ag–Zr and Ag–Cu systems have been assessed thermodynamically. The excess Gibbs energy of the solution phases in the Cu–Ag–Zr system was modeled assuming random mixing of components. The ternary phase was defined as a stoichiometric compound due to the lack of efficient thermodynamic data. At first, parameters capable of describing all phases in the Ag–Zr and the Ag–Cu systems were assessed. Combined with the parameters of the Cu–Zr system assessed previously, the isothermal sections of the Cu–Ag–Zr system at 1023 K and 978 K were extrapolated, which can reproduce the measured phase-relations.     

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.     

Thermodynamic evaluation and optimization of Al–Gd, Al–Tb, Al–Dy, Al–Ho and Al–Er systems using a Modified Quasichemical Model for the liquid

The Al–Gd, Al–Tb, Al–Dy, Al–Ho and Al–Er (Al–heavy rare earths) binary systems have been systematically assessed and optimized based on the available experimental data and ab-initio data using the FactSage thermodynamic software. A systematic technique (reduced melting temperature proposed by Gschneidner) was used for estimating the Al–Tb phase diagram due to lack of experimental data. Optimized model parameters of the Gibbs energies for all phases which reproduced all the reliable experimental data to satisfaction have been obtained. The optimization procedure was biased by putting a strong emphasis on the observed trends in the thermodynamic properties of Al–RE phases. The Modified Quasichemical Model, which takes short-range ordering into account, is used for the liquid phase and the Compound Energy Formalism is used for the solid solutions in the binary systems. It is shown that the Modified Quasichemical Model used for the liquid alloys permits one to obtain entropies of mixing that are more reliable than that based on the Bragg–Williams random mixing model which does not take short-range ordering into account.     

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.     

Thermodynamic description of the Sn–Ag–Au ternary system

Gibbs energy of hcp_A3 phase in the Ag–Sn binary system has been reassessed using compatible lattice stability. Combined with previous assessments of the Ag–Au and Au–Sn binary systems, the Sn–Ag–Au ternary system has been thermodynamically optimized using the CALPHAD method on the basis of available experimental information. The solution phases including liquid, fcc_A1, hcp_A3 and bct_A5, are modeled as substitutional solutions, while the intermediate compound Ag₃Sn is treated using a 2-sublattice model because Au can be dissolved to a certain degree. The solubility of Ag in the Au–Sn intermediate phases, D0₂₄, Au₅Sn, AuSn, AuSn₂ and AuSn₄, is not taken into account. Thermodynamic properties of liquid alloys, liquidus projection and several vertical and isothermal sections of this ternary system have been calculated, which are in reasonable agreement with the reported experimental data.