Phase equilibria of the Cu–Zr–Si system at 750 and 900 °C

Phase equilibria in the ternary Cu–Zr–Si system at 750 and 900 °C have been experimentally investigated via electron probe micro-analyzer (EPMA) and X-ray diffraction (XRD) analysis on the equilibrated alloys. The results show the presence of eight three-phase regions at 750 °C and seven three-phase regions at 900 °C. Four ternary phase: τ₁ (Zr₃Cu₄Si₆, tI26-Zr₃Cu₄Si₆), τ₄ (Zr₃Cu₄Si₄, oI22-Gd₃Cu₄Ge₄), τ₅ (ZrCuSi, oP12-Co₂Si), and τ₆ (Zr₃Cu₄Si₂, 2hP9-Fe₂P) were confirmed to exist in the Cu–Zr–Si ternary system at 750 and 900 °C. At 900 °C, the dark gray phase, the chemical composition of which is close to η-Cu₃Si, is confirmed to be the liquid phase. Moreover, the solubilities of Cu in ZrSi₂, SiZr and Zr₃Si₂ are considerably small. The solubility of Zr in η-Cu₃Si is determined to be negligible. The newly determined phase equilibria of the Cu–Zr–Si system in this work can provide important experimental data for the thermodynamic assessment of the Cu–Zr–Si system and to develop the Cu–Zr–Si alloys and related transition metal silicides.     

Experimental investigation and thermodynamic modeling of the Mg-Si-Zn system

The isothermal section at 327 °C for the Mg-Si-Zn system has been determined by means of X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDX). No ternary compound has been observed in this work. Five three-phase regions, (Zn)+(Si)+Mg₂Zn₁₁, Mg₂Zn₁₁+MgZn₂+Mg₂Si, Mg₂Zn₃+MgZn₂+Mg₂Si, Mg₅₁Zn₂₀+MgZn+Mg₂Si, and Mg₅₁Zn₂₀+Mg₂Si+(Mg), have been determined. No appreciable ternary solubility has been detected. An optimal set of thermodynamic parameters for the Mg-Si-Zn system has been obtained by considering the experimental data from both the present work and the literature. The agreement between calculation and experiment is reasonable.     

Re-assessment of the Mg–Zn–Ce system focusing on the phase equilibria in Mg-rich corner

The Mg–Zn–Ce alloys exhibit good creep resistance and strength at elevated temperature due to the formation of intermetallic compounds. However, the ternary compounds and phase equilibria in the Mg-rich corner are still controversial which restrains the development of Mg–Zn–Ce alloys. The present work experimentally investigated the phase equilibria in Mg-rich corner of the Mg–Zn–Ce system at 350 and 465 °C and thermodynamically assessed the Mg–Zn–Ce system. The existence of ternary compounds τ₁ and τ₃ were confirmed by a combination of X-ray diffraction (XRD) and scanning electron microscopy (SEM). The crystal structure of τ₁ was resolved as space group of Cmc21 with a = 0.9852(2)–1.0137(2) nm, b = 1.1361(3)–1.1635(3) nm and c = 0.9651(2)–0.9989(2) nm by Rietveld refinement of the XRD pattern. Three invariant reactions, L→τ₃+CeMg₃+CeMg₁₂, L+CeMg₁₂→α-Mg+τ₁ and L+τ₁→τ₂+α-Mg, were revealed by differential scanning calorimeter (DSC) measurement and microstructure characterization. Then, a set of self-consistent thermodynamic parameters was thereafter constructed by assessing the phase equilibria, solid solubilities of CeMg₁₂, τ₁, CeMg₃ and τ₃, as well as the formation enthalpies of binary and ternary compounds calculated by density functional theory. The comparison of calculated phase diagram with experimental results and the literature were discussed. The calculated isothermal section of Mg–Zn–Ce system at 465 °C agreed with our experimental data. The two three-phase equilibria, τ₁+α-Mg+CeMg₁₂ and CeMg₃+τ₃+CeMg₁₂, were confirmed in the Mg-rich corner. This thermodynamic database can be used for the further alloys design of Mg–Zn–Ce system.     

Isothermal section of Mg-Zn-Zr ternary system at 345 ° C

Isothermal section of Mg-Zn-Zr ternary system at 345 ^°C has been determined by X-ray diffraction, differential scanning calorimetry and scanning electron microscopy assisted with energy dispersive X-ray spectroscopy using a series of Mg-Zn-Zr alloys. The results show that there exist three intermetallic compounds ZnZr, Zn₂Zr₃, (Mg,Zn)₂Zr, and a liquid phase in equilibrium with the α-Mg phase. The presence of two other three-phase regions in equilibrium, Liquid+MgZn+(Mg,Zn)₂Zr and MgZn+Mg₂Zn₃+(Mg,Zr)Zn₂, has also been confirmed. The addition of Zn can significantly increase the solubility of Zr and vice-versa in the α-Mg matrix.     

Experimental investigation and thermodynamic assessment of the Zn–Cu–Sr ternary system

Zn–Cu–Sr alloys play a crucial role in the development of biodegradable implant materials based on zinc. The current study aimed to investigate the phase equilibria of the Zn–Cu–Sr ternary system in the Cu–Zn-rich region, through experimental analysis. For this purpose, fifteen and fourteen samples were respectively prepared and equilibrated at 350 and 400 °C, to determine the isothermal sections. The equilibrated alloys were then subjected to various analytical techniques such as scanning electron microscopy (SEM) equipped with energy dispersive spectrometry analysis (EDS), electron probe microanalysis (EPMA), and powder X-ray diffraction analysis (XRD). The analysis revealed the presence of five three-phase equilibria and ten two-phase equilibria in the two isothermal sections. Differential scanning calorimetry (DSC) was used to investigate the phase transformation temperature with constant values of 8 at. % Sr and 30 at. % Cu. The obtained experimental results were used to perform a thermodynamic assessment of the Zn–Cu–Sr system especial in Zn-rich region using the calculation of phase diagrams (CALPHAD) method. The modified quasi-chemical model (MQM) was used to model the liquid solution, while the compound energy formalism (CEF) was used to represent Gibbs free energies of the solid phases. The present obtained thermodynamic parameters were found to accurately reproduce the experimentally measured phase relationships in the Zn–Cu–Sr ternary system.     

Experimental investigation of phase equilibrium in the Al–Nb–Hf ternary system at 600 °C and 400 °C

The phase equilibria in the Al–Nb–Hf ternary system at 600 °C and 400 °C were experimentally investigated by X-ray diffraction (XRD), scanning electron microscope (SEM) and electron probe microanalysis (EPMA/WDS). In each isothermal sections, 13 three-phase regions were measured. And their phase region boundaries were precisely determined. Among the actually measured binary compounds, only Al₃Nb, AlNb₂ and AlNb₃ have a large range of solid solubility. In addition, two stable ternary compounds τ1-Al₁₁Nb₄Hf₅ and τ2-Al₂NbHf₂, which had certain solid solubility, were newly discovered. On the basis of the experimental results and reasonable inference, the isothermal sections of ternary system at 600 °C and 400 °C were constructed.     

Phase equilibria and thermodynamic re-assessment of the Cu–Ti system

Several as-cast and annealed Cu–Ti alloys were prepared for microstructural, compositional, structural and thermal characterizations. The formation of CuTi₂ was congruent and CuTi₃ was not found in both as-cast and annealed specimens. The temperatures of nine invariant reactions were determined. The Cu–Ti system was thermodynamically re-assessed according to the experimental phase equilibria and thermochemical properties from this work and the literature. The solution phases Liquid (L), fcc-A1 (Cu), bcc-A2 (βTi) and hcp-A3 (αTi) were treated as substitutional ones. The intermetallics compounds Cu₂Ti, Cu₃Ti₂, Cu₄Ti₃ and CuTi₂ with negligible solubility were described as line ones with the formula Cu_pTi_q, while βCu₄Ti and CuTi with remarkable solubility were modeled with the formula (Cu,Ti)_r(Cu,Ti)_s. A group of reliable thermodynamic parameters of the Cu–Ti system were obtained. The calculated results agreed reasonably well with the experimental ones.     

Thermodynamic calculation of S−Sb system and Cu−S−Sb system

Sb₂S₃ and CuSbS₂ have been proposed as alternative earth-abundant absorber materials for thin-film solar cells. However, no thermodynamic study of the S−Sb binary system and the Cu−S−Sb ternary system were investigated. In this paper, The S−Sb system and the Cu−S−Sb system are calculated utilizing the so-called CALPHAD (CALculation of PHAse Diagrams) technique. Using TEM-EDS and XRD, Cu_0.9Sb₁S₂ is experimentally confirmed at the Cu₁Sb₁S₂ and Sb₂S₃ two-phases region in the isothermal section at 673 K of the Cu−S−Sb ternary system. Given the asymmetric shape and miscibility gap of the liquidus in the S−Sb phase diagram, the associate solution model for the liquid phase is adopted. The solution phases (liquid, bcc, fcc) are treated with the Redlich–Kister equation. The compounds S₃Sb₂, Cu₃SbS₃, Cu₁₂Sb₄S₁₃, CuSbS₂, and Cu₃SbS₄ are described as a stoichiometric compound. A set of self-consistent thermodynamic parameters of the S−Sb binary system and the Cu−S−Sb ternary system are obtained. The calculated results are in good agreement with the experimental data. This study provides a set of reliable thermodynamic parameters to the Cu−Sb−S thermodynamic database, and a cost-effective tool to design material synthesis experiments and manufacturing processes.     

Thermodynamic description of the Al-Li-Zn system

The Al-Li-Zn system was critically assessed using the CALPHAD technique. The solution phases (liquid, bcc, fcc and hcp) were described by the substitutional solution model. The compounds Al₂Li₃ and Al₄Li₉ in the Al-Li system had homogeneity ranges of Zn and were treated as (Al,Zn)₂Li₃ and (Al,Zn)₄Li₉ in the Al-Li-Zn system, respectively. The compounds αLi₂Zn₃, βLi₂Zn₃, αLi₂Zn₅, βLi₂Zn₅ and αLiZn₄ in the Li-Zn system had no solubility of the third component Al in the Al-Li-Zn system. A two-sublattice model (Al,Li,Zn)_0.2(Al,Li,Zn)_0.8 was applied to describe the compound βLiZn₄ in the Al-Li-Zn system in order to cope with the order-disorder transition between hexagonal close-packed solution (hcp-A3) and βLiZn₄ with the Mg-type structure. The ternary compound τ₂ with a NaTl-type structure (B32) had the same structure with the compounds AlLi in the binary Al-Li system and LiZn in the binary Li-Zn system. In the present work, the three compounds AlLi, LiZn and τ₂ were treated as one phase by a two-sublattice model (Al,Li,Zn)_0.5(Al,Li,Zn)_0.5 in order to cope with the order-disorder transition between B32(AlLi, LiZn and τ₂) and body-centered cubic solid solution (bcc-A2). The ternary intermetallic compounds τ₁ and τ₃ in the Al-Li-Zn system were treated as the formula Li(Al,Zn)₂ and (AlLi,Zn)Zn₃, respectively. A set of self-consistent thermodynamic parameters describing the Gibbs energy of each individual phase as a function of composition and temperature in the Al-Li-Zn system was obtained.     

Thermodynamic assessment of the Ga-Sn-Zn system

The integral molar mixing enthalpy of liquid ternary Ga-Sn-Zn alloys has been investigated using drop calorimetry method along five intersections as follows: X_Ga/X_Zn = 3/1 at 720 K, x_Ga/x_Zn = 1/1 at 718 K and 720 K, x_Ga/x_Zn = 1/3 at 718 K, x_Ga/x_Sn = 3/17 at 718 K and for x_Ga/x_Sn = 1/3 at 720 K. Based on obtained thermodynamic results and those available in the literature the thermodynamic optimization was done using Thermo-Calc software. Next, the phase equilibria in the binary and ternary systems were calculated and the results were compared with those obtained using different experimental techniques.     

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.     

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.     

Experimental investigation of phase equilibria in the Co–Fe–La system at 600 and 500 °C

Phase equilibria in the Co–Fe–La ternary system have been studied using X-ray diffraction (XRD), scanning electron microscopy (SEM) and electron probe microanalysis (EPMA). Isothermal sections at 600 (in the whole concentration region) and 500 °C (in the La-rich region) for this system have been constructed. It was shown that the ternary compound La₂(Co,Fe)₁₇ (τ) (Th₂Zn₁₇-type structure) is stable at 600 °C and has homogeneity range from 67 to 72 at.% Co. It co-exists with the majority of solid phases (αFe,Co), LaCo₁₃, LaCo₅, La₂Co₇ and La₂Co₃ at 600 °C. The LaCo₁₃ phase has the widest homogeneity region and dissolves up to 32.5 at.% Fe at 600 °C. The character of phase equilibria at 500 °C in the studied region is similar to those at solidus temperature. The character of phase equilibria at 600 °C is different from those at the solidus temperature. The main difference involves the fact that the equilibrium τ + LaCo₅ which is present in the Co–Fe–La system at solidus temperature, is absent at 600 °C. Instead, the alternative equilibrium (αFe,Co) + La₂Co₇ is present at 600 °C.     

Thermodynamic modeling of Fe–Ti–Bi system assisted with key experiments

Phase equilibria of Fe–Ti–Bi ternary system have been studied in this work. Firstly, by using alloy sampling, the isothermal section of Fe–Ti–Bi ternary system at 773 K was determined, where the existence of a ternary phase Bi₂FeTi₄ was confirmed. Meanwhile, formation enthalpies of the intermediate phases BiTi₂, Bi₉Ti₈ and Bi₂FeTi₄, were obtained with first-principles calculations. Based on experimental data of phase equilibria and thermodynamic properties in literatures along with the calculated formation enthalpies in this work, thermodynamic modeling of Ti–Bi binary system and Fe–Ti–Bi ternary system were carried out with the CALPHAD approach. A set of self-consistent thermodynamic parameters to describe the Gibbs energy for various phases in Fe–Ti–Bi ternary system was finally obtained, with which solidification processes of two typical Fe–Ti–Bi alloys could be reasonably explained.