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.     

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.     

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.     

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 modeling of the Sn–V binary system

The Sn–V binary system was thermodynamically modeled using the CALPHAD approach combined with first-principles calculations. The predicted Gibbs free energy of the end-members in sublattice models of “ V ₃Sn” phase by the first-principles calculations was used to describe the lattice stabilities. A set of thermodynamic parameters for the Sn–V system was obtained using the PanOptimizer program in Pandat software. The calculated phase diagram and thermodynamic properties agree well with the reported experimental 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.     

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 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.     

The phase equilibria in the Mg–Ni–Ca system

The three binary systems Mg–Ni, Ca–Ni and Mg–Ca have been re-optimized. A self-consistent thermodynamic database of the Mg–Ni–Ca system is constructed by combining the optimized parameters of these three constituent binaries. Lattice stability values are not added to the pure elements Mg-hcp, Ni-fcc, Ca-fcc and Ca-bcc to construct this database. The Redlich–Kister polynomial model is used to describe the liquid and the terminal solid solution phases, and the sublattice model is used to describe the non-stoichiometric phase, in this system. The constructed database is used to calculate the three binary and the ternary systems. The calculated binary phase diagrams along with their thermodynamic properties such as Gibbs energy, enthalpy, entropy and activities are found to be in good agreement with experimental data from the literature. This is the first attempt to construct the ternary phase diagram of the Mg–Ni–Ca system. The established database for this system predicted three ternary eutectic, five ternary quasi-peritectic, two ternary peritectic and two saddle points.     

A thermodynamic modeling of the Pd-Ti system

The thermodynamic properties of the Pd-Ti system were optimized using the CALPHAD (CALculation of PHAse Diagram) technique. The solution phases, liquid, bcc, fcc and hcp, were described by the substitutional-solution model. Both compounds Pd₂Ti and PdTi₂ with tetragonal MoSi₂-type structure were treated as one phase with the formula (Pd,Ti)₂(Pd,Ti) by a two-sublattice model. The intermetallic compounds Pd₃Ti, Pd₃Ti₂, and PdTi₃ were treated as stoichiometric compounds. The intermetallic compound αPdTi, which had a homogeneity range, was treated as the formula (Pd,Ti)(Pd,Ti) by a two-sublattice model. A two-sublattice model (Pd,Ti)_0.5(Pd,Ti)_0.5 was applied to describe the compound βPdTi in order to cope with the order-disorder transition between βPdTi with CsCl-type structure (B2) and body-centered cubic solution (A2) in the Pd-Ti system. A set of self-consistent thermodynamic parameters was obtained.