Thermodynamic assessments of Ag–Dy and Ag–Er binary systems

Thermodynamic assessments of Ag–Dy and Ag–Er binary systems have been performed by using CALPHAD method. In order to provide necessary data for thermodynamic assessment, the formation enthalpies of Ag₂Dy, AgDy, Ag₂Er and AgEr were calculated by using projector augmented-wave (PAW) method within generalized gradient approximation (GGA) in first-principles frame. During assessments of the Ag–Dy and Ag–Er binary systems, the solution phases (liquid, fcc and hcp) were treated as substitutional solutions, of which the excess Gibbs energies were modeled by Redlich–Kister polynomial, and all intermetallic compounds were described as stoichiometric phases. Consequently, phase diagrams of these two binary systems were thermodynamically optimized and the self-consistent thermodynamic parameters of involved phases obtained.     

Thermodynamic modeling of the Au-Sb-Si ternary system

Thermodynamic optimization of the Au-Sb binary system was updated as well as the Si-Sb binary system was assessed thermodynamically using the CALPHAD method based on the critical review of the available experimental information from the published literature. The solution phases including liquid, fcc_A1(Au), diamond_A4(Si) and rhombohedral_A7(Sb), are modeled as substitutional solutions and their excess Gibbs energies are expressed by a Redlich-Kister polynomial. The solubility of Si in the intermetallic compound AuSb₂ is not taken into account because of the lack of experimental information. Combined with previous assessment of the Au-Si binary system, thermodynamic modeling of the Au-Sb-Si ternary system was performed to reproduce well the measured phase equilibria. The liquidus projection and several vertical sections of this ternary system were calculated, which are in reasonable agreement with the reported experimental data.     

Thermodynamic assessment of the Hg-Sn system

A thermodynamic assessment of the Hg-Sn system has been carried out using the CALPHAD method. The comprehensive assessment covers the extensive phase diagram data as well as the enthalpy, activity, and vapor pressure data. Two cases of intermetallic compounds in the Hg-Sn system are considered. Case 1 considers the intermetallic compounds β, γ, and HgSn₄ as having no solubility and can thus be treated as the stoichiometric phases β-HgSn₃₈, γ-HgSn₁₂, and HgSn₄. Case 2 uses a sublattice model to more accurately describe a solubility of the γ phase; it also considers the stoichiometric δ-HgSn₇ phase. The ε phase was considered to be metastable and neglected in the thermodynamic assessment. Thermodynamic parameters have been optimized using all the assessed experimental thermodynamic and phase equilibrium data. Both calculated phase diagrams of the Hg-Sn system (Cases 1 and 2) and the thermodynamic data are reasonable and satisfactory when compared with literature data. Future crucial experiments are suggested.     

Thermodynamic assessment of the Hg-Sn system

A thermodynamic assessment of the Hg-Sn system has been carried out using the CALPHAD method. The comprehensive assessment covers the extensive phase diagram data as well as the enthalpy, activity, and vapor pressure data. Two cases of intermetallic compounds in the Hg-Sn system are considered. Case 1 considers the intermetallic compounds β, γ, and HgSn₄ as having no solubility and can thus be treated as the stoichiometric phases β-HgSn₃₈, γ-HgSn₁₂, and HgSn₄. Case 2 uses a sublattice model to more accurately describe a solubility of the γ phase; it also considers the stoichiometric δ-HgSn₇ phase. The ε phase was considered to be metastable and neglected in the thermodynamic assessment. Thermodynamic parameters have been optimized using all the assessed experimental thermodynamic and phase equilibrium data. Both calculated phase diagrams of the Hg-Sn system (Cases 1 and 2) and the thermodynamic data are reasonable and satisfactory when compared with literature data. Future crucial experiments are suggested.     

Thermodynamic Reassessment of the Gallium–Lithium Phase Diagram

Thermodynamic optimization of the Ga–Li binary system was carried out using the CALculation of PHAse Diagrams (CALPHAD) method. Ga₁₄Li₃, Ga₇Li₂, Ga₈Li₃, Ga₉Li₅, and Ga₄Li₅ were treated as stoichiometric compounds, while a solution model was used to describe the liquid, ORTHORHOMBIC_CMCA (Ga), and BCC_A2 (Li) phases. The intermetallic compounds GaLi, Ga₂Li₃, and GaLi₂, which have homogeneity ranges, were treated using a two-sublattice model. The results of the calculations based on thermodynamic modeling are in good agreement with phase diagram data and experimental thermodynamic values.     

Thermodynamic assessment of the Gd–Sb system

A thermodynamic assessment of the binary Gd–Sb system was performed through the CALPHAD approach (CALculation of PHAse Diagram) based on the evaluation of all phase diagram data and available thermodynamic data in the literature. The liquid, hcp-A3 (αGd) and bcc-A2 (βGd) phases were described by a substitutional solution model. All the intermediate phases, Gd₅Sb₃, Gd₄Sb₃, βGdSb, αGdSb and Gd₁₆Sb₃₉, were treated as stoichiometric compounds. A set of self-consistent thermodynamic parameters of the Gd–Sb system has been obtained. A good agreement is obtained between the experimental and the calculated phase diagrams.     

Experimental studies and thermodynamic optimization of the Ni-Bi system

Experimental studies by electron microprobe analyses, optical microscopy, and differential scanning calorimetry were performed. New data about the liquidus in the central and the Bi-rich regions were obtained. A narrow homogeneity region (about 50–52 at.% Bi) was found for the compound NiBi while the second intermediate phase in this system (NiBi₃) was stoichiometric. Thermodynamic optimization of the Ni-Bi phase diagram was achieved by the CALPHAD method by combining phase diagram and thermodynamic data. Thus, NiBi was modeled with two sublattices, allowing mixing of Bi and Ni on one of them only. The intermetallic phase NiBi₃ was modeled as a stoichiometric compound. Redlich-Kister polynomials were used to describe the excess Gibbs energies of the solution phases (liquid, pure bismuth, and Ni-based solid solutions).     

The ternary Gd-Li-Mg system: Phase diagram study and computational evaluation

The binary Gd-Li and the ternary Gd-Li-Mg systems were studied experimentally by thermal analysis and phase equilibration and also by thermodynamic calculations using the CALPHAD method. Ternary phase equilibria at 250 °C were studied with 55 different alloys that were annealed for 400 h and analyzed by x-ray diffractometry. A thermodynamic assessment of the binary Gd-Li system was also performed and the calculated phase diagram is presented. In the Gd-Li-Mg system, ternary solubilities of Li in GdMg (up to 5 at.% Li), GdMg₂ (up to approximately 3 at.% Li), and GdMg₃ (up to 5 at.% Li) were found at 250 °C. No ternary compound was observed. Lattice parameters for different compositions are given for these phases. Thermal analysis using a ternary key sample of composition near the invariant reaction L′=L+(βGd)+GdMg provided the data that were needed to determine a thermodynamic parameter for the ternary liquid. Thermodynamic data sets for the ternary solid solution phases were also developed. Based on the present data sets and those of the binary Gd-Mg and Li-Mg systems from the literature, the phase equilibria in the entire ternary system were calculated. Isothermal and vertical sections of the phase diagram and the projection of the liquidus surface are shown. These calculated phase diagrams are well supported by the experimental data.     

The ternary Gd-Li-Mg system: Phase diagram study and computational evaluation

The binary Gd-Li and the ternary Gd-Li-Mg systems were studied experimentally by thermal analysis and phase equilibration and also by thermodynamic calculations using the CALPHAD method. Ternary phase equilibria at 250 °C were studied with 55 different alloys that were annealed for 400 h and analyzed by x-ray diffractometry. A thermodynamic assessment of the binary Gd-Li system was also performed and the calculated phase diagram is presented. In the Gd-Li-Mg system, ternary solubilities of Li in GdMg (up to 5 at.% Li), GdMg₂ (up to approximately 3 at.% Li), and GdMg₃ (up to 5 at.% Li) were found at 250 °C. No ternary compound was observed. Lattice parameters for different compositions are given for these phases. Thermal analysis using a ternary key sample of composition near the invariant reaction L′=L+(βGd)+GdMg provided the data that were needed to determine a thermodynamic parameter for the ternary liquid. Thermodynamic data sets for the ternary solid solution phases were also developed. Based on the present data sets and those of the binary Gd-Mg and Li-Mg systems from the literature, the phase equilibria in the entire ternary system were calculated. Isothermal and vertical sections of the phase diagram and the projection of the liquidus surface are shown. These calculated phase diagrams are well supported by the experimental data.     

Experimental determination and thermodynamic calculation of phase equilibria in the Fe−Mn−Al system

The phase equilibria among the face-centered cubic (fcc), body-centered cubic (bcc), and βMn phases at 800, 900, 1000, 1100, and 1200 °C were examined by electron probe microanalysis (EPMA), and the A2/B2 and B2/D0₃ ordering temperatures were also determined using the diffusion couple method and differential scanning calorimetry (DSC). The critical temperatures for the A2/B2 and B2/D0₃ ordering were found to increase with increasing Mn content. Thermodynamic assessment of the Fe−Mn−Al system was also undertaken with use of experimental data for the phase equilibria and order-disorder transition temperatures using the CALPHAD (Calculation of Phase Diagrams) method. The Gibbs energies of the liquid, αMn, βMn, fcc, and ε phases were described by the subregular solution model and that of the bcc phase was represented by the two-sublattice model. The thermodynamic parameters for describing the phase equilibria and the ordering of the bcc phase were optimized with good agreement between the calculated and experimental results. This paper was presented at the International Symposium on User Aspects of Phase Diagrams, Materials Solutions Conference and Exposition, Columbus, Ohio, 18–20 October, 2004.     

Re-investigation of the phase constitution of the system Pt-Te

The phase relations of the system Pt-Te have been investigated using the conventional sealed-capsule technique. The identification of phases present in the reaction products was made by reflected light microscopy, X-ray diffraction, and electron probe microanalysis. Four binary phases were confirmed to exist in the system: PtTe., Pt₃Te₄, Pt₂Te₃ and PtTe₂. The composition of all these appears to be constant without showing any appreciable compositional range. The Pt₂Te phase was not found in this study. The Te content in platinum and the Pt in tellurium in solid solution are negligible, less than 0.5 at.% up to 1000°C. The eutectic point between Pt and PtTe is near at 40 at.% Te and at 870°C. The Pt₂Te₃ phase is stable up to about 675°C, whereas the melting point of the Pt₃Te₄ phase is apparently above 1000°C. The most part of liquidus curve between PtTe₂ and Te exists above 1000°C. Physico-chemical properties of Pt-Te phases obtained in this study are given. The revised phase diagram of the Pt-Te system is proposed from this study.     

Assessment of the Mn-O system

Experimental data on the thermodynamics and the phase diagram of the Mn-O system were reviewed, and by application of the CALPHAD method, a consistent set of thermodynamic model parameters was optimized. The phases pyrolusite (MnO₂), bixbyite (Mn₂O₃), and hausmannite (Mn₃O₄) were described as stoichiometric compounds. Manganosite (Mn_1−x O) was described using the compound-energy model and the liquid described using the two-sublattice model for ionic liquids.     

Assessment of the Mn-O system

Experimental data on the thermodynamics and the phase diagram of the Mn-O system were reviewed, and by application of the CALPHAD method, a consistent set of thermodynamic model parameters was optimized. The phases pyrolusite (MnO₂), bixbyite (Mn₂O₃), and hausmannite (Mn₃O₄) were described as stoichiometric compounds. Manganosite (Mn_1−x O) was described using the compound-energy model and the liquid described using the two-sublattice model for ionic liquids.     

Thermodynamic Evaluation of the Co-Al-C System by Coupling Ab Initio Calculations and CALPHAD Approach

The ternary Co-Al-C system was thermodynamically assessed using the CALPHAD method based on the critical review of all experimental information in the system. The κ-carbide was described with a three-sublattice model (Al,Co)₃(Al,Co)₁(C,Va)₁. To support the assessment, the enthalpies of formation of all end-members of the κ-carbide were studied by ab initio calculations. The solubility ranges of the carbon in the κ-carbide, the αCo and the AlCo (B2) phases were well reproduced. The equilibria involving the liquid phase were reasonably described using the present set of thermodynamic parameters.     

Assessment of the Sr-Mn-O system

A thermodynamic assessment of the Sr-Mn-O system is presented. The main practical relevance of this system is that it contains the perovskite phase SrMnO₃, which is the Sr-rich end member of the phase (La,Sr) MnO₃, that finds widespread use as a cathode material for solid oxide fuel cells (SOFCs) and has recently attracted a lot of attention due to its interesting giant magnetoresistive properties. The thermodynamic parameters are optimized by applying the CALPHAD method. The SrMnO_3−z phase exists in two modifications, a layered hexagonal modification at low temperatures and a perovskite modification at high temperatures. Both modifications show considerable oxygen deficiencies, which are modeled using the compound energy model. The sublattice occupation of the phases is (Sr²⁺) (Mn³⁺, Mn⁴⁺)(O²⁻, Va)₃. On reducing Mn⁴⁺ to Mn³⁺, oxygen vacanices are formed. The phase SrMn₃O_6−z also shows an oxygen deficiency, which is modeled in an identical way. The Ruddlesden-Popper phases Sr₂MnO₄ and Sr₃Mn₂O₇, and the phases Sr₇Mn₄O₁₅ and Sr₄Mn₃O₁₀ are modeled as stoichiometric phases. The ionic liquid is modeled using the two-sublattice model for ionic liquids. The stability and thermodynamic data on many of the phases in this system are poorly known. For this reason, some aspects of this assessment must be regarded as tentative.     

Thermodynamic Modeling of the La-B and La-Bi Systems Supported by First-Principles Calculations

Thermodynamic assessments of the La-B and La-Bi systems were carried out based on the available experimental data including thermodynamic properties and phase equilibria by means of the CALPHAD method. The enthalpies of formation at 0 K for the LaB₄, LaB₆, La₂Bi, La₅Bi₃, La₄Bi₃ and LaBi were computed via first-principles calculations. These enthalpies of formation were used “key experimental data” in the CALPHAD approach in order to obtain the thermodynamic parameters with sound physical meaning. The liquid phase has been modeled with both the substitutional solution model and associate model, and two sets of self-consistent thermodynamic parameters for the La-B and La-Bi systems were finally obtained. The calculated phase diagram and thermodynamic properties agree reasonably with the literature experimental data and the present first-principles calculations.     

Thermodynamic study of phase equilibria in the Pb-Bi-Hg system

Thermodynamic modeling of the Pb-Bi-Hg ternary system was done with the help of the calculation phase diagram (CALPHAD) method. This work included a thermodynamic characterization of the three binary borders: the parameters relating to the Pb-Bi system were taken from the literature, whereas those of Pb-Hg and Bi-Hg systems were determined during this study, and were primarily based on particular calorimetric measurements. Some differential scanning calorimetry (DSC) data for the ternary system allowed us to verify the existence of a ternary compound with a composition close to Pb_0.45Bi_0.35Hg_0.2 and the presence of two peritectic invariants. With these results, it was possible to carry out the assessment of the ternary interaction parameter of the liquid phase.