Thermodynamic database of the phase diagrams in Cu-Fe base ternary systems

A thermodynamic database of the Cu-Fe-X [X: aluminum (Al), cobalt (Co), chromium (Cr), manganese (Mn), molybdenum (Mo), niobium (Nb), nickel (Ni), vanadium (V)] systems was developed by the CALPHAD (Calculation of Phase Diagrams) method, where the Gibbs energies of solution phases such as the liquid, face-centered-cubic (fcc), body-centered-cubic (bcc), and hexagonal-close-packed (hcp) phases are described by the subregular solution model, while the those of the bcc phase in the Cu-Fe-Al system and of all compounds are described by the sublattice model. The thermodynamic parameters describing Gibbs energies of the different phases in this database were evaluated by fitting the experimental data for phase equilibria and thermodynamic properties. On the basis of this database, much information concerning stable and metastable phase equilibria of isothermal and vertical sections, molar fractions of constituent phases, the liquidus projection, etc., can be predicted. This database is expected to play an important role in the design of Cu-Fe base alloys.     

Thermodynamic evaluation of the Al-H system

The thermodynamic properties of the Al-H system were assessed using models for the Gibbs energy of the individual phases, including the metastable hydride AlH₃ phase. The model parameters were obtained through optimization by best fitting to selected experimental data. Particular attention was paid to hydrogen solubility in liquid and face-centered-cubic (fcc) Al. It was shown that the hydrogen can be treated as an ideal gas under normal conditions. The hydrogen solubility in liquid and fcc Al can be described very well with a regular solution model for liquid and fcc. The present calculations show satisfactory agreement with most experimental data for hydrogen solubility in fcc Al and selected data for hydrogen solubility in liquid Al, qualifying the extension of this binary model to higher-order Al-H-bearing systems.     

Direct evidence of magnetically induced phase separation in the fcc phase and thermodynamic calculations of phase equilibria of the Co–Cr system

Two-phase equilibria between the ferromagnetic fcc and the paramagnetic fcc phase from 800 to 900 °C in the Co-rich region was determined using the diffusion couple technique. It was confirmed that a magnetically-induced miscibility gap of the fcc phase is formed along the Curie temperature.Thermodynamic calculation of the phase equilibria of the Co–Cr system was performed by optimizing the present results and the thermodynamic data in the literature. A set of thermodynamic values for describing the Gibbs energy of liquid, fcc hcp, bcc and sigma phases yielded good agreement between the calculated phase diagram and the experimental data. Moreover, the magnetically-induced miscibility gap between the ferromagnetic and paramagnetic hcp phases was also predicted. This kind of thermodynamic calculation of Co–Cr base alloys is quite useful for the alloy design of the magnetic recording media.     

A thermodynamic analysis of the Al-Re system

Phase equilibria and thermodynamic data of the Al-Re system are critically reviewed. In addition to the three solution phases, liquid, fcc Al, and hcp Re, there exist six intermetallic compounds in this binary. The thermodynamic properties of the system are analyzed using thermodynamic models for the Gibbs energy of individual phases of the system. A regular solution model is used for the three substitutional solution phases, and the intermetallic phases are treated as stoichiometric compounds. The model parameters are optimized from a limited amount of experimental data. The calculated phase diagram and thermodynamic values are in accord with the available experimental values.     

Thermodynamic assessment of the Ga–Pt system

The Ga–Pt binary system has been thermodynamically assessed by means of the computer program Thermo-Calc. The Redlich-Kister polynomial was used to describe the solution phases, liquid (L) and fcc (Pt). The compounds, Ga₆Pt, Ga₇Pt₃, Ga₂Pt, Ga₃Pt₂, GaPt, Ga₃Pt₅ and GaPt₂, were treated as stoichiometric phases. The sublattice-compound energy model was employed to describe the compound GaPt₃, with a homogeneity range. 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 Ga–Pt system has been obtained. The calculations agree well with the respective experimental data.     

Development of a diffusion mobility database for Ni-base superalloys

For the fcc phase of the Ni–Al–Co–Cr–Hf–Mo–Re–Ta–Ti–W system, diffusion data in various constituent binary systems were assessed to establish a multicomponent diffusion mobility database. The diffusion assessment relied on an existing thermodynamic database for the calculation of needed thermodynamic factors. The mobilities determined for the self-diffusion of the components in the fcc phase (a metastable state for some components) were consistent with the correlation of the diffusivity with the melting point. The general agreement of calculated and measured diffusion coefficients in the Ni–Co–Cr–Mo and Ni–Al–Cr–Mo quaternary systems demonstrated the ability of the database to extrapolate to higher order systems. Finally, the mobility database, in conjunction with an available thermodynamic database and a finite-difference diffusion code, was used to simulate a multicomponent diffusion couple between two commercial Ni-base superalloys.     

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.     

The thermodynamic properties of calcium intermetallic compounds

The thermodynamic properties of calcium alloys have been measured by emf (an original pin-point method) and calorimetry in recent years. A review of experimental results obtained for 15 binary (Ca,M) systems is presented (with M Ni, Pd, Pt, Cu, Ag, Au, Mg, Al, Ga, Si, Ge, Sn, Pb, Sb, Bi), and numerical optimization is performed for some of them. Application to the ternary (Ca,Sn,Pb) system of industrial interest, allowed calculation of the phase diagram for x(Ca) 0.25.     

A comparative study of metastable alloy formation by ion mixing and thermal annealing of multilayers in the immiscible Y–Zr system

Amorphous alloys were formed in an immiscible Y–Zr system by ion mixing and thermal annealing of multilayered films consisting of nine alternate metal layers. In addition, two metastable crystalline phases, i.e. a fcc Zr-rich and a fcc Y-rich phase, were also obtained. A compatible thermodynamic interpretation was proposed and illustrated by a Gibbs free energy diagram, which was constructed based on Miedema's model and included the free energy curve of the multilayered films possessing excess interfacial energy. The formation mechanism of the metastable crystalline phase is also discussed in terms of the electronic structure as well as the growth kinetics.     

Thermodynamic assessment of the Ni-Sb binary system

The Ni-Sb binary alloy system was thermodynamically assessed using CALPHAD approach in this article.Excess Gibbs energies of solution phases,liquid and fcc phases,were formulated using the Redlich-Kister expression.The intermediate phases were modeled by the sublattice model with (Ni,Va)0.5(Ni,Sb)0.25(Ni)0.25 for Ni3Sb_HT phase and (Ni,Va)0.3333(Sb)0.3333(Ni,Va)0.3333 for NiSb phase.The other phases including Ni3Sb,Ni7Sb3,and NiSb2 were treated as stoichiometric compound owing to their narrow composition ranges.Based on the reported thermodynamic properties and phase diagram data,the thermodynamic parameters of these phases were optimized,and the obtained values can reproduce the available experimental data well.     

热力学优化Bi-Ni二元系

基于文献报导的实验数据,采用相图计算（CALPHAD）方法,热力学优化了Bi-Ni二元系相图。该二元系的液相、fcc_A1（Ni）相和rhombohedral_A7（Bi）相用替换溶液模型来描述,其过剩吉布斯自由能用Redlich-Kister多项式来表达。考虑到晶体结构（NiAs型）以及与多组元体系热力学数据库的兼容性,中间化合物BiNi相采用亚点阵模型：（Bi）（Ni,Va）（Ni,Va）;Bi3Ni相处理为化学计量比化合物。最后,通过优化该二元系实测的相图和热力学数据,获得一组能够表达各相吉布斯自由能的自洽的热力学参数。根据这些热力学参数计算的相图和热力学数据与报导的实验数据吻合良好。     

Interface thermodynamics of nano-sized crystalline,amorphous and liquid metallic systems

Expressions for the Gibbs energies of interfaces occurring in particular for solid and/or liquid/amorphous metals or alloys in contact with each other have been developed. To consider its energetics, an amorphous alloy has been modelled as a mixture of the undercooled liquid metal components near to the glass transition temperature making use of the enthalpy of melting, the entropy of melting and the temperature-dependent contribution of the heat capacity of the undercooled melt. Gibbs surface and interface energies have been obtained on the basis of the “macroscopic atom” Miedema model, where the entropy contributions of alloys have been derived applying a recently developed formalism. The Gibbs energy of a crystalline interface phase has been formulated. The molar fractions of the components of the alloy at the surfaces have been determined by minimising the surface energy. These results provide a thermodynamic basis for unusual phenomena observed in nano-sized systems. The formalism has been applied to calculate the thermodynamic stability of interface phases in a nano-sized, multi-layered system of iron and zirconium and to explain the aluminium-induced crystallisation of amorphous silicon and the layer exchange occurring in bi-layers of crystalline aluminium and amorphous silicon.     

Thermodynamic assessment of the Al–Pd system

The Al–Pd binary system has been thermodynamically assessed by means of the computer program Thermo-Calc. The Redlich–Kister polynomial was used to describe the solution phases, liquid (L) and fcc. The sublattice-compound energy model was employed to describe the intermetallic compounds with homogeneity ranges, (AlPd), (AlPd₂), (Al₃Pd₂) and (Al₂Pd₅). The intermetallic compounds with no homogeneity ranges, Al₃Pd, Al₂₁Pd₈, Al₄Pd and Al₃Pd₅, were treated as stoichiometric phases. The parameters of the Gibbs energy expressions were optimized according to all the available experimental information on both the equilibrium data and the thermodynamic results. A set of self-consistent thermodynamic parameters of the Al–Pd system has been obtained. The calculations agree well with the respective experimental data.     

Thermodynamic Database and the Phase Diagrams of the (U,Th, Pu)-X Binary Systems

A thermodynamic database for nuclear materials, including U-Th, U-Pu, Th-Pu, and (U, Th, Pu)-X (X = Al, Co, Cr, Cu, Fe, Ga, Mg, Mn, Mo, Nb, Ni, Si, Ta, W, Zr) binary system has been developed by the Calculation of Phase Diagrams (CALPHAD) method. Thermodynamic parameters describing Gibbs free energies of different phases have been evaluated by optimizing experimental data on phase equilibria and thermodynamic properties. The present thermodynamic database can provide much-needed information such as stable and metastable phase equilibria, phase fractions, and various thermodynamic quantities that is important to the design of nuclear materials. This database is also an essential starting point to construct thermodynamic databases for the multicomponent systems.     

Modeling of phase stability of the fcc phases in the Ni–Ir–Al system using the cluster/site approximation method coupling with first-principles calculations

A combined CSA (cluster/site approximation)/FP (first-principles) calculation approach was employed to investigate the phase stability and thermodynamic properties of the face-centered cubic (fcc) phases of the Ni–Ir–Al system. For the constituent binaries of the Ni–Ir–Al system, enthalpies of formation of the Ni_xIr_1−x, Ni_xAl_1−x and Ir_xAl_1−x fcc compounds were calculated by first-principles approach at x = 0.75, 0.5 and 0.25 at 0 K, respectively. The pair exchange energies of the Ni–Ir and Al–Ir systems in the CSA model were obtained from FP calculated enthalpies of formation, while those for the Ni–Al binary were adopted from previous work. Thermodynamic model parameters of the fcc phases for the Ni–Ir–Al ternary system were then obtained from the constituent binaries via extrapolation. The calculated isothermal section at 1573 K is in good agreement with the experimental data within the uncertainties of the calculations and experiments.     

Thermodynamic modeling of the Ag–Sr system

The CALPHAD method was employed to model thermodynamic properties of the Ag–Sr system. The liquid phase was treated as a substitutional model (Ag,Sr), with the excess molar Gibbs free energy expressed by the Redlich–Kister formula. All the intermetallic phases were modeled as stochiometric compounds. The solubilities of Ag and Sr in the terminal solid phases were not considered due to their negligible values. Calculated results were then compared with available data from existing literatures. A set of self-consistent thermodynamic parameters of the Ag–Sr binary system was obtained.     

A pseudo-front tracking technique for the modelling of solidification microstructures in multi-component alloys

A two-dimensional model for the simulation of microstructure formation during solidification in multi-component systems has been developed. The model is based on a new pseudo-front tracking technique for the calculation of the evolution of interfaces that are governed by solute diffusion and the Gibbs–Thomson effect. The diffusion equations are solved in the primary solid phase and in the liquid using an explicit finite volume method formulated for a regular hexagonal grid. Volume elements located in the liquid phase undergo a transition to interfacial (or mushy) cells before being incorporated in the solid phase. This layer of interfacial elements, which always separates the solid from the liquid sub-domains, permits to handle the displacement of the interface in agreement with the flux condition at the interface. The interface curvature is obtained from the field of the signed distance to the interface, as reconstructed with a PLIC (piecewise linear interface calculation) technique. The concentrations at the solid–liquid interface are calculated using thermodynamic data provided by the phase diagram software Thermo-Calc [Sundman et al. CALPHAD 1987;9:153]. Different coupling strategies between the microstructure model and Thermo-Calc have been developed, in particular a computationally-efficient direct coupling using the TQ-interface of Thermo-Calc.After testing the accuracy of the model with respect to curvature calculation, comparisons are made with predictions obtained with the marginal stability theory, a one-dimensional front-tracking method and two-dimensional phase-field simulations of dendritic growth in binary alloys. The model is then used to describe the formation of several grains in an Al–1%Mg–1%Si alloy, as a function of the heat extraction rate and inoculation conditions. It is shown that the model is capable of reproducing the transition between globular and dendritic morphologies.