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The ternary Ti-Mo-N system is an important material used as a surface coating, hardener, and wear and corrosion protection layer. Knowledge of the phase equilibria, phase transformations, and phase stabilities of this alloy is important to realizeits potential applications. In this paper, formation energies of three intermetallic compounds, Mo2N-beta, Mo2Ngamma, and MoN-delta, were determined by ab-initio calculations.Then , the Calphad approach was applied to thermodynamically model the Mo-Ti, Mo-N, and Mo-Ti-N systems. The obtained Gibbs energies were used to calculate the phase diagram and thermodynamic properties of the Ti-Mo-N system. The present model is in good agreement with experimental data reported in the literature. The results of this work can be used as a basis for future investigations of the Ti-Mo-N system, as well as a basis for practical industrial applications.

Stacking fault energy (SFE) is of the most critical microstructure attribute for controlling the deformation mechanism and optimizing mechanical properties of austenitic steels, while there are no accurate and straightforward computational tools for modeling it. In this work, we applied both thermodynamic modeling and machine learning to predict the stacking fault energy (SFE) for more than 300 austenitic steels. The comparison indicates a high need of improving low-temperature CALPHAD (CALculation of PHAse Diagrams) databases and interfacial energy prediction to enhance thermodynamic model reliability. The ensembled machine learning algorithms provide a more reliable prediction compared with thermodynamic and empirical models. Based on the statistical analysis of experimental results, only Ni and Fe have a moderate monotonic influence on SFE, while many other elements exhibit a complex effect that their influence on SFE may change with the alloy composition.

High-entropy alloys (HEAs) are a new class of solid-solution alloys that have attracted worldwide attention for their outstanding properties. Owing to the demand from transportation and defense industries, light-weight HEAs have also garnered widespread interest from scientists for use as potential structural materials. Great efforts have been made to study the phase-formation rules of HEAs to accelerate and refine the discovery process. In this paper, many proposed solid-solution phase-formation rules are assessed, based on a series of known and newly-designed light-weight HEAs. The results indicate that these empirical rules work for most compositions but also fail for several alloys. Light-weight HEAs often involve the additions of Al and/or Ti in great amounts, resulting in large negative enthalpies for forming solid-solution phases and/or intermetallic compounds. Accordingly, these empirical rules need to be modified with the new experimental data. In contrast, CALPHAD (acronym of the calculation of phase diagrams) method is demonstrated to be an effective approach to predict the phase formation in HEAs as a function of composition and temperature. Future perspectives on the design of light-weight HEAs are discussed in light of CALPHAD modeling and physical metallurgy principles.

Thermodynamics is the key component of materials science and engineering. The manifestation of thermodynamics is typically represented by phase diagrams, traditionally for binary and ternary systems. Consequently, the applications of thermodynamics have been rather limited in multicomponent engineering materials. Computational thermodynamics, based on the CALPHAD approach developed in the last few decades, has released the power of thermodynamics and enabled scientists and engineers to make phase stability calculations routinely for technologically important engineering materials. Within the similar time frame, first-principles quantum mechanics technique based on density functional theory has progressed significantly and demonstrated in many cases the accuracy of predicted thermodynamic properties comparable with experimental uncertainties. In this paper, the basics of the CALPHAD modeling and first-principles calculations are presented emphasizing current multiscale and multicomponent capability. Our research results on integrating first-principles calculations and the CALPHAD modeling are discussed with examples on enthalpy of formation at 0 K, thermodynamics at finite temperatures, enthalpy of mixing in binary and ternary substitutional solutions, defect structure and lattice preference, and structure of liquid, super-cooled liquid, and glass.

In this paper, we report an investigation of adding a non-hydride forming element in the multicomponent Ti-V-Nb-M system. By the Calculation of Phase Diagrams approach (CALPHAD), the thermodynamic phase stability of the TiVNbT (T = Cr, Mn, Fe, Co, and Ni) was investigated, and Cr was selected as the fourth alloying element due its high tendency to stabilize body-centered cubic solid solutions (BCC). The (TiVNb)100−xCrx alloys (with x = 15, 25, and 35 at.% Cr) were synthesized by arc-melting. The structural characterization reveals that the three alloys were composed of a major BCC phase, which agrees with the thermodynamic calculations. The three alloys absorb hydrogen at room temperature without any activation treatment, achieving a hydrogen uptake of about H/M = 2. The Pressure-Composition-Isotherms curves (PCI) has shown that increasing the Cr amount increases the equilibrium pressures, indicating that tunable H storage properties can be achieved by controlling the alloys’ Cr content.

This report presents a design methodology for refractory high-entropy alloys with a body-centered cubic (bcc) structure using select empirical parameters (i.e., enthalpy of mixing, atomic size difference, Ω-parameter, and electronegativity difference) and CALPHAD approach. Sixteen alloys in equimolar compositions ranging from quinary to ennead systems were designed with experimental verification studies performed on two alloys using x-ray diffraction, energy-dispersive spectroscopy, and scanning electron microscopy. Two bcc phases were identified in the as-cast HfMoNbTaTiVZr, whereas multiple phases formed in the as-cast HfMoNbTaTiVWZr. Observed elemental segregation in the alloys qualitatively agrees with CALPHAD prediction. Comparisons of the thermodynamic mixing properties for liquid and bcc phases using the Miedema model and CALPHAD are presented. This study demonstrates that CALPHAD is more effective in predicting HEA formation than empirical parameters, and new single bcc HEAs are suggested: HfMoNbTiZr, HfMoTaTiZr, NbTaTiVZr, HfMoNbTaTiZr, HfMoTaTiVZr, and MoNbTaTiVZr.

There has been considerable technological interest in high-entropy alloys (HEAs) since the initial publications on the topic appeared in 2004. However, only several of the alloys investigated are truly single-phase solid solution compositions. These include the FCC alloys CoCrFeNi and CoCrFeMnNi based on 3d transition metals elements and BCC alloys NbMoTaW, NbMoTaVW, and HfNbTaTiZr based on refractory metals. The search for new single-phase HEAs compositions has been hindered by a lack of an effective scientific strategy for alloy design. This report shows that the chemical interactions and atomic diffusivities predicted from ab initio molecular dynamics simulations which are closely related to primary crystallization during solidification can be used to assist in identifying single phase high-entropy solid solution compositions. Further, combining these simulations with phase diagram calculations via the CALPHAD method and inspection of existing phase diagrams is an effective strategy to accelerate the discovery of new single-phase HEAs. This methodology was used to predict new single-phase HEA compositions. These are FCC alloys comprised of CoFeMnNi, CuNiPdPt and CuNiPdPtRh, and HCP alloys of CoOsReRu.

Designing high entropy alloys (HEAs) with high strength and excellent ductility has attracted extensive scientific interest. In the present work, the CALPHAD (calculation of phase diagrams) method was applied to guide the design of an (FeCoNi)92Al2.5Ti5.5 HEA strengthened by precipitation hardening. The grain size as well as the size and volume fraction of the precipitates was tailored via a thermomechanical process to optimize the mechanical properties. The uniformly dispersed nano-precipitates are Ni3(Al,Ti)-type precipitates with an L12 ordered structure presenting a fully coherent interface with the face-centered cubic (FCC) matrix. The yield strength of the alloy increases from 338.3 to 1355.9 MPa and the ultimate tensile strength increases from 759.3 to 1488.1 MPa, while the elongation maintains a reasonable value of 8.1%. The striking enhancement of strength is mainly caused by the precipitate’s hardening mechanism, which is evaluated quantitatively by various analytical models. The deformation-induced microbands and the coherent precipitates sheared by dislocations are the deformation and strengthening mechanisms contributing to the superior combination of ductility and strength in the present HEA. This investigation demonstrates that the CALPHAD method is beneficial to the design and optimization of HEAs.

The integrated computational materials engineering (ICME) has achieved great success in accelerating the rational design and deployment of new materials. It is a new route of designing new materials and processes and highlighted by Materials Genome Initiative/Engineering that stresses the high‐throughput computation in addition to high‐throughput experimentation and materials informatics. This article presents a brief review on the basic theories and multi‐scale computational tools of ICME to design advanced steel grades, including the first‐principles calculations, the CALPHAD method (i.e., computational thermodynamics) fueled by dedicated databases, diffusion and phase‐field simulations, as well as finite analysis methods and machine learning. In the ICME scheme to deal with steels, the CALPHAD method is considered as the core to readily consider multi‐component systems and integrated to link the microscopic simulations (such as diffusion and phase field method to predict microstructure evolutions in response to external conditions) and macroscopic finite analysis method to deal with mechanical properties. Two applications are also presented to address the new routes to carry out materials design, especially for advanced steels. A brief review is presented on the basic theories and multi‐scale computational tools of integrated computational materials engineering (ICME) for designing advanced steels, including the first‐principles calculations, the CALPHAD method (i.e., computational thermodynamics) fueled by dedicated databases, diffusion and phase‐field simulations, finite analysis methods and machine learning. In the ICME scheme to design steels, the CALPHAD method is considered as the core to readily consider multi‐component systems, and integrated to link microscopic simulations and macroscopic finite analysis methods.

This work presents a critical review of the application of CALPHAD techniques in the development of high entropy alloys (HEAs) and complex concentrated alloys (CCAs). This assessment covers three major themes: thermodynamics of mixtures and stability, retrospective thermodynamics, and predictive thermodynamics. Based on statistical and thermodynamic analysis, we assess the concept of entropic stabilization. A brief description of the major accomplishments of the CALPHAD technique applied to explain the stability and microstructure of HEAs and CCAs is presented. We describe the role of CALPHAD and its integration with other design tools, such as physicochemical criteria, data mining, and optimization techniques, to accelerate the discovery of new materials. Finally, we recommend future efforts in the development of the next generation of HEAs and CCAs in connection with the design of their microstructures, with an emphasis on precipitation strengthening and twinning-induced or transformation-induced plasticity (TWIP, TRIP).