Entropic stabilization in lithium-rich transition metal layered oxides – A perspective
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Burke, Sven (ORCID:0000000331245361)↗
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Discovering High Entropy Alloy Electrocatalysts in Vast Composition Spaces with Multiobjective Optimization
High entropy alloys (HEAs) are a highly promising class of materials for electrocatalysis as their unique active site distributions break the scaling relations that limit the activity of conventional transition metal catalysts. Existing Bayesian optimization (BO)-based virtual screening approaches focus on catalytic activity as the sole objective and correspondingly tend to identify promising materials that are unlikely to be entropically stabilized. Here, we overcome this limitation with a multiobjective BO framework for HEAs that simultaneously targets activity, cost-effectiveness, and entropic stabilization. With diversity-guided batch selection further boosting its data efficiency, the framework readily identifies numerous promising candidates for the oxygen reduction reaction that strike the balance between all three objectives in hitherto unchartered HEA design spaces comprising up to 10 elements.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Effects of local compositional and structural disorder on vacancy formation in entropy-stabilized oxides from first-principles
Entropic stabilization has evolved into a strategy to create new oxide materials and realize novel functional properties engineered through the alloy composition. Achieving an atomistic understanding of these properties to enable their design, however, has been challenging due to the local compositional and structural disorder that underlies their fundamental structure-property relationships. Here, we combine high-throughput atomistic calculations and linear regression algorithms to investigate the role of local configurational and structural disorder on the thermodynamics of vacancy formation in (MgCoNiCuZn)O-based entropy-stabilized oxides (ESOs) and their influence on the electrical properties. We find that the cation-vacancy formation energies decrease with increasing local tensile strain caused by the deviation of the bond lengths in ESOs from the equilibrium bond length in the binary oxides. The oxygen-vacancy formation strongly depends on structural distortions associated with the local configuration of chemical species. Vacancies in ESOs exhibit deep thermodynamic transition levels that inhibit electrical conduction. By applying the charge-neutrality condition, we determine that the equilibrium concentrations of both oxygen and cation vacancies increase with increasing Cu mole fraction. Our results demonstrate that tuning the local chemistry and associated structural distortions by varying alloy composition acts an engineering principle that enables controlled defect formation in multi-component alloys.
36 MATERIALS SCIENCE↗
Entropically engineered formation of fivefold and icosahedral twinned clusters of colloidal shapes
Fivefold and icosahedral symmetries induced by multiply twinned crystal structures have been studied extensively for their role in influencing the shape of synthetic nanoparticles, and solution chemistry or geometric confinement are widely considered to be essential. Here we report the purely entropy-driven formation of fivefold and icosahedral twinned clusters of particles in molecular simulation without geometric confinement or chemistry. Hard truncated tetrahedra self-assemble into cubic or hexagonal diamond colloidal crystals depending on the amount of edge and vertex truncation. By engineering particle shape to achieve a negligible entropy difference between the two diamond phases, we show that the formation of the multiply twinned clusters is easily induced. The twinned clusters are entropically stabilized within a dense fluid by a strong fluid-crystal interfacial tension arising from strong entropic bonding. Our findings provide a strategy for engineering twinning behavior in colloidal systems with and without explicit bonding elements between particles.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Hidden transformations in entropy-stabilized oxides
We report entropy-stabilized oxides (ESO) display a reversible entropy-driven phase transformation that can be leveraged to produce a continuum of metastable phase states, allowing for property optimization and novel functionalities. X-ray absorption spectroscopy reveals that entropic stabilization extends to the electronic structure (valence state and cation coordination) in sintered (Co,Cu,Mg,Ni,Zn)O, manifesting as a tunable lattice distortion in the entropy-stabilized phase. Co, Cu, and Zn ions reversibly transform from six-fold to four-fold coordinated structures and from low to high valence states due to the competition between electronic structures that are equilibrium and enthalpy-driven or metastable and entropy-driven. The segregation of a Cu-rich tenorite phase and a Co-rich spinel phase influences the electronic structure evolution. ESOs can adjust their electronic structures through heat treatment, providing a powerful tool for developing functional properties. These results indicate that the definition of entropy stabilization should include entropy-stabilized electronic structures, providing motivation to reassess previously studied HEO materials.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Site Disorder as a Predictor for Compositionally Complex 5RE 2 Zr 2 O 7 Ceramic Phase Stability
Here, phase formation and stability of five component compositionally complex rare earth zirconates (5RE 2 Zr 2 O 7 ) were investigated by X-ray diffraction and electron microprobe analysis. Zirconates with different rare earth compositions (LaNdSmEuDy, LaNdSmEuYb, LaNdEuErYb, LaNdDyErYb, SmEuDyYHo, LaYHoErYb, and DyYHoErYb) were synthesized at 1700°C and 2000°C by the solid-state method to investigate the effect of A-site site disorder (δ A ) on phase stability. Increased site disorder results from mixed cation occupancy with localized crystallographic strain and bond disorder. Compositions LaNdSmEuDy (δ A = 4.6) and LaNdSmEuYb (δ A = 6.0) produced a single pyrochlore phase and compositions SmDyYHoErYb (δ A = 2.8), LaYHoErYb (δ A = 6.2), and DyYHoErYb (δ A = 1.7) produced a single fluorite phase. High δ A compositions LaNdEuErYb (δ A = 6.9) and LaNdDyErYb (δ A = 7.2) produced a pyrochlore and fluorite phase mixture at 1700°C. Single phase was obtained for the latter composition at 2000°C. Of the single phase compositions calcined at 1700°C, LaNdSmEuYb and LaYHoErYb (both with largest δ A ) showed decomposition to mixed fluorite and pyrochlore phases during lower temperature anneals, indicating entropic stabilization. Comparison with prior work shows a temperature dependence of the critical δ A for phase stability, and compositions near it are expected to be entropy stabilized.
36 MATERIALS SCIENCE↗
Revisiting the Role of Entropy for Charge Separation in 1D Pi-Conjugated Semiconductors
Free carrier generation in organic donor/acceptor heterojunctions and redox-doped organic semiconductors is poorly understood, since assumed tight electron-hole binding conflicts with observed high free carrier yields. Cornerstone analyses that have guided the field for over 15 years predict that entropy can stabilize free charges in 2D and 3D pi-conjugated semiconductors but not in 1D systems. Here, the impact of entropy on charge generation in 1D pi-conjugated semiconductors is revisited by exploiting a greatly simplified system where enthalpy considerations alone should not allow for free charge generation. Noncontact solution-phase microwave conductivity is used to investigate the carrier density-dependent conductivity and dielectric constant in isolated chemically doped semiconducting single-walled carbon nanotubes in a low-dielectric solvent. Dopant chemical structure dramatically influences the carrier density-dependent complex conductivity, with bulky dopants facilitating carrier escape even at carrier densities below one carrier per nanotube. Three distinct numerical calculations show that entropic stabilization dramatically lowers the Gibbs energy barrier for free charge generation, explaining the high yield of free carriers, even in 1D. This renewed understanding of entropy's role in carrier generation has important implications for designing organic electronic devices-such as solar cells and thermoelectric energy harvesters-for enhanced carrier yield, conductivity, and performance.
36 MATERIALS SCIENCE↗
Structurally Regenerable High Entropy Aluminate Spinel Catalysts for Dry Reforming of Methane
The dry reforming of methane reaction is a promising means to convert two potent greenhouse gases, methane and carbon dioxide, into industrially valuable synthesis gas. However, the presence of reducing gases and high operating temperatures degrade conventional nickel catalysts via excessive coke formation and particle sintering. These catalysts are not readily regenerated because the oxidative heat treatments employed to remove coke further promote active particle sintering. In this work, we designed high entropy aluminate spinel oxides (MAl 2 O 4 where M = Co, Mg, Ni, and divalent site vacancies in nominal equimolar concentration) as selective and regenerable reforming catalysts. Under reaction conditions, reducible nickel and cobalt cations exsolved from the spinel lattice to form highly selective bimetallic particles on the oxide surface. Instead of sintering, these particles uniquely redissolved back into the aluminate lattice upon reoxidation and regained the original spinel structure. This phenomenon is ascribed to entropic stabilization, wherein an increase in configurational entropy creates a thermodynamic driving force for redispersing supported metal particles back into the multi‐cationic oxide structure. During the dry reforming reaction, nickel atoms similarly exsolved from a NiAl 2 O 4 sample and reduced to form metallic nickel particles. However, subsequent oxidation of this sample promoted sintering and oxidation of the nickel particles to an inactive state. High entropy materials thus provide a unique mechanism of regeneration, which is inaccessible in conventional catalysts.
coke deposition↗
Crystal structure of the $τ_{11}$ Al 4 Fe 1.7 Si phase from neutron diffraction and ab initio calculations
The intermetallic τ 11 Al 4 Fe 1.7 Si phase is of interest for high-temperature structural application due to its combination of low density and high strength. We determine the crystal structure of the τ 11 phase through a combination of powder neutron diffraction and density functional theory calculations. Using Pawley and Rietveld refinements of the neutron diffraction data provides an initial crystal structure model. Since Al and Si have nearly identical neutron scattering lengths, we use density-functional calculations to determine their preferred site occupations. The τ 11 phase exhibits a hexagonal crystal structure with space group P6 3 /mmc and lattice parameters of a = 7.478 Å and c = 7.472 Å. The structure comprises five Wyckoff positions; Al occupies the 6h and 12k sites, Fe the 2a and 6h sites, and Si the 2a sites. Here we observe site disorder and partial occupancies on all sites with a large fraction of 80% Fe vacancies on the 2d sites, indicating an entropic stabilization of the τ 11 phase at high temperature.
36 MATERIALS SCIENCE↗
A general flame aerosol route to high-entropy nanoceramics
High-entropy ceramics are an emerging class of materials with fascinating characteristics. However, elemental immiscibility and crystal complexity limit the development of a general synthesis strategy, and common methods yield bulk materials. Here, we introduce a transformative non-equilibrium flame aerosol technique for synthesizing high-entropy nanoceramics. This scalable, one-step process enables the production of high-entropy oxide nanoceramics with an unprecedented diversity of crystal structures, including fluorite-phase materials that integrate up to 22 distinct cation elements. The method’s capacity for entropic stabilization and grain refinement significantly improves the thermal stability of these nanostructures. In a representative application, a Pt-(MgCoNiCuZn)O high-entropy single-atom catalyst showed superior activity and long-term stability, maintaining constant CO 2 conversion over 670 h and dramatically outperforming conventional catalysts. Finally, the general approach opens a vast composition and structure space for the creation of high-entropy oxide nanomaterials for application across diverse fields, including catalysis, energy storage, sensing, and thermal management.
36 MATERIALS SCIENCE↗
Entropy-driven melting point depression in fcc HEAs
High Entropy Alloys (HEAs) are an increasingly dominant alloy design paradigm. The premise of entropic stabilization of single-phase alloys has motivated much of the research on HEAs. Chemical complexity may indeed help stabilize single alloy phases relative to other lower-entropy competing solid phases. Paradoxically, this complexity may de-stabilize these alloys against the liquid phase, potentially limiting the application space of HEAs at elevated temperatures. In this work, we carry out a comprehensive investigation of the phase stability in the fcc CoCrFeMnNiV-Al HEA space using a state of the art CALPHAD database. By using modern visualization techniques and statistical analysis we examine the trade-off between chemical complexity and stability against the liquid state and identify a potentially difficult to overcome barrier for development of high temperature alloys, at least within the conventional fcc HEA space. Here, limited experimental data seem to be consistent with this analysis.
36 MATERIALS SCIENCE↗
Molecular Structure and Thermodynamics of CO 2 and Water Adsorption on Mica
The adsorption of CO 2 and water on clay surfaces plays a key role in applications, such as gas storage in saline aquifers and depleted hydrocarbon reservoirs, but is not yet fully understood. Here, we study the adsorption of CO 2 and water vapor using Grand Canonical Monte Carlo and molecular dynamics simulations. At a bulk pressure of 100 bar, pure CO 2 adsorbs strongly on mica and forms extensive layers next to it. CO 2 adsorption is lowered substantially if introducing water vapor above mica and is largely eliminated when the relative humidity (RH) approaches about 60%. When pure water vapor is introduced above a mica surface, a subnanometer thick liquid water film develops on it to form apparent liquid–solid and liquid–vapor interfaces simultaneously. Using the identification of truly interfacial molecules (ITIM) analysis, we delineate how individual water layers develop in this film as RH increases. We highlight that the water film is spatially heterogeneous and the true liquid–vapor interface emerges only at an RH of 60–80%. Introducing 100 bar of CO 2 into the water vapor above the mica surface modulates water adsorption nonlinearly: at RH = 0.01%, the water adsorption is reduced by ∼30%; as RH increases, the reduction is weakened, and eventually, enhancement of water adsorption by about 7% occurs at RH = 90%. These variations are attributed to the interplay of film thinning by high-pressure CO 2 , competition of mica surface sites by CO 2 molecules, and energetic and entropic stabilization of interfacial water by CO 2 molecules.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Entropy-Driven Structural Evolution in Ceramic Oxides
High-entropy ceramics, with five or more elements randomly occupying the same cation crystallographic sites, offer vast compositional diversity and unique properties for material design and applications. However, for many dissimilar elements, entropic stabilization cannot overcome the enthalpic barrier to cation substitution. As a result, most high-entropy ceramics incorporate only a few similar elements, limiting the in-depth exploration of the effect of entropy on ceramic properties. Here, we first use density functional theory to model fluorite crystal structures composed of 1-10 elements and then experimentally present practical fluorite oxide nanostructures containing 1, 3, 8, and 15 metals, as well as a record-breaking 25-element high-entropy ceramic incorporating a diverse palette of rare-earth, transition, alkaline, p-block, and noble metals. As entropy increases, structural and configurational disorder in the solid solution rises, altering structural features such as lattice distortion, crystallinity, homogeneity, defect density, and thermal stability. This research provides new insights and understanding of the role of entropy in stabilizing compositionally complex ceramics.
Liu, Shuo↗
Multiprincipal Component P2-Na 0.6 (Ti 0.2 Mn 0.2 Co 0.2 Ni 0.2 Ru 0.2 )O 2 as a High-Rate Cathode for Sodium-Ion Batteries
Mixing transition metal cations in nearly equiatomic proportions in layered oxide cathode materials is a new strategy for improving the performances of Na-ion batteries. The mixing of cations not only offers entropic stabilization of the crystal structure but also benefits the diffusion of Na ions with tuned diffusion activation energy barriers. In light of this strategy, a high-rate Na 0.6 (Ti 0.2 Mn 0.2 Co 0.2 Ni 0.2 Ru 0.2 )O 2 cathode was designed, synthesized, and investigated, combining graph-based deep learning calculations and complementary experimental characterizations. This new cathode material delivers high discharge capacities of 164 mA g –1 at 0.1 C and 68 mAh g –1 at a very high rate of 86 C, demonstrating an outstanding high rate capability. Ex situ and operando synchrotron X-ray diffraction were used to reveal the detailed structural evolution of the cathode upon cycling. Using the climbing-image nudged elastic-band calculation and Ab initio molecular dynamics simulations, we show that the optimal transition metal composition enables a percolating network of low barrier pathways for fast, macroscopic Na diffusion, resulting in the observed high rate performance.
25 ENERGY STORAGE↗
Anomalous entropy-driven kinetics of dislocation nucleation
The kinetics of dislocation reactions, such as dislocation multiplication, controls the plastic deformation in crystals beyond their elastic limit, therefore critical mechanisms in a number of applications in materials science. We present a series of large-scale molecular dynamics simulations that shows that one such type of reactions, the nucleation of dislocation at free surfaces, exhibit unconventional kinetics, including unexpectedly large nucleation rates under compression, very strong entropic stabilization under tension, as well as strong non-Arrhenius behavior. These unusual kinetics are quantitatively rationalized using a variational transition state theory approach coupled with an efficient numerical scheme for the estimation of vibrational entropy changes. These results highlight the need for a variational treatment of the kinetics to quantitatively capture dislocation reaction kinetics, especially at low-to-moderate strains where large deformations are required to activate reactions. These observations suggest possible explanations to previously observed unconventional deformation kinetics in both molecular dynamics simulations and experiments.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Accurate prediction of oxygen vacancy concentration with disordered A-site cations in high-entropy perovskite oxides
Abstract Entropic stabilized ABO 3 perovskite oxides promise many applications, including the two-step solar thermochemical hydrogen (STCH) production. Using binary and quaternary A-site mixed {A}FeO 3 as a model system, we reveal that as more cation types, especially above four, are mixed on the A-site, the cell lattice becomes more cubic-like but the local Fe–O octahedrons are more distorted. By comparing four different Density Functional Theory-informed statistical models with experiments, we show that the oxygen vacancy formation energies ( $${E}_{V}^{f}$$ E V f ) distribution and the vacancy interactions must be considered to predict the oxygen non-stoichiometry ( δ ) accurately. For STCH applications, the $${E}_{V}^{f}$$ E V f distribution, including both the average and the spread, can be optimized jointly to improve Δ δ (difference of δ between the two-step conditions) in some hydrogen production levels. This model can be used to predict the range of water splitting that can be thermodynamically improved by mixing cations in {A}FeO 3 perovskites.
08 HYDROGEN↗
Understanding Reentrance in Frustrated Magnets: The Case of the Er 2 Sn 2 O 7 Pyrochlore
Reentrance, the return of a system from an ordered phase to a previously encountered less-ordered one as a controlled parameter is continuously varied, is a recurring theme found in disparate physical systems, yet its microscopic cause is often not investigated thoroughly. Here, through detailed characterization and theoretical modeling, we uncover the microscopic mechanism behind reentrance in the strongly frustrated pyrochlore antiferromagnet Er 2 Sn 2 O 7 . We use single crystal heat capacity measurements to expose that Er 2 Sn 2 O 7 exhibits multiple instances of reentrance in its magnetic field B vs temperature T phase diagram for magnetic fields along three cubic high symmetry directions. Through classical Monte Carlo simulations, mean field theory, and classical linear spin-wave expansions, we argue that the origins of the multiple occurrences of reentrance observed in Er 2 Sn 2 O 7 are linked to soft modes. These soft modes arise from phase competition and enhance thermal fluctuations that entropically stabilize a specific ordered phase, resulting in an increased transition temperature for certain field values and thus the reentrant behavior. Our work represents a detailed examination into the mechanisms responsible for reentrance in a frustrated magnet and may serve as a template for the interpretation of reentrant phenomena in other physical systems.
36 MATERIALS SCIENCE↗
Simulated structure and thermodynamics of decagonal Al-Co-Cu quasicrystals
Atomic structures of Al-Co-Cu decagonal quasicrystals (dQCs) are investigated using empirical oscillating pair potentials (EOPP) in molecular dynamic (MD) simulations that we enhance by Monte Carlo (MC) swapping of chemical species and replica exchange. Predicted structures exhibit planar decagonal tiling patterns and are periodic along the perpendicular direction. We then recalculate the energies of promising structures using first-principles density functional theory (DFT), along with energies of competing phases. We find that our τ -inflated sequence of QC approximants (QCAs) are energetically unstable at low temperature by at least 3 meV/atom. Extending our study to finite temperatures by calculating harmonic vibrational entropy, as well as anharmonic contributions that include chemical species swaps and tile flips, our results suggest that the quasicrystal phase is entropically stabilized at temperatures in the range 600-800 K and above. It decomposes into ordinary (though complex) crystal phases at low temperatures, including a partially disordered B2-type phase. We discuss the influence of density and composition on QC phase stability; we compare the structural differences between Co-rich and Cu-rich quasicrystals; and we analyze the role of entropy in stabilizing the quasicrystal, concluding with a discussion of the possible existence of “high entropy” quasicrystals. Published by the American Physical Society 2024
Huang, Yang (ORCID:0009000045917347)↗