Experimental study and thermodynamic modeling of the Cu–Sn–Si–O system and sub-systems

Phase equilibria between slag, Cu–Sn alloy and solid oxide phases, SnO₂ (cassiterite) or SiO₂ (tridymite, cristobalite) are important for oxidizing fire refining of black copper produced during the recycling of copper scrap and waste electrical and electronic equipment. Integrated experimental and thermodynamic modeling study is presented for the Cu–Sn–Si–O chemical system and its sub-systems. Experimental technique involved high-temperature equilibration, followed by rapid quenching and direct measurement of Cu, Sn and Si concentrations in the liquid and solid phases using the electron probe X-ray microanalysis. Experimental results and literature data have been used to develop the thermodynamic database for the system. The database works within the environment of FactSage software, as well as ChemApp, ChemSheet and SimuSage. Combined with other assessments, it can be used to optimize and develop recycling processes using the black copper route.     

Critical evaluation and thermodynamic modeling of the Fe–P and Fe–C–P system

Phosphorus is known to be a strongly segregating element in steel; even small amounts influence the solidification phenomena and product quality during casting processes. In order to provide an accurate prediction tool for process control in steelmaking, a CALPHAD-type thermodynamic optimization of the Fe–C–P system was performed including modeling of the binary Fe–P subsystem. The liquid phase was modeled using the Modified Quasichemical Model (MQM) in the pair approximation, which generally yields better results for strong short-range ordering (SRO) tendency in the solution. The solid bcc and fcc solutions were described using the Compound Energy Formalism (CEF). In addition, ab-initio calculations were performed to estimate the enthalpies of formation of the corresponding end-member for fcc and bcc, respectively. The phosphides Fe₃P, Fe₂P and FeP were treated as stoichiometric compounds. Higher order phosphides were not considered, since there is no reliable experimental information available in literature. The present model successfully reproduces most of the literature data within the experimental uncertainty in the Fe–C–P system without introducing a ternary parameter for the liquid phase. Compared with previous thermodynamic assessments, the agreement with recently published thermal analysis measurements of Fe–P and Fe–C–P alloys is significantly improved.     

Experimental investigation and thermodynamic modeling of the Al–Cu–Si system

16 ternary alloys located over the entire composition range of the Al–Cu–Si system are investigated by means of XRD, SEM/EDX and DTA. The phase equilibria associated with the kappa phase of the Cu–Si system are determined in detail and the isothermal sections at 600 and 500 ^°C are experimentally constructed. No ternary phase is observed at 600 or 500 ^°C. A thorough thermodynamic modeling for this system is then conducted based on the critically reassessed literature data and the present experimental results.     

A thermodynamic modeling of the Cu–Pd system

The phase equilibria and thermodynamic properties of the Cu–Pd system are optimized using the CALPHAD (CALculation of PHAse Diagram) technique. In the present work, the liquid and face-centered cubic (fcc) solution phases are modeled with the substitutional solution model. A two-sublattice model (Cu,Pd)_0.75(Cu,Pd)_0.25 is applied to describe the ordered Cu₃Pd phase, the one-dimensional long-period superlattice (1D-LPS) and two-dimensional long-period superlattice (2D-LPS) structures, in order to cope with the order–disorder transition between three intermetallic compounds (Cu₃Pd, 1D-LPS and 2D-LPS) and fcc solution (A1) in the Cu–Pd system. A two-sublattice model (Cu, Pd)(Cu, Pd) is used to describe the homogeneity range of CuPd phase. A set of self-consistent thermodynamic parameters is obtained and the calculated phase diagram and thermodynamic properties are presented and compared with the experimental data.     

Critical evaluation and thermodynamic optimization of the V–O system

The V–O system has been critically evaluated and thermodynamically assessed based on the available phase diagram and thermodynamic data using the CALPHAD method. The liquid phase over the whole composition range from metallic liquid to oxide melt is described by the modified quasichemical model with five species: V^II, V^III, V^IV, V^V and O, which takes short-range ordering in liquid solution into account. All solid solutions are modeled considering respective crystal structures. A set of self-consistent thermodynamic parameters of the V–O system is obtained and the available experimental data are reproduced well within experimental error limits. Especially for the VO_x solid solution, the site fractions of vacancies in both vanadium and oxygen sublattices are reproduced well using the present model and parameters.     

Experimental investigation and thermodynamic modeling of the Cr–Zr–Si system

The phase equilibria of the Cr–Zr–Si ternary system were studied combined with the key experiments and thermodynamic assessment. Thirty-five ternary alloys were prepared to determine the isothermal sections at 900 and 1000 °C by means of X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDS). Five ternary compounds, i.e., τ₁ (CrSi₂Zr), τ₂ (Cr₄Si₅Zr₂), τ₃ (Cr₄Si₇Zr₄), τ₄ (CrSiZr) and τ₅ (Cr₃SiZr₂), were confirmed. The solubilities of the third element in binary compounds were determined. Based on the experimental phase equilibria data available in the present work and the literature, as well as the thermodynamic parameters of constitutive binary systems, the Cr–Zr–Si system was evaluated by using the CALPHAD (CALculation of PHAse Diagram) method. A set of self-consistent thermodynamic parameters was obtained. Three isothermal sections and liquidus projection were calculated and the reaction scheme was constructed. The calculated results are in agreement with the experimental data.     

Experimental investigation and thermodynamic modeling of the Fe−Si−Zr system

The Fe−Si−Zr alloys have attracted considerable interests in recent decades. It is important to study this ternary phase diagram for experimental design. In this paper, the Fe−Si−Zr ternary system is investigated by combining the experiments and thermodynamic calculations. Liquidus surface projection of the Fe−Si−Zr system is characterised using X-ray powder diffraction (XRD), scanning electron microscopy (SEM) with energy dispersive spectrometer (EDS) and differential thermal analysis (DTA). The liquidus projection of this ternary system is constructed by identifying primary crystallization phases and invariant reaction temperatures in the as-cast alloys. Eleven different primary solidification regions are observed. Based on the experimental results of this work and the data from the previous work in the literature, the thermodynamic calculation of the Fe−Si−Zr system is performed using CALPHAD (CALculation of PHAse Diagrams) technique. A set of self-consistent thermodynamic parameters of the Fe−Si−Zr system is obtained. The calculated results are in good agreement with the experimental data. This study provides a set of reliable thermodynamic parameters to the Fe-based thermodynamic database, and a cost-effective tool to design experiments and manufacturing processes.     

Experimental investigation and thermodynamic modeling of the Cu–Mn–Ni system

The phase equilibria of the ternary Cu–Mn–Ni system in the region above 40 at.% Mn at 600 ^°C were investigated by means of optical microscopy, X-ray diffraction, scanning electron microscopy with energy dispersive X-ray spectroscopy and electron probe microanalysis. The isothermal section of the Cu–Mn–Ni system at 600 ^°C consists of 4 two-phase regions (cbcc_A12 +fcc_A1, cub_A13 +fcc_A1, cbcc_A12 + cub_A13, L₁₀$L{1}_0$ +fcc_A1) and 1 three-phase region (cbcc_A12 +cub_A13 +fcc_A1). The disordered fcc_A1 phase exhibits a large continuous solution between γ$\gamma$(Cu,Ni) and γ$\gamma$(Mn). The L₁₀$L{1}_0$ phase only equilibrates with fcc_A1 phase, and the solubility of Cu in L₁₀$L{1}_0$ phase is up to 16 at.%. A thermodynamic modeling for this system was performed by considering reliable literature data and incorporating the current experimental results. A self-consistent set of thermodynamic parameters was obtained, and the calculated results show a general agreement with the experimental data.     

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.     

Experimental investigation and thermodynamic calculation of the Fe–Si–Sn system

Phase equilibrium of the Fe–Si–Sn ternary system was investigated using equilibrated alloys. The samples were characterized by means of scanning electron microscopy equipped with energy dispersive X–ray spectrometry and X–ray diffraction. Isothermal sections of the Fe–Si–Sn system at 700 °C and 890 °C each consists of 5 three–phase regions. No ternary compound was found at those two temperatures. The solubility of Sn in the Fe–Si binary phases and the solubility of Si in the Fe–Sn binary phases is limited. Furthermore, thermodynamic extrapolation of the Fe–Si–Sn system was carried out. Calculated solidification path and phase relationship agreed well with experimental results.     

Experimental investigation and thermodynamic calculation of the Fe–Si–Bi system

Phase relationship of the Fe–Si–Bi ternary system was established by optical microscope, scanning electron microscope in combination with energy dispersive spectroscopy and X–ray diffraction. Isothermal sections of the Fe–Si–Bi system at 973 and 1173 K consist of 3 and 4 three–phase equilibrium regions, respectively. The liquid phase is in equilibrium with all the Fe–Si phases. No ternary compound is found and Bi is almost insoluble in the Fe–Si phases. Combining the reliable thermodynamic data from literature with the current experimental work, phase relationship of the Fe–Si–Bi system have been thermodynamically extrapolated. The calculated results are in good agreement with the experimental results.     

Experimental investigation and thermodynamic reassessment of the Fe–Si–Zn system

Based on the critical evaluation of the experimental data available in the literature, the isothermal section of the Fe–Si–Zn system at 873 K was measured using a combination of X-ray analysis and scanning electron microscopy with energy-dispersive X-ray analysis. No ternary phase is observed at 873 K. A thermodynamic modeling for the Fe–Si–Zn system was then conducted by considering the reliable experimental data from the literature and the present work. All the calculated phase equilibria agree well with the experimental ones. It is noteworthy that a stable liquid miscibility gap appears in the computed ternary phase diagrams although it is metastable in the three boundary binaries.     

Experimental measurements and thermodynamic modeling of the Ce–Co–Fe ternary system

The experimental determinations of the isothermal section at 823 K and the supplementary measurements of the liquidus projection of the Ce-Co-Fe ternary system were presented in the present study. In the Ce-Co-Fe ternary system, in consideration of the temperature dependent solubilities of the linear phases such as Ce₂(Co,Fe)₁₇ and Ce(Co,Fe)₂, as well as the specific locations of the univariant lines between each two primary solidification surfaces, it is necessary to study more than one isothermal section and some particular as-cast alloys to construct the phase equilibria in the temperature-composition space of the Ce-Co-Fe system. The samples for determining the liquidus projection were prepared by arc-melting method under high purity argon atmosphere in a water-cooled copper hearth, and then those for measuring the isothermal section at 823 K were isothermally treated and quenched in ice water. The microstructures and the phase compositions of samples were measured by means of scanning electron microscopy (SEM), X-ray diffraction (XRD) and electron probe micro-analyzer (EPMA). Some primary solidification regions and univariant lines of the Ce-Co-Fe ternary system were complementally determined, and the reasonability of the liquidus projection reported in previous literature was further confirmed. The phase equilibrium relations at 823 K were determined, including two-phase and three-phase equilibria. No ternary compounds were discovered in the present study. Based on the experimental results of both the previous literature reports (the reported liquidus projection and isothermal sections at 723 and 1173 K) and the present experimental study, the Ce-Co-Fe ternary system was thermodynamically assessed using the CALPHAD method. The isothermal sections, the vertical sections and the liquidus projection were calculated using the present optimized thermodynamic parameters, and a reasonable agreement between the calculated results and the experimental data was obtained.     

Experimental investigation and thermodynamic modeling of the Mg–Cu–Ca ternary system

The isothermal section in the Mg–Cu rich region of Mg–Cu–Ca ternary system at 300 °C was investigated in the present work. Two ternary compounds named as P1 and Mg_25-xCu₇₅Ca_x were observed. The solid solubility limit of the compound Mg_25-xCu₇₅Ca_x was found to be 8.29 ≤ x_Ca ≤ 15.71 with a constant value of about 75 at. % Cu at 300 °C. A narrow solid homogeneity range of the compound P1 was found to be Mg₁₉Cu₄₀Ca₄₁ to Mg₂₁Cu₄₂Ca₃₇ (in at. %). The maximum solid solubility of Ca in the terminal compound MgCu₂ (C15) was determined to be 10.20 at. % at 300 °C. The maximum ternary solid solubility of binary terminal compounds Mg₂Ca, Mg₂Cu, Cu₅Ca and CuCa were determined to be less than 2 at. %. For the more, thermodynamic modeling of the Cu–Ca binary and Mg–Cu–Ca ternary systems have been carried out by calculation of phase diagram (CALPHAD) method. The liquid solution was described using the modified quasi-chemical model (MQM). The compound energy formalism (CEF) was used for the solid phases. A self-consistent thermodynamic database of the Mg–Cu–Ca ternary system have been constructed in the present work.     

Thermodynamic assessment and database for the Cu–Fe–O–S system

The previously obtained thermodynamic databases for the Cu–Fe–S, Cu–Fe–O, Fe–O–S and Cu–O–S ternary systems have been combined and used to predict thermodynamic equilibria in the quaternary Cu–Fe–O–S system. The available experimental data were compared with model predictions. Minor modifications of model parameters were required to better describe the experimental points in the quaternary system; the effect of these changes was verified in the ternary subsystems. The procedure was developed to calculate the isothermal sections of the phase diagram of the quaternary system inside the tetrahedron. The liquid phase over the whole composition range from metallic liquid to sulfide melt to oxide melt has been described by a single model developed within the framework of the quasichemical formalism. The obtained self-consistent set of model parameters can be used as a basis for the development of a thermodynamic database for simulation of copper smelting and converting.     

Critical evaluation and thermodynamic optimization of Fe–Cu,Cu–C,Fe–C binary systems and Fe–Cu–C ternary system

Development of an efficient process for recycling ferrous scrap containing Cu requires reliable thermodynamic knowledge of Fe–Cu based alloy system. It is shown that there still remain discrepancies in existing databases from known experimental data. In order to provide an accurate prediction tool for the process development, a CALPHAD type thermodynamic modeling for the Fe–Cu–C system is presented with re-optimization of its binary sub-systems, Fe–Cu, Cu–C, and Fe–C. Liquid phase was modeled using the Modified Quasichemical Model in the pair approximation which generally gives better results in systems exhibiting positive deviation from ideality (such as in Fe–Cu). Solid solutions such as fcc and bcc were described using Compound Energy Formalism. A supplement experimental work was carried out in order to provide more accurate solid/liquid equilibria in Fe–Cu binary system. The obtained model parameters along with the model equations were shown to reproduce significantly better correspondence to the experimental data, such as the phase equilibria, activity of component in the Fe–Cu–C system, liquidus projections etc., within experimental uncertainty. High temperature stabilization of bcc phase in Fe–C binary system in previous thermodynamic modeling was revisited, and was resolved in the present study.