Thermodynamic assessment of the Cu-Ti-Zr system. I. Cu-Ti system

The CALPHAD method is used for the thermodynamic assessment of the Cu-Ti system that bounds the ternary Cu-Ti-Zr system, which is capable of forming amorphous alloys. The self-consistent parameters of thermodynamic models of the phases are obtained from data on the phase equilibria and thermodynamic properties of liquid alloys and intermetallic compounds. The Gibbs energy of the liquid phase is described using the associated ideal solution model. To describe the thermodynamic properties of the Cu₄Ti and CuTi intermetallic compounds with homogeneity range, sublattice models are used. The calculated phase diagram of the system and the thermodynamic properties of the phases are in good agreement with experimental data.     

Thermodynamic assessment of the copper-hafnium system

The thermodynamic properties of phases and phase equilibria in the Cu-Hf system are described with the CALPHAD method. The set of self-consistent model parameters is based on the thermodynamic properties of liquid alloys, intermetallic compounds, and phase equilibria. The excess Gibbs energy of the liquid phase is described using an ideal associated solution model. The models of thermodynamic properties are used to describe possible metastable transformations such as glass formation in rapid quenching from the melt, formation of bulk amorphous alloys, and formation of supersaturated terminal solid solutions.     

A thermodynamic assessment of the Fe-Mn-C system

The thermodynamic properties of the Fe-Mn-C system have been analyzed by using thermodynamic models for the Gibbs energy of individual phases. The model parameters have been evaluated from the available thermodynamic and phase diagram information and by using computerized optimization. Most of the experimental information was satisfactorily described by the present set of parameters. Comparisons between the calculations and experiments are presented.     

A thermodynamic evaluation of the Cr-Fe-N system

The thermodynamic properties of the Cr-Fe-N system have been analyzed using thermodynamic models describing the Gibbs energy of the individual phases. A two-sublattice model has been used for the interstitial solution phases and a substitutional solution model for the liquid phase. The analysis involves a combination of predictions from recent assessments of the binary sides with computerized optimization of new ternary parameters. A set of parameters describing the Gibbs energy of the body-centered cubic (bcc), face-centered cubic (fcc), ∈, CrN, Fe₄N, and liquid phases is given. Using this set of parameters, any type of phase equilibria can be calculated. A number of diagrams are presented comparing the results from the calculations with available experimental data, and the agreement is discussed. Most experimental data are well accounted for. The present study is also compared with a previous evaluation.     

Phase equilibria and thermodynamics of binary copper systems with 3d-metals. II. The copper-vanadium system

Thermodynamic assessment of the Cu-V system was carried out using the CALPHAD method. The excess heat capacity of the liquid phase was taken into account in the model of its excess Gibbs free energy. Excess thermodynamic properties of limiting solid solutions were represented by regular solution models. A self-consistent set of thermodynamic parameters was obtained using data on the mixing enthalpy and information on the phase equilibria. The thermodynamic properties of the phases and the phase diagram along with its metastable extension were calculated using this set of parameters. The thermodynamic model of the system was used in order to predict the composition limits of formation of supersaturated solid solutions prepared by highly nonequilibrium methods of synthesis. __________ Translated from Poroshkovaya Metallurgiya, Nos. 5–6(449), pp. 71–79, May–June, 2006.     

Experimental study and modeling of the thermodynamic properties of Cu-Fe-Ni melts

The partial mixing enthalpy of nickel in ternary liquid Cu-Fe-Ni alloys is studied at 1873 K along sections characterized by ratios x _Cu: x _Fe = 3, 1, and 1/3 at x _Ni = 0–0.55. The investigations are undertaken using a high-temperature isoperibolic calorimeter. The temperature and composition dependence of the excess mixing Gibbs energy of liquid Cu-Fe-Ni alloys are described in terms of the Muggianu-Redlich-Kister model using the data obtained, the literature data on the activities of liquid alloy components, and the thermodynamic properties of melts of the boundary binary systems. This model is used to calculate isotherms of the thermodynamic properties of the liquid alloys over the entire composition range. The contribution of a ternary interaction to the integral mixing enthalpy of liquid Cu-Fe-Ni alloys is found to be mainly positive.     

Thermodynamic assessment of the CaO-MgO-SiO2 system

The phase equilibrium and thermodynamic information of the CaO-MgO-SiO₂ system at 1 atm was reviewed and assessed by using thermodynamic models for the Gibbs energy of all the phases. The assessment was based on recent assessments of the CaO-MgO, CaO-SiO₂, and MgO-SiO₂ systems. Two thermodynamic models were used: the two-sublattice model for ionic liquids for the liquid phase, and the compound energy model for the solid solution phases. The model parameters were evaluated by fitting to the selected experimental data by means of a computer program, which can accommodate a variety of experimental data. A consistent set of parameters was obtained that sat-isfactorily described most of the experimental information. The models were found to be well-suited for the present system, and only a small number of adjustable parameters were needed. Extensive comparisons were made between the calculations and experimental data. Formerly Research Associate, Royal Institute of Technology     

Calculation of the equilibrium phase diagrams and the spinodally decomposed structures of the FeCuNi system

Thermodynamic stability of ternary systems with miscibility gaps is discussed and applied to the f.c.c. phase of FeCuNi alloys. The stability of the system with respect to infinitesimal composition fluctuation is described. The direction most likely for initial composition fluctuation is defined as the one with the largest negative curvature on the Gibbs energy surface. Along this direction, zero-time wavelength at initial stage of spinodally decomposed alloy structure may be calculated. The thermodynamic values of the f.c.c. FeCuNi alloys are obtained from limited amount of thermochemical and phase equilibrium data. It is found that the ternary interaction parameters for both the f.c.c. and liquid phases of FeCuNi may be approximated from the binary interaction parameters of the constituent binaries.     

A Phase-Field Model for Phase Transformations in Glass-Forming Alloys

A phase-field model is proposed for phase transformations in glass-forming alloys. The glass transition is introduced as a structural relaxation, and the competition between the glass and crystalline phases is investigated. The simulations are performed for Cu-Zr alloys, employing thermodynamic and kinetic parameters derived from reported thermodynamic modeling and molecular dynamics simulation results,[1?C3] respectively. Four distinct phase fields are treated with a multi-phase-field approach, representing the liquid/glass, Cu₁₀Zr₇, CuZr, and CuZr₂ phases. In addition, a continuum-field method is applied to the liquid to accommodate the liquid?Cglass transformation. The combined phase-field approach is used to investigate the glass formation tendency, and critical cooling rates are estimated and compared with the reported experimental values.     

Phase equilibria calculation of LaI3-MI （M=Na, K, Cs） binary systems

The Gibbs energies of liquid phases in the LaI3-MI (M=Na, K, Cs) systems were described by the modified quasi-chemical model. From the measured phase equilibrium data of these binary systems, a set of thermodynamic functions were optimized by using the CAL-PHAD technique. The enthalpy of mixing and the interaction parameter of the liquid phase were predicted from known data for the LaI3-MI systems.     

FeS-PbS和PbS-ZnS二元系的热力学优化

采用ＲｅｄｌｉｃｈＫｉｓｔｅｒ多项式描述体系液相的过剩自由焓,根据试验相图和已知的热力学数据优化得到了ＦｅＳＰｂＳ和ＰｂＳＺｎＳ二元系的热力学参数。用优化结果计算的相图与试验测量值吻合较好。     

The Fe-Cu system: A thermodynamic evaluation

Thermochemical and phase diagram data in the Fe-Cu system have been critically evaluated by using phenomenological models for the Gibbs energy of various phases. A set of thermodynamic parameters more consistent with most of the selected experimental data than previous assess-ments has been obtained by a computerized least-squares method. Stable and metastable phase equilibria,T ₀ curves, and thermodynamic properties are calculated with the optimized param-eters. The calculated liquid/face-centered cubic (fcc)T ₀ curve and metastable liquid spinodal seem to permit an accurate prediction of maximum solid solubility obtained upon melt quenching in this system.     

Thermodynamic analysis of the dominant phase equilibria in <Emphasis Type="Italic">M</Emphasis>(Si,Cr, Al)-O-C systems

Various approaches are proposed for developing thermodynamic models of dominant phase equilibria. It is noted that, as a thermodynamic analysis of the phase equilibria in M(Si, Cr, Al)-O-C systems is performed, the equilibrium concentrations and the stability of the phases should be calculated by minimizing the Gibbs energy for the systems at a given temperature and pressure.     

A thermodynamic evaluation of the Cr-Mn and Fe-Cr-Mn systems

A thermodynamic evaluation of the Cr-Mn and Fe-Cr-Mn systems has been made by using thermodynamic models for the Gibbs energy of the individual phases. An optimized set of thermodynamic parameters was obtained taking into consideration related experimental information. The thermodynamic parameters of the Cr-Mn and Fe-Cr-Mn systems and comparisons between calculation and experimental data are presented.