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.     

CALPHAD assessment of bio-oriented Ti–Zr–Sn system and experimental validation in Ti/Zr-rich alloys

The development of CALPHAD-type thermodynamic database for Ti or Zr based biomedical alloys has been spurred by the increased interest in efficiently tailoring an alloy composition to obtain high stability of β_bcc, low Young's modulus, and free of detrimental phases. However, the thermodynamic prediction is not adequate to be performed without the information of key sub-ternary Ti–Zr–Sn system. In present work, the thermodynamic assessment of Ti–Zr–Sn system is performed via a critical evaluation of phase equilibria and microstructure development in this ternary system. The partial isothermal sections at 1323 K and 1473 K with Sn content below 40 at. % are obtained by analyzing chemical compositions and crystal structures of individual phases in the annealed alloys. The composition homogeneity range of most phases is validated to favor a ternary extension paralleling to the Ti–Zr axis. Particularly, β_bcc and η phases (with the chemical composition (Ti, Zr)₅Sn_3+x) show complete solubility of Ti and Zr from Ti–Sn edge to Zr–Sn edge. With the database, negligible ternary solubility of Zr₄Sn phase, microstructure development in the as-cast samples, and the controversial conclusions in literature are discussed. Most of the experimental findings, including equilibrium phase constitution, solidification sequence, DSC signals, projections of liquidus, are reproduced in a self-consistent way. The work moves towards the completeness of multi-component Ti/Zr thermodynamic database. It can be used for composition design of novel metastable β-type biomedical alloys.     

Thermodynamic modeling of the Mg–Nd–Sr ternary system with key experimental investigation

The phase equilibria in the Mg-rich region of the Mg–Nd–Sr ternary system at 300 and 350 °C were established using equilibrated-sample method. Powder X-ray diffraction (XRD) technique and scanning electron microscopy (SEM) equipped with energy-dispersive spectroscopy (EDS) were used for phase composition determination. Four three-phase equilibria and four two-phase equilibria have been experimentally determined at both isothermal sections of 300 and 350 °C. The phase equilibria relationships in the Mg-rich side were studied. The major invariant reaction temperatures of vertical sections with 80 at. % Mg and 10 at. % Sr were determined with differential scanning calorimetry (DSC) test. Moreover, thermodynamic modeling of Mg–Nd–Sr ternary system has been carried out by CALPHAD method based on the present key experimental results. The liquid solution was described using the modified quasi-chemical model in the pair approximation (MQMPA). The compound energy formalism (CEF) was used for the solid phases. The present obtained thermodynamic database of Mg–Nd–Sr ternary system will provide an important support for the Mg-based biodegradable implant development.     

Experimental investigation and thermodynamic calculation of the Mg–Mn–Ni system

Based on the critical review of the ternary Mg–Mn–Ni system, 12 alloys were prepared using a powder metallurgy method in a glove box. The isothermal section of the Mg–Mn–Ni system at 400 °C was determined. Ternary compound τ (Mg₃MnNi₂) was confirmed in the present work. In order to obtain the phase transition temperatures, differential scanning calorimetry (DSC) was applied to the selected alloys using sealed Ta crucibles. The invariant reaction temperatures for two invariant reactions in the Mg-rich corner were measured. Considering the experimental data from present work and literature, the Mg–Mn–Ni system was optimized and a set of thermodynamic parameters was obtained. Calculated results fit well with the experimental data.     

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.     

Experimental investigation and thermodynamic modeling of the Mo–Co–B ternary system

Among the ternary borides, the Mo–Co–B system is of great interest because of its excellent hardness, toughness, and stability performance. Eight samples with 60 at.% Co were designed to investigate the isothermal section of Mo–Co–B system at 1073 K in the Co-rich portion. Scanning electron microscopy, energy-dispersion spectroscopy, electron probe microanalysis, differential scanning calorimetry, and X-ray diffraction were used to investigate the phase equilibria of the samples. The formation enthalpies of the ternary borides were obtained by first-principles calculations to serve as key information for thermodynamic assessment. By coupling the reviewed experimental data from the literature, the presently determined phase equilibria, and the calculated formation enthalpies of the compounds, the thermodynamic parameters for the Mo–Co–B ternary system were optimized and used to calculate the isothermal sections, vertical section, and liquidus projection of the system. Comprehensive comparisons showed that the calculated results are in reasonable agreement with the reported phase diagram and thermodynamic data.     

Thermodynamic description and phase selection for the Mo–Ti–Zr biomedical alloys

Thermodynamic information of the Mo–Ti–Zr ternary system is extremely useful to provide guidance for biomedical alloy development. In the present work, the experimental phase diagram data available from the literature were critically reviewed, and a thermodynamic modeling of the Mo–Ti–Zr system was performed using the CALPHAD (CALculation of PHAse Diagram) approach. The solution phases including liquid, bcc_A2 (β) and hcp_A3 (α) were modelled by the substitutional solution model, and the laves_C15 phase was modelled using a two sublattice model. A set of self-consistent thermodynamic parameters was developed. Comprehensive comparisons between the calculated and measured phase diagrams demonstrate that the experimental information is satisfactorily accounted for by the present thermodynamic modeling. The discrepancies between the calculated and measured phase equilibria have been well explained in this work. With regard to the β phase, the miscibility gap and related phase relations are well described by the present calculation. The liquidus projection and Scheil solidification simulation were generated using the present thermodynamic parameters. The presently calculated phase diagrams of the Mo–Ti–Zr alloys can be used to guide the development of Mo–Ti–Zr biomedical alloys. Based on the present calculations, two guidelines were formulated to avoid the formation of laves phase in these frequently studied Mo–Ti–Zr biomedical alloys.     

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.     

Diffusion behaviors and atomic mobilities in Mg–Sc hcp and bcc alloys: Investigation via single-phase and multi-phase diffusion couples

Diffusion behaviors in Mg–Sc hcp and bcc solid solutions between 773 and 873 K were investigated using both single-phase and multi-phase diffusion couple techniques. The EPMA detected composition-distance profiles were smoothed and fitted using the error function expansion (ERFEX). The interdiffusion coefficients were extracted using Sauer–Freise integral. The interdiffusion coefficients in hcp phase showed a slightly parabolic composition dependence at the Mg-rich part and the maximum value was around 2–3 at. % Sc. However, the interdiffusion coefficients in the bcc phase monotonously decreased with the increase of solubility of Sc. The determined inter- and impurity diffusion coefficients in the hcp Mg–Sc alloys were assessed to develop the atomic mobility database, and their validity was justified by reproducing the composition profiles and diffusion fluxes obtained in this diffusion couple experiment. Meanwhile, the development of bcc atomic mobility was realized via the Maclaurin approximation, extrapolation, and optimization. The results make up for the missing data of Mg–Sc diffusion kinetics.     

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.     

Phase diagram of Ag–Pb–Sn system

The Ag–Pb–Sn ternary system is an important material system for both electronic packaging and thermoelectric applications. However, there is no experimental phase equilibria information of the ternary system. Ag–Pb–Sn alloys are prepared and their phase equilibria at various temperatures were determined. The focus was on the 500, 350, and 200 °C isothermal sections. Additional information was also obtained for 400, and 300 °C. Several samples were studied by DSC studies. No ternary compounds were found in the ternary system. The Ag–Sn binary compounds, Ag₃Sn(ε) and Ag₄Sn(ζ) at 350 °C and Ag₄Sn(ζ) at 500 °C, exhibit very small Pb solubility. The thermodynamic assessment of the ternary Ag–Pb–Sn system was carried out using the above mentioned 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.