Thermodynamic assessment of the Ni–Co–Cr system and Diffusion Study of its fcc phase

In the present work, the liquidus and solidus for a series of Ni_xCo_1-2xCr_x alloys were measured by means of differential scanning calorimetry, and the first-principles calculations were performed to obtain total energies for all solid solutions and end-members of the intermediate phases in the Ni–Co–Cr ternary system. Various types of data from the present work and the literature were used in the assessments of the Ni–Co–Cr ternary system and sub-binary systems by the CALPHAD method, and were well reproduced by the present thermodynamic database. In addition, diffusion couples of fcc Co–Cr and Ni–Co–Cr alloys were assembled and annealed at different temperatures to extract interdiffusion coefficients. Experimental diffusion data from the present work and the literature, in conjunction with thermodynamic parameters, were adopted to assess the atomic mobilities of the fcc phase in the Ni–Co–Cr system. The calculated and experimental diffusion coefficients reach a satisfactory agreement. The diffusional kinetic database developed was further validated by appropriate predictions of composition profiles and diffusion paths.     

Thermodynamic optimization of the Ni–Al–Nd ternary system

Thermodynamic optimization of the Ni-Al-Nd ternary system and Al-Nd binary systems have been conducted in the present work. A self-consistent set of thermodynamic parameters for the Al-Nd binary system and Ni-Al-Nd ternary system have been optimized using CALPHAD method. Isothermal sections at 600 and 700 °C as well as the liquidus projection have been reproduced. Isopleths with 93 at% Al, 9 at% Ni and 3 at% Nd, have been calculated also. The calculated thermodynamic and phase equilibria data for both the binary and the ternary systems agree fairly well with the experimental data. This work can be used as multi-component thermodynamic database for Ni-based alloys.     

A critical thermodynamic assessment of the Mg–Ni, Ni–Y binary and Mg–Ni–Y ternary systems

A thorough review and critical evaluation of phase equilibria and thermodynamic data for the phases in the Mg–Ni–Y ternary system have been carried out over the entire composition range from room temperature to above the liquidus. This system is being modeled for the first time using the modified quasichemical model which considers the presence of short range ordering in the liquid. The Gibbs energies of the different phases have been modeled, and optimized model parameters that reproduce all the experimental data simultaneously within experimental error limits have been obtained. For the liquid phases, the modified quasichemical model is applied. A sublattice model within the compound-energy formalism is used to take proper account of the structures of the binary intermediate solid solutions. The Mg–Ni and Ni–Y binary systems have been re-optimized based on the experimental phase equilibrium and thermodynamic data available in the literature. The optimized thermodynamic parameters for the Mg–Y system are taken from the previous thermodynamic assessment of the Mg–Cu–Y system by the same authors. The constructed database has been used to calculate liquidus projection, isothermal and vertical sections which are compared with the available experimental information on this system. The current calculations are in a good agreement with the experimental data reported in the literature.     

Experimental study and thermodynamic calculation of the Y–Co–Fe system

In this work, the phase equilibria of the Y–Co–Fe ternary system were studied experimentally by scanning electron microscope (SEM) with energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD). The phase transition temperatures and phase formation of Y–Co–Fe alloys were examined by differential thermal analysis (DTA) and SEM-EDS. No ternary intermetallic compounds were detected. The continuous solid solution phases Y₂(Co, Fe)₁₇, Y(Co, Fe)₃ and Y(Co, Fe)₂ were formed from the respective Y–Co and Y–Fe binary intermetallic compounds. The solubility of Fe in YCo₅ and Y₂Co₇ and the solubility of Co in Y₆Fe₂₃ were determined. Based on the experimental results determined in this work and reported in the literature, the thermodynamic calculation of the Y–Co–Fe ternary system was performed using the CALPHAD method in combination with the previous assessments of three Y–Co, Y–Fe and Co–Fe binary systems. The liquidus projection, isothermal sections and vertical sections of this ternary system were calculated. The good agreement between the calculated results and the experimental results was achieved. A set of self-consistent thermodynamic parameters for describing various phases in the Y–Co–Fe ternary systems was obtained finally, which would provide a good basis for the development of the thermodynamic database of multi-component Y–Co–Fe based alloy systems.     

The phase equilibria of the Cu–Cr–Ni and Cu–Cr–Ag systems: Experimental investigation and thermodynamic modeling

The phase equilibria of the Cu–Cr–Ni and Cu–Cr–Ag systems were investigated by a combination of key experiments and thermodynamic modeling. Eleven and fourteen ternary alloys were prepared to determine the isothermal sections of the Cu–Cr–Ni system at 800 and 1000 °C, and the Cu–Cr–Ag system at 500, 600, 650 and 700 °C, respectively, by means of X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDX). The three- and two-phase regions were determined. The solubility of the third elements in the phases of the binary systems was measured. No ternary compound was found in these two ternary systems. Based on the experimental equilibria data from the literature and the present work, a thermodynamic modeling of the Cu–Cr–Ni and Cu–Cr–Ag systems was performed by the CALPHAD (CALculation of PHAse Diagrams) method. The substitutional solution model was used to describe the solution phases. A set of self-consistent thermodynamic parameters of the Cu–Cr–Ni and Cu–Cr–Ag systems was obtained. Most of the reliable experimental data can be well reproduced by the present thermodynamic modeling.     

Predictions of the Al-rich region of the Al–Co–Ni–Y system based upon first-principles and experimental data

A thermodynamic database has been produced for the Al–Co–Ni–Y quaternary system, with an emphasis on the Al-rich region of the Al–Ni–Y ternary system. The database was created using the CALPHAD method, combining existing binary systems with relevant experimental and first-principles information for selected Al–Ni–Y and Co-containing compounds. The thermodynamic database was used to produce equilibrium and non-equilibrium Scheil simulations to determine the phases present in Al–Co–Ni–Y alloys. The values for the Scheil simulation show good agreement, when compared with experimentally determined phase fractions of intermetallic particles dispersed in an Al matrix for three Al-rich quaternary alloys.     

Polynomial regression and interpolation of thermodynamic data in Al–Si–Mg–Fe system

A numerical technique for constructing thermodynamic databases has been proposed. This technique offers accurate calculations of solidification temperature, phase fractions, and solute concentrations of specific alloys in quaternary systems. The thermodynamic data is extracted by calling the TQ-interface (Thermodynamic Calculation Interface) from Thermo-Calc software, and modeled through efficient computational approaches such as polynomial regression and interpolation. This method is described in three parts. First, the applicability of regression functions is demonstrated on the Al–Si binary phase diagram. Second, the way of combining polynomial regression and interpolation is applied to model the Al–Si–Mg ternary system. Finally, the A356 alloy, which belongs to the Al–Si–Mg–Fe system, is modeled by a series of sub-ternary systems using regression and interpolation. The valid accuracy of the method is demonstrated by comparing the present results with those calculated using Thermo-Calc software. The application of the TQ-interface to solidification processes in Scheil and lever-rule models is also included. The results indicate that this method can offer accurate thermodynamic parameters for the A356 alloy in Al–Si–Mg–Fe system and reduce CPU time significantly when applied to solidification simulation. Several problems and the corresponding strategies for high order functions, unsmooth variations of thermodynamic information and partition coefficients are discussed to improve this method. This technique can also be applied to other specific alloys with small variations of thermodynamic variables in quaternary systems.     

Experimental investigations and thermodynamic modelling of the Cr–Nb–Sn–Zr system

This work reports the Calphad modelling of the Cr–Nb–Sn–Zr quaternary system. In a previous paper, the thermodynamic modelling of the Cr–Nb–Sn system was presented. Since no experimental data were available for the Cr–Sn–Zr ternary system, new experimental data are provided, within this study, on the isothermal section at 900 °C. A ternary C14 phase has been identified on the Sn-poor side of the phase diagram. In addition to these experimental data, Density Functional Theory (DFT) calculations are carried out in order to determine formation enthalpies of the stable and metastable compounds. At last, the Special Quasirandom Structures (SQS) method is jointly used with DFT calculations in order to estimate the mixing enthalpies of the A2 and A3 binary solid solutions. Finally, these experimental and calculated data in addition to those from the literature, are used as input data for the Calphad modelling of the Cr–Zr, Nb–Zr and Sn–Zr binary systems and the Cr–Nb–Zr, Cr–Sn–Zr and Nb–Sn–Zr ternary systems. A complete database for the Cr–Nb–Sn–Zr quaternary system is provided.     

Experimental study and thermodynamic assessment of the Cu–Ni–Ti system

The Cu–Ni–Ti ternary system has been systematically investigated combining experimental measurements with thermodynamic modeling. With selected equilibrated alloys, the equilibrium phase relations in the Cu–Ni–Ti system at 850 °C were obtained by means of SEM/EDS (Scanning Electron Microscopy/Energy Dispersive Spectrum), EPMA (Electron Probe Micro-Analysis) and XRD (X-ray Diffractometry). Phase transformation temperatures were measured by DSC (Differential Scanning Calorimetry) analysis in order to construct various vertical sections in the Cu–Ni–Ti system. The liquidus projection of the ternary system was determined by the identifying primary crystallization phases in the as-cast alloys and from the liquidus temperatures obtained from the DSC analyses. Based on the available data of the binary systems Cu–Ni, Cu–Ti, Ni–Ti and the ternary system Cu–Ni–Ti from the literature and the present work, thermodynamic modeling of the Cu–Ni–Ti ternary system was performed using the CALculation of PHAse Diagram (CALPHAD) approach. A new set of self-consistent thermodynamic parameters for the Cu–Ni–Ti ternary system was obtained with an overall good agreement between experimental and calculated results.     

An overview on phase equilibria and thermodynamic modeling in multicomponent Al alloys: Focusing on the Al-Cu-Fe-Mg-Mn-Ni-Si-Zn system

Knowledge of thermodynamics and phase diagram is a prerequisite for understanding many scientific and technological disciplines. To establish a reliable thermodynamic database, an integrated approach of key experiments and thermodynamic modeling, supplemented with first-principles calculations, can be utilized. In this paper, first investigations of phase diagram and thermodynamics of technologically important Al alloys (focusing on the Al-Cu-Fe-Mg-Mn-Ni-Si-Zn system, which covers the major elements in most commercial Al alloys) is reviewed with an emphasis on the need of the integrated approach. Second, the major experimental methods (X-ray diffraction, metallography, electron probe microanalysis, differential thermal analysis, diffusion couple method, and calorimetry), which are widely employed to provide phase diagram and thermodynamic data, are briefly described. Third, the basics of the first-principles calculations and CALPHAD are presented focusing on the integration of these two computational approaches. Case study for the representative Al-Fe-Ni ternary system is then demonstrated, followed by a thermodynamic modeling of the quinary Al-Fe-Mg-Mn-Si system and a brief summary to our recent activities on investigations of phase equilibria in multicomponent Al alloys.