Thermodynamic assessment of the Si–Zn,Mn–Si,Mg–Si–Zn and Mg–Mn–Si systems

The binary Si–Zn and Mn–Si systems have been critically evaluated based upon available phase equilibrium and thermodynamic data, and optimized model parameters have been obtained giving the Gibbs energies of all phases as functions of temperature and composition. The liquid solution has been modeled with the Modified Quasichemical Model (MQM) to account for the short-range-ordering. The results have been combined with those of our previous optimizations of the Mg–Si, Mg–Zn and Mg–Mn systems to predict the phase diagrams of the Mg–Si–Zn and Mg–Mn–Si systems. The predictions have been compared with available data.     

Thermodynamic modeling of the Al–Bi,Al–Sb,Mg–Al–Bi and Mg–Al–Sb systems

All available thermodynamic and phase diagram data of the binary Al–Bi and Al–Sb systems and ternary Mg–Al–Bi and Mg–Al–Sb systems were critically evaluated, and all reliable data were used simultaneously to obtain the best set of the model parameters for each ternary system. The Modified Quasichemical Model used for the liquid solution shows a high predictive capacity for the ternary systems. The ternary liquid miscibility gaps in the Mg–Al–Bi and Mg–Al–Sb systems resulting from the ordering behaviour of the liquid solutions can be well reproduced with one additional ternary parameter. Using the optimized model parameters, the experimentally unexplored portions of the Mg–Al–Bi and Mg–Al–Sb ternary phase diagrams were more reasonably predicted. All calculations were performed using the FactSage thermochemical software package.     

Experimental investigation and thermodynamic modeling of the Mg–Sn–Sr ternary system

The isothermal sections of the Mg–Sn–Sr ternary system in the Mg-rich region at 415 and 350 °C have been determined using the scanning electron microscopy (SEM) equipped with energy dispersive X-Ray spectrometry (EDS). The existence of the MgSnSr ternary compound was confirmed in these two isothermal sections. Two new compounds, named Mg₅Sn₃Sr and Mg₂₅Sn₂₄Sr_14, were found in the present work based on the SEM/EDS results. Thermodynamic optimization of the Sn–Sr binary and Mg–Sn–Sr ternary systems were carried out using the CALPHAD (CALculation of PHAse Diagrams) technique. The Modified quasi-chemical model (MQM) was used for the liquid solution which exhibits a high degree of short-range ordering behavior. The solid phases were described with the Compound energy formalism (CEF). Finally, a self-consistent thermodynamic databases for the Mg–Sn–Sr ternary system has been constructed in the present work, which can be an efficient and convenient guidance to investigate and develop the Mg-based alloys.     

Measurement and thermodynamic assessment of the phase equilibria in the Mg–Hg–Ga ternary system

Phase relations in the Mg–Hg–Ga ternary system have been experimentally and thermodynamically studied. At first, the isothermal sections of the Mg–Hg–Ga system in the Mg-rich region at 673 K and 473 K were investigated by using powder X-ray diffraction (XRD) and scanning electron microscope (SEM) with X-ray energy dispersive spectroscope (EDS). A ternary compound Mg₂₁Ga₅Hg₃ of tetragonal structure was detected and its homogeneity was determined. Then, based on the experimental literature, a thermodynamic assessment of the Mg–Hg–Ga ternary system was carried out by the CALPHAD approach. Consequently, a self-consistent set of thermodynamic parameters describing this system was obtained, which leads to a good fit between the calculated and experimental data.     

A thermodynamic description of the Gd–Mg–Sm system

The Mg–Sm, Gd–Sm and Gd–Mg–Sm systems were thermodynamically optimized using the CALPHAD technique. The solution phases, liquid, bcc, hcp and rhombohedral, were described by the substitutional solution model. The isostructural compounds, MgGd in the Gd–Mg system and MgSm in the Mg–Sm system with a B2 structure was assumed to form a continuous range of solid solutions in the Gd–Mg–Sm system. The order–disorder transition between the bcc solution with an A2 structure and compound Mg(Gd, Sm) with a B2 structure in the system has been taken into account and thermodynamically modeled. The other isostructural compounds Mg₅Gd and Mg₅Sm, Mg₃Gd and Mg₃Sm, Mg₂Gd and Mg₂Sm in the Gd–Mg–Sm system were described according to the formulae Mg₅(Gd,Sm), Mg₃(Gd,Sm), and Mg₂(Gd,Sm), respectively. The compound Mg₄₁Sm₅ with a homogeneity range was treated as a line compound Mg₄₁(Gd,Sm)₅ in the Gd–Mg–Sm system. Based on the experimental data in the Mg-rich corner of the Gd–Mg–Sm system, a set of thermodynamic parameters describing the Gibbs energies of individual phases of the Gd–Mg–Sm system as functions of composition and temperature was obtained. In addition, the complete ternary phase diagram of the Gd–Mg–Sm system were predicted.     

Thermodynamic description of the Mg–Eu binary system

Thermodynamic assessment of the Mg–Eu binary system has been carried out by combining first-principles calculations and Miedema’s theory with CALPHAD method. Firstly, the mixing enthalpy of the liquid alloys was calculated by using Miedema’s theory, and formation enthalpies of the intermetallic compounds were calculated by using the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). Subsequently, the liquid phase was described employing a simple substitutional model, of which the excess Gibbs energy was formulated with a Redlich-Kister expression. And the solubility of Eu in HCP_(Mg) and Mg in BCC_(Eu) were neglected. While the intermetallic compounds Mg₁₇Eu₂, Mg₅Eu, Mg₄Eu, Mg₂Eu and MgEu, were treated as stoichiometric compounds. Consequently, a set of self-consistent thermodynamic parameters for all stable phases in the Mg–Eu binary system were obtained, which can reproduce most of the thermodynamic and phase boundary data.     

Critical evaluation and thermodynamic optimization of the Al–Ce,Al–Y,Al–Sc and Mg–Sc binary systems

New critical evaluations and optimizations of the Al–Ce, Al–Y, Al–Sc and Mg–Sc systems are presented. The Modified Quasichemical Model is used for the liquid phases which exhibit a high degree of short-range ordering. A number of solid solutions in the binary systems are modelled using the Compound Energy Formalism. All available and reliable experimental data such as enthalpies of mixing in liquid alloys, heats of formation of intermetallic phases, phase diagrams, etc. are reproduced within experimental error limits. It is shown that the Modified Quasichemical Model reproduces the partial enthalpy of mixing data in the liquid alloys better than the Bragg–Williams random mixing model which does not take short-range ordering into account.     

Assessment of the atomic mobility in fcc Al–Cu–Mg alloys

Various experimentally measured diffusivities of fcc Al–Mg, Cu–Mg and Al–Cu–Mg alloys available in the literature are critically reviewed in the present work. The first-principles calculations coupled with a semi-empirical correlation is employed to derive the temperature dependence of impurity diffusivity for Mg in fcc Cu. Atomic mobilities for the above fcc alloys are then evaluated as a function of temperature and composition by means of DICTRA (DIffusion Controlled TRAnsformation) software. Comprehensive comparisons between calculated and measured diffusivities show that most of the experimental data can be well reproduced by the presently obtained atomic mobilities. The concentration profiles and diffusion paths are predicted with the mobility parameters in a series of binary and ternary diffusion couples. A good agreement is obtained between experiment and simulation.     

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.     

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.     

Diffusional mobility for fcc phase of Al–Mg–Zn system and its applications

Diffusional mobility for fcc phase of the Al–Mg and Al–Mg–Zn systems was critically assessed by using the DICTRA software (Diffusion Controlled Transformation). Good agreement was obtained from comprehensive comparisons between the calculated and experimental diffusion coefficients. The developed mobility database enables reasonable prediction of diffusion and solidification behaviours resulting from interdiffusion, such as concentration profile of diffusion couples and solidification curve of the Al–Mg alloys.