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Direct Measurement of Diffusion Coefficients: Evidence for Diffusive Stochastic Heating in Collisionless Plasmas

Open questions in collisionless plasma dissipation can be addressed using space-based observations in different astrophysical environments, with implications for both astrophysical and laboratory plasma systems. We study a low-𝛽, highly imbalanced, sub-Alfvénic stream observed by Parker Solar Probe (PSP) to identify and distinguish between signatures of stochastic heating (SH) and resonant heating (RH) by parallel ion cyclotron waves (∥-ICWs). Prior work studying this stream [Trevor A. Bowen et al., Stochastic heating in the sub-Alfvénic solar wind, Phys. Rev. Lett. 135, 255201 (2025)] showed that the SH rate, accounting for intermittency, matched the amplitude of the local energy transfer (LET) rate, while the RH rate did not. This comparison relied on a number of assumptions regarding the nature of the diffusive process and the calculation of the LET rate. We introduce a novel technique of inverting the proton guiding center equation to empirically measure velocity-space diffusion coefficients using three-dimensional proton velocity distribution functions, from the ion electrostatic analyzer (the Solar Probe Analyzer for Ions) on PSP. Measured diffusion coefficients are used to determine phase-space heating rates, leading to a calculation of a fully kinetic heating rate independent of assumptions made in prior work. We show that scale-dependent analytic expressions for SH via noncoherent fluctuations match the empirical measurements from PSP data, provided that we account for intermittency in the heating calculation. In contrast, the derived heating rates for SH that accounts for the effects of the helicity barrier and heating rates for RH via ∥-ICWs do not peak in the same region of velocity space as the empirical measurements, nor do they reach the required magnitude. Our approach provides novel methodology to uniquely identify and constrain heating processes in collisionless plasmas and shows evidence of a Fokker-Planck-like diffusive process in the near-Sun solar wind.

Plasma kinetic theory

Challenges in Pulsed-Field Gradient Nuclear Magnetic Resonance on Magnetically Heterogeneous Interfaces: Sequence and Field-Dependent Apparent Diffusion Coefficients

It is well known that the internal gradient (gi) that exists within pores haunts the diffusion coefficient (D) as measured by the pulsed-field gradient (PFG) nuclear magnetic resonance (NMR). Several PFG-NMR methods developed to determine an accurate D were not successful. Then, the steady-state diffusion coefficient (Dapp,8) for the cation [C4mim]+ of [C4mim][Tf2N]; [1-butyl-3-methylimidazolium][bis(trifluoromethylsulfonyl)imde] ionic liquid confined in ordered mesoporous carbon (OMC) were determined by comparing Dapp,8 obtained from 1H PFG-NMR performed with three different stimulated echo sequences: STE, APFG, and MPFG under the two external magnetic field strength, B0 = 9.4 and 14.1 Tesla. The measured Dapp,8 which is an order of magnitude smaller than D of bulk [C4mim][Tf2N], is in good agreement between APFG and MPFG both in B0 = 9.4 and 14.1 Tesla. However, the strong gi artifact, which caused apparent diffusion coefficient (Dapp) depending strongly and weakly on B0 and temperature, respectively, in diffusion-time dependent Dapp, Dapp(?) obtained from a sequence with monopolar gradients (STE) was suppressed by using sequences employing bipolar gradients (APFG and MPFG) in the region of steady-state diffusion. But incompletely suppressed gi artifact resulting in the different behaviors of the early part of Dapp(?) between the sequences leads a ˜ 0.6 and 0.9 in MPFG and APFG, respectively, in the relationship between mean squared displacement and diffusion time: = 2Dta, where a = 0.5 and 1 for 1-dimensional single file diffusion and 3-dimensional bulk diffusion, respectively. The above observations clearly show that the diffusion behavior of ions/molecules within the pores and pore structure, such as the surface-to-volume ratio? (D?_app (?)=D_0 [1-4/(9vp) S/V v(D_0 ?)]) and tortuosity (T = D0/Dapp,8), are possible to be misunderstood, especially in the systems with a non-negligible gi. This work demonstrates that it may be necessary to test several PFG sequences under multiple external magnetic fields for the correct determination of the diffusion behavior of ions/molecules in the pores with a larger internal gradient, gi.

Han, Kee Sung

Multitiered computational methodology for extracting three-dimensional rotational diffusion coefficients from x-ray photon correlation spectroscopy data without structural information

X-ray photon correlation spectroscopy (XPCS) is a powerful technique for analyzing particle systems by investigating their dynamics in suspensions across a broad range of temporal and spatial scales. This is done by illuminating samples with coherent x-ray beams and calculating the correlation function of the obtained x-ray scattering images. XPCS is uniquely suited for studying Brownian dynamics, consisting of translational and rotational diffusion. While traditional XPCS image analysis techniques can extract translational diffusion components, they are unable to estimate rotational diffusion coefficients. Here, we introduce a methodology that combines the angular-temporal cross-correlation analysis and a algorithmic framework called Multi-Tiered Estimation for Correlation Spectroscopy in 3D for estimating three-dimensional rotational diffusion coefficients from XPCS images of three-dimensional particle systems. We demonstrate our methodology for extracting rotational diffusion coefficients from XPCS data by applying it to simulated noisy x-ray images of systems of crossing nanotubes and proteins that evolve under translational and rotational Brownian motion for different diffusion rates. Furthermore, our results show that our approach determines rotational diffusion coefficients within a few percent error.

97 MATHEMATICS AND COMPUTING

Henry’s Solubility and Diffusion Coefficients for 29 Volatile Organic Compounds in Polydimethylsiloxane Sylgard 184 at 293 K

Two-dimensional (2D) inverse gas chromatography (IGC) enables simultaneous determination of Henry’s solubility and Fickian diffusion coefficients for volatile organic compounds (VOCs) in polymer films. This technique offers a significant advantage over traditional cylindrical column IGC by providing precise control and measurement of the film thickness (here, 0.064 ± 0.002 mm), which is the critical length scale for accurate diffusivity determination. We apply this methodology to characterize VOC transport in Sylgard 184, a widely used polydimethylsiloxane (PDMS)-based polymer containing substantial silica filler content. At room temperature (20 °C), we measured solubility and diffusion coefficients for 29 common VOCs spanning diverse chemical functionalities, including alkanes, aromatics, chlorinated solvents, ketones, esters, and alcohols. Comparison with literature data for pure PDMS reveals that VOC solubility in Sylgard 184 is generally higher; for most non-hydrogen-bonding compounds it remains within a factor of 2 of pure PDMS, whereas alcohols are enhanced by roughly 1.8 to 3.7 times, which we attribute to favorable interactions with residual silanol groups on the silanized silica filler. Diffusion coefficients range from 1.0 × 10 –6 cm 2 /s (n-undecane) to 8.9 × 10–5 cm 2 /s (acetonitrile) and align well with extrapolated literature values for PDMS. This study provides essential thermodynamic and transport data for predicting VOC permeation in Sylgard 184 while demonstrating the utility of 2D IGC as a robust technique for characterizing rubbery polymer membranes across diverse industrial applications.

organic

Construction of generalized quasilinear diffusion coefficient using neural networks with physical restrictions

The quasilinear diffusion coefficient (D QL ) derived from our machine learning framework shows comparable trends with the ground truth D QL obtained from GENRAY-CQL3D simulations. Additionally, for the strong absorption cases, the radial current drive profiles generated using the D QL from our model exhibit consistent behavior with those obtained from the original simulation. These findings indicate the potential of our surrogate modeling approach with physical restrictions to replicate key wave–plasma interaction characteristics while reducing computational costs. Traditionally, calculating D QL for wave–particle interactions relies on computationally intensive wave simulations coupled with Fokker–Planck solvers. To address this challenge, we developed a machine learning-based surrogate model with physical restrictions derived from cold plasma theory and bounce-averaged damping effects. First, we establish the propagation domain of Lower Hybrid Waves in the (N∥, ρ) space by identifying the accessibility limit and determining the upper and lower bounds of N∥ using the Potential Power Deposition (PPD) method. Subsequently, leveraging a database constructed using Latin hypercube sampling alongside the underlying physical restrictions (e.g. PPD), machine learning methods including U-Net and Recurrent Neural Networks are employed to design a physics-restricted machine learning framework capable of reconstructing D QL .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Diffusion coefficients predicting facet-dependent crystallization in amorphous silicon nitride

Amorphous silicon nitride is a common material in microelectronics devices, which acts as an insulating barrier. Extended annealing times at elevated temperature can initiate crystallization of α-Si 3 ⁢ N 4 , which does not possess the same barrier properties. Molecular dynamics can resolve the fundamental mechanism for α-Si 3 ⁢N 4 crystallization and the influence of local environments. Here, we compare two interatomic potentials and conclude that these models predict structural features (e.g., angular distributions and densities) which span the range of experimental measurements. We confirmed these models reproduce experimental estimates of activation energy and leveraged these models to identify crystallization drivers. We conclude that near-T g , facet-dependent silicon nitride crystal growth rates can be predicted directly by either bulk or interfacial diffusion properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Mixing by internal gravity waves in stars: assessing numerical simulations against theory

ABSTRACT Here we present a study of radial chemical mixing in non-rotating massive main-sequence stars driven by internal gravity waves (IGWs), based on multidimensional hydrodynamical simulations with the fully compressible code MUSIC. We examine two proposed mechanisms of material mixing in stars by IGWs that are commonly quoted, relating to thermal diffusion and sub-wavelength shearing. Thermal diffusion provides a non-restorative effect to the waves, leaving material displaced from its previous equilibrium, while shearing arising within the waves drives weak localized flows, mixing the fluid there. Using IGW spectra from the simulations, we evaluate theoretical predictions of mixing rates due to these mechanisms. We show, for $20\, \mathrm{M}_\odot$ main-sequence stars, that neither of these mechanisms are likely to create mixing sufficient to correct inaccuracies in current stellar evolution models. Furthermore, we compare these predictions to results obtained from Lagrangian tracer particles, following a method recently used for global simulations of stellar interiors to measure mixing by IGWs in their radiative zones. We demonstrate that tracer particle methods face significant numerical challenges in measuring the small diffusion coefficients predicted by the aforementioned theories, for which they are prone to yielding artificially enhanced coefficients. Diffusion coefficients based on such methods are currently used with stellar evolution codes for asteroseismic studies, but should be viewed with caution. Finally, in a case where tracer particles do not suffer from numerical artefacts, we suggest that a diffusion model is not suitable for time-scales typically considered by 2D numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS

Electrode and Microstructure Dependence of Oxygen Diffusion in Ferroelectric Hafnium Zirconium Oxide Thin Films

Hafnia-based ferroelectrics hold promise to reduce energy demand for computing by enabling compute-in-memory and as non-volatile memories. The ferroelectric phase in this material system is, in part, stabilized by oxygen vacancies. While oxygen vacancies may be a necessity for phase stability, they limit device endurance through diffusion and accumulation into conducting channels. Herein, it is shown that oxygen diffusion is spatially variable within individual grains of ferroelectric hafnium zirconium oxide (HZO). Using 18 O tracers and finite difference modeling, it is shown that grain boundaries and regions near electrode interfaces allow for relatively rapid oxygen diffusion, with values as much as 10 4 larger than the grain cores. Further, the selection of electrode material affects the diffusion coefficients across all microstructural regions. HZO films in contact with TiN electrodes result in more oxygen-deficient HZO films and higher oxygen diffusion coefficients. Tungsten electrodes result in fewer vacancies and lower diffusion coefficients. Diffusion activation energy differences between the HZO with the two electrodes is reconciled by differing populations of charged and uncharged oxygen vacancies. This insight into the local vacancy populations and diffusion pathways provides a platform for designing hafnia-based films, deposition processes, and integration strategies to reduce vacancy gradients and improve performance.

36 MATERIALS SCIENCE

In situ investigation of high-pressure hydrogen-induced swelling in elastomers and its correlation with material properties

The resistance of elastomeric materials to high-pressure hydrogen-induced damage is essential for ensuring the reliability of hydrogen infrastructure. Here, in this study, we systematically investigated the swelling behavior and hydrogen transport properties of four elastomer types – EPDM, NBR, FKM, and HNBR – using a custom in-situ view cell system capable of real-time monitoring during decompression from pressures up to 96.5 MPa. Each elastomer was formulated with and without fillers and plasticizers to assess the effects of formulation on swelling response. Thermal desorption analysis (TDA) was employed to determine equilibrium hydrogen content and diffusion coefficients, providing insight into gas uptake and mobility within each material. Correlation analyses using Pearson and Spearman coefficients revealed that the diffusion coefficient showed a stronger relationship with swelling behavior than hydrogen content, highlighting the dominant role of hydrogen mobility. Filled elastomers, particularly those with carbon black, consistently showed reduced swelling due to enhanced stiffness and reduced diffusivity. These results deepen our understanding of diffuso-mechanical interactions in elastomers and support the rational design of sealing materials for high-pressure hydrogen systems.

EPDM

PySIDT: Subgraph Isomorphic Decision Trees for Molecular Property Prediction

Accurate molecular property prediction is important across all fields of chemistry. Deep neural networks (DNNs) have become increasingly popular due to their ability to train automatically, avoiding the incredibly tedious process of constructing and extending traditional property estimation schemes. However, DNNs require large amounts of training data, are challenging to interpret, require large amounts of memory to load even during inference, and have severe difficulties incorporating qualitative chemical knowledge, which are often desired for molecular property prediction tasks. Here, in this study, we present PySIDT (https://github.com/zadorlab/PySIDT), a software for training and running inference on Subgraph Isomorphic Decision Trees (SIDTs). SIDTs are graph-based decision trees made of nodes associated with molecular substructures. Inference is done by descending target molecular structures down the decision tree to nodes with matching subgraph isomorphic substructures and making predictions based on the final (most specific) nodes matched. SIDTs scale down well to dataset sizes much smaller than is feasible for DNNs. As trees of molecular substructures, SIDTs are inherently readable and easy to visualize, making them easy to analyze. They are also straightforward to extend and retrain, facilitate uncertainty estimation, and enable easy integration of expert knowledge. We demonstrate the SIDT approach discussing its application to a diverse range of molecular prediction tasks: rate coefficient estimation, diffusion coefficient estimation, thermochemistry estimation, transition state bond stretch prediction, p K a prediction, stability of molecular structures, stability of surface structures, and prediction of surface lateral interaction energetics. Additionally, we demonstrate the power of the SIDT algorithms in two direct learning curve vanilla comparisons with the popular DNN-based software Chemprop and the popular gradient boosted trees-based software XGBoost on enthalpy of formation and rate coefficient prediction tasks. In particular, in the enthalpy of formation case, vanilla PySIDT is able to outperform vanilla Chemprop and XGBoost across the full range of training/validation set sizes out to 11,560 data points.

Johnson, Matthew Sean [Sandia National Laboratorie

Diffusion and phase formation in the γ-uranium-technetium system

Phase formation in the U-Tc binary system at 800 °C was investigated using a diffusion couple experiment. Scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) identified four novel potential intermetallic phases - U 7 Tc 3 , U 13 Tc 12 , U 3 Tc 5 , and UTc 4 . Diffusion coefficients were calculated for the intermetallic phases using the Boltzmann-Matano method and were respectively found to be – 120, 38.2, 15.6, and 1.51 × 10 −18 m 2 /s. Tc also exhibits a solid-solution phase with high penetration into the U with a diffusion coefficient of ∼ 10 −14 m 2 /s. Furthermore, these findings expand the number of known U-Tc phases and provide the first diffusion coefficients for the U-Tc system, and contribute valuable data to the broader field of actinide metallurgy.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Analysis of Silver Release from Furnace-Tested TRISO Particles

High temperature testing of intact TRISO particles previously irradiated in the AGR-5/6/7 experiment was performed in the Furnace for Irradiated TRISO Testing (FITT) to directly confirm diffusive release of silver and europium from intact TRISO particles. Testing was conducted from 1,100–1,600°C for exposure times up to 100 h to directly confirm silver through layer release below safety testing temperatures. The FITT analysis showed highest levels of silver release at 1,300–1,400°C which confirms athermal release behaviors previous observed in step-wise and transient safety tests. Additionally, release was non-uniform with some particles releasing a majority of their inventory while others did not appear to release silver under identical testing conditions, which was consistent with historic observations. An assessment of the effective silver diffusion coefficient in the SiC layer was conducted and indicated maximum values in the 1,300–1,400°C range. The magnitude of the calculated diffusion coefficients also exceeded currently accepted diffusion coefficients. The release behavior of europium from intact particles was also analyzed in FITT for at 1,450–1,550°C for 500 h to 750 h. Direct confirmation of europium release below safety testing temperatures was confirmed absent contributions from matrix release. The analysis indicated europium release follows a general Arrhenius behavior and suggests general uniform release and indicates irradiation conditions influence observed release response. Calculated diffusion kinetics agree well with historic experiments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Cosmic-ray transport in inhomogeneous media

A theory of cosmic-ray transport in multiphase diffusive media is developed, with the specific application to cases in which the cosmic-ray diffusion coefficient has large spatial fluctuations that may be inherently multiscale. We demonstrate that the resulting transport of cosmic rays is diffusive in the long-time limit, with an average diffusion coefficient equal to the harmonic mean of the spatially varying diffusion coefficient. Thus, cosmic-ray transport is dominated by areas of low diffusion even if these areas occupy a relatively small, but not infinitesimal, fraction of the volume. On intermediate time-scales, the cosmic rays experience transient effective subdiffusion, as a result of low-diffusion regions interrupting long flights through high-diffusion regions. In the simplified case of a two-phase medium, we show that the extent and extremity of the subdiffusivity of cosmic-ray transport is controlled by the spectral exponent of the distribution of patch sizes of each of the phases. We finally show that, despite strongly influencing the confinement times, the multiphase medium is only capable of altering the energy dependence of cosmic-ray transport when there is a moderate (but not excessive) level of perpendicular diffusion across magnetic-field lines.

Astronomy and Astrophysics

Hydrogen diffusion induced dislocation transformations in a nickel superalloy

The diffusion of hydrogen in metals and alloys induces embrittlement that can adversely affect the structural properties. We examine the adsorption and diffusion of hydrogen in Inconel-718 (IN-718), and scrutinize the ensuing effects on the dislocation behavior in the alloy to elucidate the fundamental mechanisms of hydrogen-microstructure interactions from classical molecular simulations. Hydrogen adsorption increases with time until the surface saturates, while hydrogen diffusion exhibits strong temperature dependence, with diffusion coefficients converging above 1300 K regardless of the initial hydrogen concentration in the alloy. The diffusion in IN-718 is significantly sluggish than in pure Ni, Fe, or Cr, and is strongly impacted by hydrogen concentrations, resulting in an order of magnitude higher diffusion coefficient for hydrogen (10-14 m2/s relative to 10-15 m2/s) at high concentrations, especially below 600 K. Hydrogen diffusion coefficient varies from 10-12 to 10-15 m2/s in IN-718 depending on temperature (500–1400 K). More critically, our results reveal that increasing hydrogen concentration induces microstructural changes in the alloy, transforming perfect dislocations into stair-rods and Shockley partials, with higher temperatures favoring the latter. The results are significant for hydrogen fuel applications to gain insights into the materials chemistry for designing safer and more efficient propulsion systems, particularly in high-performance environments related to controlled hydrogen combustion applications.

Banerjee, Tanumoy

Investigating Morphology and Diffusion in Simulations of Precise Anion-Conducting Polymers

Using atomistic molecular dynamics simulations, we investigate the morphology and transport properties of a new class of polymers which are functionalized with quaternary ammonium groups for use as anion exchange membranes. The polymers are precision polyolefins with either a trimethylammonium (p5CNMe3) or a dimethyl-hexyl ammonium (p5CNMe2Hx) pendant group at every fifth carbon along a polyethylene backbone. Simulations are performed at hydration levels of 5, 10, 15, and 20 water molecules per ammonium group. The hydrated polymers form nanoscale, percolated hydrophilic domains (water channels) in the hydrophobic polymer matrix that become wider with increasing water content. Water and hydroxide anion diffusion coefficients also increase with increasing water content. The morphology of the water domains is similar in both polymers, while the diffusion coefficients are somewhat lower in p5CNMe2Hx at fixed water content. Furthermore, the diffusion coefficients in both polymers fall on the same curve as a function of the fractal dimension of the percolated water channels, which appears to be a useful scalar measure of the effects of the nanoscale morphology on water and hydroxide anion transport.

Anion exchange membrane

Vacancy-Dependent Diffusion Mechanism in Oxygen-Defective SrFeO 3 Perovskite Materials: First-Principles Density Functional Theory and Experimental Approach

Understanding oxygen diffusion at the atomic scale in SrFeO 3−δ perovskites is crucial for developing oxygen storage materials with optimal performance. Such materials are required to have high stability, corrosion resistance, and acceptable oxygen storage capacity at moderate operating temperatures and pressures. Here, in this study, we used first-principles density functional theory and thermogravimetric analysis to study the vacancy-dependent oxygen diffusion in oxygen-deficient SrFeO 3−δ (δ = 0, 0.065, 0.125, 0.25, 0.5) perovskites. The electronic structures, including the partial- and spin-resolved density of states, for different SrFeO 3−δ phases were calculated and compared with available experimental and theoretical results. By mapping the migration pathways, we investigated diffusion mechanisms and calculated the energy barriers for oxygen diffusion in cubic, orthorhombic, and brownmillerite phases of SrFeO 3−δ perovskites. Using the calculated energy barriers, we deduced the diffusion time scales and diffusion coefficients within SrFeO 3−δ . A diffusion coefficient on the order of 10 –8 m 2 /s was obtained for SrFeO 2.875 . We experimentally investigated the roles of temperature and oxygen partial pressures on the redox kinetics and deduced the kinetics rate and diffusion density, which agreed well with the calculated values for the density of diffusing oxygen vacancy in the lattice. Our results showed that the energy barrier tends to reduce at higher oxygen concentrations. Our results serve as an important guideline for designing oxygen storage materials with optimal redox kinetics.

chemical looping with oxygen uncoupling (CLOU)

Nanodomain Formation and Temperature-Dependent Diffusion in Deep Eutectic Solvents Revealed by Single-Molecule Tracking

Deep eutectic solvents (DESs) are typically regarded as homogeneous liquids; however, recent work shows that many exhibit nanoscale structural heterogeneity. Most studies attribute these nanoscale features to short-range chemical interactions. It is still unclear whether a long-range physical mechanism also plays a role. Here, in this study, we examined the nanoscale structure in two hydrophobic DESs, 1:3 tetrabutylammonium bromide: l-menthol (DES-butyl) and 1:3 tetraoctylammonium bromide: l-menthol (DES-octyl). The notation 1:3 represents the molar ratio of the hydrogen bond acceptors to hydrogen bond donors used in the synthesis of the DESs. Single-molecule tracking (SMT) coupled with maximum entropy method (MEM) analysis was used to measure the number of diffusion populations of a dilute concentration of an added fluorescent probe. The presence of more than one population of diffusion coefficients indicates the existence of multiple local environments for the fluorescent probe (i.e., nanoscale structures in the DES). DES-butyl showed a relatively narrow diffusion coefficient distribution centered at 0.55 μm 2 /s, whereas DES-octyl displayed two distinct diffusing populations at 20 °C, with diffusion coefficients of 0.12 μm 2 /s and 0.53 μm 2 /s for the slow and fast populations, respectively. As DES-octyl was heated, the slow-diffusing population steadily diminished and disappeared above ∼30 °C, indicating that the nanodomains present at lower temperatures collapse as the liquid becomes more thermodynamically mixed. This temperature-dependent homogenization is consistent with a physical mechanism of nanostructure formation, for example, liquid–liquid phase separation (LLPS), wherein the structure is not driven solely by specific chemical interactions. The SMT-MEM results suggest that a long-range physical mechanism is the most plausible origin of the measured nanoscale structure in DES-octyl.

Opare-Addo, Jemima [Ames Laboratory (AMES), Ames,

Larger than uncorrelated vacancy diffusion contributions in chemically disordered crystalline materials

Arising from a variational approach to compute diffusion coefficients, we introduce “superkinetic kinosons”, which are contributions to the diffusion flux of mobile defects and atomic species by single jump mechanisms that can exceed their uncorrelated values. In vacancy-mediated diffusion in crystalline random and high entropy materials, these contributions primarily arise from intermittent jumps of slow moving atoms that remove the vacancy out of correlation traps and enable a quantification of such effects on the diffusion coefficients. They can be significant contributors to diffusion, even when faster moving atoms have infinite percolation networks. Furthermore, their existence and importance provide fundamental insights about underlying aspects of vacancy diffusion such as formation of localized correlation traps and deviation of vacancy diffusion from percolation behavior.

36 MATERIALS SCIENCE