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DOE OSTI2015

Theory of activated penetrant diffusion in viscous fluids and colloidal suspensions

We heuristically formulate a microscopic, force level, self-consistent nonlinear Langevin equation theory for activated barrier hopping and non-hydrodynamic diffusion of a hard sphere penetrant in very dense hard sphere fluid matrices. Penetrant dynamics is controlled by a rich competition between force relaxation due to penetrant self-motion and collective matrix structural (alpha) relaxation. In the absence of penetrant-matrix attraction, three activated dynamical regimes are predicted as a function of penetrant-matrix size ratio which are physically distinguished by penetrant jump distance and the nature of matrix motion required to facilitate its hopping. The penetrant diffusion constant decreases the fastest with size ratio for relatively small penetrants where the matrix effectively acts as a vibrating amorphous solid. Increasing penetrant-matrix attraction strength reduces penetrant diffusivity due to physical bonding. For size ratios approaching unity, a distinct dynamical regime emerges associated with strong slaving of penetrant hopping to matrix structural relaxation. A crossover regime at intermediate penetrant-matrix size ratio connects the two limiting behaviors for hard penetrants, but essentially disappears if there are strong attractions with the matrix. Activated penetrant diffusivity decreases strongly with matrix volume fraction in a manner that intensifies as the size ratio increases. We propose and implement a quasi-universal approach for activated diffusion of a rigid atomic/molecular penetrant in a supercooled liquid based on a mapping between the hard sphere system and thermal liquids. Calculations for specific systems agree reasonably well with experiments over a wide range of temperature, covering more than 10 orders of magnitude of variation of the penetrant diffusion constant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Non-diffusive thermal transport in GaAs at micron length scales

In this study, we use a transient thermal grating technique in reflection geometry to measure the effective thermal diffusivity in GaAs as a function of heat transfer distance at three temperatures. Utilizing heterodyne detection, we isolate the “amplitude” grating contribution of the transient grating signal, which encodes the thermal transport dynamics. As the thermal grating period decreases, and thus the heat-transfer distance, we observe a reduction in the effective thermal diffusivity, indicating a departure from diffusive behavior. Non-diffusive behavior is observed at room temperature, as well as low temperature (180 K) and high temperature (425 K). At the shortest thermal grating period measured corresponding to a heat transfer distance of approximately 1 μm, the effective diffusivity drops to a value roughly 50% of the bulk thermal diffusivity. These measurements show the utility of the reflection transient thermal grating technique to measure thermal transport properties of opaque materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Effects of surface diffusion in electrocatalytic CO 2 reduction on Cu revealed by kinetic Monte Carlo simulations

We report Kinetic Monte Carlo (KMC) methods are frequently used for mechanistic studies of thermally driven heterogeneous catalysis systems but are underused for electrocatalysis. Here, we develop a lattice KMC approach for electrocatalytic CO 2 reduction. The work is motivated by a prior experimental report that performed electroreduction of a mixed feed of 12 CO 2 and 13 CO on Cu; differences in the 13 C content of C2 products ethylene and ethanol (Δ 13 C) were interpreted as evidence of site selectivity. The lattice KMC model considers the effect of surface diffusion on this system. In the limit of infinitely fast diffusion (mean-field approximation), the key intermediates 12 CO* and 13 CO* would be well mixed on the surface and no evidence of site selectivity could have been observed. Using a simple two-site model and adapting a previously reported microkinetic model, we assess the effects of diffusion on the relative isotope fractions in the products using the estimated surface diffusion rate of CO* from literature reports. We find that the size of the active sites and the total surface adsorbate coverage can have a large influence on the values of Δ 13 C that can be observed. Δ 13 C is less sensitive to the CO* diffusion rate as long as it is within the estimated range. We further offer possible methods to estimate surface distribution of intermediates and to predict intrinsic selectivity of active sites based on experimental observations. This work illustrates the importance of considering surface diffusion in the study of electrochemical CO 2 reduction to multi-carbon products. Our approach is entirely based on a freely available open-source code, so will be readily adaptable to other electrocatalytic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Simulation study of the effects of polymer network dynamics and mesh confinement on the diffusion and structural relaxation of penetrants

The diffusion of small molecular penetrants through polymeric materials represents an important fundamental problem, relevant to the design of materials for applications such as coatings and membranes. Polymer networks hold promise in these applications because dramatic differences in molecular diffusion can result from subtle changes in the network structure. In this paper, we use molecular simulation to understand the role that cross-linked network polymers have in governing the molecular motion of penetrants. By considering the local, activated alpha relaxation time of the penetrant and its long-time diffusive dynamics, we can determine the relative importance of activated glassy dynamics on penetrants at the segmental scale vs entropic mesh confinement on penetrant diffusion. We vary several parameters, such as the cross-linking density, temperature, and penetrant size, to show that cross-links primarily affect molecular diffusion through the modification of the matrix glass transition, with local penetrant hopping at least partially coupled to the segmental relaxation of the polymer network. This coupling is very sensitive to the local activated segmental dynamics of the surrounding matrix, and we also show that penetrant transport is affected by dynamic heterogeneity at low temperatures. To contrast, only at high temperatures and for large penetrants or when the dynamic heterogeneity effect is weak, does the effect of mesh confinement become significant, even though penetrant diffusion more broadly empirically follows similar trends as established models of mesh confinement-based transport.

Chemistry↗

DOE OSTI2025

Translational diffusion in supercooled water at and near the glass transition temperature—136 K

The properties of amorphous solid water at and near the calorimetric glass transition temperature, T g , of 136 K have been debated for years. One hypothesis is that water turns into a “true” liquid at T g (i.e., it becomes ergodic) and exhibits all the characteristics of an ergodic liquid, including translational diffusion. A competing hypothesis is that only rotational motion becomes active at T g , while the “real” glass transition in water is at a considerably higher temperature. To address this dispute, we have investigated the diffusive mixing in nanoscale water films, with thicknesses up to ∼100 nm, using infrared (IR) spectroscopy. The experiments used films that were composed of at least 90% H 2 O with D 2 O making up the balance and were conducted under conditions where H/D exchange was essentially eliminated. Because the IR spectra of multilayer D 2 O films (e.g., thicknesses of ∼3–6 nm) embedded within thick H 2 O films are distinct from the spectrum of isolated D 2 O molecules within H 2 O, the diffusive mixing of (initially) isotopically layered water films could be followed as a function of annealing time and temperature. The results show that water films with total thicknesses ranging from ∼20 to 100 nm diffusively mixed prior to crystallization for temperatures between 120 and 144 K. The translational diffusion had an Arrhenius temperature dependence with an activation energy of 40.8 ± 3.5 kJ/mol, which indicates that water at and near T g is a strong liquid. The measured diffusion coefficient at 136 K is 6.25 ± 1.4 × 10 −21 m 2 /s.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Molecular dynamics based study on the effects of cation size on the local structure and diffusion in polymerized ionic liquids

We have used coarse-grained molecular dynamics simulations to understand the effect of cation size on ion diffusion in polymerized ionic liquids at temperatures well above the glass transition temperature of the polymers. We investigated dependencies of the diffusion constant on the cation radius and static dielectric constant and interpreted these results in terms of underlying structural changes, and decoupling phenomenon. We have found non-monotonic effects of the cation radius on the diffusion constant, with a maximum at an intermediate radius resulting from two different size dependent effects. Changes in the radial distribution functions characterizing spatial distribution of cations with respect to anions result in a monotonic increase in the coordination number. This yields an increase in the effective interaction energy as a function of cation radius, which can explain the decrease in the diffusion constant. This increase is counteracted at small cation radii by a corresponding increase in decoupling of cation and anion dynamics. In addition, the diffusion constant is found to increase on increasing the static dielectric constant for all radii of the cations. These results highlight the significant role of decoupling in designing polymerized ionic liquids with an enhanced diffusion constant of cations.

Gillespie, Colin [ORNL] (ORCID:0000000320287080)↗

DOE OSTI2017

Validation of a mixture-averaged thermal diffusion model for premixed lean hydrogen flames

The mixture-averaged thermal diffusion model originally proposed by Chapman and Cowling is validated using multiple flame configurations. Simulations using detailed hydrogen chemistry are done on one-, two-, and three-dimensional flames. The analysis spans flat and stretched, steady and unsteady, and laminar and turbulent flames. Quantitative and qualitative results using the thermal diffusion model compare very well with the more complex multicomponent diffusion model. Comparisons are made using flame speeds, surface areas, species profiles, and chemical source terms. Once validated, this model is applied to three-dimensional laminar and turbulent flames. For these cases, thermal diffusion causes an increase in the propagation speed of the flames as well as increased product chemical source terms in regions of high positive curvature. The results illustrate the necessity for including thermal diffusion, and the accuracy and computational efficiency of the mixture-averaged thermal diffusion model.

Schlup, Jason↗

DOE OSTI2024

Simulating hindered grain boundary diffusion using the smoothed boundary method

Abstract Grain boundaries can greatly affect the transport properties of polycrystalline materials, particularly when the grain size approaches the nanoscale. While grain boundaries often enhance diffusion by providing a fast pathway for chemical transport, some material systems, such as those of solid oxide fuel cells and battery cathode particles, exhibit the opposite behavior, where grain boundaries act to hinder diffusion. To facilitate the study of systems with hindered grain boundary diffusion, we propose a model that utilizes the smoothed boundary method to simulate the dynamic concentration evolution in polycrystalline systems. The model employs domain parameters with diffuse interfaces to describe the grains, thereby enabling solutions with explicit consideration of their complex geometries. The intrinsic error arising from the diffuse interface approach employed in our proposed model is explored by comparing the results against a sharp interface model for a variety of parameter sets. Finally, two case studies are considered to demonstrate potential applications of the model. First, a nanocrystalline yttria-stabilized zirconia solid oxide fuel cell system is investigated, and the effective diffusivities are extracted from the simulation results and are compared to the values obtained through mean-field approximations. Second, the concentration evolution during lithiation of a polycrystalline battery cathode particle is simulated to demonstrate the method’s capability.

Materials Science↗

DOE OSTI2019

Electron drift and longitudinal diffusion in high pressure xenon-helium gas mixtures

We report new measurements of the drift velocity and longitudinal diffusion coefficients of electrons in pure xenon gas and in xenon-helium gas mixtures at 1-9 bar and electric field strengths of 50-300 V/cm. In pure xenon we find excellent agreement with world data at all E/P, for both drift velocity and diffusion coefficients. However, a larger value of the longitudinal diffusion coefficient than theoretical predictions is found at low E/P in pure xenon, below the range of reduced fields usually probed by TPC experiments. A similar effect is observed in xenon-helium gas mixtures at somewhat larger E/P. Drift velocities in xenon-helium mixtures are found to be theoretically well predicted. Although longitudinal diffusion in xenon-helium mixtures is found to be larger than anticipated, extrapolation based on the measured longitudinal diffusion coefficients suggest that the use of helium additives to reduce transverse diffusion in xenon gas remains a promising prospect.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Eddy diffusivity operator in homogeneous isotropic turbulence

Here, we use the recently developed macroscopic forcing method to compute the scale-dependent eddy diffusivity characterizing ensemble-averaged scalar and momentum transport in incompressible homogeneous isotropic turbulence. For scales larger than the energy containing eddies, eddy diffusivity is found to be constant and consistent with the Boussinesq approximation. However, for small scales eddy diffusivity is found to vanish inversely proportional to the wave number. Behavior at all scales is reasonably captured by a nonlocal eddy diffusivity operator modeled as D/$\sqrt{I - l^2∇^2}$, where D is the eddy diffusivity in the Boussinesq limit, and l is a constant on the order of the large-eddy length. These results present a direct measurement of eddy diffusivity in turbulence with implications in turbulence modeling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Strongly extended diffusion length for the nonequilibrium magnons in Y 3 F e 5 O 12 by photoexcitation

Y 3 Fe 5 O 12 (YIG) is known for its long magnon diffusion length. Although it has the known lowest damping rate, an even longer diffusion distance is still highly desired since it may lead to a much more efficient information transmission and processing. While most of previous works focused on the generation and detection of magnons in YIG, here we demonstrate how to depress the damping rate during the diffusion of magnon. By selectively exciting the spin state transition of the Fe ions in YIG, we successfully increase magnon diffusion length by one order of magnitude, i.e., from the previous reported ~10 μm up to ~156 μm (for the sample prepared by liquid phase epitaxy) and ~180 μm (for the sample prepared by pulsed laser deposition) at room temperature. The diffusion length, determined by nonlocal geometry, is ~30 μm for the magnons induced by visible light and above 150 μm for the laser of 980 nm. In addition to thermal gradient, light excitation affects the electron configuration of the Fe 3+ ion in YIG. Long-wavelength laser is more effective since it causes a transition of the Fe 3+ ions in FeO 6 octahedron from a high spin to a low spin state and thus causes a magnon softening which favors a long-distance diffusion. Furthermore, the present work paves the way toward an efficient tuning of magnon transport which is crucially important for magnon spintronics.

36 MATERIALS SCIENCE↗

DOE OSTI2024

In situ counter-diffusion crystallization and long-term crystal preservation in microfluidic fixed targets for serial crystallography

Compared with batch and vapor diffusion methods, counter diffusion can generate larger and higher-quality protein crystals yielding improved diffraction data and higher-resolution structures. Typically, counter-diffusion experiments are conducted in elongated chambers, such as glass capillaries, and the crystals are either directly measured in the capillary or extracted and mounted at the X-ray beamline. Despite the advantages of counter-diffusion protein crystallization, there are few fixed-target devices that utilize counter diffusion for crystallization. In this article, different designs of user-friendly counter-diffusion chambers are presented which can be used to grow large protein crystals in a 2D polymer microfluidic fixed-target chip. Methods for rapid chip fabrication using commercially available thin-film materials such as Mylar, propylene and Kapton are also detailed. Rules of thumb are provided to tune the nucleation and crystal growth to meet users' needs while minimizing sample consumption. These designs provide a reliable approach to forming large crystals and maintaining their hydration for weeks and even months. This allows ample time to grow, select and preserve the best crystal batches before X-ray beam time. Importantly, the fixed-target microfluidic chip has a low background scatter and can be directly used at beamlines without any crystal handling, enabling crystal quality to be preserved. The approach is demonstrated with serial diffraction of photoactive yellow protein, yielding 1.32 Å resolution at room temperature. Fabrication of this standard microfluidic chip with commercially available thin films greatly simplifies fabrication and provides enhanced stability under vacuum. These advances will further broaden microfluidic fixed-target utilization by crystallographers.

Liu, Zhongrui↗

DOE OSTI2024

Constrained Local Approximate Ideal Restriction for Advection-Diffusion Problems

Herein this paper focuses on developing a reduction-based algebraic multigrid (AMG) method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure advection to pure diffusion. Initial motivation comes from a new reduction-based AMG approach, $\ell \text{AIR}$ (local approximate ideal restriction), that was developed for solving advection-dominated problems. Though this new solver is very effective in the advection-dominated regime, its performance degrades in cases where diffusion becomes dominant. This is consistent with the fact that in general, reduction-based AMG methods tend to suffer from growth in complexity and/or convergence rates as the problem size is increased, especially for diffusion-dominated problems in two or three dimensions. Motivated by the success of $\ell \text{AIR}$ in the advective regime, our aim in this paper is to generalize the AIR framework with the goal of improving the performance of the solver in diffusion-dominated regimes. To do so, we propose a novel way to combine mode constraints as used commonly in energy-minimization AMG methods with the local approximation of ideal operators used in $\ell \text{AIR}$. The resulting constrained $\ell \text{AIR}$ algorithm is able to achieve fast scalable convergence on advective and diffusive problems. In addition, it is able to achieve standard low complexity hierarchies in the diffusive regime through aggressive coarsening, something that was previously difficult for reduction-based methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Characterization of Thermal, Hydraulic, and Gas Diffusion Properties in Variably Saturated Sand Grades

Core Ideas This study provides physical, hydraulic, and thermal properties of five sand grades. An extended three‐region thermal conductivity model is proposed. A gas diffusivity‐based variable tortuosity parameter is examined. Useful parametric functions and descriptive models were tested. Detailed characterization of partially saturated porous media is important for understanding and predicting vadose zone transport processes. While basic properties (e.g., particle‐ and pore‐size distributions and soil‐water retention) are, in general, essential prerequisites for characterizing most porous media transport properties, key transport parameters such as thermal conductivity and gas diffusivity are particularly important to describe temperature‐induced heat transport and diffusion‐controlled gas transport processes, respectively. Despite many experimental and numerical studies focusing on a specific porous media characteristic, a single study presenting a wide range of important characteristics, together with the best‐performing functional relationships, can seldom be found. This study characterized five differently textured sand grades (Accusand no. 12/20, 20/30, 30/40, 40/50, and 50/70) in relation to physical properties, water retention, hydraulic conductivity, thermal conductivity, and gas diffusivity. We used measured basic properties and transport data to accurately parameterize the characteristic functions (particle‐ and pore‐size distributions and water retention) and descriptive transport models (thermal conductivity, saturated hydraulic conductivity, and gas diffusivity). An existing thermal conductivity model was improved to describe the distinct three‐region behavior in observed thermal conductivity–water saturation relations. Applying widely used parametric models for saturated hydraulic conductivity and soil‐gas diffusivity, we characterized porous media tortuosity in relation to grain size. Strong relations among average particle diameter, characteristic pore diameter from soil‐water retention measurements, and saturated hydraulic conductivity were found. Thus, the results of this work are useful toward better describing, linking, and predicting mass transfer and pore network properties in variably saturated porous media.

Chamindu Deepagoda, T. K. K.↗

DOE OSTI2016

Isotope Fractionation by Diffusion in Liquids (Final Technical Report)

The overall objective of the DOE-funded research by grant DE-FG02-01ER15254 was document and quantify kinetic isotope fractionations during chemical and thermal (i.e., Soret) diffusion in liquids (silicate melts and water) and in the later years to include alloys and major minerals such as olivine and pyroxene. The research involved both laboratory experiments and applications to natural settings. The key idea is that major element zoning on natural geologic materials is common and can arise for either changes in melt composition during cooling and crystallization or from diffusion. The isotope effects associated with diffusion that we have documented are the key for determining whether or not the zoning observed in a natural system was the result of diffusion. Only in those cases were the zoning is demonstrably due to diffusion can use independently measured rates of diffusion to constrain the thermal evolution of the system.

58 GEOSCIENCES↗

DOE OSTI2017

High-Throughput Study of Diffusion and Phase Transformation Kinetics of Magnesium-Based Systems for Automotive Cast Magnesium Alloys

The objective of the proposed study is to establish a scientific foundation on kinetic modeling of diffusion, phase precipitation, and casting/solidification, in order to accelerate the design and optimization of cast magnesium (Mg) alloys for weight reduction of U.S. automotive fleet. The team has performed the following tasks: 1) study diffusion kinetics of various Mg-containing binary systems using high-throughput diffusion multiples to establish reliable diffusivity and mobility databases for the Mg-aluminum (Al)-zinc (Zn)-tin (Sn)-calcium (Ca)-strontium (Sr)-manganese (Mn) systems; 2) study the precipitation kinetics (nucleation, growth and coarsening) using both innovative dual-anneal diffusion multiples and cast model alloys to provide large amounts of kinetic data (including interfacial energy) and microstructure atlases to enable implementation of the Kampmann-Wagner numerical model to simulate phase transformation kinetics of non-spherical/non-cuboidal precipitates in Mg alloys; 3) implement a micromodel to take into account back diffusion in the solid phase in order to predict microstructure and microsegregation in multicomponent Mg alloys during dendritic solidification especially under high pressure die-casting (HPDC) conditions; and, 4) widely disseminate the data, knowledge and information using the Materials Genome Initiative infrastructure (http://www.mgidata.org) as well as publications and digital data sharing to enable researchers to identify new pathways/routes to better cast Mg alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2019

First-principles Studies of Tritium Reactivity and Diffusivity on Defective and Carbon Doped Surfaces of $\gamma$-LiAlO 2 Pellets (Tritium Science Program Report FY 2019 )

In tritium-producing burnable absorber rods (TPBARs), tritium ($^{3}_{1}$H,T) is produced in 6 Li isotope enriched γ-LiAlO 2 ceramic pellet. However, a better understanding of $^{3}_{1}$H transport through the pellets, getters and the barrier/cladding system is hampered by a lack of fundamental data about the $^{3}_{1}$H solubility and diffusivity. In the process of $^{3}_{1}$H diffusion from bulk γ-LiAlO 2 to its surface, it is possible that $^{3}_{1}$H atoms bind with surface atoms or become trapped at vacancies sites. By increasing the number of $^{3}_{1}$H diffused from bulk to surface, upon recombination and desorption from surface sites, they will escape from the γ-LiAlO 2 surface to form different $^{3}_{1}$H species (possibly being as T, T 2 , T 2 O, OT, or CT x (x=1-4, with C impurity present at a 100-600 ppm level in pellets) that need to be identified and can become captured by the getter. Therefore, exploring the $^{3}_{1}$H diffusion from bulk to surface, corroborated with surface adsorption, diffusion and recombination and followed by desorption from surface as various types of $^{3}_{1}$H species becomes a very important task as an integral part of the study of $^{3}_{1}$H solubility and diffusivity in the pellets.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Calibration of the Diffusivity Predictions of Centipede Using Approximate Bayesian Computation and Applications in Nyx (Engineering Scale) and Xolotl-MARMOT (Meso-Scale) Simulations

Fission gas evolution and release in UO 2 nuclear fuel are important fuel performance metrics and occur in several distinct stages: 1) nucleation, growth and resolution of intra-granular bubbles, 2) diffusion to grain boundaries and 3) nucleation and growth of bubbles at grain boundaries, which eventually form a connected network (percolation) enabling release of gas from grain boundaries through connections to triple junctions, grain edges or free surfaces. The NE-SciDAC project is developing several computational tools to model this problem, which are connected in a hierarchical multi-scale framework. The information transfer in the multi-scale framework is a critical step that, in addition to best-estimates, should include uncertainty quantification. Despite taking a first-principles multi-scale approach, there is a need to perform parameter calibration to ensure consistency with available experimental data. In the present study, uncertainty quantification (UQ) and parameter calibration is demonstrated for one of the lower length scale codes in the multi-scale framework (Centipede) and then the results, including instances of the propagated uncertainties, are used in other codes within the framework, specifically Nyx and Xolotl-MARMOT. We calibrated the model parameters in Centipede, a computer code used to predict diffusivities of uranium (U) and xenon (Xe) in the context of the simulation of fission gas in uranium oxide (UO 2 ) nuclear fuel. The Centipede code depends on 183 parameters, all of which are subject to uncertainty. The three data sets used in our calibration effort are taken from the literature. This data is available as a set of measurements, including measurement errors. Our goal is to calibrate a statistical model that predicts both the value of the measurement and the uncertainty associated with the measurement. We perform a Bayesian calibration of the model parameters using a dedicated approximate Bayesian computation (ABC) likelihood function. To avoid excessive computational costs, we replace the expensive Centipede simulation code by a higher-order surrogate model, constructed using only the 9 most important parameters. These important parameters are identified by a preliminary global sensitivity analysis (GSA) study. Among the important parameters are T0 (the temperature at which UO 2 is perfectly stoichiometric) and Hf_pO2 (the temperature dependence of the oxygen (O) partial pressure) that should be considered as operating conditions to be estimated along with the other parameters. We consider two different cases: one where we define one set of these operating conditions for all data sets, and one where we define distinct operating condition parameters for each data set. The Xe diffusivities predicted by the latter case show distinct features that could not be observed in the former. Next, we use the diffusivity predictions by Centipede as input to Nyx, a reduced order fuel performance code focused on gas behavior alone, in order to estimate quantities associated with inter-granular bubble formation at conditions specified by the experiments. Finally, the diffusivities obtained from the calibrated Centipede runs were used in coupled Xolotl-MARMOT simulations of intra- and inter-granular gas evolution. The results are compared to simulations using the baseline diffusivities from Turnbull et al.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗