Valence Electron Concentration Research Articles

CALPHAD and rule-of-mixtures: A comparative study for refractory high entropy alloys

Present work studies 126 quaternary and 126 quinary equiatomic refractory high entropy alloys (RHEAs), made from Group IV (Ti, Zr, Hf), Group V (V, Nb, Ta) and Group VI (Cr, Mo, W) elements. Rule-of-mixtures (ROM) technique is used to calculate liquidus temperature, density (ρ), Young's modulus (E), % atomic size difference (δ), valence electron concentration (VEC) and specific heat at constant pressure and at 1273 K (Cp). CALPHAD technique is used to predict the number of phases formed at 298 K, ρ and liquidus temperature. ROM calculated densities are matching perfectly with CALPHAD values. Densities and E are directly proportional to the VEC and liquidus temperature of the alloys. Ti, Zr, Hf are ductilizing the alloys and making them light; whereas Cr, Mo and W, are reducing the alloys' ductility and making them heavy. For quinary RHEAs, Cp shows six distinct groups with δ, but a similar trend is not observed in quaternary RHEAs. A methodology is developed to screen a large number of alloys based on various properties. Correlations between those properties are also studied.

СТРУКТУРА И КОРРОЗИОННО-ЭЛЕКТРОХИМИЧЕСКИЕ СВОЙСТВА ЛИТЫХ ВЫСОКОЭНТРОПИЙНЫХ СПЛАВОВ НА ОСНОВЕ ЖЕЛЕЗА

The structure, electrochemical behavior, and corrosion resistance of samples of cast high-entropy alloys systems Fe – Cr – Cu – Ni – Mn – Si and Fe – Co – Cu – Ni – Mn – Si in a neutral solution of sodium chloride were studied. Selection of components of the studied alloys was carried out on the basis of the criteria adopted in the literature for the high-entropy alloys composition based on calculation of the entropy and enthalpy of mixing, valence electron concentrations as well as the difference between the atomic radii of the components. Using X-ray diffraction analysis, the phase composition and crystal lattice parameters of the investigated high-entropy alloys were determined. It was established that the Fe5CоCuNiMnSi alloy is a solid solution with a face-centered cubic lattice, while the Fe5CrCuNiMnSi alloy contains two solid solutions with a face-centered and solid solution with body-centered cubic lattices. The values of stationary potentials and areas of electrochemical stability of alloys, as well as the density of corrosion currents, are determined. It has been shown that samples of the Fe5CrCuNiMnSi alloy behave inertly in corrosion tests.

Theoretical and Experimental Studies of the Structural, Phase Stability and Elastic Properties of AlCrTiFeNi Multi-Principle Element Alloy.

The fundamental challenge for creating the crystal structure model used in a multi-principle element design is the ideal combination of atom components, structural stability, and deformation behavior. However, most of the multi-principle element alloys contain expensive metallic and rare earth elements, which could limit their applicability. Here, a novel design of low-cost AlCrTiFeNi multi-principle element alloy is presented to study the relationship of structure, deformation behavior, and micro-mechanism. This structured prediction of single-phase AlCrTiFeNi by the atomic-size difference, mixing enthalpy and valence electron concentration (VEC), indicate that we can choose the bcc-structured solid solution to design the AlCrTiFeNi multi-principle element alloy. Structural stability prediction by density functional theory calculations (DFT) of single phases has verified that the most advantageous atom occupancy position is (FeCrNi)(AlFeTi). The experimental results showed that the structure of AlCrTiFeNi multi-principle element alloy is bcc1 + bcc2 + L12 phases, which we propose as the fundamental reason for the high strength. Our findings provide a new route by which to design and obtain multi-principle element alloys with targeted properties based on the theoretical predictions, first-principles calculations, and experimental verification.

Local order in high-entropy alloys and associated deuterides – a total scattering and Reverse Monte Carlo study

Many of the materials properties of high-entropy alloys (HEAs), like increased hardness, reduced thermal and electrical conductivity, and interesting hydrogen storage properties, are proposed to be related to local lattice distortions of the crystal structure due to the significant size differences between the elements of the alloy. However, direct evidence of this effect is very limited in the literature, and it therefore remains a hypothesis. This work presents a detailed assessment of the local lattice distortion in three body-centered cubic (bcc) HEAs TiVNb, TiVZrNb and TiVZrNbHf with varying atomic size differences using total scattering measurements and Reverse Monte Carlo structure modelling. The analysis indicates that the amount of local lattice distortion in the alloys increases with the elemental size difference in the alloy. The amount of lattice distortion is relieved when dideuterides with CaF2-type structures (Fm3¯m) are formed from the bcc (Im3¯m) HEAs. Analyses of the local environments around the deuterium atoms reveal an interesting correlation between the valence-electron concentration (VEC) of the nearest-neighbour metals and the stability of tetrahedral interstices with respect to deuterium occupation. Moreover, there is a tendency towards Ti/Nb short-range order in TiVNbD5.7 where the mixing entropy is lowest. In TiVZrNbHfD10, about 6 % of the deuterium atoms are displaced from the tetrahedral interstices with smaller volumes to octahedral interstices.

AlxCoCrFeNiSi high entropy alloy coatings with high microhardness and improved wear resistance

AlxCoCrFeNiSi (x = 0.5, 1.0, 1.5, and 2.0 in molar ratio) high-entropy alloy (HEA) coatings are prepared by atmospheric plasma spraying and laser re-melting. The effects of Al addition on the formation of different crystal structures and the mechanical properties of this series of HEA coatings are evaluated in terms of microhardness and wear resistance. The phase formation of the AlxCoCrFeNiSi coatings is analysed based on the rules of HEAs. With an increase in Al content, the crystal structures transform from body-centred cubic (BCC) and face-centred cubic (FCC) to B2/BCC and Cr3Si phases. The formation of a simple solid solution is governed by the combined effects of mixing entropy (∆S), mixing enthalpy (∆H), atom-size difference (δ) and valence electron concentration (VEC). For high Al contents (x = 2.0), the maximum microhardness reaches 1255 HV. Simultaneously, the coefficient of friction reaches its lowest value of 0.25 when the worn surface is smooth with minimal debris. Moreover, the main wear mechanism is abrasive wear, and the wear resistance of the HEA coatings is enhanced.

Influence of alloying elements on mechanical and electronic properties of NbMoTaWX (X = Cr, Zr, V, Hf and Re) refractory high entropy alloys

NbMoTaW refractory high entropy alloy (RHEA) has shown great potential applications for high temperature components due to its high temperature mechanical strength. However, the brittleness at room temperature hinders its engineering application and further development. To overcome this deficiency, refractory alloying elements with melting temperatures over 1850 °C, i.e., Cr, Zr, V, Hf, and Re, were chosen to enhance the mechanical performance of NbMoTaW RHEA in the present work. The effects of refractory alloying elements on the strength and ductility of NbMoTaW RHEA were investigated via a combination of theory and experiment. To be specific, the first-principle calculations based on density functional theory were employed to predict the mechanical properties of the alloyed NbMoTaWX (X = Cr, Zr, V, Hf and Re) RHEAs and explain the alloying effect from the atomic and electronic level. Moreover, the phase structures of the alloyed RHEAs were determined based on the formation enthalpy and cohesive energy, as well as some empirical parameters, such as the average valence electron concentration VEC and atomic size difference δ. In combination with the experimental results, the calculated elastic constants and modulus indicated that most of these alloying elements enhanced the strength of NbMoTaW RHEA, while only Zr-alloying significantly improved the ductility. The strengthening mechanism of different elements was well analyzed based on the total and partial density of states, overlapping Mulliken population, charge density contour, and atomic distance. The improvement of the ductility for Zr-alloying was attributed to the formation of Zr–Zr metallic bonds in the alloyed NbMoTaWX RHEAs. The theoretic predictions were confirmed by the experimental investigations. The present work provides a good guidance for design and construction of NbMoTaW RHEA.

New approach to model the yield strength of body-centered cubic solid solution refractory high-entropy alloys

A simple fitting approach is used for modeling the compressive yield strength of body centered cubic (bcc) solid solution high entropy alloys in Al-Hf-Nb-Mo-Ta-Ti-V-Zr system. It is proposed that the yield strength could be modeled by a polynomial where the experimental data can be used for finding the polynomial coefficients. The results show that the proposed polynomial could model the yield strength of solid solution alloys relatively well. The developed polynomial is used for predicting the strength of RHEAs in Hf-Mo-Nb-Ta-Ti-V-Zr system. It is observed that the yield strength of alloys within this system increases with the additions of Mo and Zr and decreases with the addition of Ti. Furthermore, the model predicts that the yield strength increases with increasing the value of parameters valence electron concentration (VEC) and atomic size difference (ASD). Although the developed polynomial does not consider the mechanisms involved in the strengthening of alloys, it can be considered as a straightforward method for assessing the strength of solid solution RHEAs.

The functioning mechanism of Al valid substitution for Co in improving the cycling performance of Zr–Co–Al based hydrogen isotope storage alloys

In order to optimize the hydrogen isotope storage properties of ZrCo alloy and promote its application in the storage and delivery system (SDS), ZrCo alloy is modified by partial substitution of Co with Al and subsequent melt spinning process. The microstructure and hydrogen isotope storage properties, especially the cycling performance, of ZrCo1-xAlx (x = 0–0.15) samples were thoroughly investigated. It is found that all as-cast Al-substituted alloys are consisted of a main phase of ZrCo, while the segregation of Al element at grain boundary is more serious with the increase of Al doping content, which restrains the valid substitution content of Al for Co in ZrCo phase. The initial activation performances of the Al-substituted alloys are enhanced and excellent hydriding kinetics are maintained. With the increase of Al substitution content in ZrCo phase of ZrCo1-xAlx (x = 0–0.15) alloys, the initial saturated hydrogen capacities of α solid-solution phase are improved significantly, which is attributed to the decline of valence electron concentrations (VEC) for Al-substituted alloys. Further analysis shows that the hydrogenation-dehydrogenation process of ZrCo1-xAlx (x = 0–0.15) alloys after multiple cycles has been altered as intercalation and de-intercalation of hydrogen atoms between ZrCo phase and α phase, leading to cycling capacity stabilization. More importantly, the improved terminal saturated hydrogen capacities of α phase in the Al-substituted alloys, which represents enhanced final cycling stable capacities, is linked with the increase of initial saturated hydrogen capacities of α phase after Al substitution for Co in ZrCo phase. In addition, the valid substitution content of Al for Co in ZrCo phase is further increased without any element segregation for ZrCo0.9Al0.1 alloy processed by melt spinning, which behaves further optimized final cycling stable capacity of 0.93 wt%, and its variation of the hydrogenation and dehydrogenation paths is similar to those of the above samples. In this work, the mechanism of cycling capacity stabilization has been explored in detail, which provides guidance to improve the cycling stability of ZrCo-based hydrogen isotope storage alloys from point of phase structure of ZrCo alloy.

Prediction of Face-Centered Cubic Single-Phase Formation for Non-Equiatomic Cr–Mn–Fe–Co–Ni High-Entropy Alloys Using Valence Electron Concentration and Mean-Square Atomic Displacement

Prediction of Face-Centered Cubic Single-Phase Formation for Non-Equiatomic Cr–Mn–Fe–Co–Ni High-Entropy Alloys Using Valence Electron Concentration and Mean-Square Atomic Displacement

Unraveling the abnormal dependence of phase stability on valence electron concentration in Ni–Mn-based metamagnetic shape memory alloys

Valence electron concentration (e/a) dependence of phase transition temperature TM, i.e., a higher e/a leading to an elevated TM, is a well-accepted criterion for the Ni–Mn-based alloys. However, this tendency is not always obeyed by certain alloy systems, such as the Ni2Mn(Ga, Z) alloys (Z = Si, Ge, and Sn). The origin of this abnormal behavior remains uncovered. In this work, by first-principles calculations, the origin of the abnormal e/a dependence of phase stability in the Ni2MnGa1−xSix (x = 0–1) alloys is elucidated through examining the electronic structure, phonon, and magnetism. We find that the abnormal e/a dependence of phase stability intrinsically originated from the chemical composition change. The composition variation brings about a reduction of the minority-spin electronic states near the Fermi energy and the weakness of the Fermi surface nesting. Moreover, the substitution of Si for Ga leads to a decreased magnetization of austenite and an increased magnetization of martensite, which also makes a non-negligible contribution to the abnormal phase stability. The conclusions drawn for the Ni2MnGa1−xSix alloys can be well extended to understand the structural transition in other abnormal alloying systems, such as the Ni2MnGa1−xZx alloys (Z = Ge and Sn). This work clarifies the origin of the abnormal dependence of phase stability on e/a in the Ni–Mn-based alloys and provides solid knowledge for the design of advanced magnetic shape memory alloys.

Correlation between fracture characteristics and valence electron concentration of sputtered Hf-C-N based thin films

Hard protective coating materials based on transition metal nitrides and carbides typically suffer from limited fracture tolerance. To further tune these properties non-metal alloying – substituting C with N – has been proven favorable for magnetron sputtered Hf-C-N based thin films. A theoretically predicted increase in valence electron concentration (from 8.0 to 9.0 e/f.u. from HfC to HfN) through nitrogen alloying lead to an increase in fracture toughness (KIC obtained during in-situ SEM cantilever bending) from 1.89 ± 0.15 to 2.33 ± 0.18 MPa·m1/2 for Hf0.43C0.57 to Hf0.35C0.30N0.35, respectively. The hardness remains close to the super-hard regime with values of 37.8 ± 2.1 to 39.9 ± 2.7 GPa for these specific compositions. Already the addition of small amounts of nitrogen, while sputtering a ceramic HfC target, leads to a drastic increase of nitrogen on the non-metallic sublattice for fcc single phased structured HfC1-xNx films, where x = N/(C + N). The here obtained results also provide experimental proof for the correlation between fracture characteristics and valence electron concentration.

Theoretical study on novel orthorhombic ternary monocarbides M0.5Re0.5C (M=V, Nb, Ta) from first-principles calculations

A new type of ternary monocarbides M0.5Re0.5C (M = V, Nb, Ta) with outstanding mechanical properties were firstly reported by introducing the Re into their well-known hard parent compounds MC to tune the valence electron concentration (VEC). By an efficient structure searching method, a universal orthorhombic structure with space group of Cmc21 has been uncovered and demonstrated to be the ground-state phase of these three monocarbides, which can be sustained up to the ultrahigh pressure of 300 GPa for V0.5Re0.5C and Nb0.5Re0.5C. The thermodynamic and dynamical stabilities of the predicted phases were confirmed by the formation enthalpy and phonon spectra calculations. The structural, mechanical as well as electronic properties of M0.5Re0.5C in comparison with their parent compounds MC were thus fully investigated using first-principles density functional theory (DFT) calculations. Compared to their parent compounds MC, results on the mechanical calculations indicated that they not only possess larger Vickers hardness and ideal indentation shear strength values but also exhibit much smaller elastic and ideal strength anisotropy which are advantageous to their potential applications. Detailed analysis of electronic structures reveals that the origin of the improved mechanical properties of M0.5Re0.5C is mainly attributed to the enhanced hybridization of metals-d and C-2p orbitals by locating the fermi level at the valley of the pseudogap.

From Zintl to Wade: Ba3LiGa5 – A Structure Pattern with Pyramidal Cluster Chains –[Ga5]n–

Investigation of the correlation between the crystal structure, electronegativity difference and valence electron concentration in intermetallic gallides lead to the discovery of the new compound Ba3LiGa5 (space group Immm, a = 6.2720(2) Å, b = 6.5872(2) Å, c = 12.6878(8) Å). A combination of quantum chemical bonding analysis with NMR study revealed the gallium substructure to be formed of chains built of the interconnected pyramidal [Ga5] clusters. Analysis of chemical bonding by means of the electron localizability approach confirmed the presence nido‐[Ga5] Wade clusters. Lithium species are not only required for the purpose of charge compensation, but also – analogous to a transition metal – occupies partially the same crystallographic position as gallium.

A single-phase V0.5Nb0.5ZrTi refractory high-entropy alloy with outstanding tensile properties

A ductile V0.5Nb0.5ZrTi refractory high-entropy alloy (RHEA) with relatively low density (~6 g/cm−3) is investigated, designed by controlling its valence electron concentration. The homogenized alloy exhibits a stable BCC structure, significant work hardening rate and considerable tensile stress (787 MPa) and elongation (21.9%). The solid-solution strengthening effect is estimated to be ~575 MPa by simplifying into a pseudo-binary alloy, which is in accordance with the test results. These findings can inspire a new strategy to design RHEA with a balanced matching of strength and ductility.

First-principles study on a new type of quaternary carbonitride VWCN with outstanding mechanical properties

Ceramics with outstanding mechanical properties have great potential applications in industrial fields ranging from cutting tools to scratch and wear resistant films. Here, a new type of transition-metal carbonitride VWCN is proposed by introducing the fourth element W into the ternary V2CN system. The value of valence electron concentration (VEC) per two atoms was tuned to enhance the hardness and the corresponding ideal strengths as well as the electronic stability. By an improved structure searching method, an orthorhombic Pmm2 structure of VWCN was firstly uncovered and verified as its ground-state phase. The relative formation enthalpy calculations show that it is the most energetically favorable phase in the pressure range of 0–300 GPa. The lattice dynamical stability was also checked by the phonon spectrum calculations. The systematic study of mechanical property showed this Pmm2-VWCN not only has a great improvement of hardness value from 23 GPa for V2CN to 35 GPa, but also has a large pure shear strength of 31 GPa. Meanwhile, it also exhibited surprisingly high ductility and toughness relative to V2CN. Electronic analysis revealed that the mechanical enhancement induced by the introduction of the element W mainly stems from the variation of structure and the consequent presence of hybridizations between TM-d and LE-p orbitals, which is also responsible for the minimized EF DOS by exactly separating the bonding and antibonding states.

Surface electronic structure and elastic property of (Ti,Zr)(C,N) coatings by laser carburization

Change in the mechanical properties of (Ti,Zr)(C,N) coatings by laser carburization was investigated in terms of bonding state and valence electron concentration (VEC). The doped carbon was analyzed for the formation of amorphous carbon phase with ID/IG of 0.85 and sp2/sp3 ratio of 2.13. The formation of carbide phase (TiC and ZrC) was substituted for nitrogen. The ratios of TiC/TiN and ZrC/ZrN were verified to be 0.10 and 0.26 by the analysis of the bonding environment using photoelectron spectroscopy. VEC was calculated to be 8.85 due to the transformation from (Ti,Zr)N (VEC = 9) to (Ti,Zr)(C,N). The decreased VEC was correlated with the decrease of the metallic state and the increase of p-d hybridized bond in valence band. As the measured elastic modulus and hardness increased from 420.3 GPa and 32.4 GPa for VEC = 9 to 442.1 GPa and 37.6 GPa for VEC = 8.85 before and after carbon doping, the change in resistive properties against the elastic strain was identified due to the increase in hybridized bonds.

Designing of Fe-containing (Ti33Zr33Hf33)-(Ni50Cu50) high entropy alloys developed by equiatomic substitution: phase evolution and mechanical properties

Novel (Ti33Zr33Hf33)x(Ni50Cu50)100−x with x=40–80at.%, high entropy alloys (HEAs) developed by equiatomic substitution, each element is varied with five levels so that their microstructure and mechanical properties could be compared to define the effect of different contents. Above all, the (Ti33Zr33Hf33)60(Ni50Cu50)40 HEA exhibits enhanced the plasticity with maintaining high strength due to the occurrence of the C14-type phase of homogeneity morphology.Consequently, in this series of HEAs with equiatomic substitution selected composition with a relatively simple phase, and proceeded with the addition of other elements with good chemical compatibility factors such as atomic size different, valence electron concentration, and mixing enthalpy to induce phase transformation.

Understanding microstructure and mechanical properties of (AlTa0.76)xCoCrFeNi2.1 eutectic high entropy alloys via thermo-physical parameters

(AlTa0.76)xCoCrFeNi2.1 (x values in molar ratio, x = 0.1, 0.3, 0.5, 0.7, 1.0, and 1.5) alloys were designed to investigate the microstructure and mechanical properties of the eutectic high entropy alloys (EHEAs) consisting of FCC, B2, and Laves phases. Depending on the compositional variatio, clear microstructural variation was observed, as follows: (1) Group 1: FCC dendrite + Laves interdendrite (x = 0.1), (2) Group 2: FCC dendrite + fine-eutectic structure consisting of FCC and Laves phases (x = 0.3, 0.5 and 0.7), (3) Group 3: B2 dendrite + bimodal eutectic structure [FCC/B2 +Laves] (x = 1.0), (4) Group 4: Laves dendrite + eutectic structure consisting of B2 and Laves phases (x = 1.5). As the fraction of Laves or B2 phases increases, yield stress increases from 293 to 2336 MPa, while the plastic strain decreases from 50 % to 2%. Thermo-physical parameters, such as mixing entropy (ΔSmix), mixing enthalpy (ΔHmix), valence electron concentration (VEC), and atomic size difference (δr), were calculated to understand the microstructural variation. Two criteria (δr - VEC and δr - ΔHmix) were utilized to elucidate the formation of the eutectic structures in the present EHEAs, revealing the usefulness of the thermo-physical parameters in the development of EHEAs.

First principle calculation of the effect of Cr, Ti content on the properties of VMoNbTaWMx (M = Cr, Ti) refractory high entropy alloy

The influence of Cr and Ti content on the phase structure, elastic constants, elastic properties and anisotropy of VMoNbTaWMx (M = Cr, Ti) refractory high entropy alloy was studied by the first principle method in this paper. Based on the plane wave pseudo-potential and density functional theory, the structure model of solid solution was established by virtual crystal approximation (VCA). By calculating the atom size difference (δ), valence electron concentration (VEC) and atom distribution (λ), it was indicated that the VMoNbTaWMx (M = Cr, Ti, 0 < x < 2) maintain a single BCC solid solution structure. The calculation results showed that with the increase of Cr content, the strength of the alloy increased, the plasticity presented a certain fluctuation, and the anisotropy first decreases and then increases. The anisotropy of VMoNbTaWCr was the lowest, VMoNbTaWCr1.75 had the highest plasticity and VMoNbTaWCr2 had the highest strength. With the increase of Ti element, the strength of the alloy decreased, the plasticity first decreased and then increased, and the anisotropy decreased first and then increased. VMoNbTaW had the best strength and plasticity and VMoNbTaWTi1.75 had the lowest anisotropy.

Formation of γ-brass type pseudo-binary Ni2Zn11-4δXδ (0≤δ≤~0.13) (X = In and Ga) by an exchange mechanism

The solid solution phases with general formula Ni2Zn11-4δXδ (0≤ δ ≤~0.13) (X ​= ​In, Ga) have been synthesized by high-temperature solid-state synthesis. Their structures have been characterized by X-ray diffraction and elemental analysis. The phases crystallize in the cubic space group I¯43m and adopt cubic γ-brass-type Ni2Zn11 structure, which is made of 26 atom γ-cluster. The unit cell of the Ni2Zn11-4δXδ contains 50–52 atoms depending upon the composition of the compounds. The pseudo-binary phases in Ni–Zn-X (X ​= ​In, Ga) are formed by the insertion of In or Ga in the structure of Ni2Zn11 by an exchange mechanism. Instead of direct substitution of Zn, In/Ga occupy at the empty centre of γ-cluster, probably, due to the large size difference in the atomic radii of Zn and In metals. The insertion of trivalent In or Ga is accompanied by the sharp depletion of bivalent Zn atoms from the γ-cluster to keep the valence electron concentration constant throughout the entire range of solid solution.