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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Cantor-derived medium-entropy alloys: bridging the gap between traditional metallic and high-entropy alloys

The year 2004 marked the beginning of a new era in the design of metallic materials, as the concept of multiple principal component alloys, commonly known as High-Entropy Alloys (HEAs), was proposed by Cantor and Yeh. The unexpected single-phase microstructure, instead of the expected brittle intermetallic compounds, was attributed to the large entropy of mixing and immediately caught the attention of the scientific community. Today, HEAs are considered important advanced materials and a broad range of alloys using nominally the same design principle have been investigated. Despite that, the CrMnFeCoNi (Cantor) alloy stands out as the most successful HEA due to its outstanding mechanical properties and microstructure. In this scenario, variants of the Cantor alloy, named medium-entropy alloys (MEAs), are gaining significant interest as they display a better industrial potential than both HEAs and traditional alloys. These variants of the Cantor alloy with only three or four main elements result in 15 possible combinations. The microstructure of these alloys is discussed in terms of advanced characterization as well as thermodynamic parameters and computational simulation. Their phase stability is addressed over a wide range of temperatures and strain rates. The mechanical properties, especially the fracture toughness, of the CrFeCoNi and CrCoNi alloys have been reported to be even superior to those of the Cantor alloy and most modern engineering alloys. This is associated with the formation of a continuous sequence of strengthening mechanisms, including hierarchical twin networks, which serve to prolong the strain hardening. The present article reviews and critically assesses, for the first time, recent advances in these Cantor-derived MEAs.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Defect-Driven Configurational Entropy in the High-Entropy Oxide Li 1.5 MO 3-δ

Layered lithiated oxides are promising materials for next generation Li-ion battery cathode materials; however, instability during cycling results in poor performance over time compared to the high capacities theoretically possible with these materials. Here, in this paper, we report the characterizations of a Li 1.47 Mn 0.57 Al 0.13 Fe 0.095 Co 0.105 Ni 0.095 O 2.49 high-entropy layered oxide (HELO) with the Li 2 MO 3 structure where M = Mn, Al, Fe, Co, and Ni. Using electron microscopy and X-ray spectroscopy, we identify a homogeneous Li 2 MO 3 structure stabilized by the entropic contribution of oxygen vacancies. This defect-driven entropy would not be attainable in the LiMO 2 structure sometimes observed in similar materials as a secondary phase owing to the presence of fewer O sites and a 3+ oxidation state for the metal site; instead, a Li 2-γ MO 3-δ is produced. Beyond Li 2 MO 3 , this defect-driven entropy approach to stabilizing novel compositions and phases can be applied to a wide array of future cathode materials including spinel and rock salt structures.

25 ENERGY STORAGE↗
DOE OSTI2020

Entropy-stabilized single-atom Pd catalysts via high-entropy fluorite oxide supports

Single-atom catalysts (SACs) have attracted considerable attention in the catalysis community. However, fabricating intrinsically stable SACs on traditional supports (N-doped carbon, metal oxides, etc.) remains a formidable challenge, especially under high-temperature conditions. Here, we report a novel entropy-driven strategy to stabilize Pd single-atom on the high-entropy fluorite oxides (CeZrHfTiLa)O x (HEFO) as the support by a combination of mechanical milling with calcination at 900 °C. Characterization results reveal that single Pd atoms are incorporated into HEFO (Pd1@HEFO) sublattice by forming stable Pd–O–M bonds (M = Ce/Zr/La). Compared to the traditional support stabilized catalysts such as Pd@CeO 2 , Pd 1 @HEFO affords the improved reducibility of lattice oxygen and the existence of stable Pd–O–M species, thus exhibiting not only higher low-temperature CO oxidation activity but also outstanding resistance to thermal and hydrothermal degradation. This work therefore exemplifies the superiority of high-entropy materials for the preparation of SACs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A cosine-based correlation information entropy approach for building automatic fault detection baseline construction

Building automatic fault detection and diagnosis (AFDD) technologies have shown great potential for energy savings. To enable AFDD, a baseline depicting the normal operation mode is needed to detect whether the building operation deviates from normality. Existing research using physics-based knowledge and models for AFDD has mainly taken a trial-and-error approach to determine if a given baseline is sufficient via empirical experiments. A mechanism to support decisions such as how many samples and what samples should be included in the baseline is currently lacking. In this study, a data-driven method for AFDD baseline construction based on information entropy is developed. The entropy is derived based on cosine similarity among typical building automation system measurements in conjunction with outdoor weather information. The performance of the proposed method is evaluated using real building data. Evaluation results indicate that the fault detection strategy adopting the proposed method has similar or better accuracy in detecting faults compared to the same fault detection strategy using the baseline construction method from the literature. Additionally, the use of entropy enables the proposed method to automatically construct and assess the baseline consisting of information-rich samples.

42 ENGINEERING↗
DOE OSTI2026

High entropy oxides prediction and discovery by the Mixed Enthalpy-Entropy Descriptor

The vast, high-dimensional composition space of high-entropy oxides (HEOs) offers exceptional opportunities for functional materials discovery, yet it also poses a fundamental challenge: the rational and efficient prediction of stable, synthesizable compositions and the corresponding structure–property relationships. Despite growing interest, the field still lacks broadly applicable, physically grounded descriptors capable of navigating various large chemical spaces. Here, we introduce a Mixed Enthalpy–Entropy Descriptor (MEED) that enables rapid, first-principles–based prediction of HEOs synthesizability across diverse chemistries. Using MEED, we perform high-throughput screening of two distinct HEO families: rocksalt oxides and perovskite oxides. The predicted top candidates in each family were experimentally validated. MEED reveals unifying thermodynamic and structural principles governing stability across both chemical compositions and polymorphs, providing mechanistic insight into the formation of high-entropy phases. This work significantly broadens the accessible chemical design space for HEOs and establishes a data-efficient framework for accelerating the discovery of next-generation functional materials.

Yu, Liping [University of Central Florida]↗
DOE OSTI2026

A Comparative Study of Thermal Oxidization Resistance of a High-Entropy Metal Boride and a High-Entropy Metal Carbide

We present a systematic study of thermal oxidation resistance of transition metal borides and carbides up to 1300 °C in a dry air environment. A High-Entropy Metal Boride (HEMB), of composition (Hf 0.2 , Mo 0.2 , Nb 0.2 , Ta 0.2 , Zr 0.2 )B 2 , and a similar High-Entropy Metal Carbide (HEMC) (Hf, Mo, Nb, Ta, Zr)C 5 were synthesized from precursor mixtures, under 30 MPa of pressure at a temperature of 1800 °C using a Spark Plasma Sintering Device. The synthesized phases were confirmed via X-ray Diffraction analysis, which showed a pure hexagonal AlB 2 -type structure for HEMB and a face-centered cubic (FCC) structure for HEMC, with lattice parameters, a = 3.10 Å and c = 3.37 Å for HEMB and a = 4.524 Å for HEMC. Oxidation resistance was evaluated using a simultaneous thermogravimetric analysis and differential scanning calorimetry (TGA/DSC) stage in which HEMB and HEMC were heated up to 1300 °C at a rate of 2 °C/min in a dry air environment. Scanning electron microscopy (SEM) was used to analyze the resulting oxidized material. Our study demonstrates that HEMB shows better thermal oxidation resistance as compared to a similar metal composition HEMC at high temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Computationally aided, entropy-driven synthesis of highly efficient and durable multi-elemental alloy catalysts

Multi-elemental alloy nanoparticles (MEA-NPs) hold great promise for catalyst discovery in a virtually unlimited compositional space. However, rational and controllable synthesize of these intrinsically complex structures remains a challenge. Here, we report the computationally aided, entropy-driven design and synthesis of highly efficient and durable catalyst MEA-NPs. The computational strategy includes prescreening of millions of compositions, prediction of alloy formation by density functional theory calculations, and examination of structural stability by a hybrid Monte Carlo and molecular dynamics method. Selected compositions can be efficiently and rapidly synthesized at high temperature (e.g., 1500 K, 0.5 s) with excellent thermal stability. We applied these MEA-NPs for catalytic NH 3 decomposition and observed outstanding performance due to the synergistic effect of multi-elemental mixing, their small size, and the alloy phase. We anticipate that the computationally aided rational design and rapid synthesis of MEA-NPs are broadly applicable for various catalytic reactions and will accelerate material discovery.

36 MATERIALS SCIENCE↗
NASA NTRS2019

Approximate Entropy and Sample Entropy: A Comprehensive Tutorial

Approximate Entropy and Sample Entropy are two algorithms for determining the regularity of series of data based on the existence of patterns. Despite their similarities, the theoretical ideas behind those techniques are different but usually ignored. This paper aims to be a complete guideline of the theory and application of the algorithms, intended to explain their characteristics in detail to researchers from different fields. While initially developed for physiological applications, both algorithms have been used in other fields such as medicine, telecommunications, economics or Earth sciences. In this paper, we explain the theoretical aspects involving Information Theory and Chaos Theory, provide simple source codes for their computation, and illustrate the techniques with a step by step example of how to use the algorithms properly. This paper is not intended to be an exhaustive review of all previous applications of the algorithms but rather a comprehensive tutorial where no previous knowledge isrequired to understand the methodology.

Delgado-Bonal, Alfonso↗
DOE OSTI2021

Magnetic Texture in Insulating Single Crystal High Entropy Oxide Spinel Films

Magnetic insulators are important materials for a range of next-generation memory and spintronic applications. Structural constraints in this class of devices generally require a clean heterointerface that allows effective magnetic coupling between the insulating layer and the conducting layer. However, there are relatively few examples of magnetic insulators that can be synthesized with surface qualities that would allow these smooth interfaces and precisely tuned interfacial magnetic exchange coupling, which might be applicable at room temperature. In this work, we demonstrate an example of how the configurational complexity in the magnetic insulator layer can be used to realize these properties. The entropy-assisted synthesis is used to create single-crystal (Mg 0.2 Ni 0.2 Fe 0.2 Co 0.2 Cu 0.2 )Fe 2 O 4 films on substrates spanning a range of strain states. These films show smooth surfaces, high resistivity, and strong magnetic responses at room temperature. Furthermore, local and global magnetic measurements further demonstrate how strain can be used to manipulate the magnetic texture and anisotropy. These findings provide insight into how precise magnetic responses can be designed using compositionally complex materials that may find application in next-generation magnetic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Computational exploration of biomedical HfNbTaTiZr and Hf 0.5 Nb 0.5 Ta 0.5 Ti 1.5 Zr refractory high-entropy alloys

Refractory high entropy alloys (RHEAs) have been proven to be a potential candidate in the biomedical field due to their balanced mechanical properties and biocompatible composition. Recent experimental findings show that RHEAs like HfNbTaTiZr and Hf 0.5 Nb 0.5 Ta 0.5 Ti 1.5 Zr have good mechanical properties such as high polarization and wear resistance than others which establish them as potential materials for biomedical application. In this work, we performed first-principles density functional theory calculations on the mechanical and thermal properties of HfNbTaTiZr and Hf 0.5 Nb 0.5 Ta 0.5 Ti 1.5 Zr. The predicted lattice constant, density, Young's modulus, and Vickers hardness are consistent with the available experimental report, which verifies the accuracy of the applied model. The thermal coefficient of linear expansion of both RHEAs has been investigated by utilizing the Debye theory. The present methods could be applied to study other future RHEAs on exploration of their physical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2021

High Density of Strong yet Deformable Intermetallic Nanorods Leads to an Excellent Room Temperature Strength-Ductility Combination in a High Entropy Alloy

This paper introduces a new microstructural template for high entropy alloys (HEAs), where the face centered cubic (FCC) complex concentrated solid solution is reinforced with a high density of strong, yet deformable, nanorods of an ordered multi-component intermetallic L12 compound. Thermodynamic modeling has been employed to design this HEA with a large L12 volume fraction. Thermo-mechanical processing by isothermal annealing of the conventionally processed bulk cold-rolled alloy directly at precipitation temperatures, has been applied to produce a high density of uniformly distributed L12 nanorods within refined FCC grains, resulting from concomitant recrystallization and discontinuous precipitation processes. The nanorod morphology of the discontinuous L12 product has been established from three-dimensional atom probe tomography. The refined grains result in a complete coverage of the microstructure with discontinuously precipitated intermetallic nanorods. This nanorod strengthened HEA exhibits an exceptionally high room temperature yield strength of ~1630 MPa, good tensile ductility of ~15%, and an ultimate tensile strength of ~1720 MPa. Furthermore, a single L12 phase alloy, melted based on the precipitate composition in the two-phase FCC + L12 HEA, exhibits very high compressive deformability and strain hardenability, unusual for ordered intermetallic compounds. These results open a new strategy for design of fine-grained microstructures strengthened via ordered intermetallic phases, exploiting the beneficial effects of discontinuous precipitation, for achieving very high room temperature tensile strengths while maintaining good ductility.

Gwalani, Bharat↗
DOE OSTI2021

Uncertainty Quantification and Error Propagation in the Enthalpy and Entropy of Surface Reactions Arising from a Single DFT Functional

Accounting for parametric uncertainty in models is essential for quantifying the models’ predictive ability. Recently, approaches have been introduced to estimate parametric uncertainty in kinetic models while accounting for correlations among energy parameters. However, correlations have been estimated indirectly and correlations in entropies have not been accounted for. For surface-catalyzed microkinetic models of >C2 (more than two carbon-containing) molecules, which consist of thousands of reaction steps and intermediate surface species, first-principles density functional theory (DFT) is costly, and thus, estimation of thermochemistry and reaction barriers requires surrogate methods of DFT, such as group additivity and Brønsted–Evans–Polanyi relationships, respectively. For such parametrization, model uncertainty is unclear. This work develops a framework to overcome these gaps using group additivity and a single DFT functional. We estimate correlations in parameters of kinetic models and quantify uncertainty for thermochemistry, reaction barriers, reaction paths, and ultimately reaction rates, accounting also for the contribution of entropic uncertainty. Furthermore, the approach is illustrated on propane combustion and ethane oxidative dehydrogenation reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Resolving Configurational Disorder for Impurities in a Low-Entropy Phase

Hematite (α-Fe 2 O 3 ) exerts a strong control over the transport of minor but critical metals in the environment and is used in multiple industrial applications; the photocatalysis community has explored the properties of hematite nanoparticles over a wide range of transition metal dopants. Nonetheless, simplistic assumptions are used to rationalize the local coordination environment of impurities in hematite. Here, we use ab initio molecular dynamics (AIMD)-guided structural analysis to model the extended X-ray absorption fine structure (EXAFS) of Cu 2+ - and Zn 2+ -doped hematite nanoparticles. Specific defect–impurity associations were identified, and the local coordination environments of Cu and Zn both displayed considerable configurational disorder that, in aggregate, approached Jahn–Teller-like distortion for Cu but, in contrast, maintained hematite-like symmetry for Zn. This study highlights the role of defects in accommodating impurities in a nominally low-entropy phase and the limits to traditional shell-by-shell fitting of EXAFS for dopants/impurities in unprecedented bonding environments.

36 MATERIALS SCIENCE↗