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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

First-Principles Studies on Sc 2 RuZ (Z = Si, Ge, Sn) Inverse Heusler Alloys: Structural, Electronic, and Transport Properties

The continuous demand for efficient, nontoxic, and thermally stable materials for room-temperature energy conversion motivates the exploration of novel thermoelectric systems beyond the traditional magnetic Heusler alloys. While full and half-Heusler compounds, especially Co-, Ni-, and Mn-based systems, have demonstrated promising thermoelectric properties, their typically high operating temperatures and magnetic complexities limit their applicability in ambient thermal management. In this context, we investigate whether Sc-based inverse Heusler alloys can offer a viable nonmagnetic alternative with competitive thermoelectric performance. In this work, we perform a systematic first-principles study of the inverse Heusler compounds Sc 2 RuZ (Z = Si, Ge, Sn), focusing on their structural, electronic, mechanical, and thermodynamic-thermoelectric properties. Density Functional Theory (DFT) was employed to compute optimized lattice structures and band dispersion, while dynamical stability was assessed via phonon calculations. Thermoelectric transport coefficients, including Seebeck coefficient, electrical conductivity, and thermal conductivity, were estimated using the semiclassical Boltzmann transport theory within the constant relaxation time approximation. Our results show that all Sc 2 RuZ compounds are thermodynamically stable semiconductors with indirect band gaps of 0.12–0.16 eV and exhibit high elastic moduli, especially Sc 2 RuSn, which demonstrates superior stiffness and incompressibility. Importantly, all compounds display promising room-temperature thermoelectric characteristics, including high Seebeck coefficients and power factors. These findings reveal that Sc 2 RuZ alloys represent a rare class of stable, nonmagnetic inverse Heusler semiconductors with intrinsic thermoelectric potential at room temperature, unlike many existing Heusler systems optimized for spintronics or high-temperature operation. This work expands the known design space for Heusler-based thermoelectrics and offers a theoretical basis for experimental realization of efficient, low-temperature, nonmagnetic thermoelectric materials.

alloys↗
DOE OSTI2026

Quaternary i-MAX Phases (Mo 2/3 RE 1/3 ) 2 AlC (RE: Dy, Tb, Er): Experimental Characterization and First-Principles Insights into their Fundamental Properties

Rare earth (RE)-based materials have unique electronic, magnetic, and optical properties, leading to the recent discovery of atomically layered solids with the chemical formula (M' 2/3 RE 1/3 ) 2 AlC, which have since garnered significant attention in the scientific community. This study aims to synthesize, characterize, and investigate the structural and thermal stability of the RE i-MAX phases. We prepared i-MAX phases using molybdenum (Mo) as M′ and RE elements as Dy, Tb, and Er, namely (Mo 2/3 Dy 1/3 ) 2 AlC, (Mo 2/3 Tb 1/3 ) 2 AlC, and (Mo 2/3 Er 1/3 ) 2 AlC. Structural characterization through x-ray diffraction (XRD) and Raman spectroscopy confirms the formation of the RE-based i-MAX phase, along with the presence of minor impurity phases in the alloys. Thermogravimetric analysis (TGA) conducted up to 1000°C under ambient conditions reveals that the i-MAX phases remain thermally stable up to approximately 450°C, beyond which oxidation leads to a noticeable weight gain in all samples. Differential scanning calorimetry (DSC) measurements during heating and cooling cycles show endothermic and exothermic peaks for (Mo 2/3 Dy 1/3 ) 2 AlC i-MAX in the 410–420°C range, indicating a temperature-induced minor atomic arrangement. In contrast, these peaks are absent in the Tb- and Er-based i-MAX phases. These findings offer valuable insights into the thermal behavior and stability of these i-MAX phases under thermal stress, contributing to a deeper understanding of their unique properties. Furthermore, first-principles density functional theory (DFT) calculations were performed to investigate the electronic and optical properties of the i-MAX phases. The results reveal their metallic nature, with pronounced contributions from Mo and RE elements near the Fermi level and within the conduction band.

Rare earth↗
DOE OSTI2026

A first principles approach for determining solute effect on electrical resistivity of Aluminum solid solution

There are no general approaches for predicting the effect of solutes on electrical resistivity changes in aluminum (Al) solid solutions. Here, we introduce a first principles-based approach for predicting temperature-dependent electrical resistivity of Al solid solutions. A combination of electronic structure methods was applied to calculate electronic scattering effects on chemical disorder and temperature induced atomic vibrations or phonons. Our calculations are validated by contrasting experimental resistivity measurements for two elements in Al solid solution: at 0.3 at. % concentration, Sn (an sp-valence solute) increases the residual resistivity by 0.2 μΩ·m, whereas Zr (a d-valence solute) causes a 2.5 μΩ·m increase. This trend may deviate for solute elements in Al that form semiconductors in pure state, like Si. Our findings provide an understanding of the role of valence electron character of solute atoms in determining electrical resistivity of Al alloys.

Samolyuk, German [ORNL] (ORCID:0000000168778255)↗
DOE OSTI2025

First-Principles Statistical Mechanics Study of Magnetic Fluctuations and Order–Disorder in the Spinel LiNi 0.5 Mn 1.5 O 4 Cathode

While significant magnetic interactions exist in lithium transition metal oxides, commonly used as Li-ion cathodes, the interplay between magnetic couplings, disorder, and redox processes remains poorly understood. In this work, we focus on the high-voltage spinel LiNi 0.5 Mn 1.5 O 4 (LNMO) cathode as a model system on which to apply a computational framework that uses first principles-based statistical mechanics methods to predict the finite temperature magnetic properties of materials and provide insights into the complex interplay between magnetic and chemical degrees of freedom. Density functional theory calculations on multiple distinct Ni–Mn orderings within the LNMO system, including the ordered ground-state structure (space group P4332), reveal a preference for a ferrimagnetic arrangement of the Ni and Mn sublattices due to strong antiferromagnetic superexchange interactions between neighboring Mn 4+ and Ni 2+ ions and ferromagnetic Mn–Mn and Ni–Ni couplings, as revealed by magnetic cluster expansions. These results are consistent with qualitative predictions using the Goodenough-Kanamori-Anderson rules. Simulations of the finite temperature magnetic properties of LNMO are conducted using Metropolis Monte Carlo. We find that a “semiclassical” Monte Carlo sampling method based on the Heisenberg Hamiltonian accurately predicts experimental magnetic transition temperatures observed in magnetometry measurements. This study highlights the importance of a robust computational toolkit that accurately captures the complex chemomagnetic interactions and predicts finite temperature magnetic behavior to help analyze experimental magnetic and magnetic resonance spectroscopy data acquired ex situ and operando.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

First-principles Study of the Tritium Species Diffusion Across Ni-Zircaloy-4 Getter Interface

Tritium is a critical fuel component for experimental nuclear fusion reactors (like tokamaks), typically used in combination with deuterium. In tritium-producing burnable absorber rods (TPBARs), due to its high lithium density, LiAlO2 is used in the form of an annular ceramic pellet enriched with the Li_6 isotope located between the Zircaloy-4 liner and nickel-plated Zircaloy-4 tritium getter. Employing DFT, we explored the tritium diffusion across the pellet and getter.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Photoinduced electronic excitations drive polymerization of carbon monoxide: A first-principles study

Under pressure, carbon monoxide (CO) transforms into a polymer that can be recovered to ambient conditions. While this transformation can occur without additional stimuli, experimental observations have shown that laser irradiation can induce a similar transformation at reduced pressure. The resulting polymeric phase, which is metastable under ambient conditions, releases energy through decomposition into more stable configurations. Using time-dependent density functional theory and Born–Oppenheimer molecular dynamics simulations, we investigate the mechanism by which electronic excitation facilitates CO polymerization. Our calculations reveal that electronic excitation enhances carbon–carbon bonding, enabling polymerization at pressures significantly lower than those required by conventional compression methods. In conclusion, these findings suggest that a photo-assisted approach could be employed to synthesize novel, potentially energetic materials under less demanding pressure conditions.

Born-Oppenheimer molecular dynamics↗
DOE OSTI2024

Impacts of point defects on shallow doping in cubic boron arsenide: A first principles study

Cubic boron arsenide (BAs) stands out as a promising material for advanced electronics, thanks to its exceptional thermal conductivity and ambipolar mobility. However, effective control of p- and n-type doping in BAs poses a significant challenge, mostly as a result of the influence of defects. In the present study, we employed density functional theory (DFT) to explore the impacts of the common point defects and impurities on p-type doping of Be B and Si As , and on n-type doping of Si B and Se As . We found that the most favorable point defects formed by C, O, and Si are C As , O B O As , Si As , C As Si B , and O B Si As , which have formation energies of less than 1.5 eV. While the O impurity detrimentally affects both p- and n-type dopings, C and Si impurities are harmful for n-type dopings, making n-type doping a potential challenge. Interestingly, the antisite defect pair A s B B As benefits both p- and n-type doping. Finally, the doping limitation analysis presented in this study can potentially pave the way for strategic development in the area of BAs-based electronics.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Performance of Heterostructural TaC/AlGaN Schottky Diodes Based on First Principles Electronic Structure Properties

Advances in ultra-wide bandgap materials, such as high Al-content AlxGa1-xN (AlGaN), are essential for next generation power electronics, but the requirement for lattice matched substrates is currently a significant obstacle. Recently, conductive TaC has emerged as a promising virtual substrate for AlGaN heteroepitaxy, with wurtzite (0001) AlxGa1-xN lattice-matched to rocksalt (111) TaC at x ~ 0.5. Thus, understanding and controlling the electronic properties of the TaC/AlGaN interface is key for developing technological applications based on TaC/AlGaN devices. Using density functional theory and electronic structure calculations, we here investigate TaC/Al0.5Ga0.5N interfaces, where we include explicit alloy models in the slab calculations. We predict the Schottky barrier height and the electric field discontinuity resulting from interface charges. Considering all possible combinations of (Ta, C) substrate termination, (Al/Ga, N) nucleation, and (Al/Ga, N) polarity, we construct a chemical potential phase diagram to identify the stable interfaces that can be accessed through variation of the synthesis conditions. The predicted interface electronic properties are implemented in device performance simulations to demonstrate a practical design for a strain-free, high-efficiency TaC/AlGaN Schottky diode with a low barrier height and without interface charges, underscoring the potential of TaC as a substrate for ultra-wide bandgap devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Effect of Ni deposition on CrI 3 monolayer: First-principles study

In our recent experimental work, we demonstrated that Ni thin film deposition can be used to tune the surface magnetic states in bulk CrI 3 . Here, we present the results of a computational study of Ni deposition on a CrI 3 monolayer. In particular, we compare structural, electronic, and magnetic properties of three different systems: a pristine CrI 3 monolayer, a CrI 3 monolayer with partial Ni coverage, and a CrI 3 monolayer with full Ni coverage. The corresponding cells used in our calculations are Cr 2 I 6 , Cr 2 I 6 Ni 1 , and Cr 2 I 6 Ni 3 . In Cr 2 I 6 Ni 1 , the Ni atom is positioned over the hollow site, which corresponds to the lowest energy configuration. In Cr 2 I 6 Ni 3 , the three Ni atoms are positioned over the single hollow site, and over the two Cr sites. Our calculations indicate that the partial coverage of CrI 3 monolayer with Ni retains the semiconducting nature of the parent compound, but results in a strong reduction of the energy band gap. At the same time, the full coverage of CrI 3 monolayer with Ni results in a metallic transition, with a highly spin-polarized (possibly half-metallic) electronic structure. The magnetic alignment of the CrI 3 monolayer with the deposited Ni is ferrimagnetic, due to the anti-aligned magnetic moments of Cr and Ni atoms. While the partial coverage of the CrI 3 monolayer with Ni has a moderate impact on the lattice parameter of the parent compound, full coverage by Ni results in a significant increase of the lattice constant. For both partial and full coverages, the lowest energy configuration corresponds to the Ni atoms being approximately aligned with the out-of-plane coordinate of the surface iodine layer. In addition, in the full coverage mode, the Cr layer exhibits a significant shift away from the Ni atoms, effectively “detaching” the Ni / I atomic layer from the rest of the cell.

2D magnetism↗
DOE OSTI2026

Vibrational and electronic properties of Np 2 O 5 from experimental spectroscopy and first principles calculations

High-valence actinide oxides are critical to understanding the behavior of 5f-electrons, yet their structural and electronic properties remain poorly understood due to challenges in synthesis and handling. We report the first Raman spectroscopic study of single-crystalline Np 2 O 5 and the first scanning tunneling spectroscopy (STS) measurement on any neptunium-containing material. Hydrothermally synthesized crystals were structurally verified by X-ray diffraction. Raman spectra revealed sharply resolved vibrational features, including previously unreported low-frequency modes. STS measurements revealed a band gap of 1.5 eV. Density functional theory (DFT) enables vibrational mode assignments, reveals neptunium-dominated low-frequency phonons, oxygen-dominated high-frequency modes, and predicts an indirect band gap of 1.68 eV. This predicted value is in excellent agreement with the experimentally measured STS gap. This combined Raman, DFT, and STS approach provides a robust framework for correlating lattice dynamics and electronic structure in actinide materials, providing benchmark data for Np 2 O 5 , and opening new avenues for probing structure–property relationships in complex f-electron materials.

36 - MATERIALS SCIENCE↗
DOE OSTI2025

High-Temperature Gas Sensor Materials with Properties Predicted via First-Principles Calculations with Machine Learning Modeling and Experimental Corroboration

Understanding the temperature dependence of functional properties of sensing materials is vital for their applications in combustion environments. The electron-phonon coupling that derives the electronic structure change with temperatures is a key property of interest as it affects other sensing responses. Herein, we first assess the temperature dependence of band gap renormalization in sensing materials by employing Allen-Heine-Cardona (AHC) theory with density functional theory (DFT) simulations corroborated with experimental observation. As the AHC calculations are impractical for high-throughput screening of materials, we employ data-driven Gaussian process regression to predict the parameters employed in the O’Donnell empirical model from a set of physical features. To mitigate the reliability issues arising from the small size of the dataset, we apply a Bayesian technique to improve the generalizability of the data-driven models as well as to quantify the uncertainty associated with theoretical predictions. These models capture well the overall trend of the O’Donnell parameters with respect to a reduced feature set obtained by transforming the available physical features. Quantifying the associated uncertainty helps us understand the reliability of the predictions and, therefore, the variation of bandgap as a function of temperature for other novel materials. The predicted candidates from machine learning models are further validated by experiments and DFT calculations.

bandgap renormalization↗
DOE OSTI2024

First-principles investigation of lanthanides diffusion in HCP zirconium via vacancy-mediated transport

The diffusion of lanthanide fission products plays an important role in the growth of the fuel-cladding chemical interaction (FCCI) region in metallic fuels. The use of a Zr interdiffusion barrier may mitigate the transport of lanthanides from the fuel to the cladding, but the efficacy of such a liner is not yet known. In this paper, the stability and vacancy-mediated diffusion of La, Ce, Pr, and Nd in hexagonal close-packed (HCP) Zr is investigated via density functional theory (DFT) calculations and self-consistent mean field (SCMF) analysis. DFT is used to calculate the formation, binding, and migration energies of vacancies and vacancy-solute pairs. The DFT energetics are used in the KineCluE code to calculate the Onsager transport coefficients. La is found to be the fastest diffusing species in HCP Zr and experiences an almost isotropic diffusion behavior. The other three species (Ce, Pr, and Nd) demonstrate anisotropic diffusion where the diffusion in the basal planes is significantly faster than that along the c-axis. Further, the calculated lanthanide diffusivities in HCP Zr are fitted to an Arrhenius relation and the activation energies and prefactors are reported for the first time. Furthermore, the vacancy drag and the segregation tendencies were analyzed using the calculated off-diagonal transport coefficients. According to our vacancy-mediated diffusion model, lanthanides are expected to be enriched at vacancy sinks at low temperatures, while at high temperatures, lanthanides are depleted at sinks and will preferably diffuse into the bulk. The enrichment/depletion transition temperature depends on the diffusion direction (basal or axial) and hence will be controlled by the grain texture and orientation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

First-Principles Evaluation of Proton Hopping in Tetrahedral Oxide Motifs

Proton-conducting oxides (PCOs) are important materials used as ionic conductors for energy conversion technologies. Existing research efforts on PCO optimization and discovery generally focus on complex perovskite-based oxides that require doping and alloying to engineer oxygen deficiency and high proton conductivity. However, the variety of chemical compositions and coordination environments in oxides poses challenges for efficient materials design. In this computational study, we construct a database of simplified motifs to elucidate the relationship between fundamental materials chemistry and proton kinetics. Specifically, we focus on the zincblende crystal structure as a proxy for tetrahedral metal–oxide (M–O) coordination environments. We systematically quantified the effects of cation type, oxidation states, and M–O bond lengths on the proton hopping barrier, and found that strong M–O bonds and metal cations with large and variable oxidation states (e.g., Mo 6+ , V 5+ ) lead to smaller proton hopping barriers. By mapping the candidate cations and their preferred bond geometries onto materials databases such as the Inorganic Crystal Structure Database (ICSD) and Materials Project, we identified real materials containing the corresponding metal–oxide units. In general, we observed good agreement between the calculated proton hopping barriers obtained in real crystal structures and those predicted by our motif database. We also discuss the limitations of our model and possible future extensions to improve its predictive capabilities. Overall, our model provides a first step for the rational design and quick screening of energy-efficient PCOs.

organic↗
DOE OSTI2025

First-Principles Insights into the Thermocatalytic Cracking of Ammonia-Hydrogen Blends on Fe(110). 2. Kinetics

Ammonia (NH 3 ) is an energy-rich molecule that is routinely synthesized from nitrogen (N 2 ) and hydrogen (H 2 ). NH 3 ’s more favorable physical properties compared to H 2 suggests it may offer a way to more conveniently store, transport, and, when needed, extract H 2 via thermal decomposition. However, the high kinetic barrier and endoergicity to decompose to H 2 and N 2 require high temperatures. The standard reaction free energy indicates nearly 100% thermodynamic conversion to the diatomic molecules only at ~673 K and higher. However, even at these temperatures, a catalyst, e.g., iron (Fe), is needed for favorable kinetic conversion. Here, in this study, we explore via density functional theory the kinetics of NH 3 decomposition on the most stable facet of body-centered cubic Fe, namely, (110), under typical high-temperature and finite-pressure operando conditions. We predict coverage-dependent energetics of elementary surface reactions, often neglected in atomic-scale modeling. From these models, we find the recombinative desorption of adsorbed N as N 2 is rate-determining at 573.15–773.15 K and even at an extreme case of 1173.15 K. From microkinetic modeling, we find that the steady-state turnover frequencies (TOFs) for N 2 and H 2 generation rates (r$_{H_2}$) depend exponentially on temperature. The catalyst achieves a steady-state TOF of 36.4 s –1 and an r$_{H_2}$ of 0.107 μmol cm –2 s –1 for a feed of 1.8 bar NH 3 with 0.2 bar H 2 at 1173.15 K. However, at 773.15 K, with the same feed composition and velocity, the steady-state TOF and r$_{H_2}$ decrease to 0.14 s –1 and 4.10 × 10 –4 μmol cm –2 s –1 , respectively, as the process is significantly hindered by slow N 2 desorption. Although at first glance counterintuitive, our simulations suggest that surface modifications that reduce Fe’s reactivity toward NH x species should enhance its overall NH 3 decomposition activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

First principles investigation of dopants and defect complexes in CdSe$_x$Te$_{1-x}$

Se alloying is a common approach to improve the performance of CdTe solar cells by tuning the bandgap, defect levels, and carrier density. A fundamental understanding of these improvements, specifically the effect of Se alloying on the behavior of defects and dopants in CdTe, remains unclear. Here, in this work, we present a density functional theory (DFT) study of point defect energetics in CdTe and CdSe x Te 1-x with x = 0.25, leading to a comparison of how native defects, dopants (As and Cu), impurities (Cl and O), and related defect complexes behave in CdTe vs CdSe x Te 1-x . Our calculations, performed by combining semi-local and nonlocal hybrid functionals, show a general lowering of the formation energies of native defects as well as substitutional defects formed by As and Cl upon Se addition. For successful p-type doping with As, destabilizing Cl-based defects in the CdSeTe lattice would be essential. We find evidence for some low-energy defect complexes of As, Cl, and O in CdSe 0.25 Te 0.75 . The computed defect formation energies further enable estimates of temperature-dependent defect concentrations and self-consistent Fermi levels. A comparison of defect energetics with the energies of impurity phases reveals that As, Cu, Cl, and O overwhelmingly prefer being segregated to unwanted As 2 O 5 , AsCl 3 , Cd 2 AsCl 2 , and CuO x phases rather than remain at defect sites, but such segregation is less likely to happen in CdSe 0.25 Te 0.75 than in CdTe. Overall, our work presents a list of likely defects and complexes in CdTe and Se-incorporated CdTe, paving the way to explain and mitigate limited dopant activation in experimental observations.

CdTe↗
DOE OSTI2024

First Principles Study of Aluminum Doped Polycrystalline Silicon as a Potential Anode Candidate in Li‐ion Batteries

Addressing sustainable energy storage remains crucial for transitioning to renewable sources. While Li‐ion batteries have made significant contributions, enhancing their capacity through alternative materials remains a key challenge. Micro‐sized silicon is a promising anode material due to its tenfold higher theoretical capacity compared to conventional graphite. However, its substantial volumetric expansion during cycling impedes practical application due to mechanical failure and rapid capacity fading. A novel approach is proposed to mitigate this issue by incorporating trace amounts of aluminum into the micro‐sized silicon electrode using ball milling. Density functional theory (DFT) is employed to establish a theoretical framework elucidating how grain boundary sliding, a key mechanism involved in preventing mechanical failure is facilitated by the presence of trace aluminum at grain boundaries. This, in turn, reduces stress accumulation within the material, reducing the likelihood of failure. To validate the theoretical predictions, capacity retention experiments are conducted on undoped and Al‐doped micro‐sized silicon samples. In conclusion, the results demonstrate significantly reduced capacity fading in the doped sample, corroborating the theoretical framework and showcasing the potential of aluminum doping for improved Li‐ion battery performance.

25 ENERGY STORAGE↗
DOE OSTI2025

Temperature-Dependent Mechanical Properties of Ni-Based Concentrated Alloys: Insights from First-Principles Calculations

The present work focuses on predicting temperature-dependent mechanical properties of Ni-based concentrated alloys Ni 18 Cr 10 Co 10 Fe 6 M 4 (abbreviated by X 44 M 4 , with M = Al, V, Mn, Fe, Nb, Mo, and W) using density functional theory (DFT). These predictions are based on shear (plastic) and elastic deformations, utilizing the special quasirandom structure (SQS), the phonon-based quasiharmonic approach (QHA), and the quasistatic approach. The resulting properties include coefficient of thermal expansion via QHA, ideal shear strength (τ IS ), and stable and unstable stacking fault energies (γ SF and γ US ) through pure alias shear deformation, and elastic constants (c ij ), bulk modulus (B 0 ), and shear modules (G 0 ) via elastic deformation. Notably, predicting accurate γ SF is challenging due to uncertainties that can exceed the γ SF values. τ IS and γ US exhibit a strong linear relationship, enabling the accurate prediction of γ US based on the precisely determined τ IS . All mechanical properties of X 44 M 4 decrease with increasing temperature, except for some γ SF cases such as X 44 M 4 with M = V, Mn, Fe, Mo, and W. Among the X 44 M 4 alloys, X 44 Nb 4 exhibits the lowest τ IS , γ US , and G 0 values, and the highest B 0 /G 0 ratio, while X 44 Mn 4 has the lowest B 0 and B 0 /G 0 ratio. We found that volume is a crucial descriptor for understanding and modeling mechanical properties (except B0 and maybe also γ SF ) affected by alloying elements and temperature. Ni-based dilute alloys (e.g., Ni 11 M 1 and Ni 31 M 1 ) and concentrated alloys (e.g., X 44 M 4 ) show similar trends in mechanical properties influenced by alloying elements and temperature, simplifying the analysis and design of Ni-based alloys.

Elastic properties↗