Valence Electron Concentration Research Articles

Characterization of an Al-Cu-Mg-Zn multi principal element alloy by experimental and computational screening methods

We present a combined experimental and computational investigation of phase stability and mechanical properties in the Al-Cu-Mg-Zn quaternary system. Samples containing different relative compositions were prepared using magnetron sputtering and investigated by electron microscopic and X-ray based methods. To classify the technical relevance of the samples, the indentation hardness was measured. The phase stability was studied computationally using a cluster expansion approach based on density functional theory (DFT) methods in a comprehensive screening of the structural and stoichiometric configuration space. Upon decreasing Cu concentration, a transition from an FCC to a mixed FCC/BCC crystal system and significant changes in the mechanical properties depending on Valence Electron Concentration (VEC) and atomic size differences (δr) was observed experimentally. The corresponding crystallographic phases were assigned by XRD and the experimentally observed phase transition was confirmed by the computational screening of formation energies. Since to date, quaternary complex light metal alloy systems cannot be reliably predicted, this is an important step towards a priori modelling of this class of materials.

PyMPEALab Toolkit for Accelerating Phase Design in Multi-principal Element Alloys

Multi-principal element alloys (MPEAs) occur at or nearby the centre of the multicomponent phase space, and they have the unique potential to be tailored with a blend of several desirable properties for the development of materials of future. The lack of universal phase diagrams for MPEAs has been a major challenge in the accelerated design of products with these materials. This study aims to solve this issue by employing data-driven approaches in phase prediction. A MPEA is first represented by numerical fingerprints (composition, atomic size difference , electronegativity , enthalpy of mixing , entropy of mixing , dimensionless Omega parameter, valence electron concentration and phase types ), and an artificial neural network (ANN) is developed upon the datasets of these numerical descriptors. A pyMPEALab GUI interface is developed on the top of this ANN model with a computational capability to associate composition features with remaining other input features. With the GUI interface, an user can predict the phase(s) of a MPEA by entering solely the information of composition. It is further explored on how the knowledge of phase(s) prediction in composition-varied hbox {Al}_xCrCoFeMnNi and hbox {CoCrNiNb}_x can help in understanding the mechanical behavior of these MPEAs.Graphic

Theoretical and experimental study on phase stability of TiVZrMoW refractory high entropy alloy

ABSTRACT An equiatomic quinary TiVZrMoW refractory high entropy alloy (RHEA) is selected for studying phase evolution and stability. The prediction of phases that may form on synthesis is made by (i) Semi-empirical /empirical methods (based on extended Hume-Rothery rules), (ii) CALPHAD and (iii) ab-initio methods. Mixing enthalpy (calculated by Miedema method) and valence electron concentration predicted the formation of the BCC phase (; and VEC = 5). However, the atomic mismatch factor, δ (7.17%) value being higher than the desired value, can de-stabilize the lattice to form a multi-phase structure. CALPHAD technique predicted that at room temperature three BCC and two Laves phases would form. The enthalpy of mixing (4.25 kJ/mol) calculated using Density Functional Theory (DFT) also suggests phase separation at room temperature. The phases and microstructure that evolved in the as-cast and annealed samples are studied by X-ray diffraction (XRD), scanning electron and transmission electron microscopy (TEM) techniques. Two BCC phases and a minor amount of ordered B2 and C15 type Laves phase are found to co-exist in the as-cast sample. The primary BCC phase (BCC#1) is rich in Mo and W (a = 3.17 ± 0.02 Å), while the minor BCC phase (BCC#2) is rich in Zr and Ti (a = 3.65 ± 0.02 Å). The annealed sample shows the transformation of both the disordered BCC phase to the ordered B2 phases and the increase in the amount of C15 Laves phase. The phase evolution and their relative stability in this RHEA has been discussed after analysing the experimental and theoretical results.

Effects of Bi-doping on electronic structure and martensitic transformation in Ni2MnGa and Mn2NiGa MSMAs: A theoretical approach

The effects of Bi-doping on the electronic structure, martensitic transformation and magnetic properties of Heusler alloys Ni2MnGa1-xBix and Mn2NiGa1-xBix (x = 0, 0.25, 0.5, 0.75, 1) were investigated theoretically. The substitution of Bi for Ga has a negative effect on the martensitic transformation. The total energy difference ΔEM between the martensite and austenite decreases gradually with the doping of Bi. When x = 0.5, 0.75 and 1.0 in Ni2MnGa1-xBix and x = 1.0 in Mn2NiGa1-xBix, the martensite phase becomes higher in energy comparing with the austenite. Thus the doping of Bi can lower the martensitic transformation temperature TM and finally suppresses it. The possible reasons for this trend are related to the increasing valence electron concentration e/a and cell volume V with Bi-doping. The competition between them may be ascribed further by the electron density, which combines the effect of valence electron concentration and size effect. The electron densities of Ni2MnGa1-xBix and Mn2NiGa1-xBix decrease monotonously with increasing Bi content. This agrees well with the variation of ΔEM or TM. The doping of Bi does not change the magnetic structure of Ni2MnGa1-xBix and Mn2NiGa1-xBix. The former is ferromagnetic and the latter is ferrimagnetic in both martensite and austenite state. These results can help to introduce new component like Bi to Heusler alloys and discover new functional materials in them.

Criteria for laves-phase formation in refractory high-entropy alloys

ABSTRACT The refractory high-entropy alloys (RHEAs) have been the subject of considerable research in recent years. Since the Laves phase usually leads to a dramatic decrease in the malleability of RHEAs at ambient temperatures, it is critical to identifying the Laves-phase formation. Here, a facile and effective criterion is proposed to predict the phase stability based on the empirical parameters of reported RHEAs. The results indicate that the small atomic size difference is a sufficient condition for determining the stability of solid solution but not a necessary one. In general, the Laves-phase precipitates can be inhibited by decreasing the atomic-size difference, the enthalpy of mixing, and the valence electron concentration. These criteria can be easily adapted to design new RHEAs with the desired phase structure.

High deformation ability induced by phase transformation through adjusting Cr content in Co-Fe-Ni-Cr high entropy alloys

To understand the phase transformation and its effect on mechanical properties of high entropy alloys (HEAs) during deformation, Co40Fe20Ni40-xCrx (x = 10, 20, 30 at%, hereinafter simplified as HCr10, HCr20 and HCr30, respectively) HEAs were prepared, and the microstructure and tensile properties were investigated. The results show that HEAs are mainly composed of face-centered cubic (FCC) phase, and the σ phase forms in HCr30 due to the valence electron concentration (VEC) decreasing from 8.8 to 8.0 with increasing Cr content. For HCr10, the phase transforms from FCC to hexagonal closed-packed (HCP), but for HCr20 and HCr30, the phase transforms from FCC to HCP and σ phases during tensile deformation. The volume fraction of HCP phase firstly increases from 4.29 to 15.40 vol%, then decreases to 7.67 vol%, and σ phase increases from 0 to 28.89 vol% with the increase of Cr content. The stacking faults (SFs) probability increases with the increase of Cr content, contributing to the occurrence of the phase transformations. Tensile testing shows that the yield strength increases by 50% in HCr30 compared with HCr10, and the ultimate strength and elongation reach the maximum values (718 MPa and 59.05%) in HCr20. HCr20 shows a high strain hardening exponent (n = 0.95) after tensile deformation. The phase transformation induced by tensile deformation mainly accounts for the strength-ductility improvement, whereas an increase in σ phases will reduce the ductility.

A machine learning-based alloy design system to facilitate the rational design of high entropy alloys with enhanced hardness

Trapped by time-consuming traditional trial-and-error methods and vast untapped composition space, efficiently discovering novel high entropy alloys (HEAs) with exceptional performance remains a great challenge. Herein, we present a machine learning-based alloy design system (MADS) to facilitate the rational design of HEAs with enhanced hardness. Initially, a hardness database was constructed, and then the key features affecting the hardness of HEAs were screened out by performing a four-step feature selection. Five descriptors including the average deviation of the atomic weight (ADAW), the average deviation of the column (ADC), the average deviation of the specific volume (ADSV), the valance electron concentration (VEC), and the mean melting point (Tm) were identified as the key features related to the hardness of as-cast HEAs. Furtherly, a hardness prediction model based on the support vector machine was constructed with the five features as the inputs. The Pearson correlation coefficients of the well-trained model reach 0.94 for both the testing set and the leave-one-out cross validation (LOOCV). Subsequently, several optimized compositions recommended by inverse projection and high-throughput screening were synthesized by experiments. The best performer exhibits ultra-high hardness, which is 24.8% higher than the highest one in the original dataset. Moreover, the Shapley additive explanation (SHAP) was introduced to boost the model interpretability, which manifests that VEC plays an important role in the prediction for hardness. Notably, VEC has a positive effect on hardness when VEC < 7.5.

Phase prediction and new parametric approach for multi-component alloys with using deep learning API: Keras

In this work phase prediction was estimated by deep learning algorithm using Keras. 400 alloys were randomly selected from the literature. The valence electron concentration (VEC), atomic size difference (δ), electronegativity difference (∆χ) and κ values are calculated for each alloy and a dataset has been created. Here κ value was defined as a new parametric value to be used in phase estimation. The κ value defined in this study will be an important tool in phase estimations. 320 multi-components’ data was used to train and 80 multi-components’ data was used as validation data. Here three different adaptive optimizers were used: Adam, Adagrad and RMSprop. Most important key feature of adaptive optimizers is that do not require a tuning of the learning rate. The aim of the machine-learning is to develop the capability of the models’ generalisation. Estimation of the models must be succeeded in the data that never seen before. Critical point for machine-learning model is overfitting. In this study; simple hold-out validation was used to avoid overfitting. 320 data used for training and 80 data used for validation. A second check was applied using dropout regularization techniques to avoid overfitting. Adam, Adagrad and RMSprop estimation achieved 90%, 66% and 88% respectively. After all these processes, the physical parameters of the 58 multi-component alloy were entered, which are not in 400 data, and predicted that it had an amorphous or crystalline structure. The κ value defined in this study has shown that it is a simple and easily calculable limit value in phase estimation for multi-component alloys.

A molecular dynamics study of the influence of nucleation conditions on the phase selection in Fe50Mn30Cr10Co10 high entropy alloy

Non-equiatomic high entropy alloys with single or multiphase microstructures offer opportunities to optimize the mechanical properties through compositional variation. The Fe-Mn-Cr-Co alloys have shown the potential to activate nanotwinning at large strains even at room temperatures, thereby enhancing both ductility and strength. This paper presents a molecular dynamics study of phase formation during solidification of Fe50Mn30Cr10Co10 using a modified embedded atom method potential. The evolution of the phases has been investigated using adaptive common neighbour analysis, composition analysis, and radial distribution function. In contrast to the reported microstructures containing FCC and HCP phases, a BCC phase with the average composition of the alloy has resulted under homogeneous conditions. On the other hand, heterogeneous nucleation from an initial FCC seed resulted in a dual-phase microstructure of FCC and HCP at 300 K in agreement with the experiments. Interestingly, annealing at 900 K did not alter the phase fractions in samples from both nucleation conditions. Analysis based on the empirical thermodynamic parameter suggested by Ye et al. [Materials Today (2016), Vol19, p349–362] and valence electron concentration (VEC) supports the formation of both types of microstructures observed here. Hence, biasing the nucleation process is believed to strongly influence the type of phases formed in this alloy.

Effect of Cu segregation on the phase transformation and properties of AlCrFeNiTiCux high-entropy alloys

In this work, the effect of Cu on the phase transformation, microstructure, and properties of AlCrFeNiTiCux high-entropy alloys (HEAs) was investigated. Meanwhile, the formation mechanism of the FCC solid solution was discussed. The results showed that it was a beneficial effect on the formation of the FCC solid solution for the addition of Cu into HEAs from the perspective of valence electron concentration (VEC), enthalpy of mixing (ΔHmix) and difference in atom size (δ), which was confirmed by X-ray diffraction and Scanning Electron Microscope analysis. In addition, the increment of Cu content in the alloys promoting the segregation of Al, Ni and Ti in dendrite and Fe, Cr segregated into particles distributed in dendrite and inter-dendrite. The micro-hardness of the HEAs decreased with increasing Cu content and as the Cu content increased, oxidative wear intensified. However, the friction coefficient was significantly reduced, which was related to the lubricity of Cu itself. Besides, the segregation of Cu increased the corrosion current density of the passivation zone of the HEAs, thereby reducing the corrosion resistance of the HEAs in 0.5 mol/L H2SO4 solution.

Consequences of Co-doping on the magnetic and magnetofunctional behavior of the antiferromagnetic Mn5Si3 alloy

The structural, magnetic, and electrical dc transport properties of Co-doped hexagonal Mn5Si3 alloys of nominal compositions Mn5−xCoxSi3 (x = 0.1, 0.3, 0.5) have been investigated. The doped alloys were found to crystallize in hexagonal D88 type structure. The shift in the collinear to non-collinear antiferromagnetic transition temperature towards the lower temperature is found to be slow with increasing Co-concentration compare to the Ni-doped alloys. However, both Ni and Co-doping provide positive chemical pressure in the system. Slower change in the valence electron concentration (e∕a ratio) with Co-doping plays the crucial role behind such observation. Incomplete field-induced non-collinear to collinear antiferromagnetic transition in the Co-doped alloys is another critical observation of the present work. A possible explanation for such behavior has been mooted in terms of local minimas’ disappearance between parent and product phases in the free energy landscape. Besides, various vital properties of Mn5Si3 alloy like, inverted hysteresis behavior, magnetocaloric effect, and magnetoresistance are found to be significantly affected by Co-doping.

Study of martensitic transition temperature on Ni54Fe19Ga23X4 Heusler glass-coated microwires doped by X = B, Al, Ga, in

The influence of alloying in Ni54Fe19Ga23X4 Heusler glass-coated microwires doped by X = B, Al, Ga, In is presented in this work. Even though the alloys exhibit different chemical compositions, the valence electron concentration (e/a) was constant. Furthermore, basic magnetic and resistivity measurements have been performed to determine the chemical doping effect on the magnetic properties and the associated structural transformation. Results point to the fact that the fine-tuning of the chemical composition may be a suitable tool for adjusting the Curie temperature, transformation temperature, and magnetocaloric properties of the glass-coated microwires. In the case of Ga and the Al-doped alloy, a thermal hysteresis can be distinguished in the M(T) dependences at saturation magnetic field, pointing to the presence of the structural transformation. Moreover, the 4% Al doping shifts the structural transformation temperature and the Curie temperature almost to the same position. On the other hand, B and In doping may lead to the disappearance or shift of the structural transformation out of the measurement range (100–400 K). Resistivity measurements proved these results.

Structure and Physical Properties of Cast and Splat-Quenched CoCr0.8Cu0.64FeNi High Entropy Alloy

The article investigates the structure and physical properties of the multicomponent high-entropy alloy CoCr0.8Cu0.64FeNi in the cast and quenched state. The composition of the alloy under study is analyzed using the criteria available in the literature for predicting the phase composition of high-entropy alloys. These parameters are based on calculations of the entropy and enthalpy of mixing and also include the concentration of valence electrons, the thermodynamic parameter Ω, which takes into account the melting point, entropy of mixing, and enthalpy of mixing. Another important parameter is the difference in atomic radii between the alloy components δ. Cast samples of the CoCr0.8Cu0.64FeNi alloy of nominal composition were prepared on a Tamman high-temperature electric furnace in an argon flow using a copper mold. The weight loss during the manufacture of ingots did not exceed 1%, and the average cooling rate was ~ 102K/s. Thereafter, the cast ingot was remelted, and films were obtained from the melt. The splat quenching technique used in this work consisted of the rapid cooling of melt droplets when they collide with the inner surface of a rapidly rotating (~ 8000 rpm) hollow copper cylinder. The cooling rate, estimated from the film thickness, was ~ 106 K / s. X-ray structural analysis was performed on a DRON-2.0 diffractometer with monochromatic Cu Kα radiation. Diffraction patterns were processed using the QualX2 program. The magnetic properties of the samples were measured using a vibrating sample magnetometer at room temperature. The microhardness was measured on a PMT-3 device at a load of 50 g. In accordance with theoretical predictions confirmed by the results of X-ray diffraction studies, the structure of the alloy, both in the cast and in the quenched state, is a simple solid solution of the FCC type. The lattice parameters in the cast and liquid-quenched states are 0.3593 nm and 0.3589 nm, respectively. Measurements of the magnetic properties showed that the CoCr0.8Cu0.64FeNi alloy can be classified as soft magnetic materials. In this case, quenching from a liquid state increases the coercivity. On quenched samples, increased microhardness values were also obtained. This can be explained by internal stresses arising during hardening.

Investigating the mechanism of magnetic phase transition temperature of FeRh thin films by doping copper impurities

In this work, we study the magnetic phase transition (from antiferromagnetic (AFM) to ferromagnetic (FM) states) temperature (TAFM-FM) of iron-rhodium (FeRh) thin films and its tuning by doping copper impurities up to 4.5 at.%. The thin epitaxial FeRh films are prepared by DC magnetron sputtering on the MgO (001) substrate and the doping is performed by simultaneously co-sputtering Cu impurities. More importantly, the doping of Cu impurities drastically decreases the TAFM-FM of FeRh films by more than 100 K, which cannot be precisely described either by strain measurement or change in the valence electron concentration as published by previous works. To explain this unique phenomenon, we proposed a hypothesis to determine the reduction of long-range order of AFM and correlated the change in transition temperature exponentially as a function of doping different concentrations of Cu impurities. Overall, this study concludes that lattice strain, valence electrons per atom, existence of mixed phase and short range order of AFM altogether attribute to the significant decrease of the TAFM-FM.

Correlating structure and orbital occupation with the stability and mechanical properties of 3d transition metal carbides

The development of novel transition metal carbides for improved hard coating technologies requires a detailed understanding of the factors influencing their stability and mechanical performance. To this end, we carried out first principles calculations based on density functional theory to tabulate the electronic structures, formation energies, and phonon dispersion curves of 3d transition metal carbides adopting zincblende, rocksalt, and cesium chloride structures. By analyzing the corresponding results, we outline a theoretical framework that describes how valence electron concentration and bonding configuration control the stability of these compounds. Many early transition metal carbides are predicted to be stable in the rocksalt and zincblende structures, enabled by filled bonding states, whereas the cesium chloride structure shows persistent instability. For compounds that are predicted to be stable, mechanical properties were investigated through calculation of elastic tensors, from which observable properties including Vicker’s hardness and ductility were derived. A robust mechanical performance is shown to be correlated with complete filling of bonding orbitals as illustrated for rocksalt TiC and VC, which have calculated hardnesses of 25.66 and 22.63 GPa respectively. However, enhanced ductility and toughness can be achieved by allowing partial occupation of the antibonding states as in CrC, which has a relatively low Pugh’s ratio of 0.51.

Method to identify the phase structures of high entropy alloys with modified lattice distortion enthalpy

Severe lattice distortion is one of important characteristics of high entropy alloys (HEAs) and exercises considerable influence over phase structures, and atomic volume V is thought to be the key factor for lattice distortion. In the present work, the calculation of V was modified by taking the stacking density effects into consideration, and the calculation of lattice distortion enthalpy (∆HLD) caused by elastic lattice distortion for HEAs was optimized accordingly. With this method, two phase structure formation rules were proposed: valence electron concentration(VEC)−∆HLD rule for crystal structure of solid solution and chemical enthalpy(∆Hchem)−∆HLD rule for phase composition. The prediction effect of these two rules were verified by analyzing 100 existing HEAs, and the intrinsic effect of lattice elastic distortion on the phase formation of HEAs were discussed. The results of the research would be helpful in the composition design of HEAs.

Development of single-phase bcc UHfNbTi high-entropy alloy with excellent mechanical properties

Based on the theory of mixing enthalpy of i,j element pairs (ΔHij) and atomic-size difference δ, we designed a uranium-containing equiatomic UHfNbTi high-entropy alloy with a single-phase bcc structure. The alloy showed good room-temperature compressive plastic properties. They with stood at least 60% of compression strain without fracture. We investigated the effect of average valence electron concentration (VEC) on the mechanical properties of the alloy. Reducing the VEC number is expected to produce uranium-containing high-entropy alloys with high ductility.

Entropy Landscaping of High-Entropy Carbides.

The entropy landscape of high-entropy carbides can be used to understand and predict their structure, properties, and stability. Using first principles calculations, the individual and temperature-dependent contributions of vibrational, electronic, and configurational entropies are analyzed, and compare them qualitatively to the enthalpies of mixing. As an experimental complement, high-entropy carbide thin films are synthesized with high power impulse magnetron sputtering to assess structure and properties. All compositions can be stabilized in the single-phase state despite finite positive, and in some cases substantial, enthalpies of mixing. Density functional theory calculations reveal that configurational entropy dominates the free energy landscape and compensates for the enthalpic penalty, whereas the vibrational and electronic entropies offer negligible contributions. The calculations predict that in many compositions, the single-phase state becomes stable at extremely high temperatures (>3000 K). Consequently, rapid quenching rates are needed to preserve solubility at room temperature and facilitate physical characterization. Physical vapor deposition provides this experimental validation opportunity. The computation/experimental data set generated in this work identifies "valence electron concentration" as an effective descriptor to predict structural and thermodynamic properties of multicomponent carbides and educate new formulation selections.

Machine learning assisted prediction of the Young\u2019s modulus of compositionally complex alloys

We identify compositionally complex alloys (CCAs) that offer exceptional mechanical properties for elevated temperature applications by employing machine learning (ML) in conjunction with rapid synthesis and testing of alloys for validation to accelerate alloy design. The advantages of this approach are scalability, rapidity, and reasonably accurate predictions. ML tools were implemented to predict Young’s modulus of refractory-based CCAs by employing different ML models. Our results, in conjunction with experimental validation, suggest that average valence electron concentration, the difference in atomic radius, a geometrical parameter λ and melting temperature of the alloys are the key features that determine the Young’s modulus of CCAs and refractory-based CCAs. The Gradient Boosting model provided the best predictive capabilities (mean absolute error of 6.15 GPa) among the models studied. Our approach integrates high-quality validation data from experiments, literature data for training machine-learning models, and feature selection based on physical insights. It opens a new avenue to optimize the desired materials property for different engineering applications.

Microstructure and tensile properties of Co-free Fe4CrNi(AlTi)x high-entropy alloys

According to parameters of atomic size difference (δ), valence electron concentration (VEC) and the cost effectiveness, a series of high Fe-content and Co-free Fe4CrNi(AlTi)x (x = 0.2, 0.6 and 1.0) high-entropy alloys (HEAs) were designed. Effects of the content of Al and Ti on the microstructure and tensile properties were investigated. It is found that the constituent phases change from the single face-centered cubic (FCC) phase to FCC + body-centered cubic (BCC) + L21 phases and BCC + L21 phases as the Al and Ti content increases from 0.2 to 0.6 and 1.0, respectively. With increasing the Al and Ti content, the strength increases but the tensile plasticity decreases. Specifically, Fe4CrNi(AlTi)0.6 exhibits a good combination of a high strength of 858 MPa and a large tensile plasticity of 12.8%. The excellent tensile properties of this alloy are attributed to the synergetic effects of a soft FCC phase and hard BCC/L21 phases, and moreover, the uniform distribution of high-density L21 nanoparticles in the BCC phase also benefits the tensile properties. In addition, the phase-evolution principles in the current HEAs and in many previously-reported HEAs are well discussed within the framework of δ and VEC parameters. These findings are believed to promote the development of low-cost HEAs with high performance for practical applications.