Phase formations in low density high entropy alloys

Phase formations in high entropy alloys (HEAs) with at least two light elements in literature are predicted by CALPHAD (CALculation of PHAse Diagrams) thermodynamic calculations and the results are compared with experimental observations. The comparison suggests that the applicability of traditional CALPHAD calculations depends on the manufacturing processes of HEAs. Factors such as solute trapping, energies of defects need to be considered while predicting phases in HEAs prepared by non-equilibrium processes. The effects of light elements (Al, Ti, Si, alkali and alkaline earth metals) on the phase formations in HEAs are discussed. Especially, intermetallics predicted for Si-containing HEAs by traditional CALPHAD calculation can be suppressed in rapid solidification process, due to the solute trapping effect. Mg or other alkali and alkaline earth metals can lead to the formations of various intermetallics in HEAs prepared by conventional casting, but could be dissolved into solid solutions by non-equilibrium processes such as mechanical alloying. It is proposed that non-equilibrium processes may be an effective way to introduce light elements Si, alkali and alkaline earth metals into HEAs.     

Thermodynamic and diffusion kinetic studies of the Fe-Co system

The phase equilibria, thermodynamic properties and diffusion mobilities of the Fe-Co system were carefully assessed through the CALPHAD methods. As an indispensable tool, the first-principles calculations were carried out to study the magnetic moments and the enthalpies of mixing of the bcc_A2, bcc_B2, fcc_A1 and hcp_A3 phases as well as the point defect types of the bcc_B2 phase. In order to verify the heat capacities reported in the literature, new measurements were conducted in a high-temperature calorimetric apparatus using the three-dimensional calorimetric method. Because of the revision of the thermodynamic parameters in the present work, the diffusion mobilities for the fcc_A1 phase were reassessed. The diffusion mobilities for the bcc_A2 phase were established for the first time based on the experimental diffusion coefficients. For the low-temperature bcc_B2 phase, the diffusion couple experiments conducted in the present work show that the diffusion process is sluggish and the interdiffusion coefficients are difficult to determine. Therefore the tracer diffusivities of Co and Fe in the Fe-Co alloys were used to assess the diffusion mobilities for the bcc_B2 phase, while the composition-distance profile of one diffusion couple was served as a validation of its diffusion mobilities.     

Thermodynamic assessment of Fe–Ti–S ternary phase diagram

A thermodynamic analysis of the Fe-Ti-S ternary system was performed by incorporating first-principles calculations into the calculation of phase diagrams (CALPHAD) method. To evaluate the Gibbs energy, the Debye-Grüneisen model was applied for some sulfides of the Ti-S binary system. In addition, the cluster expansion and cluster variation methods were used for the solid solution phases in the Ti-S binary and (Fe,Ti)S phases. The calculated Ti-S binary phase diagram showed good agreement with the experimental results. The very low solubility of the Ti solid solution in the Ti-S system, as reported by Murray, agreed well with our calculated results. A binodal phase decomposition of the liquid phase was expected in the S-rich region. The Gibbs energy curve of (Fe,Ti)S between FeS and TiS was found to be convex downward. This is characteristic of an isomorphic solid solution, attributed to the attractive interaction between Fe and Ti in (Fe,Ti)S. The vertical phase diagram between FeS and TiS, obtained using the thermodynamic database, was in good agreement with the experimental results of Mitsui et al. The solubility products of (Fe,Ti)S have been experimentally estimated previously. The calculated solubility product agreed with the experimental value of TiS.     

Ferromagnetic ordering and mobility end-members for impurity diffusion in bcc Fe

Based on the experimental data available in the literature, the mobility end-members for impurity diffusion of twelve elements, i.e. Ag, Al, As, Au, Cu, Mo, Nb, Sb, Sn, Ti, W and Zn, in bcc Fe have been critically studied. The effect of ferromagnetic ordering is taken into consideration, which allows the dramatic change of kinetic behaviors around the Curie temperature to be considered. Comprehensive comparisons between the calculated and experimentally measured impurity diffusion coefficients are made, where the good agreement confirms not only the parameters obtained in this work but also the model developed by Jönsson. This work contributes to the establishment of a general mobility database to computationally study microstructure evolution upon heat treatment and performance prediction during service.     

Thermodynamic Modeling of the Succinonitrile-Water System

Succinonitrile-water (SCN-H₂O) system is a widely used transparent metallic alloy system due to its analog solidification behavior to metals. In the present work, Gibbs energy of pure succinonitrile was derived utilizing temperature as well as enthalpy of transformations, and temperature dependencies of heat capacity available in the literature. The phase diagram for the binary SCN-H₂O system was assessed via the CALPHAD approach using phase equilibrium data available in the literature. Self-consistent thermodynamic parameters were obtained. A good agreement between the experimental and calculated data for the phase diagram has been achieved. The present work contributes to the development of the thermodynamic database of the SCN-H₂O system that can be incorporated into thermodynamic and kinetic codes for computational simulations.     

Hydrogen storage in TiZrNbFeNi high entropy alloys,designed by thermodynamic calculations

The hydrogen storage properties of the novel equiatomic TiZrNbFeNi and non-equiatomic Ti₂₀Zr₂₀Nb₅Fe₄₀Ni₁₅ high entropy alloys (HEAs) were studied. These alloys were designed with the aid of thermodynamic calculations using the CALPHAD method due to their tendency to form single C14 Laves phase, a phase desirable for room-temperature hydrogen storage. The alloys, which were synthesized by arc melting, showed a dominant presence of C14 Laves phases with the (Zr, Ti)₁(Fe, Ni, Nb, Ti)₂ constitution and small amounts of cubic phases (<1.4 wt%), in good agreement with the thermodynamic predictions. Hydrogen storage properties, examined at room temperature without any activation procedure, revealed that a maximum hydrogen storage capacity was reached for the equiatomic alloy in comparison to the non-equiatomic alloy (1.64 wt% vs 1.38 wt%) in the first cycle; however, the non-equiatomic alloy presented superior reversibility of 1.14 wt% of hydrogen. Such differences on reversibility and capacity among the two alloys were discussed based on the chemical fluctuations of hydride-forming and non-hydride-forming elements, the volume per unit cell of the C14 Laves phases and the distribution of valence electrons.     

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.