CALPHAD Calculations Research Articles

IMPROVEMENT OF THE ALLOY STRUCTURE OF THE Ni-Cr-Со-W-Mo-Al-Ti-C SYSTEM

Purpose. Establishing the specifics of the influence of alloying elements on the formation of carbides in the structure, their shape and the possibility of separating TLC phases for the system of the Ni-Cr-Co-W-Mo-Al-Ti-C type using the CALPHAD calculation method of prediction in comparison with data obtained by the method of raster electron microscopy. Research methods. The results of experimental and calculated data, formed on the basis of experimental and results taken from open sources, are presented. The chemical composition was determined on a REM-106I scanning electron microscope equipped with an energy dispersive analysis. Experimental values were processed by the method of least squares with obtaining correlation dependencies of the “parameter-property” type and establishing mathematical equations of regression models that optimally describe these dependencies. Results. It was established that when the concentration of titanium is more than 4 % and molybdenum is more than 6 % and 15 % chromium, the formation of TSC phases (Р, s and m- phases) is possible, which reduce the operational properties of the alloy. It was found that when the alloy contains more than 25 % chromium, a solid chromium-based solution is formed, which reduces the properties of the alloy (mechanical and corrosion). It is shown that the obtained dependences correspond to reality and coincide with experimental data at the level of 10 %. Scientific novelty. Obtained dependences of the influence of alloying elements on the chemical composition of carbides will allow predicting properties without conducting experiments. It was established that changes in the course of dependencies are closely correlated with the processes occurring in the structure of alloys. Practical value. The obtained dependencies can be used both for the development of new heat-resistant alloys and for the improvement of the compositions of industrial alloys.

Optimizing toughness in high entropy alloys using a genetic algorithm: A combined computational and experimental approach

A genetic algorithm (GA) was developed to search for high entropy alloys (HEAs) with good combinations of mechanical properties. The algorithm was designed find single-phase face-centered cubic (FCC) HEAs, already known for their ductility, with high Hall-Petch constants (K) and high critical resolved shear stresses (τY). The objective was to develop a methodology that allows the design of HEAs in a multi-objective environment, focusing on alloys that exhibit enhanced ductility and strength, achieved through an increase in its yield point without significant loss of its ultimate deformation via adjustments of K and τY values, resulting in an alloy with high toughness. The most promising alloy suggested by the genetic algorithm was an unconventional composition (Co32.73Cu15.11Fe0.72Hf0.72Mn35.97Mo3.96Ni10.43Sn0.36), with eight different elements in non-equiatomic ratios with maximized K and τY values. This alloy was then experimentally produced and characterized by scanning electron microscopy (SEM), synchrotron x-ray diffraction (XRD), transmission electron microscopy (TEM) and microhardness, with the objective of validating the predictions made by the GA. An advantage of the proposed method is the possibility of more systematically identifying and exploring new compositions in the complex composition space characteristic of these multicomponent alloys, as it directs its search towards domains that can be used to solve challenging problems involving multi-objective optimization. However, the thermodynamic parameters used for single-phase FCC prediction, namely the valence electron concentration (VEC) and the dimensionless thermodynamic parameter φ, exhibited limitations. These limitations were further explored in the present study, as evidenced by the fact that the microstructure of the selected alloy was not single-phase, which hindered the study of the mechanical properties, predicted exclusively for monophasic FCC alloys. Therefore, this work highlights the necessity for the development of novel thermodynamic equations for phase prediction, or even the integration of the genetic algorithm with other methodologies, such as CALPHAD calculations, to achieve enhanced results.

Effect of hot-rolling process on the microstructure, mechanical and corrosion behaviors of dual-phase Co-based entropic alloys

Two compositions from dual-phase Co-based entropic alloys with high corrosion resistance were chosen, and the effect of hot-rolling process on the microstrcture, mechanical property and corrosion resistance was investigated in this work. The processing parameters were designed and optimized by CALPHAD calculations. For the case of hot-rolled alloys, fcc + hcp dual-phase structures were confirmed by different characterization techniques, including XRD, ECCI, and EBSD. After testing various mechanical properties and electrochemical corrosion behaviors at room temperature, the hot-rolled alloys exhibit an outstanding mechanical and corrosion resistance property. The hot-rolling process improves the electrochemical corrosion resistance slightly and promotes hardness as well as strength-ductility greatly. The experimental characterizations provide plentiful information about microstructure, crystallographic orientation, lattice misorientation, grain boundaries, and so on. More details for the strengthening and hardening mechanisms could be obtained from the EBSD analysis. The current work shed lights on the design of new alloy recipe as well as the synthesis of novel grade dual-phase entropic alloys with excellent combination of mechanical properties and corrosion resistance which could be applied in harsh environments.

Liquid AlCoCrFeNi and AlCoCrFeNiX (X = Mo, Ta) high-entropy alloys on graphite: Wetting, reactivity and CALPHAD modelling

Wettability and interfacial reactivity with graphite of three equimolar High-Entropy Alloys (HEAs), namely AlCoCrFeNi (HEA-base), AlCoCrFeNiMo (HEA-Mo) and AlCoCrFeNiTa (HEA-Ta), were investigated for the first time, aiming to support industrial sectors involving liquid-phase processing routes. Isothermal high-temperature wettability tests were performed at 1400 °C for HEA-base and HEA-Mo, and at 1580 °C for HEA-Ta. The samples were then analysed by SEM-EDS. Based on the in-house-built GHEA thermodynamic database, CALPHAD calculations were used to simulate and discuss liquid-solid interactions occurring at high temperatures as well as transformations taking place in the samples during cooling. HEA-base wetted the graphite well after 5 min and the wetting behaviour significantly improved for HEA-Mo after the same contact time. HEA-Ta, after initial melting and wetting stage, solidified due to high-melting phases formation. All the graphite/HEA samples formed refractory carbides. For HEA-base and HEA-Mo, such carbides were found homogeneously dispersed in the whole drop. In HEA-Ta, TaC formed a compact layer separating two liquids of different compositions, with only one of these being in contact with the graphite substrate. The here proposed combination of experiments and thermodynamic calculations allowed to understand and discuss both high-temperature reactivity and evolution of the systems over cooling. Overall, a remarkable agreement between equilibrium calculations and experimental findings was observed for these complex dynamic systems.

Decreased Metal Dusting Resistance of Ni-Cu Alloys by Fe and Mn Additions

Ni-Cu alloys are promising for application at temperatures between 400–900 °C and reducing atmospheres with high C-contents. Typically, under such conditions, metallic materials in contact with the C-rich atmosphere are degraded by a mechanism called metal dusting (MD). Ni-Cu-alloys do not form protective oxide scales, but their resistance is attributed to Cu, which catalytically inhibits the C-deposition on the surface. Adding other alloying elements, such as Mn or Fe, was found to enhance the MD attack of Ni-Cu alloys again. In this study, the effect of the Mn and Fe is divided into two affected areas: the surface and the bulk. The MD attack on binary Ni-Cu alloys, model alloys with Fe and Mn additions, and commercial Monel Alloy 400 is experimentally demonstrated. The surface electronic structure causing the adsorption and dissociation of C-containing molecules is investigated for model alloys. Analytical methods such as scanning electron microscopy combined with energy-dispersive X-ray spectroscopy, electron probe microanalysis combined with wavelength-dispersive X-ray spectroscopy, X-ray diffraction analysis, and near-edge X-ray absorption fine structure measurements were used. The results are correlated to CALPHAD calculations and atomistic simulations combining density functional theory calculations and machine learning. It is found that the Cu content plays a significant role in the surface reaction. The effect of Mn and Fe is mainly attributed to oxide formation. A mechanism explaining the enhanced attack by adding both Fe and Mn is proposed.

An integrated modeling framework with open architecture for phase field simulation of multi-component alloys

An integrated modeling framework (PanPhaseField) has been developed, which enables a direct and fast coupling between CALPHAD calculations and large-scale phase field simulations for multi-component alloys. It adopts an open architecture allowing for integration of user-defined phase field models in a plug-and-play manner by taking full advantage of the user-friendly graphical interface of Pandat software. The developed modeling platform becomes an enabling tool that can be used to simulate the evolution of spatially varying microstructures of industrial complex alloys for various engineering applications.

Computational thermodynamics-guided alloy design and phase stability in CoCrFeMnNi-based medium-and high-entropy alloys: An experimental-theoretical study

A computational thermodynamics approach has been employed to design CoCrFeMnNi-based medium- and high-entropy alloys (M/HEAs) with systematically varied compositions (Co((80-X)/2)Cr((80-X)/2)FeXMn10Ni10 with x = 30, 40, and 50 at.%) and phase stability. Since the formation of sigma phase, usually brittle and undesirable, is a common concern, when this class of alloys is subjected to elevated temperatures (600–1000 °C), predicting its formation becomes essential. Thus, its formation and the phase equilibria were studied using the CALPHAD method, and two empirical methods, namely, valence electron concentration (VEC) and paired sigma-forming element (PSFE). Isothermal aging treatments at 900–1100 °C for 20 h were performed, since CALPHAD and VEC/PSFE predictions diverged. Both prediction methods were compared with experimental characterization by a combination of scanning electron microscopy and high-energy synchrotron X-ray diffraction. The predictions from the VEC/PSFE and CALPHAD calculations (depending on the database used) were shown to be quite accurate.

Experimental and theoretical investigation on refining mechanism of Mg2Si by Y addition in the Mg-Al-Si alloys

Aiming at development of new lightweight and high-strength magnesium alloys, a combined experimental and theoretical study on refining mechanism of Mg2Si by Y addition in the Mg-Al-Si alloys was performed. Two alloys, Mg63.32Al22.83Si13.85 and Mg62.56Al22.55Si14.36Y0.52 (wt.%), were prepared and investigated by combining experimental characterization with quantum-mechanical and CALPHAD calculations. The experimental results indicated that Y can refine the Mg2Si phase in Mg-Al-Si alloys but it is rather sensitive to the preparation procedure of the alloys. It was observed that Al4MgY is surrounded by Mg2Si in the as-cast alloys with Y, but it undergoes separation after homogenization annealing. First-principles calculations revealed that the mechanism of Y refining the Mg2Si phase is direct adsorption on the Mg2Si surface rather than indirect adsorption in the form of the elements atomic substitution or entering the center interstitial sites of Mg2Si. The significant refinement of the Mg2Si phase after annealing is attributed to recrystallization within the grains, eliminating the original grain boundaries, and the surface activity is reduced with Y adsorption, resulting in the formation of new and smaller Mg2Si phases. The mechanism behind the Al4MgY phase being surrounded by Mg2Si in the as-cast state but subsequent separation after homogenization annealing is not heterogeneous nucleation, but maybe due to liquid entrapment.

Laser powder bed fusion of oxide dispersion-strengthened IN718 alloys: A complementary study on microstructure and mechanical properties

In this study, two new grades of oxide dispersion strengthened (ODS) Inconel 718 (IN718) alloys were designed by the thermochemical CALPHAD method and produced by laser powder bed fusion (LPBF) technique. Alloys designated as IN718-YF and IN718-YFH, that consist Y2O3–FeO and Y2O3–FeO–Hf, respectively, were fabricated with >99.9 % densification using optimized process parameters. CALPHAD calculations were highly consistent with experimental findings, highlighting the formation of Al-containing Y–Ti–O and Y–Hf–O nano-oxides in both alloy types. Texture analyzes revealed no significant texture development in as-built (AB) or heat-treated (HT) alloys. Heat treatment was applied at 1050 °C for 1 h to enhance nano-oxide density. The nano-oxide number density remained similar in IN718-YF while it decreased in IN718-YFH alloy as a result of carbide formation after the heat treatment. Besides, formation of secondary γ′ particles was observed in the IN718-YFH/HT alloy. Even though the yield strengths of IN718-YF and IN718-YFH alloys in both AB and HT conditions were similar, the ductility of IN718-YFH was ∼50 % less in almost all conditions compared to the ductility of IN718-YF. This has been shown to be as a result of irregular shaped micron-sized Y-Hf-O oxides, martensite formation in AB condition, increased amount of carbides and existence of secondary γ′ particles in HT condition in IN718-YFH. High density of stacking faults (SF) forming at the interface of the nano-oxides have been detected in IN718-YF alloys. Besides dislocation/nanoparticle interactions, SFs which are responsible for the delocalization of the deformation improve the ductility of IN718-YF alloys. Overall, high temperature mechanical tests exhibit that both alloys have higher strength with improved ductility compared to the standard IN718 alloys, indicating the contribution of the nano-oxides.

High entropy alloys (FeCoNi)0.75Cr0.25-xCux – thermal stability and physical properties

The paper reports on the phase stability of the (FeCoNi)0.75Cr0.25-xCux HEA system with equimolar ratio of Fe, Co and Ni by differential scanning calorimetry (DSC) and measurements of physicochemical properties: density, electrical resistivity, Seebeck coefficient, thermal conductivity, and magnetic behaviour in a broad temperature region as well as hardness and elastic modulus at room temperature as a function of the gradual substitution of chromium by copper in a series of (FeCoNi)0.75Cr0.25-xCux alloys with different mole fraction of Cu (x = 0, 0.05, 0.1, 0.15 and 0.2). DSC measurements showed that all alloys are thermally stable. Increasing content of Cu was found (i) to increase the formation of a fcc Cu-rich phase, (ii) to strengthen ferromagnetic interactions, resulting in rising ordered magnetic moments, as well as in growing ferromagnetic transition temperatures, and (iii) to distinctly change physical properties like electrical resistivity, thermal expansion, and mechanical properties. Experimental data regarding the phase stability are supported by CALPHAD calculations.

Unraveling the formation of L12 nano-precipitates within the FCC-phase in AlCoCrFeNi2.1 eutectic high entropy alloy

The present study investigates the formation mechanism of L12 nano-precipitates within the FCC phase during the solidification process of the AlCoCrFeNi2.1 eutectic high entropy alloy. For this purpose, advanced characterization techniques, including high-energy synchrotron X-ray diffraction, transmission electron microscopy, and atom probe tomography were employed, along with CALPHAD calculations. The solidified microstructure of the AlCoCrFeNi2.1 eutectic high entropy alloy consists of five phases: disordered FCC, disordered BCC, ordered B2 BCC, ordered L12 FCC, and sigma (σ). The dendritic regions of the disordered FCC phase were formed due to non-equilibrium solidification, while the L12 nano-precipitates were uniformly embedded within the disordered FCC matrix. These nano-precipitates were enriched with Al and Ni, while being depleted in Co, Cr, and Fe. These nano-precipitates might form around the critical temperature of 600 °C due to short-range diffusion of Al and Ni because of nucleation and growth mechanism during the solidification process.

Integration of CALPHAD calculations and nanoindentation test for the design of low-modulus near-β titanium

Integration of CALPHAD calculations and nanoindentation test for the design of low-modulus near-β titanium

Experimental and computational analysis of stacking fault energy in B-doped Fe50−XMn30Co10Cr10BX multi-principal elements alloys

The effect of boron doping in Fe50−XMn30Co10Cr10BX multi-component alloys on the resulting stacking fault energy has been experimentally and computationally assessed to understand the alloys' deformation mechanisms from structural and thermodynamic perspectives. Firstly, the fcc and hcp phases were identified together with stacking faults along their (110) planes using high-resolution transmission electron microscopy. At the same time, they were theoretically predicted through thermodynamic CALPHAD and ab initio calculations. The average stacking fault energy for the boron-free alloy was 23.9 ± 2.4 mJ/m2, suggesting that the deformation mechanisms relate to dislocation slip and deformation twinning. The average stacking fault energy for the highest boron content (5.4 at%) was 50.1 ± 14.1 mJ/m2, indicating dislocation glide as the possible deformation mechanism. The boron content in the solid solution was modelled. The modelling suggested that the presence of Cr-B, Mn-B and Fe-B bonds points towards forming (Cr,Fe)2B borides, which was experimentally confirmed. The borides, fcc phase stability, and the boron in solid solution contribute to increased stacking fault energy, preventing the motion of Shockley partial dislocations and influencing the ɛ-hcp martensitic transformation.

Combinatorial Alloy Design and Microstructure Evolution in Laser-cladded Al–Co–Cr–Fe–Ni–Ti Compositionally Complex Alloys

In this work, we propose a strategy for high-throughput design and development of compositionally complex alloys combining theoretical and experimental alloy screening. This methodology was applied for the exploration of the (Co2CrFeNi2)1-x-yTixAly subsystem of so-called high entropy superalloys in the Al–Co–Cr–Fe–Ni–Ti alloy system. Alloy design was guided by thermodynamic calculations based on the CALPHAD approach. The evolution of the microstructure with increasing Al and Ti content was analyzed in the as-built, homogenized and age-hardened conditions by means of scanning electron microscopy, energy-dispersive X-ray spectroscopy and electron backscattered diffraction. Additionally, the evolution of the sample hardness with increasing Al and Ti contents was determined for all conditions. Based on the experimental results, the reliability of the CALPHAD calculations was assessed. Generally, a good agreement between calculations and experiments is achieved in the homogenized state. In the aged conditions, the CALPHAD predictions of the precipitation processes are partly inaccurate and need improvement. Optimal Al and Ti concentrations are derived for age hardening through L12 and combined L12 + B2 precipitations.

Simulations of self- and Xe diffusivity in uranium mononitride including chemistry and irradiation effects

A combination of density functional theory and empirical potential atomic scale simulations have been used to determine a model for defect stability and mobility in uranium mononitride (UN), as a function of temperature (T) and N2 partial pressure (pN2). Using the model, predictions of hypo-stoichiometry under U-rich conditions compare favorably to CALPHAD calculations using the TAF-ID database. Furthermore, our predictions of U and N self-diffusivity are in good agreement with experiments carried out as a function of T at specific partial pressures under thermal equilibrium. The validated atomic scale data have then been implemented within a cluster dynamics method to simulate irradiation-enhanced defect concentrations. All defects and clusters studied have significantly enhanced concentrations, with respect to thermal equilibrium, as T is lowered. The irradiation-enhanced Xe diffusivity is compared to post-irradiation annealing and in-pile experiments. The contributions of various defects and clusters to non-stoichiometry, self-diffusivity, and Xe diffusivity are discussed.

Influence of chemical composition on coarsening kinetics of coherent L12 precipitates in FCC complex concentrated alloys

In this study, we report the experimental coarsening kinetics at 850, 900 and 950 °C of four complex concentrated alloys in the Al–Ti–Cr–Fe–Co–Ni senary system with different chemical compositions but a similar γ’ (L12) volume fraction (∼35 % at 950 °C) in a face-centered cubic (γ, FCC) matrix. The selected alloys were specifically designed to investigate the influence of Fe additions and Ni–Co substitutions on Ostwald ripening kinetics. Atom Probe tomography (APT) was used to determine the compositions of the FCC and L12 phases, which agree very well with Calphad calculations at thermodynamic equilibrium. Thermo-kinetic modeling of L12 precipitation was carried out using the Prisma module developed by Thermo-Calc and compared with experimental results. Apparent activation energies were determined and discussed in light of diffusion-controlled coarsening models to identify the key parameters affecting Ostwald ripening. We suggest that the abnormally high apparent activation energies results from composition-dependent parameters. When the latter are accounted for, the corrected activation energies for coarsening are in better agreement with available diffusion data.

A comparative study on nanocrystalline soft magnetic Fe-Si-B-Nb-Cu alloys made of pure elements and ferro-alloys

In the present study, we report a cost-effective method of flux-shielded air induction melting using commercial grade master alloys to produce nanocrystalline soft magnetic Fe73.5Si13.5B9Nb3Cu1 alloy. For comparison, the alloy was made from highly pure raw materials as well. The structure and soft magnetic properties of the commercial grade alloy is similar to the pure one. Air induction melting process with flux not only removed impurities through chemical reactions, it also provided protection from oxidation. Studies of glass formation through experimental findings and Glass Forming Ability (GFA) calculations through ΔT value, α-parameter and PHSS parameter and studies using Calphad (Calculation of Phase Diagram) method have shown that the impurities present in the commercial grade alloy did not affect the glass formation compared to the pure grade alloy. Impurities present in the commercial grade alloy increase the activation energy of crystallization of Fe3Si phase, which in turn influences the volume fraction and grain size of Fe3Si phase during annealing treatment. Amorphous phase TC was found to decrease due to the impurities present in the amorphous phase and this decreased exchange interaction between Fe-Fe atoms. Saturation magnetization and coercivity of commercial grade alloy are almost equivalent to the alloys prepared with pure elements and they are independent of type and concentration of impurities. Lowest coercivity in commercial grade alloy can be achieved in less annealing time which can lead to increase the productivity and reduce the cost further.

Composition- and temperature-dependence of β to ω phase transformation in Ti-Nb alloys

ω phases have shown great effects on the superelasticity and modulus of metastable β-Ti alloys. In this study, the microstructure evolution during cooling and aging for β → ω phase transformation is investigated by integrating a thermodynamic database with phase field simulations. Our CALPHAD calculations based on an available thermodynamic database give the Gibbs energies of metastable β (Nb-lean β1 + Nb-rich β2 produced via spinodal decomposition) and ω phases in Ti-Nb. Informed by the results, our phase field simulations show that the formation mechanisms of ω exhibit dependence on the composition and temperature. The ω can form in Ti-26 at.% Nb without the assistance of spinodal decomposition. Further analysis shows that the precursory spinodal decomposition in the β phase occurs in Ti-50 at.% Nb, and could induce geometrically confined ω. The novel transformation pathway could create unique morphology of ω. This study could elucidate new insights into the ω phase transformation in Ti-Nb alloys and metastable β-Ti alloys having spinodal decomposition.

Probing phase stability in CrMoNbV using cluster expansion method, CALPHAD calculations and experiments

High entropy alloys (HEA), a novel class of materials with multiple principal elements, allow us to tune the properties within a wide composition range where the solid-solution phase is stable. However, it is difficult to experimentally determine the boundaries of the single-phase region. In this paper, we calculate the phase diagram of the CrMoNbV quaternary system, as well as its constituent binary and ternary subsystems, using a combination of the cluster expansion method and CALPHAD calculations. We further verify these results by carrying out experiments at two different compositions of the full quaternary system. Our work shows how these computational tools can enable efficient discovery and development of new HEAs.

Phase stability behavior of (Ti,Al,Si)N multi-principal nitrides regulated by the Si content: Thermodynamics and first principles calculations

The cubic (B1) (rock salt-type) Ti(1−x)AlxN system is one of the most important protective coatings in industry due to properties such as hardness and thermal stability. Moreover, different alloying elements have been studied to increase its working temperature. Silicon has been demonstrated as an interesting option, since it can improve the oxidation resistance and stabilize the system in the hexagonal (B4 wurtzite-type) phase. Different experimental studies have been developed to understand the role of Si in the conformation of Ti(1−x-y)AlxSiyN pseudo-ternary coatings. However, some results seem to be contradictory. Here, we used ab initio and CALPHAD calculations to understand the Si incorporation effects on the phase stability and the critical Si composition. We found that the maximum mixing enthalpy for B1 falls on the TiN-AlN side of the ternary diagram and continues until almost equimolar composition. The B1-B4 phase transition point shifted significantly from x(AlN) = 0.71 without Si to x(AlN) = 0.21 with x(SiN) = 0.4. The critical composition of x(SIN) = 0.06 was found, where the miscibility gap region increased, demonstrating unfavorable results if going higher in Si content.The ab-initio calculations showed that the inclusion of silicon reduced the mechanical properties of the B1 phase, but at the critical threshold of 10 at% of silicon content, the mechanical properties did not significantly diminished. Calculated diagrams at equilibrium conditions mapped out the phase evolution to determine the phase transition paths and phase dependence on common coating deposition parameters. These results could serve as a reference for the experimental obtaining of improved hard coatings based on the (Ti,Al,Si)N multi-principal nitride.