Configurational Entropy Research Articles

High Entropy Activated and Stabilized Nickel-based Prussian Blue Analogue for High-performance Aqueous Sodium-ion Batteries

Aqueous sodium-ion batteries (SIBs) represent a cost-effective, safe, and reliable candidate for grid-scale energy storage towards a low-carbon society. The development of cathode materials for aqueous SIBs that have both high capacity and good cycling stability still remains a big challenge. This study proposes a high entropy strategy to boost both specific capacity and capacity retention by introducing equimolar Fe, Co, Mn, and Cu at the Ni sites in the Prussian blue analogue (PBA) frameworks. Attributing to the hybridization of 3d energy levels and improved valence electron concentration deriving from the exotic equimolar four transition metals, significantly increase the number of electrochemically active sites and raised the configuration entropy of PBA frameworks, contributing intensive valence electron transport to faster Faraday reaction and more stable hosts for Na+ ion (de)intercalation. Therefore, the high-entropy PBA (HE-PBA) cathode delivers an enhanced capacity of 118.6 mAh g−1 at the current density of 100 mA g−1, which is nearly 1.6 times higher than that of Ni-PBA, resulting in a high energy density of 74.8 Wh kg−1. Moreover, the HE-PBA demonstrates stable operation over 1800 cycles at a high rate of 5 C. This high entropy strategy provides a feasible strategy for the practical application of aqueous SIBs.

Pattern formation by the drying of saline droplets on pillars

The application of saline solutions for surface coating is pertinent across multiple biomedical fields, various technological sectors, and industries, including agriculture. The drying of salt solution droplets is key to understanding and controlling morphological structures on surfaces. In this paper, we report the study of pattern formation from the evaporation of saline drops (NaCl, CsCl, and KCl) placed on pillars. Our findings indicate that regardless of saline concentration and type, the drying process can be categorized into three modes: stable, metastable, and unstable. In both the stable and metastable modes, the droplet fixes to the pillar during the drying process and ensuing pattern formation; however, the crucial distinction lies in the metastable mode, where the droplet additionally undergoes mass loss through fluid drainage from the walls of the pillars. Conversely, in the unstable drying mode, the droplet undergoes rapid collapse, leading to a substantial loss of mass. The distinct drying modes dictate the resulting patterns on the pillars. We employ measurements of configurational entropy and fractal dimension as quantitative metrics to assess the complexity, reproducibility, and similarity of patterns. The texture analysis reveals that, at low concentrations of both CsCl and KCl, significant differences emerge among the patterns produced by the different drying modes, especially highlighting differences in patterns of the stable drying mode. Finally, we analyze fertilizer deposition patterns to prove that all three drying modes can occur in complex fluids.

High-entropy relaxor ferroelectric ceramics for ultrahigh energy storage

Dielectric ceramic capacitors with ultrahigh power densities are fundamental to modern electrical devices. Nonetheless, the poor energy density confined to the low breakdown strength is a long-standing bottleneck in developing desirable dielectric materials for practical applications. In this instance, we present a high-entropy tungsten bronze-type relaxor ferroelectric achieved through an equimolar-ratio element design, which realizes a giant recoverable energy density of 11.0 J·cm−3 and a high efficiency of 81.9%. Moreover, the atomic-scale microstructural study confirms that the excellent comprehensive energy storage performance is attributed to the increased atomic-scale compositional heterogeneity from high configuration entropy, which modulates the relaxor features as well as induces lattice distortion, resulting in reduced polarization hysteresis and enhanced breakdown endurance. This study provides evidence that developing high-entropy relaxor ferroelectric material via equimolar-ratio element design is an effective strategy for achieving ultrahigh energy storage characteristics. Our results also uncover the immense potential of tetragonal tungsten bronze-type materials for advanced energy storage applications.

Regulation of d‐Orbital Electron in Fe‐N4 by High‐Entropy Atomic Clusters for Highly Active and Durable Oxygen Reduction Reaction

AbstractSimultaneously improving activity and stability is a crucial yet challenge in the development of metallic single‐atom‐based catalysts. In current work, a novel approach is introduced to address this issue by combining post‐adsorption and secondary pyrolysis techniques to create a synergistic catalytic system, in which the single atoms (SAs) Fe sites played in the NC matrix (Fe─NC) are coupled with high‐entropy atomic clusters (HEACs). Theoretical calculations reveal that the incorporation of HEACs lead to a rehybridization of the 3d orbital configuration of Fe‐N4, which helps to balance the adsorption/desorption energy of oxygenated intermediates. In situ spectroscopy further reveals that the rate‐limiting step of OH* desorption on HEAC/Fe─NC in oxygen reduction reaction (ORR) is more facile compared to atomic Fe─NC, implying a higher ORR activity. Moreover, the synergistic effect of diffusion activation barriers and configuration entropy contributes to the structural stability of HEAC/Fe─NC, resulting in remarkable durability. Consequently, this unique catalyst exhibits half‐wave potentials of 0.927 and 0.828 V in an aqueous solution of KOH (0.1 m) and HClO4 (0.1 m), respectively, along with excellent durability. The findings propose a novel strategy for modulating the electronic structure of metallic SAs catalysts and enhancing their stability through strong interactions between SAs and HEACs.

Role of Electronegativity on the Elemental Diversity in High-Entropy Alloys.

High-entropy alloys (HEAs) or multi-principal element alloys (MPEAs) have found extensive applications in high-precision devices. While the increased configurational entropy for HEAs favors more elemental diversity, it also increases the possibility of phase separation into multiple heterogeneous systems. This article reports that these two mutually competing effects are balanced for 3- and 4-component alloys. Analysis of all of the n-component ABCD···-type (∼5 × 105) available compounds in the materials' database shows that more than 70% are either 3- or 4-component ones. Their high propensity is explained on the basis of their optimal average difference of electronegativity (EN) ∼0.5-1.0 and the average sum of electronegativity (EN) ∼5.0-6.5 between the constituent atoms in the Oganov scale. Effectively, these 3- and 4-component alloys lie in the intermediate (centroid) region of the van Arkel-Ketelaar triangle, indicating their metalloid nature.

Tuning Ion Mobility in Lithium Argyrodite Solid Electrolytes via Entropy Engineering.

The development of improved solid electrolytes (SEs) plays a crucial role in the advancement of bulk-type solid-state battery (SSB) technologies. In recent years, multicomponent or high-entropy SEs are gaining increased attention for their advantageous charge-transport and (electro)chemical properties. However, a comprehensive understanding of how configurational entropy affects ionic conductivity is largely lacking. Herein we investigate a series of multication-substituted lithium argyrodites with the general formula Li6+x[M1aM2bM3cM4d]S5I, with M being P, Si, Ge, and Sb. Structure-property relationships related to ion mobility are probed using a combination of diffraction techniques, solid-state nuclear magnetic resonance spectroscopy, and charge-transport measurements. We present, to the best of our knowledge, the first experimental evidence of a direct correlation between occupational disorder in the cationic host lattice and lithium transport. By controlling the configurational entropy through compositional design, high bulk ionic conductivities up to 18 mS cm-1 at room temperature are achieved for optimized lithium argyrodites. Our results indicate the possibility of improving ionic conductivity in ceramic ion conductors via entropy engineering, overcoming compositional limitations for the design of advanced electrolytes and opening up new avenues in the field.

Understanding the phase stability in a multi-principal-component AlCuFeMn alloy

Method(s) that can reliably predict phase evolution across thermodynamic parameter space, especially in complex systems, are of critical significance in academia as well as in the manufacturing industry. In the present work, the phase stability in an equimolar AlCuFeMn multi-principal-component alloy (MPCA) was predicted using complementary first-principles density functional theory calculations and ab initio molecular dynamics (AIMD) simulations. The temperature evolution of completely disordered, partially ordered, and completely ordered phases was examined based on the Gibbs free energy. Configurational, electronic, vibrational, and lattice mismatch entropies were considered to compute the Gibbs free energy of the competing phases. Additionally, elemental segregation was studied using AIMD. The predicted results at 300 K align well with room-temperature experimental observations using x-ray diffraction and scanning and transmission electron microscopy on a sample prepared using commercially available pure elements. The adopted method could help in predicting plausible phases in other MPCA systems with complex phase stability.

Higher entropy-induced strengthening in mechanical property of Cantor alloys/Zr-3 joints by laser in-situ eutectic high-entropy transformation

To effectively regulate the grain boundary infiltration in CoCrFeMnNi high-entropy alloy (Cantor alloys, HEA) caused by the violent atomic interdiffusion, the higher configuration entropy on Cantor alloys surface was designed and realized via eutectic high-entropy (EHEA) transformation. Meanwhile, to effectively alleviate the residual stress caused by the notable difference in the thermal expansion coefficient (CTE) between Cantor alloys and Zr-3 alloys, a cladding layer was applied to the HEA surface using laser cladding technology of Nb, followed by brazing to Zr-3 alloys with Zr63.2Cu filler. The cladding layer's microstructure comprised Nbss and FCC+(Co,Ni)2Nb eutectic structure, resulting from an in-situ reaction between Cantor alloys and Nb. The Nbss and FCC demonstrated good plasticity, and the (Co,Ni)2Nb Laves phase provided increased strength, endowing both good plastic deformation ability and strength of the cladding layer. Notably, the existence of EHEA in the laser cladding layer made the Cantor alloy entropy from 1.61 R to 1.77 R, greatly enhancing its thermal stability and suppressing the grave grain boundary infiltration. Joints produced via laser cladding with Nb-assisted brazing exhibited a complex microstructure (HEA/Nbss + FCC + (Co,Ni)2Nb/(Zr,Nb)(Cr,Mn)2 + (Zr,Nb)ss/(Zr,Nb)2(Cu,Ni,Co,Fe) + (Zr,Nb)(Cr,Mn)2 + (Zr,Nb)ss/Zr-3 and a significantly improved shear strength of 242.8 MPa at 1010 °C for 10 min, 42.4 % higher than that of directly brazed joints. This improvement was attributed to reduced grain boundary infiltration, alleviated residual stress due to CTE disparity, and eliminated micro-cracks in the brazing seam. This study presents an effective solution for reducing residual stresses and achieving reliable bonding between Cantor alloys and Zr-3 alloys, with potential applications in brazing CoCrFeNi-based HEA and Zr-3 due to the beneficial eutectic reaction between CoCrFeNi and Nb.

High Entropy Spinel Oxide (AlCrCoNiFe2)O as Highly Active Oxygen Evolution Reaction Catalysts.

The advancement of water electrolyzer technologies and the production of sustainable hydrogen fuel heavily rely on the development of efficient and cost-effective electrocatalysts for the oxygen evolution reaction (OER). High entropy ceramics, characterized by their unique properties, such as lattice distortion and high configurational entropy, hold significant promise for catalytic applications. In this study, we utilized the sol-gel autocombustion method to synthesize high entropy ceramics containing a combination of 3d transition metals and aluminum ((AlCrCoNiFe2)O). We then compared their electrocatalytic performance with other series of synthesized multimetal and monometallic oxides for the OER under alkaline conditions. Our electrochemical analysis revealed that the high entropy ceramics exhibited excellent performance and the lowest charge transfer resistance, Tafel slope (29 mV·dec-1), and overpotential (η10 = 230 mV). These remarkable results can be primarily attributed to the high entropy effect induced by the addition of Al, Cr, Co, Ni, and Fe, which introduces increased disorder and complexity into the material's structure. This, in turn, facilitates more efficient OER catalysis by providing diverse active sites and promoting optimal electronic configurations for the reaction. Furthermore, the strong electronic interactions among the constituent elements in the metallic spinels further enhance their catalytic activity in the initiation of the OER process. Combined with the reduced charge transfer resistance, these factors collectively play pivotal roles in enhancing the OER performance of the electrocatalysts. Overall, our study provides valuable insights into the design and development of high-performance electrocatalysts for sustainable energy applications. By harnessing the high entropy effect and leveraging strong electronic interactions, electrocatalytic materials can be tailored to improve efficiency and stability, thus advancing the progress of clean energy technologies.

Theoretical approach of hydrogen absorption isotherms on C14–Zr(Cr0.5Ni0.5)2 Laves phases

Theoretical studies on the total energy, and hydrogen absorption thermodynamics on Zr(Cr0.5Ni0.5)2 intermetallic compound were performed using absorption models on the most stable sites. In the first stage, Density Functional calculations provide the absorption energies corresponding to hydrogen in different environments. From there, 28 hydrogen absorption locations were found and the corresponding absorption energies were specifically determined. Then, with this information, a theoretical approximation based on the concept of local absorption isotherm and Fermi-Dirac statistics was applied to study the thermodynamics of the system. In this case, and due to the absence of lateral interactions, exact expressions of the thermodynamic functions can be derived. The process was monitored by following the surface coverage as a function of the chemical potential (absorption isotherm), the energy and configurational entropy of the adsorbed phase and the differential heat of absorption. Interesting behaviours were observed and discussed in terms of the absorption microscopic properties (energy distribution of the absorption sites).

Turning bad into good: A medium-entropy double perovskite oxide with beneficial surface reconstruction for active and robust cathode of solid oxide fuel cells

The cathodes of solid oxide fuel cells (SOFCs) often suffer from detrimental cation segregations and associated impurities poisoning, leading to insufficient electroactivity and poor stability. Here we developed a medium-entropy double perovskite GdBa(Co1.2Mn0.2Fe0.2Ni0.2Cu0.2)O5-δ (ME-GBCO) for promising SOFC cathode. The increased configuration entropy can effectively tailor the surface composition with in situ formed active BaCoO3-δ (BCO) species, rather than inert and deleterious BaOx segregation on parent GdBaCo2O5-δ (GBCO) surface. Accordingly, the layered ME-GBCO cathode with beneficial surface reconstruction exhibited not only high oxygen reduction activity but excellent durability against CO2 impurity, enabling it a very attractive cathode for intermediate temperature SOFCs (IT-SOFCs). Our study provides a new idea for development of efficient and durable cathodes via configurational entropy induced rational surface reconstruction.

Effects of B′‐site configurational entropy on structure and microwave dielectric characteristics in Ba(B′1/3Nb″2/3)O3 complex perovskite ceramics

AbstractBa[(Ca0.2Mg0.2Zn0.2Co0.2Ni0.2)1/3Nb2/3]O3 and Ba[(Mg0.25Zn0.25Co0.25Ni0.25)1/3Nb2/3]O3 perovskite single‐phase ceramics were synthesized by a solid‐state reaction method, and they were annealed at different temperatures in order to investigate the effect of B′‐site configurational entropy on phase stability, ordered domain structure and microwave dielectric characteristics. By comparing the B′‐site high‐entropy composition with B′‐site medium‐entropy and low‐entropy compositions, the entropy‐dominated phase‐stabilization effect and sluggish diffusion effect were observed in Ba[(Ca0.2Mg0.2Zn0.2Co0.2Ni0.2)1/3Nb2/3]O3. These effects enhanced the temperature stability of the B‐site 1:2 ordered structure. Ba[(Ca0.2Mg0.2Zn0.2Co0.2Ni0.2)1/3Nb2/3]O3 even reached a higher Qf value after annealing above the order‐disorder transition temperature (To‐d). This research extends the entropy regulation to ordered complex perovskite and provides a promising way to modify the performances of complex perovskite dielectric ceramics.

On the Phase Configurational Entropy of Dual-Phase γ/γ′ Multi-principal Element Alloys: A Case Study on the Al–Cu–Fe–Ni–Ti System

On the Phase Configurational Entropy of Dual-Phase γ/γ′ Multi-principal Element Alloys: A Case Study on the Al–Cu–Fe–Ni–Ti System

Chemical Environment and Structural Variations in High Entropy Oxide Thin Film Probed with Electron Microscopy.

We employ analytical transmission electron microscopy (TEM) to correlate the structural and chemical environment variations within a stacked epitaxial thin film of the high entropy oxide (HEO) Mg0.2Co0.2Ni0.2Cu0.2Zn0.2O (J14), with two layers grown at different substrate temperatures (500 and 200 °C) using pulsed laser deposition (PLD). Electron diffraction and atomically resolved STEM imaging reveal the difference in out-of-plane lattice parameters in the stacked thin film, which is further quantified on a larger scale using four-dimensional STEM (4D-STEM). In the layer deposited at a lower temperature, electron energy loss spectroscopy (EELS) mapping indicates drastic changes in the oxidation states and bonding environment for Co ions, and energy-dispersive X-ray spectroscopy (EDX) mapping detects more significant cation deficiency. Ab initio density functional theory (DFT) calculations validate that vacancies on the cation sublattice of J14 result in significant electronic and structural changes. The experimental and computational analyses indicate that low temperatures during film growth result in cation deficiency, an altered chemical environment, and reduced lattice parameters while maintaining a single phase. Our results demonstrate that the complex correlation of configurational entropy, kinetics, and thermodynamics can be utilized for accessing a range of metastable configurations in HEO materials without altering cation proportions, enabling further engineering of functional properties of HEO materials.

A multicationic-substituted configurational entropy-enabled NASICON cathode for high-power sodium-ion batteries

Na-superionic-conductor (NASICON)-type Na3V2(PO4)3 is considered as one of the potential cathodes for sodium-ion batteries (SIBs), but its inherent low electronic conductivity and non-adjustable voltage plateau is an urgent issue hindrance to its practical application. Hereof, the concept of multicationic-substituted high-entropy doping is innovatively utilized to modify the fine structure within crystals, enhance electronic conductivity, and achieve excellent local diffusion kinetics and high redox activity according to theoretical calculations. The carbon-free Na3V1.8(CrMnFeZnAl)0.2(PO4)3 (HE-NVP-0.2) cathode exhibits a maximum specific capacity of 119.8 mA h g−1, achieved through V3+/V4+/V5+ redox reactions, while maintaining an impressive capacity retention rate of 80 % after 3000 cycles at 10 C. Moreover, the in-situ X-ray diffraction (XRD) analysis reveals that the incorporation of multi-(high entropy) elements induces a stable transition state, facilitating rapid phase transitions. Combined with in-situ digital image correlation (DIC), reversible structural evolution has been verified at both micro and macro scales. More competitively, coupling with a hard carbon (HC) anode, the HE-NVP-0.2//HC full cells exhibit exceptional energy density/power density characteristics while simultaneously maintaining excellent high-rate performance and prolonged cycle life (2000 stable cycles at 50 C). The regulation of configurational entropy enables the realization of an intermediate phase in the equilibrium state and makes the unlikely potential regulation possible, presenting innovative approaches to expedite the commercialization of high-power SIBs.

Thermodynamic and structural characterization of high-entropy garnet electrolytes for all-solid-state battery

This study explores multi-component garnet-based materials as solid electrolytes for all-solid-state lithium batteries. Through a combination of computational and experimental approaches, we investigate the thermodynamic and structural properties of lithium lanthanum zirconium oxide garnets doped with various elements. Applying density functional theory, the influence of dopants on the thermodynamic stability of these garnets was studied. Probable atomic configurations and their impact on materials’ properties were investigated with the focus on understanding the influence of these configurations on structural stability, phase preference, and ionic conductivity. In addition to the computational study, series of cubic-phase garnet compounds were synthesized and their electrochemical performance was evaluated experimentally. Our findings reveal that the stability of cubic phase in doped Li-garnets is primarily governed by enthalpy, with configurational entropy playing a secondary role. Moreover, we establish that the increased number of doping elements significantly enhances the cubic phase’s stability. This in-depth understanding of materials’ properties at atomic level establishes the basis for optimizing high-entropy ceramics, contributing significantly to the advancement of solid-state lithium batteries and other applications requiring innovative material solutions.

High-Entropy Alloy Electrocatalysts Bidirectionally Promote Lithium Polysulfide Conversions for Long-Cycle-Life Lithium-Sulfur Batteries.

High-entropy alloys (HEAs) have attracted considerable attention, owing to their exceptional characteristics and high configurational entropy. Recent findings demonstrated that incorporating HEAs into sulfur cathodes can alleviate the shuttling effect of lithium polysulfides (LiPSs) and accelerate their redox reactions. Herein, we synthesized nano Pt0.25Cu0.25Fe0.15Co0.15Ni0.2 HEAs on hollow carbons (HCs; denoted as HEA/HC) by a facile pyrolysis strategy. The HEA/HC nanostructures were further integrated into hypha carbon nanobelts (HCNBs). The solid-solution phase formed by the uniform mixture of the five metal elements, i.e., Pt0.25Cu0.25Fe0.15Co0.15Ni0.2 HEAs, gave rise to a strong interaction between neighboring atoms in different metals, resulting in their adsorption energy transformation across a wide, multipeak, and nearly continuous spectrum. Meanwhile, the HEAs exhibited numerous active sites on their surface, which is beneficial to catalyzing the cascade conversion of LiPSs. Combining density functional theory (DFT) calculations with detailed experimental investigations, the prepared HEAs bidirectionally catalyze the cascade reactions of LiPSs and boost their conversion reaction rates. S/HEA@HC/HCNB cathodes achieved a low 0.034% decay rate for 2000 cycles at 1.0 C. Notably, the S/HEA@HC/HCNB cathode delivered a high initial areal capacity of 10.2 mAh cm-2 with a sulfur loading of 9 mg cm-2 at 0.1 C. The assembled pouch cell exhibited a capacity of 1077.9 mAh g-1 at the first discharge at 0.1 C. The capacity declined to 71.3% after 43 cycles at 0.1 C. In this work, we propose to utilize HEAs as catalysts not only to improve the cycling stability of lithium-sulfur batteries, but also to promote HEAs in energy storage applications.

Unveiling the Structure of Oxygen Vacancies in Bulk Ceria and the Physical Mechanisms behind Their Formation.

Understanding the structures of oxygen vacancies in bulk ceria is crucial as they significantly impact the material's catalytic and electronic properties. The complex interaction between oxygen vacancies and Ce3+ ions presents challenges in characterizing ceria's defect chemistry. We introduced a machine learning-assisted cluster-expansion model to predict the energetics of defective configurations accurately within bulk ceria. This model effectively samples configurational spaces, detailing oxygen vacancy structures across different temperatures and concentrations. At lower temperatures, vacancies tend to cluster, mediated by Ce3+ ions and electrostatic repulsion, while at higher temperatures, they distribute uniformly due to configurational entropy. Our analysis also reveals a correlation between thermodynamic stability and the band gap between occupied O 2p and unoccupied Ce 4f orbitals, with wider band gaps indicating higher stability. This work enhances our understanding of defect chemistry in oxide materials and lays the groundwork for further research into how these structural properties affect ceria's performance.

Thermal Stability of High-Entropy Alloy Nanoparticles Evaluated by In Situ TEM Observations.

High-entropy alloy (HEA) nanoparticles (NPs) have attracted attention in several fields because of their fascinating properties. The high mechanical strength, good thermal stability, and superior corrosion resistance of HEAs, which are derived from their high configurational entropy, are attractive features. Herein, we investigated the thermal stability of FeCoNiCuPd HEA NPs on reduced graphene oxide via in situ transmission electron microscopy observations at elevated temperatures. The HEA NPs maintained their structure, size, and composition at 700 °C, and their size gradually decreased accompanied by the preferential sublimation of Cu. On the contrary, the deterioration of the monometallic Pd NPs begins at temperatures greater than 700 °C according to Ostwald ripening, which involves the migration of adatoms or mobile molecular species. Theoretical calculations revealed that the detachment of adatoms from clusters (i.e., the first step of Ostwald ripening) was suppressed in the case of HEA NPs because of the high-configuration-entropy effect.

High-Entropy CeNbO4+δ-Based Ceramics with Ultrahigh Comprehensive Thermosensitive Performances.

Next-generation advanced high-temperature sensors rely heavily on negative temperature coefficient thermosensitive ceramics with low cost, small volume, high sensitivity, and fast response. However, thus far, the enormous challenge of achieving ultrahigh stability and accuracy has become a critical bottleneck restricting the development of thermosensitive ceramics in high-temperature sensor applications. Here, we propose a high-entropy strategy to design a "cation valence self-equilibrium" system in CeNbO4+δ-based ceramics introducing redox couple compensation and ultrahigh density dislocations to solve the problem of temperature-dependent oxygen nonstoichiometry that restricts the performances of high-temperature thermosensitive ceramics. Ferroelastic domains are generated by enhancing the configurational entropy at both A and B sites, resulting in a dramatic increase of dislocation density to >1010 mm-2, which ultimately optimizes the thermosensitive performances. Extreme temperature measurement accuracy with R2 as high as 999.98‰ and RSS as low as 0.011 and high-temperature stability with ΔR/R0 as low as 0.23% after aging at 873 K for 1000 h are realized in high-entropy CeNbO4+δ-based ceramics, indicating a breakthrough in the comprehensive performances of thermosensitive ceramics. This work opens up an effective way to design thermosensitive materials with ultrahigh comprehensive performance to meet the requirements of advanced high-temperature sensors.