Valence Electrons Research Articles

Review of Extrinsic Factors That Limit the Catalytic Performance of Transition Metal Dichalcogenides (TMDs) in Hydrogen Evolution Reactions (HER)

AbstractTransition metal dichalcogenides (TMDs) have garnered attention as potential catalysts for water splitting owing to their unique structures, diverse electronic properties, and composition from earth‐abundant elements. While certain TMD catalysts, notably MoS2, have shown promising activity for hydrogen evolution reactions (HER), achieving performance comparable to traditional platinum catalysts remains a challenge. While significant effort has been invested into understanding the effect of TMD's structural properties, such as defectiveness and crystalline phases, recent work has emphasized the role of extrinsic factors on HER. This review summarizes the current understanding of the impact of commonly overlooked electrocatalytic effects that exhibit an enhanced importance in TMD‐based HER. By combining recent advances in theoretical modeling and experimental work, we review the dominating effects of extrinsic factors including electronic resistance, interfacial barriers, surface roughness, oxidation, and valence impurities. Our work aims to provide insights into optimizing TMDs as highly efficient catalysts for HER, facilitating future advancements in hydrogen generation technology.

In situ tuning of platinum 5d valence states for four-electron oxygen reduction

The oxygen reduction reaction (ORR) catalyzed by efficient and economical catalysts is critical for sustainable energy devices. Although the newly-emerging atomically dispersed platinum catalysts are highly attractive for maximizing atomic utilization, their catalytic selectivity and durability are severely limited by the inflexible valence transformation between Pt and supports. Here, we present a structure by anchoring Pt atoms onto valence-adjustable CuOx/Cu hybrid nanoparticle supports (Pt1-CuOx/Cu), in which the high-valence Cu (+2) in CuOx combined with zero-valent Cu (0) serves as a wide-range valence electron reservoir (0‒2e) to dynamically adjust the Pt 5d valence states during the ORR. In situ spectroscopic characterizations demonstrate that the dynamic evolution of the Pt 5d valence electron configurations could optimize the adsorption strength of *OOH intermediate and further accelerate the dissociation of O = O bonds for the four-electron ORR. As a result, the Pt1-CuOx/Cu catalysts deliver superior ORR performance with a significantly enhanced four-electron selectivity of over 97% and long-term durability.

Designing cobalt-free face-centered cubic high-entropy alloys: A strategy using d-orbital energy level

High-entropy alloys (HEAs) are promising materials for high-temperature structural applications such as nuclear reactors due to their outstanding mechanical properties and thermal stability. Instead of the trial-and-error method, it is efficient to design and prepare single-phase face-centered cubic (FCC) structured HEAs using semi-empirical phase formation rules. However, almost all of phase formation rules were proposed without taking into account the cobalt-free situation. The HEAs containing cobalt are unsuitable for nuclear applications because of the long-term activation of cobalt. Here, six parameters, d-orbital energy level, valance electron concentration, entropy of mixing, enthalpy of mixing, atom size differences, and parameter of the entropy of mixing (Ω) were calculated to determine the solid solution phase, especially the FCC phase formation rules in cobalt-free HEAs. HEAs of 4 components were arc melted to verify the newly developed phase formation rules. The nanomechanical properties of produced HEAs were evaluated using nanoindentation. Among the six parameters, the d-orbital energy level and valance electron concentration are the critical factors that determine the FCC phase stability in cobalt-free alloys. Interestingly, the d-orbital energy level can be alone used as a benchmark for developing mechanical properties.

Borozenes: Benzene-Like Planar Aromatic Boron Clusters.

ConspectusWith three valence electrons and four valence orbitals, boron (2s22p1) is an electron-deficient element, resulting in interesting chemical bonding and structures in both borane molecules and bulk boron materials. The electron deficiency leads to electron sharing and delocalization in borane compounds and bulk boron allotropes, characterized by polyhedral cages, in particular, the ubiquitous B12 icosahedral cage. During the past two decades, the structures and bonding of size-selected boron clusters have been elucidated via combined photoelectron spectroscopy and theoretical investigations. Unlike bulk boron materials, finite boron clusters have been found to possess 2D structures consisting of B3 triangles, dotted with tetragonal, pentagonal, or hexagonal holes. The discovery of the planar B36 cluster with a central hexagonal hole provided the first experimental evidence for the viability of 2D boron nanostructures (borophene), which have been synthesized on inert substrates. The B7-, B8-, and B9- clusters were among the first few boron clusters to be investigated by joint photoelectron spectroscopy and theoretical calculations, and they were all found to possess 2D structures with a central B atom inside a Bn ring. Recently, the B73- (C6v), B82- (D7h), and B9- (D8h) series of closed-shell species were shown to possess similar π bonding akin to that in the C5H5-, C6H6, and C7H7+ series, respectively, and the name "borozene" was coined to highlight their analogy to the classical aromatic hydrocarbon molecules.Among the borozenes, the D7h B82- species is unique for its high stability originating from both its double aromaticity and the fact that the B7 ring has the perfect size to host a central B atom. The B82- borozene has been realized experimentally in a variety of MB8 and M2B8 complexes. In particular, the B82- borozene has been observed to stabilize the rare valence-I oxidation state of lanthanides in LnB8- complexes, as well as a Cu2+ species in Cu2B8-. The B6 ring in B73- is too small to host a B atom, resulting in a slight out-of-plane distortion. Interestingly, the bowl-shaped B7 borozene is perfect for coordination to a metal atom, leading to the observation of a series of highly stable MB7 borozene complexes. On the other hand, the B8 ring is slightly too large to host the central B atom, such that a low-lying and low-symmetry isomer also exists for B9-. Even though most 2D boron clusters are aromatic, the B73-, B82-, and B9- borozenes are special because of their high symmetries and their analogy to the series of C5H5-, C6H6, and C7H7+ prototypical aromatic compounds. This Account discusses recent experimental and theoretical advances on the investigations of various borozene complexes. It is expected that many new borozene compounds can be designed and may be eventually synthesized.

The silicon doped B10Si2 and isovalent boron clusters: Quasi-degenerate 2D and 3D isomers and electron model for rectangular cuboid

The DFT/PBE functional and coupled-cluster theory CCSD(T) computations were used to explore properties of the isovalent B12H2, B11SiH and B10Si2 clusters. Diverse approaches for analysing quasi-degenerate isomers pointed out that while the ribbon-like isomer achieves aromaticity, its spatial effects diminish it with increasing ribbon size. Doping of two H atoms into B12 does not reduce the σ aromaticity of B12H12. Remarkably, the lowest-lying isomer of B10Si2 exhibits a novel 3D structure whose shape and electrons can be simulated by a rectangular cuboid. The spectrum of the whole set of valence electron of this 3D B10Si2 was elucidated by this model.

Advances in Nickel-Containing High-Entropy Alloys: From Fundamentals to Additive Manufacturing.

High-entropy alloys (HEAs) are recognized as a class of advanced materials with outstanding mechanical properties and corrosion resistance. Among these, nickel-based HEAs stand out for their impressive strength, ductility, and oxidation resistance. This review delves into the latest advancements in nickel-containing HEAs, covering their fundamental principles, alloy design strategies, and additive manufacturing techniques. We start by introducing HEAs and their unique properties, emphasizing the crucial role of nickel. This review examines the complex relationships between alloy composition, valence electron concentration (VEC), and the resulting crystal structures. This provides insights into design principles for achieving desired microstructures and mechanical properties. Additive manufacturing (AM) techniques like selective laser melting (SLM), electron beam melting (EBM), and laser metal deposition (LMD) are highlighted as powerful methods for fabricating intricate HEA components. The review addresses the challenges of AM processes, such as porosity, fusion defects, and anisotropic mechanical properties, and discusses strategies to mitigate these issues through process optimization and improved powder quality. The mechanical behavior of AM-processed nickel-based HEAs is thoroughly analyzed, focusing on compressive strength, hardness, and ductility. This review underscores the importance of microstructural features, including grain size, phase composition, and deformation mechanisms, in determining the mechanical performance of these alloys. Additionally, the influence of post-processing techniques, such as heat treatment and hot isostatic pressing (HIP) on enhancing mechanical properties is explored. This review also examines the oxidation behavior of nickel-containing HEAs, particularly the formation of protective oxide scales and their dependence on aluminum content. The interplay between composition, VEC, and oxidation resistance is discussed, offering valuable insights for designing corrosion resistant HEAs. Finally, this review outlines the potential applications of nickel-based HEAs in industries such as aerospace, automotive, and energy, and identifies future research directions to address challenges and fully realize the potential of these advanced materials.

DFT study on doping effect of different transition metals on MoS2 for enhancing the formation of S vacancies

MoS2 modification by doping transition metals is an effective way to change the Mo–S bond energy by taking advantage of the electronic variability of the d orbitals of transition metals. Herein, this study investigates the doping effect of different transition metals onto MoS2 edge sites through DFT calculations. To screen out the metal additive effect, different transition metals were doped to the MoS2 edge sites to see the effect on generating S vacancies that were generally regarded as the active sites. DFT simulation results proved that the ability of the valence electrons to populate the orbitals with the greatest overlap with the orientation of the edge Mo–S bond was a major factor in how simple it was to create S vacancies at the Mo-edge and S-edge sites. For the transition metals, the vacancy formation energy increases with the increase of periodic number for the same group, while decreases with the increase of the atomic weight for the same period. This implied that the upper right corner transition metals in the Periodic Table could be selected to modify MoS2 to obtain the minimum vacancy formation energy. Therefore, nickel and cobalt are the best choice as the doping element for modifying MoS2.

Development and Mechanical Characterization of a CoCr-Based Multiple-Principal-Element Alloy

The development and mechanical characterization of a CoCr-based multiple-principal-element alloy are presented and discussed. In this work, ab initio synthesis and mechanical characterization of the (CoCr)100-x(TiNbZr)x (x = 0, 48 60, 78 and 100 % at) alloy family is reported; these include the calculation of thermodynamic parameters such as mixing entropy (ΔSmix), mixing enthalpy (ΔHmix), valence electron concentration (VEC), Ω and δ factors. The alloys were melted in a vacuum arc furnace; rod-shaped ingots were produced by suction casting. Phase characterization was carried out using optical microscopy, scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), and X-ray diffraction. Mechanical characterization was done via compressive and hardness tests. Calculation of phase diagrams was performed using Thermo-Calc © software. Yang’s model for phase prediction predicted a BCC solid solution. Multicomponent simulations predicted a more complex structure, with Laves (C14 and C15), Theta (C16), BCC 1, 2 and 3, Mu, CoTi2, CoZr3 and TiZr2. Contrary to Yang’s model for phase prediction, the experimentally obtained phases agreed reasonability well with those obtained by the Thermo-Calc simulation. The suction cast process cooling rate suppressed the nucleation and growth of some equilibrium phases, i.e., Laves (C14) or BCC 3 for the (CoCr)100-x(TiNbZr)x (x = 0, 48 60, 78 and 100 % at) alloys. The hardness test results were strongly related to the intermetallic phase formation, showing an increase of 331% with the x = 78 alloy. The BCC 1 phase played an important role in the yield strength behavior, as the (CoCr)22(TiNbZr)78 alloy, with a considerable amount of this phase, showed the highest yield strength value.

Understanding stacking fault energy of NbMoTaW multi-principal element alloys by interpretable machine learning

Stacking fault energy (SFE) is a crucial property influencing the deformation mechanisms of multi-principal element alloys (MPEAs). However, experimentally measuring SFE and exploring composition space of MPEAs is challenging. This study explores the SFE in NbMoTaW by integrating machine learning force fields (ML-FF), molecular dynamics simulations (MD), neural networks, and symbolic regression (SR) methods. A SFE dataset containing 2000 different NbMoTaW compositions were generated by combining ML-FF and MD. Then the neural-network model was developed for SFE prediction with an accuracy of 0.981 and a mean absolute error of 0.020. Using SR, the valence electron concentration (VEC), average shear modulus (G), radii gamma (γ) were identified as the key descriptors to determine SFE with the relationship of SFE=0.307·VEC+0.352·(G+γ). This work demonstrated a significant impact of chemical composition on SFE and established an accurate mathematical expression for SFE prediction, enhancing the understanding and alloy design of MPEAs.

Multifaceted investigation into the impact of Ga substitution for Al in V[formula omitted]MnAl inverse Heusler alloys

This study investigates the impact of Ga substitution for Al in V2MnAl inverse Heusler alloys, focusing on lattice parameter variations. Despite similar valence electrons, Ga’s distinct size and surface energy prompt questions about its role in alloy characteristics. Experimental synthesis of V2Mn1Al1−xGax alloys (x = 0 to 0.60) reveals crystal parameter changes. Theoretical exploration using density functional theory (DFT) probes how Ga doping at the Al site influences the density of states, altering the half-metallic properties of V2MnAl. Additionally, machine learning, with a dataset of 391 entries, predicts lattice constants based on atomic properties, enhancing our ability to maneuver material characteristics. This multifaceted approach aims to deepen our understanding of Ga’s impact on Heusler alloys, bridging experimental and theoretical realms for comprehensive insights into materials design and behavior.

Mechanistic investigation of methanol-to-olefins conversion catalyzed by H-ZSM-5 zeolite: a DFT study.

The mechanisms for the formation of the first C - C bond and lower olefins on methanol to olefins (MTO) conversion on H-ZSM-5 had been focused in dispute. In this paper, density functional theory has been used to study the reaction mechanisms of methanol to olefins on ZSM-5. The configurations of reactants, intermediates, products and transition state of the numerous reactions involved in such a process have been optimized, as well as the elementary reactions related to these configurations were determined by the calculation of corresponding activation energy barriers and reaction heats. Here, two different kinds of the mechanisms were proposed for the formation of dimethylether (DME), one involving an associative interaction of two methanol molecules with the zeolite Brønsted acid sites and the other occurring via a surface methoxy species and a methanol molecule. A critical intermediate of the methoxy methyl cation was theoretically verified by the reaction of the methoxy species and dimethylether. Besides, it was found that the first intermediates containing a C - C bond were 1,2-dimethoxyethane and 2-methoxy-ethanolare, in which the former was formed from methoxy species with dimethyl ether and the latter was formed from methanol by onium ions((CH3)2O+CH2CH2OCH3), respectively. For the whole reaction mechanism, the results in this paper indicated that the ethene formation is more favorable than propylene formation due to the low activation energy barrier for ethene formation (123.49 vs. 162.09kJ.mol-1). From these calculations, it would be concluded that ethene is the first alkene product that induces the occurrence of the hydrocarbon pool mechanism. All the periodic density function theory (DFT) calculations were performed by the Vienna Ab Initio Simulation package (VASP). The interaction between nucleus and valence electron was described using the pseudopotentials found in the projector augmented wave (PAW) method. PBE-D3 was used in the whole DFT calculations and CI-NEB was used to locate transition state.

Ring Structures of Metal Atom Doped C9, C11, and C13 Clusters from Ab Initio Calculations-The Finding of a Gd@C13 Magnetic Superatom Ring.

Pure C9 clusters have a linear chain structure. However, here, we report using ab initio calculations the transformation of a chain into a cyclic ring structure with the capping of Ca, Sr, and Ba atoms. Further calculations on neutral and charged clusters doped with Sc, Y, and La atoms show stabilization of a cation C9 isoelectronic cyclic ring capped with the metal (M) atom, but anion clusters doped with these trivalent atoms form a C10 like MC9 ring, which deforms to a necklace structure. Both the ring structures correspond to electronic shell closing with 20 delocalized valence electrons in a disk jellium model and have a large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap. Calculations of IR and Raman spectra show no imaginary frequency, suggesting that the structures are stable. Addition of two C atoms to the ring structure of LaC9 leads to a capped ring structure of the cation LaC11 and an open ring structure of the LaC11 anion. Further addition of two C atoms leads to a La@C13 cation as well as Ca@C13 and Sr@C13 neutral wheel-shaped rings with endohedral doping of the M atom. These novel ring structures have a large HOMO-LUMO gap of more than 4 eV and are magic with electronic shell closing corresponding to 28 delocalized valence electrons in a disk jellium model. There is π aromaticity in this ring satisfying 4n+2 (n = 3) Hückel's rule with 14 valence electrons. Interestingly, when the dopant is a Gd atom, there is a formation of a magnetic superatom ring Gd@C13 + with 7 μB magnetic moments due to seven 4f up-spin states of Gd being fully occupied. Bonding in these novel ring structures is discussed.

Regulating coordination environment around transition metal (Fe, Co) single atom catalysts for efficient Hg0 adsorption

Elemental mercury (Hg0) is one of the main pollutants released during coal combustion, which is difficult to remove due to its hydrophobicity and volatility, resulting in serious environmental pollution. Therefore, it is urgent to develop a low-cost and high-performance catalyst to remove Hg0. In this work, using first-principles study, the effect of nonmetal (NM = B, C and O) coordination environment on the charge distribution of graphene-supported transition metal single atom catalysts (TM-N4-SAC) has been investigated. It is found that regulating the TM-N4-SAC with NM coordination atoms with fewer valence electrons than N atom can cause TM atoms to lose more electrons, and the charge distribution in the active center to be locally deviated. Moreover, in-depth analysis of the adsorption configuration, charge density difference, charge transfer, adsorption energy and density of state of Hg0 adsorption on NM modified TM-N4-SAC confirmed that the adsorption of Hg0 can be effectively enhanced only when TM atoms lose more electrons. Thus, Fe-N3B- and Co-N3B-SAC have the strongest ability to adsorb Hg0 because they have the most negative adsorption energy of −1.13 and −0.49 eV. This work provides theoretical guidance for the design of SAC for efficient adsorption of Hg0.

Structure and chemical bonding in high-pressure potassium silver alloys

The high-pressure structures of K-Ag alloys were examples of pressure-induced electron transfer from the electropositive potassium to the electronegative silver. We re-examined the crystal and electronic structures of KAg2, K2Ag, and K3Ag using powder X-ray diffraction and theoretical calculations. Our findings establish a connection between the morphologies of these three phases and the precursor face-centered cubic Ag. For K2Ag, we discovered a disordered structure that better matches the X-ray pattern. Valence electron density distributions obtained from the maximum entropy method, along with charge density calculations, provide a comprehensive understanding of the evolution of chemical bonding in these systems. It was found that K atoms share their valence electrons during alloy formation, contributing to K-Ag and Ag-Ag bonds in K2Ag and KAg2, while no Ag-Ag bonds are present in K3Ag. These results indicate the Zintl-Klemm model may be too simplistic to describe the structure and bonding in high-pressure binary intermetallic compounds.

A robust sandwich structural catalyst of (Cu/CuCo-MOF)2/MXene double heterojunction with outstanding activity toward hydrogen generation

Non-noble metal catalysts have exhibited promising prospects in ammonia borane (NH3BH3) hydrolysis, but their activity and stability still need to be further improved. Herein, a 2D sandwich heterostructural catalyst with Cu/CuCo-MOF and MXene-MOF double heterojunction has been prepared by coupling Ti3C2Tx MXene with bimetal organic framework nanosheets using a facile in situ growth strategy. The optimized CuCo-MOF/MX exhibits unprecedented activity with a turnover frequency (TOF) of 82.3 min–1 and excellent cycle stability, comparable to precious metal catalysts. Spectroscopic characterization and density functional theory (DFT) calculations reveal that Cu/CuCo-MOF heterojunction provides CuCo dual active sites for catalysis, and MXene-MOF heterojunction modulates the electronic structure and valence states of Cu sites via the Ti3C2Tx interlayer with 2D electron promoter effect to improve the synergistic effect of CuCo dual active sites. These modulation optimize the adsorption and dissociation of reactants, leading to a lower reaction barrier. This work provides insight into the 2D electron promoter effect, proposes a novel strategy for improving the performance of non-precious metal catalysts through constructing double heterojunction with 2D electron promoter effect.

Mechanism of Gd doping on microstructure and mechanical properties of FeCrNiCuTi0.4 high entropy alloy

The study focused on investigating the impact of rare earth element Gd content on both the microstructure and mechanical properties of FeCrNiCuTi0.4Gdx (x = 0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.08, 0.1, 0.12, and 0.15, in mole ratio) high-entropy alloys, as well as elucidating the underlying mechanisms involved. The microstructure analysis revealed that the alloy exhibited a diphase structure consisting of FCC and BCC phases at low Gd content, and precipitation of the Cu5Gd phase occurred alongside the FCC and BCC phases at x = 0.05. The phase evolution of the current alloy system was assessed using the Ω - δ, △χ, and VEC (valence electron concentration) criteria. The mechanical properties indicated that the Vickers hardness increased with the increase of Gd content. Additionally, the compressive strength, yield strength, and plastic strain exhibit an initial increase followed by a decrease, while the average friction coefficient and wear demonstrated an initial increase followed by a subsequent decrease. The fracture mechanism shifted from plastic fracture to ductile fracture, ultimately transitioning to dissociative fracture with ductile fracture as the predominant mode. Similarly, the wear mechanism progressed from abrasive wear to a combination of abrasive wear with oxidation wear. The strengthening mechanisms of the present alloys included solid solution strengthening, fine crystal strengthening, and second-phase strengthening.

Intermediate Intercluster Bond Orders. Electronic Communication in Au38(SR)24 Superatomic Molecules.

Ligand-protected gold clusters remain potential building blocks for envisaged molecular materials. The archetypal Au38(SR)24 cluster can be viewed as a robust template for the fusion of two Au25(SR)18 - cluster units, retaining a bi-icosahedral Au23 core. Via electrochemical properties, the overall charge state can be selectively tuned, enabling the access of 14 valence electron (ve) species featuring a single intercluster bond and nearby charge from -1 to +3, achieving related species bearing 15- to 11-ve with variable intercluster bond orders. Here, we explore the characteristics of intermediate intercluster bond orders in order to provide insights into the plausible electron communication between the constituent building blocks, with Au38(SR)24, as a representative template. Our results denote a small structural variation along -1 to +3 charge states, provided by the core-protecting ligand interaction, which is enhanced towards more oxidized species. The remaining unpaired electron from intermediate intercluster bond orders of 1.5 for Au38(SR)24 1-, 1.5 for Au38(SR)24 1+, and 2.5 for Au38(SR)24 3+, holds delocalized characteristics between the building block units, favoring electron communication for conductive and cooperative cluster aggregates. Such features are relevant for the formation of molecular electronic device applications, favoring the rationalization prior to engaging in explorative synthesis of larger ligand-protected cluster aggregates.

DFT and machine learning studies on a multi-functional single-atom catalyst for enhanced oxygen and hydrogen evolution as well as CO2 reduction reactions

In this contribution, the design of a graphene-supported high-entropy single-atom catalyst (HESAC) composed of Fe, Co, Ni, and Ru metal atoms (FeCoNiRu-HESAC) is proposed. Negative formation energy and positive dissociation potentials indicate such materials' thermodynamic and electrochemical stability. Based on density functional theory (DFT) calculations, Co active sites lead to the overpotentials of 0.28 VRHE for oxygen evolution reaction (OER), 0.16 VRHE for hydrogen evolution reaction (HER), and 0.25 VRHE for CO2 reduction reaction (CO2RR) towards CO formation. These surpass the activity of CoN4 single-atom catalyst. More interestingly, the low CO2RR and HER overpotentials enable the FeCoNiRu-HESAC to produce syngas (CO + H2). In addition, the Fe, Ni, and Ru sites simply serve as counterparts to modify the performance of Co active sites through non-bonding interactions. Besides, machine learning (ML) implies that, the valence electrons of intermediates as well as the d orbital electrons of metal sites are the most important parameters affecting the reaction intermediates’ Gibbs free energy. According to these DFT and ML results, a strategy to design multifunctional HESACs electrocatalysts is developed.

Prediction of thermodynamic properties oflanthanide/transition metal alloys by deep learning

The utilization of machine learning, especially deep learning, in solving materials science issues bring an opportunity to accelerate the development process of new materials and draw the attention of researchers all over the world. In this work, we present our study on applying deep neural networks to represent and predict thermodynamic quantities including formation energy, convex hull distance, and to recognize potential thermodynamical stabile materials. We employ our novel material descriptor, named orbital field matrix (OFM), to determine the feature vectors for materials. The OFM descriptors were developed based on the information of valence electron configuration and the Voronoi analysis of the atomic structures of materials. Our experiments show that deep neural networks can accurately predict formation energyand convex hull distancewith the mean absolute error around 0,124eV/atom and 0,105 eV/atom, respectively. In addition,the classification neural network can yield an accuracy of 92% in distinguishing the stable and unstable materials.

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.