Valence Electron Concentration Research Articles

The eutectic compositional space in Al-Cr-Fe-Ni system utilizing the high-throughput Calphad approach

Eutectic High-Entropy Alloys (EHEAs) show promise in balancing strength and ductility, along with excellent castability and chemical homogeneity. However, identifying optimal eutectic compositions in HEAs has been a persistent challenge, primarily due to the lacuna of multi-component phase diagrams. In addressing this challenge, the eutectic compositional space in Al-Cr-Fe-Ni is unveiled for the first time as a case study using the High-Throughput Calphad methodology. By integrating the Python application programming interface into Thermo-Calc, Latin Hypercube Sampling generated 100,000 compositions examined for eutectic formation based on thermodynamic parameters. This analysis revealed the significant correlation of valence electron concentration, enthalpy of mixing, and atomic size difference on eutectic formation. Moreover, the predictions of the proposed design methodology were compared with reported eutectic compositions, exhibiting excellent agreement. Further, a novel dual-phase eutectic alloy featuring an FCC+B2 combination predicted through the proposed design framework has been successfully cast, providing further experimental validation.

Phase stability and elastic properties of NbMoTaWMx (M = Al, V, Zr, Tc, Re and Ir) RHEAs: A first-principles assessment

Using the exact muffin-tin orbital (EMTO) method in combination with the coherent potential approximation (CPA), we studied the influence of alloying elements Al, V, Zr, Tc, Re and Ir on the phase stability, lattice parameters, densities, and elastic properties of NbMoTaWMx (M = Al, V, Zr, Tc, Re, Ir; 0 ≤ x ≤ 1.0) refractory high entropy alloys. The predicted lattice parameter and elastic parameters agree with the available experimental and theoretical data. We calculated the atomic size difference (δ), the valence electron concentration (VEC) and the total energy of face-centered cubic (fcc), body-centered cubic (bcc) and hexagonal closed-pack (hcp) structures. We found that all studied NbMoTaWMx (M = Al, V, Zr, Tc, Re, Ir; 0 ≤ x ≤ 1.0) systems have the bcc structure. We showed that Al and Ir decrease the stability of the bcc structure and Zr significantly enlarges the lattice parameter of the host. Vanadium increases the ductility of NbMoTaW system. On the other hand, Al and Ir have strongly non-linear effect on the ductility, with clear minimum at x = 0.55. The present results provide consistent theoretical data and call for experimental investigation for these alloys.

Field-assisted sintering of high-entropy alloy-reinforced aluminium matrix composites: phase identification and microstructural properties

AbstractThis study investigates the design, phase identification, and microstructural properties of high-entropy alloy (HEA)-reinforced aluminium (Al) matrix composites. Thermophysical expressions for HEAs were employed during the design phase of the HEA; both theoretical frameworks and experimental analyses were used to anticipate stable phases while a field-assisted sintering technique was employed to consolidate the samples. Calculation of phase diagram (CALPHAD) predictions for the phases present in the HEA align with valence electron concentration (VEC) calculations as both predicted the presence of BCC and FCC phases. The microhardness results reveal a substantial increase in the hardness value of the composites as compared to the pure Al, such that as low as 5 wt% HEA addition resulted in over a 100% improvement, while the densification of the composites was found to decrease with an increase in the wt% of HEA. SEM micrographs and XRD analyses show fair dispersion, bonding, and phase integration in the HEA-reinforced composites.

Unravelling the Role of the BCC-B2 Transition and V Occupancies in the Contradictory Magnetism-Ductility Relationship of FeCoV Alloys

The contradictory relationship between magnetism and ductility restricts further applications of FeCoV alloys in high-performance electrical machines. The role of the BCC-B2 transition, accompanied by vanadium (V) site occupancies, in magnetic moments and ductility has been explored using first-principles calculations. The variations in magnetism and ductility of FeCoV alloys are attributed to the coupling of the BCC-B2 transition and V occupancies. When V replaces Fe atoms in the equiatomic B2-FeCo alloy, the superior magnetism observed in B2-Fe50-cCo50Vc alloys is a consequence of the enhanced local magnetic moment of Fe and the ferrimagnetic-ferromagnetic transition in the magnetic state. Moreover, due to the preferential V occupancy in the B2 phase, the B2-Fe46Co50V4 alloy exhibits comparable ductility to the BCC-Fe50Co46V4 alloy. The results indicate that the increased brittleness in the B2 phase arises from the raised Peierls stress and the enhanced covalent component in interatomic bonding, which is caused by the strong hybridization between Fe and Co atoms. Pearson correlation analysis illustrates that valence electron concentration (VEC) and V content are significant factors in the contradictory relationship between magnetization and ductility. The theoretical results demonstrate that tuning the V content and atomic occupancies is helpful to achieve a trade-off between magnetization and ductility in B2-FeCoV alloys.

Regulation of chemical microenvironment to overcome strength-ductility trade-off in FeCrVTiSix high-entropy alloys coating

Developing metallic materials with both high strength and ductility is an enormous challenge in the field of materials science and engineering due to commonly known “strength-ductility trade-off”. In this work, we proposed a regulation strategy of the chemical microenvironment through changing valence electron concentration (VEC) to achieve simultaneous improvement of the strength and ductility of metallic materials. Taking FeCrVTiSix system as a proof-of-concept model, we first predicted the influence of Si on the chemical microenvironment through density functional theory calculations. These calculations unveiled that Si atoms effectively modify the bonding state among alloy elements, resulting in an enhancement of the strength within the FeCrVTi alloy system while maintaining its ductility. Building upon this insight, we successfully synthesized FeCrVTiSix alloys coating using laser cladding techniques. Subsequent tests, including nanoindentation, Vickers hardness, and tensile assessments, unequivocally demonstrated that the introduction of Si significantly increases the strength of the alloy while maintaining its ductility. Si atoms play a pivotal role in modulating the slip behavior of high-entropy alloys (HEAs) by reshaping the chemical microenvironment, thus enabling the elevation of strength in HEAs while preserving ductility. This work provides a novel approach for designing HEAs that effectively circumvent the “strength-ductility trade-off”, potentially broadening the horizons of engineering applications for HEAs coating.

Excellent specific strength-ductility synergy in novel complex concentrated alloy after suction casting

Lightweight alloys are known to improve the fuel efficiency of the structural components due to high strength-to-weight ratio, however, they lack formability at room temperature. This major limitation of poor formability is most of the time overcome by post-fabrication processing and treatments thereby increasing their cost exponentially. We present a novel Ti50V16Zr16Nb10Al5Mo3 (all in at. %) complex concentrated alloy (Ti-CCA) designed based on the combination of valence electron concentration theory and the high entropy approach. The optimal selection of constituent elements has led to a density of 5.63 gm/cc for Ti-CCA after suction casting (SC). SC Ti-CCA displayed exceptional room temperature strength (UTS ∼ 1.25 GPa) and ductility (ε ∼ 35 %) with a yield strength (YS) of ∼ 1.1 GPa (Specific YS = 191 MPa/gm/cc) without any post-processing treatments. The exceptional YS in Ti-CCA is attributed to hetero grain size microstructure, whereas enormous strength-ductility synergy is due to the concurrent occurrence of slip and deformation band formation in the early stages of deformation followed by prolonged necking event due to delayed void nucleation and growth. The proposed philosophy of Ti-CCA design overcomes the conventional notion of strength-ductility trade-off in such alloy systems by retaining their inherent characteristics.

Phase stability and mechanical properties of the six-principal element TiVNbCrCoNi alloys

This study designed a series of six-principal element TiVNbCrCoNi alloys according to the maximum entropy principle under the constraint of valence electron concentration (VEC). The phase stability and mechanical properties were investigated. It was showed that at VEC levels below 5.2, the body-centered cubic (BCC)-structured solid-solution phase remained stable at room temperature. As VEC exceeded 8.0, the face-centered cubic (FCC)-structured solid-solution phase stabilized. In the VEC range of 5.2–8.0, (Co, Ni)Ti and Ni3Nb intermetallic compounds formed combining with the solid-solution phases. Both yield strength and ductility increased with increase of VEC in the BCC-structured solid-solution alloys. The phase stability was elucidated through First-principle and thermodynamic calculations, while the evolution of mechanical properties of solid-solution alloys was evaluated in terms of multiple parameters. The thermodynamic calculation achieved satisfactory accuracy after being adjusted to utilize atomic bond enthalpy instead of atomic electronegativity difference.

Hardness of single phase high entropy carbide ceramics with different compositions

Five high entropy carbide ceramics, (Hf0.2,Nb0.2,Ta0.2,Ti0.2,Zr0.2)C, (Cr0.2,Hf0.2,Ta0.2,Ti0.2,Zr0.2)C, (Hf0.2,Mo0.2,Ta0.2,Ti0.2,Zr0.2)C, (Hf0.2,Ta0.2,Ti0.2,W0.2,Zr0.2)C, and (Hf0.2,Mo0.2,Ti0.2,W0.2,Zr0.2)C, were synthesized by carbothermal reduction of oxides and direct current sintering. The five high entropy carbide ceramics were determined to be nominally phase-pure with relative densities of more than 98.9% and mean grain sizes of less than 5 μm. Average Vickers hardness values ranged from 19.2 ± 0.4 GPa for (Hf0.2,Nb0.2,Ta0.2,Ti0.2,Zr0.2)C at a load of 2 kgf to 43.5 ± 0.4 GPa for (Hf0.2,Mo0.2,Ti0.2,W0.2,Zr0.2)C at a load of 0.05 kgf. Hardness generally increased with increasing the valence electron concentration and strain as measured by the Williamson–Hall analysis. However, neither correlation was conclusive enough to be a clear indicator of hardness. Instead, it was determined that a combination of effects that includes the valence electron concentration, lattice strain, and grain size all contribute to the hardness of high entropy carbide ceramics.

Evolution of tensile strength and ductility of the non-equimolar TiVNbMoCr alloys with maximum entropy under the VEC constraint

In this work, a series of non-equimolar TiVNbMoCr alloys were designed according to the maximum entropy principle under the valence electron concentration (VEC) constraint. The effect of the physical parameters on tensile strength and elongation was experimentally investigated and comprehensively discussed. It was found that the lattice constant a and the average grain size d vary with relative changes in the content of each component, and exhibit negative correlations to VEC. Whereas, the self-interstitial formation energy Ei, the atomic radius mismatch δ, the shear modulus mismatch η and the shear modulus G exhibit positive correlations to VEC. These parameters have a significant impact on tensile properties of the alloys. Except for Burgers vector magnitude, the critical physical parameters in the Senkov and Labusch-Maresca-Curtin's strengthening models are positively correlated to the yield strength. The ductility of the solid-solution TiVNbMoCr alloys is related to VEC, a, d and the grain boundary characteristics in strain accommodation, which respectively belong to intrinsic, crystallography structural and microstructural types of parameters.

Characterization of cosputtered (TiZrHfY)Nx films

Medium-entropy TiZrHfY alloy films and corresponding nitride (TiZrHfY)Nx films were fabricated through cosputtering. The Ti0.24Zr0.23Hf0.27Y0.26 film had the form of a hexagonal close-packed (HCP) solid solution with a mixing enthalpy of 9.09 kJ/mol, mixing entropy of 11.50 J/mol·K (1.38 R), atomic size difference of 7.72 %, and valence electron concentration of 3.73. Moreover, this film had a hardness of 6.0 GPa and an elastic modulus of 106 GPa. (TiZrHfY)Nx films with various stoichiometric ratios (x) were fabricated by adjusting the reactive gas flow ratio fN2 [N2/(N2 + Ar)] in the range 0.1–0.7. Adding N to the TiZrHfY matrix resulted in a change of phase from an HCP structure to a face-centered cubic phase. The (Ti0.23Zr0.18Hf0.24Y0.35)N0.71 film (with fN2 = 0.2) exhibited the most favorable mechanical properties, having a hardness of 19.1 GPa and an elastic modulus of 244 GPa. Moreover, the film had the highest critical loads (LC3 = 46.6 N) among the films analyzed in the scratch test. The anticorrosive properties of the TiZrHfY and (TiZrHfY)Nx films were evaluated using potentiodynamic polarization curves, obtained in 3.5 wt% NaCl aqueous solution. High polarization resistance of 1.1 × 106 Ω·cm2 was obtained for the (Ti0.23Zr0.18Hf0.24Y0.35)N0.71 film, which was 145 times higher than that of the bare SUS420 substrate. The (Ti0.23Zr0.18Hf0.24Y0.35)N0.71 film had the most favorable mechanical and anticorrosive properties of the surveyed (TiZrHfY)Nx films.

Body-centered cubic phase stability in cobalt-free refractory high-entropy alloys

Cobalt-free refractory high-entropy alloys (RHEAs) are strong contenders for structural materials in nuclear reactors because they do not exhibit cobalt activity under irradiation. The mechanical properties and thermal stability of RHEAs are primarily attributed to the solid solution phase, which is essentially the body-centered cubic (BCC) phase. The BCC phase formation rules thus became the basic criterion in the compositional design of RHEAs. In this paper, the BCC phase formation rules in cobalt-free RHEAs were determined via the calculation of six semiempirical parameters, namely, the entropy of mixing, enthalpy of mixing, atomic size difference, Ω-parameter, d-orbital energy level and valance electron concentration. The mixing enthalpy and atomic size differences are more effective than other semiempirical parameters for predicting BCC phase stability in cobalt-free RHEAs. The presence of aluminum is found to cause a notable alteration in the range of phase stability in cobalt-free RHEAs.

Improving the performance of machine learning model predicting phase and crystal structure of high entropy alloys by the synthetic minority oversampling technique

It is critical to select the suitable integration of elements that has an influence on phase formation when selecting the proper High Entropy Alloys (HEAs) with desired qualities. Machine Learning (ML) models were used to predict the phase and crystal structure of HEAs in this study. Trained on extensive experimental datasets, the set of input characteristics includes Atomic size difference, Mixing Enthalpy, Mixing Entropy, Valence Electron concentration, Electronegativity difference, Ω and Average Melting Temperature. The phase is divided into three categories: Solid solution (S), Dual phase (D), and Intermetallic (Im). Crystal structure classifications include BCC, FCC, and FCC+BCC. For phase and crystal structure prediction, five ML algorithms were used: Decision Tree (DT), K Nearest Neighbour (KNN), Random Forest (RF), Gradient Boosting (GB) and eXtreme Gradient Boosting (XG Boosting), The classification of the HEAs phase has been predicted with great accuracy using an XG Boosting (80 %) and Random Forest exhibits the highest accuracy (94 %) for crystal structure prediction when model is trained on an experimental dataset. Even though the ML model predicts the classes with a better degree of accuracy (>80 %), the F1 value of each class varies more dramatically. This issue has arisen as a result of an imbalance in the dataset's class distribution. To boost performance, this work uses an ML model in conjunction with the Synthetic Minority Oversampling Technique (SMOTE). According to this approach, XG boosting identified the crystal structure with 93 % accuracy and predicted the phase of HEAs with 84 % accuracy. Additionally, it has been noted that each class's F1 score improved and the difference between them was reduced after using the SMOTE technique. It is evident that the SMOTE approach has improved the ML model's ability to differentiate between the various classes.

Microstructure characterization and phase evolution of equiatomic AlCoMoFeNi high entropy alloy synthesized by mechanical alloying

The present study deals with the fabrication of a novel AlCoMoFeNi high-entropy (HEA) alloy using mechanical alloying techniques. The developed HEA was characterized by X-ray diffraction, differential scanning calorimetry (DSC), scanning electron microscopy (SEM) equipped with energy dispersive x-ray spectroscopy (EDX), and transmission electron microscopy (TEM). The crystallite size of the high-entropy alloy solid solution was determined to be 20 ± 1 nm, with a lattice strain of 0.467 ± 0.03 % and a lattice parameter of 3.98 ± 0.08 Å. A number of characteristics, including melting point, mixing enthalpy change, mixing entropy change, atomic size difference, electronegativity difference, and valence electron concentration, were computed in order to ascertain the conditions regulating the formation of high-entropy alloys. A HEA with BCC and FCC solid solution was obtained after mechanical alloying, which was confirmed by experimental findings as well as thermodynamic calculations.

Machine learning guided prediction of the yield strength and hardness of multi-principal element alloys

Background Multi-Principal Element Alloys (MPEAs) have better properties, such as yield strength, hardness, and corrosion resistance compared to conventional alloys. Compositional optimization is a challenging task to obtain desired properties of MPEAs and machine learning is a potential tool to rapidly accelerate the search and design of new materials. Methods We have implemented different machine learning models to predict the yield strength and Vickers hardness of MPEAs at room temperature and quantify the uncertainty of the predictions. Results Our results suggest that valence electron concentration (VEC) is the key feature dominating the yield strength and hardness of MPEAs. Our predicted yield strength and hardness values for the experimental validation set show < 15 % error for most cases with respect to the experimental values. Conclusions Our machine learning model can serve as a useful tool to screen half a trillion MPEAs and down select promising compositions for useful applications.

Structural and mechanical properties of magnetron sputtered (NbxMo1-x)C thin films

While transition metal carbides (TMCs) exhibit favourable mechanical properties, alloying according to the valence electron concentration (VEC) has the potential to further enhance the properties of these hard but inherently brittle materials. This study investigates the influence of alloying on the microstructure and mechanical properties of (NbxMo1-x)C carbide films, including binary references and ternary compositions with varying metal ratios (x between 0.35 and 0.53). Furthermore, the influence of various substrate materials is studied by comparing films deposited on Al2O3, MgO and SiO2. All films exhibit a NaCl-type carbide structure and X-ray photoelectron spectroscopy revealed the presence of small amounts of an additional amorphous carbon (a-C) phase. Hardness values around 20 ± 2 GPa were obtained for the films on Al2O3 and MgO, whereas a reduced hardness of 11 ± 1 GPa was observed for the films on SiO2 which is attributed to larger crystallite size and more polycrystalline structure. Overall no clear trend as a function of composition can be noted, indicating that microstructure effects dominate the mechanical properties in this study overshadowing the effect of varying the metal content.

Predicting and understanding the ductility of BCC high entropy alloys via knowledge-integrated machine learning

Despite the fact that body-centered cubic high entropy alloys (BCC HEAs) exhibit exceptional strengthening mechanisms over a wide temperature range, their application is often hindered by poor room temperature ductility. Consequently, the accurate prediction of BCC HEAs′ ductility becomes critical in alloy design but is challenged by the intricate nature of these alloy systems. In this study, a comprehensive machine learning (ML) strategy with integrated material knowledge is proposed to address this problem. By referring to plasticity theories, thermodynamics as well as atomic properties, we develop a set of cost-effective material descriptors with various mathematical forms such as averaging, mismatching, maximum-minimum ranging and averaging as binary pairs for HEAs. These descriptors are proved to effectively incorporate material knowledge into ML modelling. They also offer potential alternatives to those obtained from costly first principles calculations. Classification and regression tasks are conducted to predict the ductility of BCC HEAs, and Gradient boosting algorithm exhibiting the best performance for both tasks is eventually selected. The established optimized models achieve high predictive accuracies exceeding 0.85. Through feature engineering, five key features related to valence electron concentration (VEC) and atomic size are screened out. These features lay the foundation for explicit formulae developed via Symbolic Classification, enabling the straightforward numerical prediction of BCC HEAs′ ductility. These key features are further analyzed by an interpretable ML method and compared against experimental and computational plasticity factors, elucidating their influences on various plasticity mechanisms. An in-depth exploration of why the proposed ML models outperform conventional plasticity criteria for HEAs is also presented. This study highlights an effective knowledge-integrated ML approach in predicting material properties resulting from complex mechanisms, with a particular focus on HEAs that often exhibit sparse data.

Effective Descriptor for Screening Single-Molecule Conductance Switches.

The adsorption-type molecular switch exhibits bistable states with an equivalently long lifetime at the organic/inorganic interface, promising reliable switching behavior and superior assembly ability in the electronic circuits at the molecular scale. However, the number of reported adsorption-type molecular switches is currently less than 10, and exploring these molecular switches poses a formidable challenge due to the intricate interplay occurring at the interface. To address this challenge, we have developed a model enabling the identification of diverse molecular switches on metal surfaces based on easily accessible physical characteristics. These characteristics primarily include the metal valency electron concentration, the work function of metal surfaces, and the electronegativity difference of molecules. Using this model, we identified 56 new molecular switches. Employing the gradient descent algorithm and statistical linear discriminant analysis, we constructed an explicit descriptor that establishes a relationship between the interfacial structure and chemical environment and the stability of molecular switches. The model's accuracy was validated through density functional theory calculations, achieving a 90% accuracy for aromatic molecular switches. The conductive switching behaviors were further confirmed by nonequilibrium Green's function transport calculations.

Effects of Mo target power on the structure and tribological properties of AlB2 Ta1-xMoxB films by magnetron sputtering

In this paper, magnetron sputtering from TaB2 and Mo stoichiometric targets is used to prepare AlB2 ternary Ta1-xMoxB films. The films with various Mo contents were obtained by adjusting the Mo target powers. It was discovered that the contents of Mo have an obvious impact on the crystallinity and phase structure stability of Ta1-xMoxB films. When x = 0.43, the (001) and (002) orientation is improved, while stabler AlB2 structure is maintained simultaneously. While increasing x to 0.59, the films show amorphous structure. Meanwhile, as Mo contents rise, the hardness of films first decreases and then increases, eventually drops a lot. The Ta1-xMoxB films with x = 0.44 exhibit the superhardness (H = 49.9 ± 1.5 GPa) and elastic modulus (E = 520 ± 4.7 GPa), which benefit from the structure of Transition-metal diboride (TMB2) and solid solution strengthening effect. Alloying Mo can increase the Valence electron concentration (VEC) of films and therefore enhanced films toughness, higher fracture toughness (KIC = 1.13 MPa·m1/2) and elasticity (85.805%) were achieved when x = 0.44, the films showed better ability to resist plastic deformation even in 500 gf load. In addition, the Ta0.56Mo0.44B films obtain higher wear resistance (4.5 × 10−7 mm3/Nm) in air, but excess Mo atoms lead to deterioration of mechanical properties (H = 25.0 GPa、E = 240.0 Gpa for Mo90). Ta1-xMoxB ternary films with appropriate Mo content show a good potential as a hard protective coating.

Correlations to improve high-temperature strength and room temperature ductility of refractory complex concentrated alloys

Correlations were explored between mechanical, thermodynamic and physical properties of refractory complex concentrated alloys (RCCAs). Experimentally measured yield strengths (σy) and ductility were taken from the open literature and were compared against liquidus, solidus and solvus temperatures, elastic properties (Young’s, shear and bulk moduli), density (ρ), surface energy (γ) and valence electron concentration (VEC). If not publicly available, the thermodynamic properties were calculated using CALPHAD while the other properties listed above were estimated using a rule-of-mixtures average of the constituent element properties. This analysis emphasized tensile ductility. Based on the identified correlations, useful criteria for selecting possibly ductile RCCA compositions with good high-temperature strength were proposed, a few ductile and strong RCCAs were made and properties of some of them were reported in this paper. Additionally, multivariate linear regression (MLR) was used to identify new insights from the high dimensional space of the present study by modeling the influence of composition and the input thermodynamic and physical properties on the high-temperature strength and room temperature ductility. Equal concentrations of Mo and Nb in RCCAs were found to give a good balance of strength and ductility. The MLR analysis identified over 50 promising RCCAs for intended high-temperature applications, pending experimental confirmation.

The effect of Hf on the microstructure, transformation temperature, and the shape memory properties of Zr–Cu-based high-entropy shape memory alloys

The microstructures, phase transformation temperatures, and shape memory properties of Hf-modified Zr50−xHfxCu25Ni7.5Co17.5 and Zr50−xHfxCu25Ni10Co15 high-entropy shape memory alloys (SMAs) were investigated. Hf additions can alter the valence electron concentration, strengthen the alloy matrix, and introduce more secondary phase particles, which significantly influence the properties of the alloys. The results reveal that high austenitic transformation temperature (over 600 K) with very small thermal hysteresis (70–80 K) can be achieved by tailoring the Hf contents, and the best shape memory recovery strain (up to 2.44%) compared with other Zr–Cu-based SMAs could be obtained in Zr42Hf8Cu25Ni10Co15 alloy. This study demonstrated that high-performance Zr–Cu-based high-entropy SMAs can be realized by incorporating Hf additions.