Thermodynamic assessments of the Ni–Pt and Al–Ni–Pt systems

The Ni–Pt system is assessed using the CALPHAD method. The four fcc-based phases, i.e. disordered solid solution phase, Ni₃Pt–L1₂, NiPt–L1₀ and NiPt₃–L1₂, are described by a four-sublattice model. The calculated thermodynamic properties and order/disorder phase transformations are in good agreement with the experimental data. In order to facilitate the assessment, first-principles pseudopotential calculations are also performed to calculate the enthalpy of formation at 0 K, and comparison with the assessed values is discussed. By combining the assessments of Al–Ni and Al–Pt, the Al–Ni–Pt ternary system is assessed within a narrow temperature range, focusing on the fcc-based phases and their phase equilibria with B2 phase.     

Thermodynamic assessment of the V–Zn system supported by key experiments and first-principles calculations

The V–Zn system was investigated by a combination of CALPHAD modeling with key experiments and first-principles calculations. Based on a critical literature review, one diffusion couple and nine alloys were designed to reinvestigate the stabilities of the phases reported in the literature. The samples were annealed and cooled under different conditions, followed by examination with X-ray diffraction and scanning electron microscopy with energy-dispersive X-ray spectrometry. Four phases ((V), (Zn), V Zn₃ and V ₄Zn₅) were confirmed to exist in the phase diagram, while V Zn₁₆ and V ₃Zn were not observed. By means of first-principles calculations, the enthalpies of formation for V Zn₃ and V ₄Zn₅ were computed to be −4.55 kJ mol-atoms⁻¹ and −4.58 kJ mol-atoms⁻¹, respectively. A set of self-consistent thermodynamic parameters for this system was obtained by considering the reliable experimental phase diagram data and the enthalpies of formation acquired from first-principles calculations. The calculated V–Zn phase diagram agrees well with the experimental data.     

Thermodynamic reassessment of the Au–Dy system supported by first-principles calculations

Based on the available experimental phase equilibria and thermodynamic data and enthalpies of formation computed via first-principles calculations, thermodynamic reassessment of the Au–Dy system was carried out by means of the CALPHAD method. The enthalpies of formation at 0 K for AuDy₂, αAuDy, βAuDy, Au₂Dy, Au₃Dy, Au₅₁Dy₁₄ and Au₆Dy were computed via first-principles calculations to supply the necessary thermodynamic data for the modeling in order to obtain the thermodynamic parameters with sound physical meaning. The solution phases, i.e. liquid, (Au), (αDy) and (βDy), were described by the substitutional solution model, and all the intermetallic compounds in the Au–Dy system were treated as stoichiometric phases. A set of self-consistent thermodynamic parameters for the Au–Dy system was finally obtained. The calculated phase diagram and thermodynamic properties agree reasonably with the literature experimental data and the present first-principles calculations.     

Phase equilibria and thermodynamic investigation of the In–Li system

Phase equilibria and thermodynamic properties of the In–Li system were analyzed by combining the first-principles approach and Computer Coupling of Phase Diagrams and Thermochemistry (CALPHAD) methodology. The enthalpies of formation for all the stable compounds were calculated by first-principles calculations based on the density functional theory (DFT). Phase diagram of the In–Li system was calculated for the first time, and a set of self-consistent thermodynamic parameters was finally obtained by CALPHAD approach coupling experimental measurements and first-principles calculations. An associate model of (In, In₂Li₃, Li) was used to describe the liquid phase, and InLi and InLi₂ were treated by sub-lattice models. Other intermediate phases were considered to be stoichiometric compounds. The calculated phase diagram, voltage curve and thermodynamic properties can reproduce the available experimental data reasonably.     

Thermodynamic modeling of the Mg–Ge–Pb system

All available thermodynamic and phase diagram data of the Mg–Ge and Mg–Pb binary systems, and the Mg–Ge–Pb ternary system have been critically evaluated and all reliable data have been simultaneously optimized to obtain one set of model parameters for the Gibbs energies of the liquid and all solid phases as functions of composition and temperature. The liquid phase was modeled using the Modified Quasichemical Model in order to describe the strong ordering in Mg–Ge and Mg–Pb liquid. Mg₂Ge–Mg₂Pb solid solution phase was modeled with consideration of a solid miscibility gap. All calculations were performed using the FactSage thermochemical software.     

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.     

Ab initio calculation of the BCC Fe–Al–Mo (Iron–Aluminum–Molybdenum) phase diagram: Implications for the nature of the phase

The metastable phase diagram of the BCC-based ordering equilibria in the Fe–Al–Mo system has been calculated via a truncated cluster expansion, through the combination of Full-Potential-Linear augmented Plane Wave (FP-LAPW) electronic structure calculations and of Cluster Variation Method (CVM) thermodynamic calculations in the irregular tetrahedron approximation. Four isothermal sections at 1750 K, 2000 K, 2250 K and 2500 K are calculated and correlated with recently published experimental data on the system. The results confirm that the critical temperature for the order–disorder equilibrium between Fe₃Al–D0₃ and FeAl–B2 is increased by Mo additions, while the critical temperature for the FeAl–B2/A2 equilibrium is kept approximately invariant with increasing Mo contents. The stabilization of the Al-rich A2 phase in equilibrium with overstoichiometric B2–(Fe,Mo)Al is also consistent with the attribution of the A2 structure to the τ₂ phase, stable at high temperatures in overstoichiometric B2–FeAl.     

Phase equilibria of the Zn-Ti system: Experiments,first-principles calculations and Calphad assessment

The phase equilibria and thermodynamic properties of the Zn-Ti system have been investigated by experiments, first-principles calculations and Calphad assessment. Differential scanning calorimetry measurement and microstructure characterization confirmed the Zn richest eutectic reaction to occur at 691.3 ± 0.4 K with about 0.27 at% Ti in the liquid. Density functional theory (DFT) calculations have been performed to calculate the finite-temperature heat capacity (C_p) of the intermetallics, providing also the absolute entropies. A full thermodynamic assessment of the Zn-Ti system has been performed by using the experimental and DFT results obtained in this work together with the collection of all available data from previous publications. In the present work, the Calphad results show good agreement not only in thermodynamic properties with DFT data, but also phase equilibria data with experimental results, especially in the Zn-rich side, which significantly improved from previous Calphad assessment. Phase diagrams including the gas phase have also been calculated and discussed.     

Thermodynamic modeling of Fe–Ti–Bi system assisted with key experiments

Phase equilibria of Fe–Ti–Bi ternary system have been studied in this work. Firstly, by using alloy sampling, the isothermal section of Fe–Ti–Bi ternary system at 773 K was determined, where the existence of a ternary phase Bi₂FeTi₄ was confirmed. Meanwhile, formation enthalpies of the intermediate phases BiTi₂, Bi₉Ti₈ and Bi₂FeTi₄, were obtained with first-principles calculations. Based on experimental data of phase equilibria and thermodynamic properties in literatures along with the calculated formation enthalpies in this work, thermodynamic modeling of Ti–Bi binary system and Fe–Ti–Bi ternary system were carried out with the CALPHAD approach. A set of self-consistent thermodynamic parameters to describe the Gibbs energy for various phases in Fe–Ti–Bi ternary system was finally obtained, with which solidification processes of two typical Fe–Ti–Bi alloys could be reasonably explained.     

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.