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.     

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.     

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.     

Thermodynamic modeling of the Na–Al–Ti–H system and Ti dissolution in sodium alanates

Thermodynamic assessments were made to optimize thermodynamic models and parameter fits to selected experimental and first principles hypothetical predicted phase data within the Na–Al–Ti–H system. This enabled thermodynamic modeling of Ti solubility within the sodium alanates: NaAlH₄ and Na₃AlH₆, and the relative stability of Ti-bearing phases. The modeling provides insights into the role of Ti originating from Ti-based activating agents commonly referred to as ‘catalysts’ in promoting reversibility of the Na–Al–H dehydrogenation and rehydrogenation reactions under moderate temperature and pressure conditions relevant to H storage applications. Preliminary assessments were made to evaluate H solubility in bcc-Ti and hcp-Ti, and stability of the hydride δ-TiH₂. To model possible Ti dissolution in NaAlH₄ and α-Na₃AlH₆, sub-lattice models were applied. A repulsive interaction is predicted by first principles calculations when Ti is dissolved in NaAlH₄ or α-Na₃AlH₆, which becomes stronger with increasing temperature. Although Ti is virtually insoluble in NaAlH₄ or α-Na₃AlH₆, a small addition of TiCl₃ will induce a thermodynamic driving force for formation of TiH₂ and/or TiAl₃. The addition of pure Ti shows a weaker effect than TiCl₃ and leads to formation of TiH₂ only. Based on a combined interpretation of present thermodynamic modeling and prior experimental observations, the TiAl₃ and TiH₂ phases are ascribed to have a catalytic effect, not a thermodynamic destabilization effect, on the reversibility of the dehydrogenation/rehydrogenation reactions in the Na–Al–H system.     

Thermodynamic evaluation and optimization of the As–Co,As–Fe and As–Fe–S systems

A critical evaluation of all available phase diagram and thermodynamic data for the As–Co and As–Fe binary systems as well as the As–Fe–S ternary system has been performed and thermodynamic assessments over the whole composition ranges are presented using the CALPHAD method. To predict thermodynamic properties and phase equilibria for these systems, the Modified Quasichemical Model (MQM) for short range ordering was used for the liquid phases. The Compound Energy Formalism (CEF) was used for the solid solutions. Since Co and Fe are ferromagnetic, magnetic contributions were added to describe the Gibbs energy of cobalt and iron rich solid solutions. Important uncertainties remain for the liquidus of As-rich regions in the binary subsystems.     

Thermodynamic assessment of the Ca–Zn,Sr–Zn,Y–Zn and Ce–Zn systems

Published experimental thermodynamic and phase diagram data for the Ca–Zn, Sr–Zn, Y–Zn and Ce–Zn systems have been critically evaluated to provide assessed thermodynamic parameters for the different phases of the systems. The parameters allow all thermodynamic properties and phase boundaries for each system to be calculated within reasonable error limits. Because a strong compound-forming tendency and pronounced minimum in the enthalpy of mixing curve is observed for the liquid phase of all the systems, the Modified Quasichemical Model (MQM) in the pair approximation has been used throughout the assessment work to treat short-range ordering in the liquid.     

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.     

Phase transition,microstructure and solidification of Ce–La–Fe and Ce–Nd–Fe alloys: Experimental investigation and thermodynamic calculation

In this work, phase transition temperatures of La–Fe and Ce–Fe alloys were determined using differential thermal analysis (DTA), while phase transition temperatures, microstructure, and phase compositions of La–Ce–Fe and Ce-Nd-Fe alloys were studied using DTA and scanning electron microscopy with energy dispersive spectroscopy (SEM-EDS). Based on the available experimental data reported in the literature and the experimental results determined in this work, the La–Fe and Ce–Fe systems were re-assessed thermodynamically using the CALPHAD (CALcuation of PHAse Diagrams) method, and then the Ce–La–Fe and Ce-Nd-Fe systems were calculated by combining the re-assessed La–Fe and Ce–Fe systems with the previously assessed Nd–Fe, Ce–La, and Ce–Nd systems. The calculated phase diagrams and thermodynamic properties of the La–Fe and Ce–Fe systems are consistent with the experimental data. The calculated isothermal sections and vertical sections in the Ce–La–Fe and Ce-Nd-Fe systems are in good agreement with the experimental results. The solidification behaviors of Ce–La–Fe and Ce-Nd-Fe as-cast alloys were analyzed through the experimental examination and thermodynamic calculation with Scheil-Gulliver non-equilibrium model. The simulated results agree well with the experimental results. It indicates that the reasonable thermodynamic parameters of the Ce–La–Fe and Ce-Nd-Fe systems were obtained finally, which would be fundamental to developing a thermodynamic database of the multi-component Nd-RE-Fe-B alloy systems and then to designing novel Nd-Fe-B permanent magnets with light rare-earth metals La and Ce.     

Study on diffusion and Kirkendall effect in diffusion triples for fcc Ni–Al–Ta alloys

In the present work based on two diffusion triples, the composition-dependent interdiffusivity matrices in the fcc Ni–Al–Ta alloys at 1373K and 1473K were efficiently deduced by using our newly developed two-dimensional (2D) inverse scheme. This scheme determines interdiffusivities from point and one-dimensional (1D) diffusion path to 2D composition region, yet requires much less experimental efforts, with the measured 2D composition profiles being well reproduced. Further, the interdiffusivities deduced from the inverse scheme were directly compared with those extracted by the traditional Sauer-Freise method and Whittle-Green method based on nine diffusion couples designed for verification. The interdiffusivities inferred from two distinct ways are fairly consistent, either at the binary boundaries or at the intersection points within the ternary composition range. Besides, the interdiffusion flux and the shift of the Kirkendall plane over the whole diffusion zone were simulated by applying the present 2D inverse scheme. The resulting 2D mapping presents a non-uniform but curved Kirkendall plane, which is in contrast to the flat shape generated in 1D diffusion couples and well explained by the calculated diffusion variables.     

Birman–Wenzl–Murakami algebra, topological parameter and Berry phase

In this paper, a 3?×?3-matrix representation of Birman?CWenzl?CMurakami (BWM) algebra has been presented. Based on which, unitary matrices A(??, ?? ₁, ?? ₂) and B(??, ?? ₁, ?? ₂) are generated via Yang?CBaxterization approach. A Hamiltonian is constructed from the unitary B(??, ??) matrix. Then we study Berry phase of the Yang?CBaxter system, and obtain the relationship between topological parameter and Berry phase.     

Predictions of the Al-rich region of the Al–Co–Ni–Y system based upon first-principles and experimental data

A thermodynamic database has been produced for the Al–Co–Ni–Y quaternary system, with an emphasis on the Al-rich region of the Al–Ni–Y ternary system. The database was created using the CALPHAD method, combining existing binary systems with relevant experimental and first-principles information for selected Al–Ni–Y and Co-containing compounds. The thermodynamic database was used to produce equilibrium and non-equilibrium Scheil simulations to determine the phases present in Al–Co–Ni–Y alloys. The values for the Scheil simulation show good agreement, when compared with experimentally determined phase fractions of intermetallic particles dispersed in an Al matrix for three Al-rich quaternary 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.