Thermodynamic modeling of the Mg–Bi and Mg–Sb binary systems and short-range-ordering behavior of the liquid solutions

In order to investigate the short range ordering behavior of liquid Mg–Bi and Mg–Sb solutions, thermodynamic modeling of the Mg–Bi and Mg-Sb binary systems has been performed. All available thermodynamic and phase diagram data of the Mg–Bi and Mg–Sb binary systems have been critically evaluated and all reliable data have been simultaneously optimized to obtain one set of model parameters for the Gibbs energies of the liquid and all solid phases as functions of composition and temperature. In particular, the Modified Quasichemical Model, which accounts for short-range-ordering of nearest-neighbor atoms in the liquid, was used for the liquid solutions. A comparative evaluation of both systems was helpful to resolve inconsistencies of the experimental data. The thermodynamic modeling shows the strong ordering behavior in the liquid Mg–Bi and Mg–Sb solutions at Mg₃Bi₂ and Mg₃Sb₂ compositions, respectively, and predicts the metastable liquid miscibility gaps at sub-solidus temperatures. All calculations were performed using the FactSage thermochemical software.     

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.     

First-principles study of binary special quasirandom structures for the Al–Cu,Al–Si,Cu–Si,and Mg–Si systems

Based on special quasirandom structures (SQS’s) and first-principles calculations, enthalpies of mixing have been predicted for four binary fcc solid solutions in the Al–Cu, Al–Si, Cu–Si, and Mg–Si systems at nine compositions (x=0.0625$x=0.0625$, 0.125, 0.1875, 0.25, 0.5, 0.75, 0.8125, 0.875, 0.9375, where x$x$ is the mole fraction of A atoms in the A–B binary system). The present results are compared with previous first-principles calculations and thermodynamic modeling results available in the literature. In order to provide insight into the understanding of mixing behavior for these solid solutions, the spatial charge density distributions in these binary solid solutions are also analyzed. The results obtained herein indicate that the SQS model can be used to estimate the thermodynamic properties of solid solutions, especially for metastable phases, the thermodynamic qualities of which are rarely measured.     

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.     

Modeling short-range ordering in liquids: The Mg–Al–Sn system

A liquid solution of components A and B may often exhibit a tendency towards short-range ordering (SRO). This may be modeled by the Modified Quasichemical Model (MQM) which attributes the SRO to the preferential formation of nearest-neighbor A–B pairs or, alternatively, by an associate model which attributes the ordering to the formation of A_nB_m associates or molecules. Although both models can often provide similar and equally good fits to experimental thermodynamic and phase equilibrium data in a binary system, the MQM provides significantly better predictions of the thermodynamic properties of ordered ternary liquid phases A–B–C solely from the optimized model parameters of the A–B, B–C and C–A binary sub-systems. This is illustrated through coupled thermodynamic/phase diagram optimization of the Mg–Al–Sn system. A similar example for the Mg–Al–Sc system is also presented.     

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.     

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.     

Experimental measurement of diffusion coefficients and assessment of diffusion mobilities in HCP Mg–Li–Al alloys

An atomic mobility database was established for the ternary HCP Mg–Li–Al system as a part of an ongoing effort to enable rapid development of novel lightweight Mg alloys. Three sets of three diffusion couples were assembled and annealed at temperatures ranging from 400 to 500 °C. Li concentration profiles were measured using a combination of Auger electron spectroscopy (AES) and inductively coupled plasma optical emission spectrometry (ICP-OES), while Al composition profiles were acquired using electron probe microanalysis (EPMA). The forward-simulation analysis (FSA) was employed to extract both interdiffusion and impurity diffusion coefficients from the collected experimental composition profiles. These measured diffusivity data were used to assess and iteratively optimize mobility parameters for the Mg–Li–Al system using the diffusion module within the Thermo-Calc Software package (DICTRA). The reliability of the assessed mobility parameters was further confirmed by two validation diffusion couples that were annealed at 425 and 475 °C for 96 and 48 h, respectively. It was observed that additions of Li increased the diffusivity of Al in HCP Mg, whereas additions of Al decreased the diffusivity of Li in HCP Mg.     

A thermodynamic assessment of Ni–Sb system

The Ni–Sb system was critically assessed by means of the CALculation of PHAse Diagram (CALPHAD) technique. The solution phases, Liq and (αNi), were modelled as the substitutional solutions with the Redlich–Kister equation. The intermediate phases, (γNiSb) and (βNi₃Sb), with homogeneity ranges were described respectively using three-sublattices (Sb)_1/3(Ni%,V a)_1/3(V a%,Ni)_1/3 and (Sb)_1/4(Ni%,V a)_1/2(Ni%,V a)_1/4 based on their structure features. Corresponding to the phase (βNi₃Sb), the two low-temperature phases of (δNi₃Sb) and (θNi₅Sb₂) with narrow homogeneity ranges were modelled as two-sublattice, (Ni)_3/4(Sb,Ni)_1/4 and (Ni)_5/7(Sb,Ni)_2/7. The intermetallic compound ζNiSb₂ with no homogeneity ranges was treated as stoichiometric compound. The phase ε$\epsilon$Sb was considered as pure Sb for the solubility of Ni in ε$\epsilon$Sb is very low. A set of self-consistent thermodynamic parameters of the Ni–Sb system was obtained. The optimized phase diagram and thermodynamic properties were presented and compared with experimental data.     

Critical assessment of the Ag–Bi–Sn ternary system

A history of system assessments was given, and all the experimental works on its thermodynamics and constitution were mentioned, as well. A dataset for preliminary optimization was constructed, all existing phases of ternary system were listed and appropriate thermodynamic models were chosen. Optimization was carried out in the subsequent steps, and ternary thermodynamic parameters of all the phases under accord were determined. Equilibrium calculations resulted in phase boundary coordinates, invariant reaction parameters and thermodynamic function values; a Scheil reaction scheme was constructed, as well. Calculated quantities were then compared to the existing experimental data displaying the excellent agreement. Suggestion on the choice of alloy compositions was given as for solder material.     

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.