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 optimization of the Mn–P and Fe–Mn–P systems

Thermodynamic modeling of the Mn–P and Fe–Mn–P systems in the full composition was carried out using the CALculation of PHAse Diagrams (CALPHAD) method based on the critical evaluation of all available phase equilibria and thermodynamic data. The liquid and solid solutions were described using the Modified Quasichemical Model and Compound Energy Formalism, respectively. The Gibbs energies of the binary stoichiometric iron and manganese phosphides were determined based on reliable experimental data. The ternary (Fe,Mn)₃P, (Fe,Mn)₂P and (Fe,Mn)P phosphides were modeled as solid solutions with mutual substitution between Fe and Mn atoms. The Gibbs energy of the liquid solution was predicted using the Toop interpolation technique with P as an asymmetric component, without any ternary parameters. The thermodynamic properties of P in the entire composition region and the liquidus of the ternary system were well reproduced. Based on the thermodynamic models with optimized parameters, unexplored phase diagrams and thermodynamic properties of the Fe–Mn–P system were predicted.     

Thermodynamic assessment of the Be–Pu and Cd–Pu systems

Thermodynamic assessment of Be–Pu and Cd–Pu systems has been developed with the application of the CALPHAD (Calculation of Phase Diagrams) method, which is established on experimental data including thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, fcc, hcp, αPu, βPu, γPu, δPu, δ′Pu, and εPu phases were described by the subregular solution model with the Redlich–Kister equation, and those of the intermetallic compounds in the Be–Pu and Cd–Pu binary systems were described by the sublattice model. A set of thermodynamic parameters was derived for describing the Gibbs free energies of solution phases and intermetallic compounds in the Be–Pu and Cd–Pu binary systems. Calculated phase equilibria and thermodynamic parameters are in good agreement with experimental data.     

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.     

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.     

Thermodynamic re-assessment and experimental confirmation for the Zn–Mn system

The Zn–Mn system has been critically re-assessed based on available experimental data from literature by CALPHAD (CALculation of PHAse Diagram) approach. Solution phases, viz. liquid, (δMn), (γMn), (βMn), (αMn) and (Zn) were described using substitutional solution model. Besides, the ε, αˊ, γ, δ, δ₁ and ζ phases were described by the sub-lattice models based on the reported crystallographic information and homogeneity ranges. The β₁ phase was treated as a stoichiometric compound since no distinct homogeneity range of this phase was reported. Thermodynamic parameters on the whole system compatible with the databases of Thermo-Calc and Pandat were first obtained. Compared with previous assessments, calculations using the presently obtained thermodynamic parameters achieved a significant improvement. To further verify the reliability of the obtained thermodynamic parameters, eight as-cast Zn–Mn alloys were prepared and the phase compositions and solidified microstructures were analyzed by X-ray diffraction (XRD) and electron probe microanalysis (EPMA). It was shown that the observed experimental results agreed well with the Scheil solidification calculations.     

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 V–Zn system supported by key experiments and first-principles calculations

The V–Zn system was investigated by a combination of CALPHAD modeling with key experiments and first-principles calculations. Based on a critical literature review, one diffusion couple and nine alloys were designed to reinvestigate the stabilities of the phases reported in the literature. The samples were annealed and cooled under different conditions, followed by examination with X-ray diffraction and scanning electron microscopy with energy-dispersive X-ray spectrometry. Four phases ((V), (Zn), V Zn₃ and V ₄Zn₅) were confirmed to exist in the phase diagram, while V Zn₁₆ and V ₃Zn were not observed. By means of first-principles calculations, the enthalpies of formation for V Zn₃ and V ₄Zn₅ were computed to be −4.55 kJ mol-atoms⁻¹ and −4.58 kJ mol-atoms⁻¹, respectively. A set of self-consistent thermodynamic parameters for this system was obtained by considering the reliable experimental phase diagram data and the enthalpies of formation acquired from first-principles calculations. The calculated V–Zn phase diagram agrees well with the experimental data.