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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Mechanism and kinetics of the oxidation of 1,3-butadien-1-yl (n-C 4 H 5 ): a theoretical study

Here, ab initio CCSD(T)-F12/cc-pVTZ-f12//B3LYP/6-311G(d,p) calculations of the C 4 H 5 O 2 potential energy surface have been combined with Rice–Ramsperger–Kassel–Marcus Master Equation (RRKM-ME) calculations of temperature- and pressure-dependent rate constants and product branching ratios to unravel the mechanism and kinetics of the n-C 4 H 5 + O 2 reaction. The results indicate that the reaction is fast, with the total rate constant being in the range of 3.4–5.6 × 10 –11 cm 3 molecule –1 s –1 . The main products include 1-oxo-n-butadienyl + O and acrolein + HCO, with their cumulative yield exceeding 90% at temperatures above 1500 K. Two conformers of 1-oxo-n-butadienyl + O are formed via a simple mechanism of O 2 addition to the radical site of n-C 4 H 5 followed by the cleavage of the O–O bond proceeding via a van der Waals C 4 H 5 O∙∙∙O complex. Alternatively, the pathways leading to acrolein + HCO involve significant reorganization of the heavy-atom skeleton either via formal migration of one O atom to the opposite end of the molecule or its insertion into the C1–C2 bond. Not counting thermal stabilization of the initial peroxy adducts, which prevails at low temperatures and high pressures, all other products share a minor yield of under 5%. Rate constants for the significant reaction channels have been fitted to modified Arrhenius expressions and are proposed for kinetic modeling of the oxidation of aromatic molecules and 1,3-butadiene. As a secondary reaction, n-C 4 H 5 + O 2 can be a source for the formation of acrolein observed experimentally in oxidation of the phenyl radical at low combustion temperatures, whereas another significant (secondary) product of the C 6 H 5 + O 2 reaction, furan, could be formed through unimolecular decomposition of 1-oxo-n-butadienyl. Both the n-C 4 H 5 + O 2 reaction and unimolecular decomposition of its 1-oxo-n-butadienyl primary product are shown not to be a substantial source of ketene.

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

Thermal gradient effect on helium and self-interstitial transport in tungsten

First-wall materials in a fusion reactor are expected to withstand harsh conditions, with high heat and particle fluxes that modify the materials microstructure. These fluxes will create strong gradients of temperature and concentration of diverse species. Besides the He ash and the hydrogenic species, neutron particles generated in the fusion reaction will collide with the material creating intrinsic defects, such as vacancies, self-interstitials atoms (SIAs), and clusters of such point defects. These defects and the He atoms will then migrate in the presence of the aforementioned gradients. In this study, we use nonequilibrium molecular dynamics to analyze the transport of He and SIAs in the presence of a thermal gradient in tungsten. We observe that, in all cases, the defects and impurity atoms tend to migrate toward the hot regions of the tungsten sample. The resulting species concentration profiles are exponential distributions, rising toward the hot regions of the sample, in agreement with irreversible thermodynamics analysis. For both He atoms and SIAs, we find that the resulting species flux is directed opposite to the heat flux, indicating that species transport is governed by a Soret effect (thermal-gradient-driven diffusion) characterized by a negative heat of transport that drives species diffusion uphill (from the cooler to the hot regions of the sample). Here, we demonstrate that the steady-state species profiles obtained accounting for the Soret effect vary significantly from those where temperature-gradient-driven transport is not considered and discuss the implications of such a Soret effect on the response to plasma exposure of plasma-facing tungsten.

36 MATERIALS SCIENCE↗
DOE OSTI2025

The effect of composition on helium bubble nucleation in complex concentrated alloys

Molecular dynamics simulations of helium implantation have been performed in the MoNbTaTi complex concentrated alloy (CCA) to determine the impact of composition on helium clustering and bubble nucleation. It was found that compositions with lower interstitial atomic volume resulted in smaller cluster sizes, higher helium-to-vacancy ratios, and larger migration barriers. As the atomic volume decreases, it is harder to accommodate additional helium in the lattice and for helium to diffuse between interstitial sites, resulting in smaller cluster sizes. In particular, increasing molybdenum directly correlated with a decreased interstitial atomic volume and increased migration barrier. Niobium exhibited the opposite trend, where more niobium in the material resulted in larger interstitial atomic volumes and cluster sizes but lower migration barriers. The atomic volume was determined to be an indicator of the susceptibility of the material to helium bubble growth and could potentially be used as a metric to screen compositions for resistance to helium damage. In this way, properties such as available interstitial volumes could be used to screen materials more rapidly given the vast compositional space of CCAs.

McCarthy, Megan Jeanne [Sandia National Laboratori↗
DOE OSTI2021

Sluggish, chemical bias and percolation phenomena in atomic transport by vacancy and interstitial diffusion in Ni-Fe alloys

In this paper, we report the results of extended atomistic modeling of intrinsic mobility of point defects and associated atomic transport in Ni-Fe model binary alloys. We consider the effects of composition and temperature and present evidence of the sluggish and chemically biased diffusion, and percolation effects occurring in atomic transport via the vacancy and interstitial migration mechanisms. The results are analyzed and discussed in the light of previous studies and some experimental observations. It is demonstrated that the sluggish diffusion, the chemically biased diffusion, and the percolation are interlinked phenomena that are defined by the chemical complexity of particular alloys. Methods for predicting these phenomena in multicomponent alloys are discussed.We report a fundamental understanding of sluggish diffusion, chemically-biased diffusion, as well as percolation phenomena, in Ni-Fe random alloys for vacancy and interstitial atom migration mechanisms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Thermodynamic and kinetic properties of layered-CaCo2O4 for the Ca-ion batteries: a systematic first-principles study

One of the more promising directions in multivalent energy storage is systems based on Ca ion intercalation due to the potential for high voltage and capacity. A major challenge for enabling such a battery is to find cathode materials capable of fast ionic diffusion and reversible insertion of Ca ions. Here, on the basis of first-principles calculations, we have demonstrated that layered CaCo 2 O 4 exhibits favorable thermodynamic and kinetic properties that should enable topotactic Ca ion intercalation reactions. The P3-type layered Ca x Co 2 O 4 (0 < x < 1) with either of space groups of P 1 or P 2 1 / m are stable at multiple Ca concentrations and show a smooth voltage plateau higher than 3 V up to X = 0.5. The energy barriers of the single Ca ion migration are as low as 0.36 eV and 0.27 eV at the dilute and high vacancy concentration limits, respectively. Therefore, although varying the vacancy environments of the diffusing atom influences the migration barriers, they do not exceed 0.6 eV. Stochastic analysis of Ca hopping events performed by ab initio molecular dynamics (AIMD) simulation has shown that the migration barriers are lower than 0.32 eV. Therefore, the Ca diffusivity at room temperature extrapolated from the AIMD results is comparable to Li diffusivity (>10 -10 cm 2 s -1 ) in conventional Li cathode materials, suggesting the feasibility of layered Ca x Co 2 O 4 as multivalent cathode materials. Finally, the structural factors that enable fast diffusion are discussed.

25 ENERGY STORAGE↗
DOE OSTI2023

Mechanism of Nitrogen-Carbon Bond Formation from Iron(IV) Disilylhydrazido Intermediates during N 2 Reduction

We recently reported a reaction sequence that activates C–H bonds in simple arenes as well as the N–N triple bond in N 2 , delivering the aryl group to N 2 to form a new N–C bond ( Nature 2020 , 584, 221). This enables the transformation of abundant feedstocks (arenes and N 2 ) into N-containing organic compounds. The key N–C bond forming step occurs upon partial silylation of N 2 . However, the pathway through which reduction, silylation, and migration occurred was unknown. Here, in this work, we describe synthetic, structural, magnetic, spectroscopic, kinetic, and computational studies that elucidate the steps of this transformation. N 2 must be silylated twice at the distal N atom before aryl migration can occur, and sequential silyl radical and silyl cation addition is a kinetically competent pathway to a formally iron(IV)–NN(SiMe 3 ) 2 intermediate that can be isolated at low temperature. Kinetic studies show its first-order conversion to the migrated product, and DFT calculations indicate a concerted transition state for migration. The electronic structure of the formally iron(IV) intermediate is examined using DFT and CASSCF calculations, which reveal contributions from iron(II) and iron(III) resonance forms with oxidized NNSi 2 ligands. The depletion of electron density from the Fe-coordinated N atom makes it electrophilic enough to accept the incoming aryl group. This new pathway for the N–C bond formation offers a method for functionalizing N 2 using organometallic chemistry.

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

Strengthening of tungsten by coherent rhenium precipitates formed during low fluence irradiation

Experimental data show that the accumulation of rhenium and osmium from transmutation reactions severely affect the microstructural evolution and property degradation of tungsten-based materials under neutron irradiation. Theory and modeling have confirmed that Re atom transport in W is by irradiation-produced migrating self-interstitial atoms. With this diffusion mode in operation, a specific microstructure evolution is realized when at relatively low neutron fluence the Re-rich precipitates are formed, while the void and interstitial loop population development is suppressed, affecting the mechanical properties. Here, this research shows the effect of small coherent Re-rich precipitates on the dislocation glide under stress, investigated using the molecular dynamics approach with empirical interatomic potentials. The results are compared with an earlier simulation of void hardening in W. It is demonstrated that small coherent Re-rich precipitates of less than 6 nm diameter represent relatively weak obstacles for moving edge dislocations. The implication of these results on the interpretation of experimental results is discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Mo Atom Rearrangement Drives Layer-Dependent Reactivity in Two-Dimensional MoS 2

Two-dimensional (2D) materials offer a valuable platform for manipulating and studying chemical reactions at the atomic level, owing to the ease of controlling their microscopic structure at the nanometer scale. While extensive research has been conducted on the structure-dependent chemical activity of 2D materials, the influence of structural transformation during the reaction has remained largely unexplored. In this work, we report the layer-dependent chemical reactivity of MoS 2 during a nitridation atomic substitution reaction and attribute it to the rearrangement of Mo atoms. Our results show that the chemical reactivity of MoS 2 decreases as the number of layers is reduced in the few-layer regime. In particular, monolayer MoS 2 exhibits significantly lower reactivity compared with its few-layer and multilayer counterparts. Atomic-resolution transmission electron microscopy (TEM) reveals that MoN nanonetworks form as reaction products from monolayer and bilayer MoS 2 , with the continuity of the MoN crystals increasing with layer number, consistent with the local conductivity mapping data. The layer-dependent reactivity is attributed to the relative stability of the hypothetically formed MoN phase, which retains the number of Mo atomic layers present in the precursor. Specifically, the low chemical reactivity of monolayer MoS 2 is attributed to the high energy cost associated with Mo atom diffusion and migration necessary to form multilayer Mo lattices in the thermodynamically stable MoN phase. In conclusion, this study underscores the critical role of lattice rearrangement in governing chemical reactivity and highlights the potential of 2D materials as versatile platforms for advancing the understanding of materials chemistry at the atomic scale.

Chemical reactivity↗
DOE OSTI2025

Nanocluster Active Sites Formed on Heterogeneous Thermal Catalysts and Electrocatalysts by Operando Reactive Environments

Here, in this Viewpoint, we summarize our recent studies in this endeavor, ending with a forward-looking perspective into the remaining challenges and open questions for consideration by the catalysis community. Through a computationally efficient framework of systematically investigating metal atom ejection from and migration onto metal surfaces, leading to the formation of metal atom clusters, we show that the surface of a metal catalyst is dynamic and much less rigid than previously thought. We suggest that the operando formed metal atom clusters are novel active sites, which can dominate the activity of steps or kinks (let aside terraces) from where their constituent atoms were ejected. Through more readily responding to reaction conditions by forming catalytically active clusters, solid metal catalysts approach not only homogeneous catalyst motifs, thus establishing a bridge between homogeneous and heterogeneous catalysis, but also liquid metals which have been suggested to be better than traditional heterogeneous catalysts.

adsorption↗
DOE OSTI2025

Selenium Migration and Local Structures in Cu‐Doped CdSeTe Solar Cells after Aging

Selenium grading plays a critical role in state-of-the-art Cadmium Telluride photovoltaic cells by enhancing long-wavelength absorption and extending minority carrier lifetimes —key to enabling the current performance record of 23.08%. However, very little is understood about selenium motion. In this study, a comprehensive, multimodal, and multiscale approach is employed to investigate Se migration and local structural changes in copper (Cu)-doped CdSeTe solar cells subjected to accelerated stress. X-ray fluorescence (XRF) microscopy shows unexpected levels of Se diffusion after 500 h under heat (75°C) and light (0.8 suns, 80 mW/cm 2 ), suggesting the coexistence of fast and slow diffusion channels even at low temperatures, with unexpectedly low activation energies (<0.85 eV). X-ray Absorption Near Edge Structure (XANES) analysis indicates a preferential migration of Se atoms to anionic lattice sites and a reduction in Se-Cl co-passivation at Te-terminated dislocation cores. Furthermore, these findings point to a reconfiguration of Se local environments and highlight the potential role of extended structural defects in enabling Se transport at low temperatures. Additionally, XANES results suggest that the presence of metallic Cu across the absorber layer may contribute to back-contact degradation and reduced hole density in both fresh and aged devices.

14 SOLAR ENERGY↗
DOE OSTI2020

Investigation of the structure and chemical nature of Pd fission product agglomerations in irradiated TRISO particle SiC

Tristructural-isotropic (TRISO)-coated fuel particles are used in high-temperature gas-cooled nuclear reactors. Although the polycrystalline 3C-SiC layer acts as the main barrier to fission product release, post-irradiation examinations have shown that certain metallic fission products are found outside of the TRISO coated particle, with no observable micro-cracks or other mechanical failure feature. In this study, an atomic resolution transmission electron microscopy investigation of a SiC layer of a neutron irradiated (19.38% fissions per initial metal atom average burnup; 1072°C time-averaged temperature) TRISO-coated particle from the first advanced gas reactor experiment at Idaho National Laboratory containing mainly Pd and U was conducted. The fission product Pd was found to be present at dislocation cores associated with twins, stacking faults, and their intersections. The Pd present at the dislocation cores were bonded to Si, suggesting that the diffusion of Pd along the SiC dislocation cores involves the formation of Pd-Si bonds. Evidence of single atom grain boundary migration was also found. Fission product agglomerations at grain boundaries most likely consist of a random solid solution containing Si-FP, Si-C, and C-C type bonding arrangements. No difference in the Si- or C-bonding environment is found for the unoccupied grain boundary adjacent to a fission product agglomeration compared to the bulk SiC.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Effect of Collective Dynamics and Anharmonicity on Entropy in Heterogenous Catalysis: Building the Case for Advanced Molecular Simulations

In this paper, we present a perspective on the computational determination of entropy and its effects and consequences on heterogeneous catalysis. Special attention is paid to the role of anharmonicity and the deviations from the standard harmonic oscillator approximations which can fail to provide a reliable assessment of entropy. To address these challenges, advanced methodologies are needed that can explicitly account for these thermodynamic drivers through the appropriate statistical sampling of reactive free energy surfaces. We discuss where anharmonicity should be expected, where it has been observed from a theoretical perspective, and the methods currently employed to address it. We concentrate on three types of systems where we have observed major, nonnegligible anharmonic effects: (1) supported nanoparticles, where the migration of metal atoms, complexes, and entire clusters exhibit anharmonic behavior in their dynamic motion; (2) porous solids where confinement effects distort potential energy surfaces and hinder molecular motions resulting in large entropic terms; and (3) solid/liquid interfaces, where interactions between solvent molecules and adsorbed species can result in large solvent organization free energy and unique reactivity.

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

Reactivity of Iridium Complexes of a Triphosphorus-Pincer Ligand Based on a Secondary Phosphine. Catalytic Alkane Dehydrogenation and the Origin of Extremely High Activity

The selective functionalization of alkanes and alkyl groups is a major goal of chemical catalysis. Toward this end, a bulky triphosphine with a central secondary phosphino group, bis(2-di-t-butyl-phosphinophenyl)phosphine ( tBu P H PP), has been synthesized. When complexed to iridium, it adopts a meridional (“pincer”) configuration. The secondary phosphino H atom can undergo migration to iridium to give an anionic phosphido-based–pincer ( tBu PPP) complex. Stoichiometric reactions of the ( tBu PPP)Ir complexes reflect a distribution of steric bulk around the iridium center in which the coordination site trans to the phosphido group is quite crowded; one coordination site cis to the phosphido is even more crowded; and the remaining site is particularly open. The ( tBu PPP)Ir precursors are the most active catalysts reported to date for dehydrogenation of n-alkanes, by about 2 orders of magnitude. The electronic properties of the iridium center are similar to that of well-known analogous ( R PCP)Ir catalysts. Accordingly, DFT calculations predict that ( tBu PPP)Ir and ( tBu PCP)Ir are, intrinsically, comparably active for alkane dehydrogenation. While dehydrogenation by ( R PCP)Ir proceeds through an intermediate trans-(PCP)IrH 2 (alkene), ( tBu PPP)Ir follows a pathway proceeding via cis-(PPP)IrH 2 (alkene), thereby circumventing unfavorable placement of the alkene at the bulky site trans to phosphorus. ( tBu PPP)Ir and ( tBu PCP)Ir, however, have analogous resting states: square planar (pincer)Ir(alkene). Alkene coordination at the crowded trans site is therefore unavoidable in the resting states. Furthermore, the resting state of the ( tBu PPP)Ir catalyst is destabilized by the architecture of the ligand, and this is largely responsible for its unusually high catalytic activity.

02 PETROLEUM↗
DOE OSTI2022

Cost-effective carbon fiber precursor selections of polyacrylonitrile-derived blend polymers: carbonization chemistry and structural characterizations

Blending polyacrylonitrile (PAN) with plastic wastes and bio-based polymers provides a convenient and inexpensive method to realize cost-effective carbon fiber (CF) precursors. In this work, PAN-based blend precursors are investigated using ReaxFF reactive molecular dynamics simulations with respect to the formation of all-carbon rings, the evolutions of oxygen-containing and nitrogen-containing species, and the migration of carbon atoms to form turbostratic graphene. From these simulations, we identify that PAN/cellulose (CL) blend manifests the highest carbon yield and the most substantial all-carbon ring formation. This ReaxFF-based finding is confirmed by Raman and TEM experiments indicating high crystallinity for PAN/CL-derived blend CFs. We trace the pathway of gasification and carbonization of PAN/CL to elaborate the mechanism of the formation of all-carbon ring networks. We discover that the acetals of CL can catalyze the cyclization of the blend precursor, allowing for the search for CL derivatives or the other kinds of bio-based polymers with similar functionalities as alternative blends. In addition, we examine the structural characteristics using the carbon–carbon (C–C) radial distribution functions, C–C bond length distributions, and sp2 C atom ratios for the four representative precursors, i.e., PAN, oxidized PAN, PAN/nylon 6,6, and PAN/CL. Our simulation results show the most extensive all-carbon ring cluster and graphitic structure growths for PAN/CL. Here, we propose PAN/CL as a cost-effective alternative CF precursor, since (a) CL is naturally abundant and eco-friendly for production, (b) the blend precursor PAN/CL does not require oxidation treatment, (c) PAN/CL has a high carbon yield with substantial all-carbon ring formation, and (d) PAN/CL based CFs potentially provide a mechanical property enhancement.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Carboxylic acid induced restructuring of the Fe 3 O 4 (001) surface

The redox properties of Fe 3 O 4 surfaces are central to many catalytic processes and enable dynamic, reduction-induced morphological restructuring during reactions. Here, we investigate the structural changes of the Fe 3 O 4 (001) surface during the decomposition of formic and acetic acids using scanning tunneling microscopy, X-ray photoelectron spectroscopy, and density functional theory (DFT) calculations. Both acids readily deprotonate, forming ordered carboxylate overlayers on the surface. Product formation pathways involve the removal of lattice oxygen, resulting in extensive surface restructuring. For formic acid, only a modest level of surface oxygen removal (∼3%) is observed, resulting in elongated pits along the octahedral Fe rows and exhibiting an aspect ratio of ∼3. In contrast, acetic acid induces more extensive reduction, with the removal of ∼20% of surface oxygen, yielding significantly larger pits while maintaining a similar aspect ratio. Repeated exposure to acetic acid further enlarges the pits, indicating preferential etching at step edges. DFT calculations reveal a mechanistic sequence in which lattice oxygen removal destabilizes adjacent Fe atoms, promoting their migration into the bulk and subsequent pit propagation and step edge formation. Together, these findings provide atomistic insights into the coupling between carboxylic acid conversion and oxide surface restructuring, underscoring the strong interplay between redox chemistry and morphological changes on catalytically active Fe 3 O 4 surfaces.

Ortiz-Garcia, José J. [Pacific Northwest National ↗
DOE OSTI2025

Unraveling the transformation pathway of the 𝛽 to 𝛾 phase transition in Ga 2 ⁢O 3 from atomistic simulations

Defect spinel 𝛾−Ga 2 ⁢O 3 is the least stable polymorph of Ga 2 ⁢O 3 , so its frequent appearance as a structural defect within or on the surface of monoclinic 𝛽−Ga 2 ⁢O 3 remains a mystery. Through first-principles calculations, we explore potential pathways for the phase transition from 𝛽−Ga 2⁢ O 3 to 𝛾−Ga 2 ⁢O 3 , and examine two key driving forces: tensile strain and Ga deficiency. When configurational entropy contributions to phase energies are included, the 𝛾 phase becomes energetically competitive with the 𝛽 phase, with the free energy difference between these phases diminishing even further under Ga-deficient conditions. Notably, a stability crossover occurs at room temperature at high vacancy concentrations ([V$^{3−}_{Ga}$]>3%) . A simple model 𝛽 → 𝛾 transformation pathway is identified, comprising two primary reactions, that enables the formation of the 𝛾 phase via simultaneous migration of Ga atoms from tetrahedral lattice sites to octahedral interstitial positions. The transformation barriers are prohibitively large in pristine Ga 2 ⁢O 3 , but can be substantially reduced by: (1) the presence of Ga vacancies, (2) elongational strains along the crystallographic 𝑎-axis, and (3) when volumetric relaxations are possible during transformation. These results elucidate prior experimental observations, where 𝛾−Ga 2⁢ O 3 is seen on damaged surfaces or in highly 𝑛-type 𝛽−Ga 2⁢ O 3 environments, which support Ga deficiency and mechanical strain. The insights into the driving forces and mechanisms of 𝛾−Ga 2⁢ O 3 formation enhance understanding of how localized strain and nonequilibrium defect concentrations may facilitate its formation from the 𝛽 phase.

Defects↗
DOE OSTI2026

Lattice vacancy migration barriers in Fe-Ni alloys, and an indication as to why Ni atoms diffuse slowly: A first-principles study

Lattice vacancy migration barriers in ferromagnetic Fe 𝑥 ⁢Ni 1−𝑥 alloys (0.4 ≤ 𝑥 ≤ 0.6) are accurately quantified within the framework of ab initio electronic structure calculations using the nudged elastic band (NEB) method. Both the atomically disordered (A1) fcc phase, as well as the atomically ordered, tetragonal L⁢1 0 phase—which is under consideration as a material for a rare-earth-free gap magnet for advanced engineering applications—are investigated. Across an ensemble of NEB calculations performed on supercell configurations spanning a range of compositions and containing disordered, partially ordered, and fully ordered structures, we find that Ni-vacancy interchanges encounter significantly higher energetic barriers than do Fe-vacancy interchanges. We contend that this aspect is a key factor in determining the differences in mobility between Fe and Ni atoms in this ferromagnetic alloy. Moreover, we are able to interpret these findings in terms of the ferromagnetic alloy's underlying spin-polarized electronic structure. Specifically, we report a coupling between the size of local lattice distortions and the magnitude of the local electronic spin polarization around vacancies. This causes Fe atoms to relax into lattice vacancies, while Ni atoms remain rigidly fixed to their original lattice positions. These results give atomic-scale insight into the longstanding experimental observation that Ni exhibits remarkably slow atomic diffusion in Fe-Ni alloys.

density functional theory↗