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DOE OSTI2024

High entropy ceramics for applications in extreme environments

Abstract Compositionally complex materials have demonstrated extraordinary promise for structural robustness in extreme environments. Of these, the most commonly thought of are high entropy alloys, where chemical complexity grants uncommon combinations of hardness, ductility, and thermal resilience. In contrast to these metal–metal bonded systems, the addition of ionic and covalent bonding has led to the discovery of high entropy ceramics (HECs). These materials also possess outstanding structural, thermal, and chemical robustness but with a far greater variety of functional properties which enable access to continuously controllable magnetic, electronic, and optical phenomena. In this experimentally focused perspective, we outline the potential for HECs in functional applications under extreme environments, where intrinsic stability may provide a new path toward inherently hardened device design. Current works on high entropy carbides, actinide bearing ceramics, and high entropy oxides are reviewed in the areas of radiation, high temperature, and corrosion tolerance where the role of local disorder is shown to create pathways toward self-healing and structural robustness. In this context, new strategies for creating future electronic, magnetic, and optical devices to be operated in harsh environments are outlined.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Robustness of entropy plateaus: A case study of triangular Ising antiferromagnets

We present that residual entropy is a key feature associated with emergence in many-body systems. From a variety of frustrated magnets to the onset of spin-charge separation in Hubbard models and fermion-Z 2 -flux variables in Kitaev models, the freezing of one set of degrees of freedom and the establishment of local constraints are marked by a plateau in entropy as a function of temperature. Yet, with the exception of the rare-earth pyrochlore family of spin-ice materials, evidence for such plateaus is rarely seen in real materials, raising questions about their robustness. Following recent experimental findings of the absence of such plateaus in the triangular-lattice Ising antiferromagnet (TIAF) TmMgGaO 4 by Li et al., we explore in detail the existence and rounding of entropy plateaus in TIAF. We use a transfer-matrix method to numerically calculate the properties of the system at different temperatures and magnetic fields, with further neighbor interactions and disorder. In conclusion, we find that temperature windows of entropy plateaus exist only when second-neighbor interactions are no more than a couple of percent of the nearest-neighbor ones, and they are also easily destroyed by disorder in the nearest-neighbor exchange variable, thereby explaining the challenge in observing such effects.

2-dimensional systems↗

DOE OSTI2018

Determining the vibrational entropy change in the giant magnetocaloric material LaFe 11.6 Si 1.4 by nuclear resonant inelastic x-ray scattering

Magnetocaloric ${\mathrm{LaFe}}_{13{-}x}{\mathrm{Si}}_{x}$-based compounds belong to the outstanding materials with potential for efficient solid-state refrigeration. We have performed temperature-dependent $^{57}\mathrm{Fe}$ nuclear resonant inelastic x-ray scattering measurements (in a field ${{\mu}}_{0}H$ of ${\sim}0.7$ T) of the vibrational (phonon) density of states, VDOS, in ${\mathrm{LaFe}}_{11.6}{\mathrm{Si}}_{1.4}$ across the metamagnetic isostructural first-order phase transition at ${T}_{C}{\sim}192$ K from the low-temperature ferromagnetic (FM) to the high-temperature paramagnetic (PM) phase, in order to determine the change in thermodynamic properties of the Fe lattice at ${T}_{C}$. The experimental results are compared with density-functional-theory-based first-principles calculations using the fixed-spin moment approach. Our combined experimental and theoretical results reveal distinct and abrupt changes in the VDOS of the Fe sublattice across ${T}_{C}$, occurring within a small temperature interval of $\mathrm{{\Delta}}T{\le}12$ K around ${T}_{C}$. This indicates that strong magnetoelastic coupling (at the atomic scale) is present up to ${T}_{C}$, leading to a pronounced lattice softening (phonon redshift) in the PM phase. These changes originate from the itinerant electron magnetism associated with Fe and are correlated with distinct modifications in the Fe-partial electronic density of states $D({E}_{F}$) at the Fermi energy ${E}_{F}$. From the experimental VDOS we can infer an abrupt increase (jump) in the Fe-partial vibrational entropy $\mathrm{{\Delta}}{S}_{\mathrm{vib}}$ of $+6.9\pm{}2.6$ J/(kg K) and in the vibrational specific heat $\mathrm{{\Delta}}{C}_{\mathrm{vib}}$ of $+2.7\pm{}1.6$ J/(kg K) upon heating. The increase in magnitude of the vibrational entropy $|\mathrm{{\Delta}}{S}_{\mathrm{vib}}|=6.9$ J/(kg K) of the Fe sublattice at ${T}_{C}$ upon heating is substantial, if compared with the magnitude of the isothermal entropy change $|\mathrm{{\Delta}}{S}_{\mathrm{iso}}|$ of 14.2 J/(kg K) in a field change $\mathrm{{\Delta}}B$ from 0 to 1 T, as obtained from isothermal magnetization measurements on our sample and using the Maxwell relation. Finally, we demonstrate that $\mathrm{{\Delta}}{S}_{\mathrm{vib}}$ obtained by nuclear resonant inelastic x-ray scattering is a sizable quantity and contributes directly and cooperatively to the total entropy change $\mathrm{{\Delta}}{S}_{\mathrm{iso}}$ at the phase transition of ${\mathrm{LaFe}}_{13{-}x}{\mathrm{Si}}_{x}$.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Entropy Measurement of a Strongly Coupled Quantum Dot

The spin 1/2 entropy of electrons trapped in a quantum dot has previously been measured with great accuracy, but the protocol used for that measurement is valid only within a restrictive set of conditions. Here, in this work, we demonstrate a novel entropy measurement protocol that is universal for arbitrary mesoscopic circuits and apply this new approach to measure the entropy of a quantum dot hybridized with a reservoir. The experimental results match closely to numerical renormalization group (NRG) calculations for small and intermediate coupling. For the largest couplings investigated in this Letter, NRG calculations predict a suppression of spin entropy at the charge transition due to the formation of a Kondo singlet, but that suppression is not observed in the experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Orbital control of metal-to-insulator transition in high-entropy nickelates

High-entropy materials have emerged as a promising platform for exploring unique electronic and structural properties. In this study, we investigated the orbital control of the metal-to-insulator transition in thin films of high-entropy nickelates, which are composed of five rare-earth elements in equi-atomic concentrations. By manipulating the levels of misfit strain through substrate choice and film thickness, we modulated the electronic properties and examined the intricate interplay between strain, orbital interactions, and the metal-to-insulator transition. Compared to other nickelates thin films like NdNi O 3 and SmNi O 3 , thin films of high-entropy nickelates exhibited remarkable resilience in maintaining control over their transport properties and orbital polarization, even in the presence of considerable A-site disorder. Further, this finding suggests that the electronic properties of A-site disordered high-entropy nickelates are still governed by the electronic bandwidth, primarily influenced by the Ni-O bonding geometry. This study provides valuable insights into the complex interplay among composition, structure, and electronic properties in perovskite oxides. These insights have the potential to guide the development of perovskite oxide materials with tailored electronic properties for a wide range of applications.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Pressureless sintering of dual-phase, high-entropy boride–carbide ceramics

Here, dual-phase, high-entropy boride–carbide ceramics were densified by pressureless sintering. Relative densities up to approximately 96% were obtained for ceramics containing about 30 vol% high-entropy boride and 70 vol% high-entropy carbide. Isostatic pressing at 200 MPa resulted in higher relative densities of both the green bodies and final ceramics compared to uniaxial pressing. The highest relative density of 96.3% was achieved for a ceramic that was isostatically pressed at 200 MPa and sintered at 2300°C for 2 h. Grain sizes of the resulting ceramics were approximately 2 µm. This is the first report of pressureless sintering of dual-phase, high-entropy boride–carbide ceramics.

36 MATERIALS SCIENCE↗

DOE OSTI2014

MO-A-BRD-02: Noise Suppression for Dual-Energy CT Through Entropy Minimization

Purpose: In dual energy CT (DECT), noise amplification during signal decomposition significantly limits the utility of basis material images. Since clinically relevant objects contain a limited number of materials, we propose to suppress noise in decomposed images through entropy minimization within a 2D transformation space. Distinct from other noise suppression techniques, the entropy minimization method does not estimate and suppress noise based on spatial variations of signals and thus maximally preserves image spatial resolution. Methods: From decomposed images, we first generate a 2D plot of scattered data points, using basis material densities as coordinates. Data points representing the same material generate a cluster with a highly asymmetric shape. We orient an axis by minimizing the entropy in a 1D histogram of these points projected onto the axis. To suppress noise, we replace the pixel values of decomposed images with center-of-mass values in the direction perpendicular to the optimized axis. The proposed method's performance is assessed using a Catphan 600 phantom and an anthropomorphic head phantom. Electron density calculations are used to quantify its accuracy. Our results are compared to those without noise suppression, with a filtering method, and with a recently developed iterative method. Results: On both phantoms, the proposed method reduces noise standard deviations of the decomposed images by at least on order of magnitude. In the Catphan study, this method retains the spatial resolution of the CT images and increases the accuracy of electron density calculations. In the head phantom study, the proposed method outperforms the others in retaining fine, intricate structures. Conclusion: This work shows that the proposed method of noise suppression through entropy minimization for DECT suppresses noise without loss of spatial resolution while increasing electron density calculation accuracy. Future investigations will analyze possible bias and incorporate spatial information into the technique for further noise reduction. The work is partially supported by the NIH under the grant number R21EB012700.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2017

Entropy and magnetocaloric effect in ferrimagnets RCo{sub 2}

The equations of state for the magnetic and elastic subsystems of a ferrimagnet are obtained in terms of the exchange–striction model. In the formulas derived for magnetic entropy, it is represented as the sum of the contributions of two magnetic sublattices of the ferrimagnet. One of the main characteristics of the magnetocaloric effect, viz., isothermal variation ΔS{sub iso} of the entropy in a magnetic field, is calculated for compounds RCo{sub 2} (R = Er, Ho, Dy) that experience a first-order magnetic phase transition and TbCo{sub 2} that experiences a second-order magnetic phase transition. It is shown that the calculated values of ΔS{sub iso} for these compounds are in satisfactory quantitative agreement with experimental results. The change in the entropy of a ferrimagnet in a strong magnetic field upon a transition from the ferrimagnetic to ferromagnetic ordering is calculated. The peculiarities in the magnetic field dependences of the magnetic entropy of a two-sublattice ferrimagnet are analyzed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Application of permutation entropy method in the analysis of chaotic, noisy, and chaotic noisy series

We have considered a permutation entropy method for analyzing chaotic, noisy, and chaotic noisy series. We have introduced the concept of permutation entropy from a survey of some features of information entropy (Shannon entropy), described the algorithm for its calculation, and indicated the advantages of this approach in the analysis of time series; the application of this method in the analysis of various model systems and experimental data has also been demonstrated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

A Regularized Entropy-Based Moment Method for Kinetic Equations

Here, we present a new entropy-based moment method for the velocity discretization of kinetic equations. This method is based on a regularization of the optimization problem defining the original entropy-based moment method, and this gives the new method the advantage that the moment vectors of the solution do not have to take on realizable values. We show that this equation still retains many of the properties of the original equations, including hyperbolicity, an entropy-dissipation law, and rotational invariance. The cost of the regularization is mismatch between the moment vector of the solution and that of the ansatz returned by the regularized optimization problem. However, we show how to control this error using the parameter defining the regularization. This suggests that with proper choice of the regularization parameter, the new method can be used to generate accurate solutions of the original entropy-based moment method, and we confirm this with numerical simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Production of Entanglement Entropy by Decoherence

We examine here the dynamics of entanglement entropy of all parts in an open system consisting of a two-level dimer interacting with an environment of oscillators. The dimer-environment interaction is almost energy conserving. We find the precise link between decoherence and production of entanglement entropy. We show that not all environment oscillators carry significant entanglement entropy and we identify the oscillator frequency regions which contribute to the production of entanglement entropy. For energy conserving dimer-environment interactions the models are explicitly solvable and our results hold for all dimer-environment coupling strengths. We carry out a mathematically rigorous perturbation theory around the energy conserving situation in the presence of small non-energy conserving interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

World Congress on High Entropy Alloys (HEA 2019) (Final Technical Report)

The World Congress on High Entropy Alloys (HEA 2019) was a new, cross-disciplinary technical forum designed to share the latest research advances in materials with high configurational entropy, including both single-phase and multiphase (compositionally complex) alloys. This inaugural World Congress on High Entropy Alloys (HEA 2019) was held in Seattle, Washington from November 17-20, 2019 with the goal of HEA 2019 to assemble the international community of HEA stakeholders – including researchers, educators, and engineers – to capture the current state-of-the-art, identify current gaps in HEA efforts, and to set the stage for the future growth and application of HEAs worldwide. HEA 2019 was the environment for leaders in this field to showcase their researc, and network with their peers to informally discuss the latest developments in high entropy alloys, while also making valuable professional connections. The goal of the organizers was to ensure a high-quality conference that held a strong international presence and aimed to highlight the important advances in HEA research on a global scale. Student participation was greatly encouraged in order to give students exposure to recent advances in this field. This meeting was open to all interested individuals and attempted to provide the most advanced technical meeting possible, with a mixture of attendees from research and development, industry, and education.

36 MATERIALS SCIENCE↗

DOE OSTI2019

A Suggestion of Converting Protein Intrinsic Disorder to Structural Entropy Using Shannon’s Information Theory

We propose a framework to convert the protein intrinsic disorder content to structural entropy (H) using Shannon’s information theory (IT). The structural capacity (C), which is the sum of H and structural information (I), is equal to the amino acid sequence length of the protein. The structural entropy of the residues expands a continuous spectrum, ranging from 0 (fully ordered) to 1 (fully disordered), consistent with Shannon’s IT, which scores the fully-determined state 0 and the fully-uncertain state 1. The intrinsically disordered proteins (IDPs) in a living cell may participate in maintaining the high-energy-low-entropy state. In addition, under this framework, the biological functions performed by proteins and associated with the order or disorder of their 3D structures could be explained in terms of information-gains or entropy-losses, or the reverse processes.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

A Robust Protocol for Entropy Measurement in Mesoscopic Circuits

Previous measurements utilizing Maxwell relations to measure change in entropy, S, demonstrated remarkable accuracy in measuring the spin-1/2 entropy of electrons in a weakly coupled quantum dot. However, these previous measurements relied upon prior knowledge of the charge transition lineshape. This had the benefit of making the quantitative determination of entropy independent of scale factors in the measurement itself but at the cost of limiting the applicability of the approach to simple systems. To measure the entropy of more exotic mesoscopic systems, a more flexible analysis technique may be employed; however, doing so requires a precise calibration of the measurement. Here, we give details on the necessary improvements made to the original experimental approach and highlight some of the common challenges (along with strategies to overcome them) that other groups may face when attempting this type of measurement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Entropy viscosity method applied to Euler equations

The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

2D High‐Entropy Transition Metal Dichalcogenides for Carbon Dioxide Electrocatalysis

Abstract High‐entropy alloys combine multiple principal elements at a near equal fraction to form vast compositional spaces to achieve outstanding functionalities that are absent in alloys with one or two principal elements. Here, the prediction, synthesis, and multiscale characterization of 2D high‐entropy transition metal dichalcogenide (TMDC) alloys with four/five transition metals is reported. Of these, the electrochemical performance of a five‐component alloy with the highest configurational entropy, (MoWVNbTa)S 2 , is investigated for CO 2 conversion to CO, revealing an excellent current density of 0.51 A cm −2 and a turnover frequency of 58.3 s −1 at ≈ −0.8 V versus reversible hydrogen electrode. First‐principles calculations show that the superior CO 2 electroreduction is due to a multi‐site catalysis wherein the atomic‐scale disorder optimizes the rate‐limiting step of CO desorption by facilitating isolated transition metal edge sites with weak CO binding. 2D high‐entropy TMDC alloys provide a materials platform to design superior catalysts for many electrochemical systems.

Cavin, John↗

DOE OSTI2016

Supersymmetric Renyi entropy in CFT 2 and AdS 3

We show that in any two dimensional conformal field theory with (2, 2) super-symmetry one can define a supersymmetric analog of the usual Renyi entropy of a spatial region A. It differs from the Renyi entropy by a universal function (which we compute) of the central charge, Renyi parameter n and the geometric parameters of A. In the limit n → 1 it coincides with the entanglement entropy. Thus, it contains the same information as the Renyi entropy but its computation only involves correlation functions of chiral and anti-chiral operators. We also show that this quantity appears naturally in string theory on AdS3.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

An entropy current in superspace

We provide a mechanism by which an entropy current can be constructed in a supersymmetric formulation of the low-energy effective action for the Schwinger-Keldysh generating functional. This mechanism allows us to define an entropy current quantum mechanically by coupling it to an external source. Such an entropy current is given by the bottom component of an entropy current superfield which is conserved in superspace, but when restricted to real space satisfies a non-conservation law. We demonstrate the validity of our mechanism in a probe limit which allows us to fully treat quantum fluctuations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗