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 description of the Ti–H system

Previous thermodynamic assessments of the Ti–H system are reviewed, and a new evaluation is carried out by taking into account the liquid phase in the system using the associate solution model. The sublattice model is utilized to depict the interstitial solution phases with various lattice ratios. The model parameters are optimized in the least square procedure by selecting most reported equilibrium solubility and thermochemical data of the Ti–H system. It is demonstrated that a credible set of thermodynamic parameters well describing the whole Ti–H system is obtained. With these parameters, the behavior of the Ti–H system was predicted at higher pressures of 10, 100 and 370 atm.     

Thermodynamic evaluation of the thixoformability of Al–Si–Cu alloys

The aim of this work was to evaluate the thixoformability of Al-(2 to 7 wt%) Si–Cu alloys by differential thermal analysis (DTA), differential scanning calorimetry (DSC) and CALPHAD simulation. Thermoanalytical data were generated for exothermic (rheocasting) and endothermic (thixoforming) cycles under different kinetic conditions (heating and cooling rates of 5, 10, 15, 20 and 25 °C/min). The findings indicate that the SSM critical temperatures and liquid fractions are directly affected by the kinetic conditions, chemical composition and heat-flow direction and that the measured values of these critical temperatures and liquid fractions vary according to the thermodynamic evaluation technique used (Calphad simulation, DSC or DTA). The SSM working window (a) became smaller as the heating/cooling rates and Si content increased; (b) was larger for rheocasting (solidification) than for thixoforming (melting) operations; (c) was on average approximately 12 °C wider and covered a range of mass fractions approximately 0.12 greater for DSC measurements than for DTA measurements; and (d) had a low sensitivity for all the conditions analyzed, indicating the thermodynamic stability of the Al–Si–Cu system. CALPHAD simulation successfully predicted several transformations and the thermodynamic behavior of the temperatures and liquid fractions analyzed. The DTA and DSC techniques yielded discrepant results for some of the critical points investigated, such as the limits of the SSM working window. The majority of the DSC cycles were more sensitive to variations in kinetic conditions, heat-flow direction and chemical composition than the corresponding DTA cycles. Furthermore, the tertiary Al₂Cu phase transformation could not be identified in many of the DTA cycles. For these reasons, DTA should be used with caution when predicting the thermodynamic behavior of potential raw materials for SSM processing.     

The isothermal section of the La–Si–Mg system at 500 C

The isothermal section of the La–Si–Mg system at 500 ^°C was constructed in the whole concentration range by means of the SEM-EDXS and XRPD characterization of about forty alloys prepared by induction melting and then annealed. Phase equilibria are characterized by the following ternary phases: τ₁-La_2+xSi₂Mg_1−x (0≤x≤0.35,tP10-Mo₂FeB₂), τ₂-LaSi₂Mg₂ (tP5-CeSi₂Mg₂), τ₃-LaSi₂Mg (structure still unknown) and τ₄-La₆SiMg₂₃ (cF120-Zr₆SiZn₂₃). The high temperature binary phase LaMg₂ (cF24-MgCu₂) has been found to be stabilized at 500 ^°C probably by a small amount of Si. Phases in binary subsystems do not generally form extended ternary solid solutions except for (La_1−xMg_x)₃Si₂ (0≤x≤0.167,tP10-U₃Si₂). Crystal structures of phases τ₁-La_2+xSi₂Mg_1−x and (La_1−xMg_x)₃Si₂ are correlated, the former being a substitution derivative of the latter.     

Experimental phase diagram study of the TiAl-rich part of the Ti–Al–Ni ternary system

Phase equilibria of the TiAl-rich part of the Ti–Al–Ni ternary system have been studied experimentally by scanning electron microscopy and electron probe micro-analysis of heat-treated alloys. Partial isothermal sections involving the liquid, β-Ti, α-Ti, α₂-Ti₃Al, γ-TiAl and τ₃-Al₃NiTi₂ phases were constructed between 1623 and 1273 K. Eight three-phase regions of the L + β + α, L + α + γ, L + β + γ, β + α + γ, L + β + τ₃, β + γ + τ₃, β + α₂ + τ₃ and α₂ + γ + τ₃ were derived. Extrapolations of these tie-triangles indicate the occurrence of three transition-type reactions; L + α = β + γ at around 1593 K, L + γ = β + τ₃ at around 1553 K, and β + γ = α + τ₃ at around 1393 K. The Ni solid solubility in the α and α₂ phase is extremely low, less than 1 at.% in all studied temperature ranges.     

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 modeling of the C–Pu system

The thermodynamic modelling of the binary C–Pu system was performed in the framework of the development of a thermodynamic database for nuclear materials, for increasing the knowledge of the physico-chemical behaviour of the fuel and surrounding materials implicated in GFR (gas cooled fast reactor) systems. The critical assessment was carried out using the CALPHAD approach, based on available experimental data on phase diagram and thermodynamic properties of the solid phases.     

Experimental investigation and thermodynamic reassessment of the Fe–Si–Zn system

Based on the critical evaluation of the experimental data available in the literature, the isothermal section of the Fe–Si–Zn system at 873 K was measured using a combination of X-ray analysis and scanning electron microscopy with energy-dispersive X-ray analysis. No ternary phase is observed at 873 K. A thermodynamic modeling for the Fe–Si–Zn system was then conducted by considering the reliable experimental data from the literature and the present work. All the calculated phase equilibria agree well with the experimental ones. It is noteworthy that a stable liquid miscibility gap appears in the computed ternary phase diagrams although it is metastable in the three boundary binaries.     

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.     

Experimental investigation and thermodynamic modeling of the Ni–Ti–V system

The liquidus surface projection and isothermal section at 1273 K of the Ni–Ti–V system were established using X-ray diffraction (XRD), scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS), electron probe micro-analyzer (EPMA) and differential thermal analysis (DTA) techniques. Six primary solidification regions and four invariant reactions were deduced in the liquidus surface projection, and six three-phase regions were derived in the isothermal section at 1273 K. No ternary compound was observed. According to the experimental results in the present work and literatures, the Ni–Ti–V system was modeled by means of the CALPHAD (CALculation of PHAse Diagram) method. Two-sublattice model (Ni,Ti)₁₀(Ni,Ti)₂₀ for binary σ phase was used, and the thermodynamic parameters of the σ and NiV₃ phases in the Ni–V system was reassessed. Solution phases (liquid, fcc, bcc and hcp) were modeled with the substitutional solution model in the Ni–Ti–V system. The compounds, Ni₃Ti, NiTi₂, Ni₃V and σ, were treated as (Ni,Ti,V)_m(Ni,Ti,V)_n, and B2 were treated as (Ni,Ti,V)_0.5(Ni,Ti,V) _0.5Va₃. A set of self-consistent thermodynamic parameters of individual phases was obtained.     

Experimental investigation and thermodynamic description of the Ni–Ti–W system

The liquidus surface projection and isothermal sections at 1173 and 1373 K of the Ni–Ti–W system were constructed on the basis of microstructure and phase constituents of as-cast and annealed alloys, which were obtained by means of scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS), X–ray diffraction (XRD). Six primary solidification regions were determined in the liquidus surface projection. Five and six three-phase regions were derived in the isothermal sections at 1173 and 1373 K, respectively. No new ternary compounds were found. Based on the present experimental data, the Ni–Ti–W system was optimized using CALPHAD (CALculation of PHase Diagram) method. The solution phases, liquid, fcc, bcc, and hcp, were treated as substitutional solution. Two compounds Ni₃Ti and NiTi₂ were treated as (Ni,Ti,W)_m(Ni,Ti,W)_n, and Ni₄W was treated as (Ni,Ti)₄W₁ by a two-sublattice model. NiTi with B2 crystal structure was treated as the ordered phase of bcc solution, and model was (Ni,Ti,W)_0.5(Ni,Ti,W)_0.5(Va)₃. A set of self-consistent thermodynamic parameters was obtained.     

Critical assessment and thermodynamic modeling of the Cu–Fe–O–Si system

The present study is the first Calphad-type assessment of the Cu–Fe–O–Si system. All relevant thermodynamic and phase equilibrium data have been critically evaluated to produce a thermodynamic database describing the Gibbs energies of all phases in the system. The predictive range of the database covers all conditions of pyrometallurgical production of copper in terms of temperature and oxygen partial pressure. Liquid oxide slag and liquid metal phases have been described using two separate solution models, both developed within the framework of the Modified Quasichemical Formalism. Slag model is expressed as [Cu⁺, Fe²⁺, Fe³⁺, Si⁴⁺][O^2-] and metal model is expressed as (Cu^I, Fe^II, O^II). They are internally consistent with the models for fcc–Cu, fcc–Fe, bcc–Fe, spinel, wüstite, CuFeO₂, Cu₂O, Fe₂SiO₄, Fe₂O₃ and SiO₂ obtained in the previous optimizations of the Cu–O, Fe–O, Cu–Fe, Cu–Fe–O, Cu–O–Si, Fe–O–Si sub-systems.