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At least 433 records · Page 24

Viscous evolution of accretion discs in the quiescence of dwarf novae

Viscous evolution of accretion disks in the quiescence of dwarf novae is investigated semi-analytically. There are two key factors: the inward flow of the initial mass in the disk and the diffusion of the material added into the disk. The results are compared with the brightness temperature distributions obtained by the eclipse mapping of Z Cha and OY Car. The functional form of the viscosity parameter a, its values, the types of outbursts, and the application to soft X-ray transients are discussed.

Mineshige, Shin↗

Electrode performance parameters for a radioisotope-powered AMTEC for space power applications

The alkali metal thermoelastic converter (AMTEC) is a device for the direct conversion of heat to electricity. Recently a design of an AMTEC using a radioisotope heat source was described, but the optimum condenser temperature was hotter than the temperatures used in the laboratory to develop the electrode performance model. Now laboratory experiments have confirmed the dependence of two model parameters over a broader range of condenser and electrode temperatures for two candidate electrode compositions. One parameter, the electrochemical exchange current density at the reaction interface, is independent of the condenser temperature, and depends only upon the collision rate of sodium at the reaction zone. The second parameter, a morphological parameter, which measures the mass transport resistance through the electrode, is independent of condenser and electrode temperatures for molybdenum electrodes. For rhodium-tungsten electrodes, however, this parameter increases for decreasing electrode temperature, indicating an activated mass transport mechanism such as surface diffusion.

Underwood, M. L.↗

Transient Flow Dynamics in Optical Micro Well Involving Gas Bubbles

The Lab-On-a-Chip Application Development (LOCAD) team at NASA s Marshall Space Flight Center is utilizing Lab-On-a-Chip to support technology development specifically for Space Exploration. In this paper, we investigate the transient two-phase flow patterns in an optic well configuration with an entrapped bubble through numerical simulation. Specifically, the filling processes of a liquid inside an expanded chamber that has bubbles entrapped. Due to the back flow created by channel expansion, the entrapped bubbles tend to stay stationary at the immediate downstream of the expansion. Due to the huge difference between the gas and liquid densities, mass conservation issues associated with numerical diffusion need to be specially addressed. The results are presented in terms of the movement of the bubble through the optic well. Bubble removal strategies are developed that involve only pressure gradients across the optic well. Results show that for the bubble to be moved through the well, pressure pulsations must be utilized in order to create pressure gradients across the bubble itself.

Johnson, B.↗

Mass Transport Limitations and Kinetic Consequences of Corn Stover Deacetylation

Alkaline pretreatment of herbaceous feedstocks such as corn stover prior to mechanical refining and enzymatic saccharification improves downstream sugar yields by removing acetyl moieties from hemicellulose. However, the relationship between transport phenomena and deacetylation kinetics is virtually unknown for such feedstocks and this pretreatment process. Here, we report the development of an experimentally validated reaction–diffusion model for the deacetylation of corn stover. A tissue-specific transport model is used to estimate transport-independent kinetic rate constants for the reactive extraction of acetate, hemicellulose and lignin from corn stover under representative alkaline conditions (5–7 g L -1 NaOH, 10 wt% solids loadings) and at low to mild temperatures (4–70°C) selected to attenuate individual component extraction rates under differential kinetic regimes. The underlying transport model is based on microstructural characteristics of corn stover derived from statistically meaningful geometric particle and pore measurements. These physical descriptors are incorporated into distinct particle models of the three major anatomical fractions (cobs, husks and stalks) alongside an unsorted, aggregate corn stover particle, capturing average Feret lengths of 917–1239 μm and length-to-width aspect ratios of 1.8–2.9 for this highly heterogeneous feedstock. Individual reaction–diffusion models and their resulting particle model ensembles are used to validate and predict anatomically-specific and bulk feedstock performance under kinetic-controlled vs. diffusion-controlled regimes. In general, deacetylation kinetics and mass transfer processes are predicted to compete on similar time and length scales, emphasizing the significance of intraparticle transport phenomena. Critically, we predict that typical corn stover particles as small as ~2.3 mm in length are entirely diffusion-limited for acetate extraction, with experimental effectiveness factors calculated to be 0.50 for such processes. Debilitatingly low effectiveness factors of 0.021–0.054 are uncovered for cobs—implying that intraparticle mass transfer resistances may impair observable kinetic measurements of this anatomical fraction by up to 98%. These first-reported quantitative maps of reaction vs. diffusion control link fundamental insights into corn stover anatomy, biopolymer composition, practical size reduction thresholds and their kinetic consequences. These results offer a guidepost for industrial deacetylation reactor design, scale-up and feedstock selection, further establishing deacetylation as a viable biorefinery pretreatment for the conversion of lignocellulosics into value-added fuels and chemicals.

09 BIOMASS FUELS↗

Local Electric Field Effects on Water Dissociation in Bipolar Membranes Studied Using Core–Shell Catalysts

The local electric field strength is thought to affect the rate of water dissociation (WD) in bipolar membranes (BPMs) at the catalyst–nanoparticle surfaces. Here, we study core–shell nanoparticles, where the core is metallic, semiconducting, or insulating, to understand this effect. The nanoparticle cores were coated with a WD catalyst layer (TiO2 or HfO2) via atomic layer deposition (ALD), and the morphology was imaged with transmission electron microscopy. Irrespective of the core material, these core–shell catalysts displayed comparable WD overpotentials at optimal mass loading, despite the hypothesized differences in the electric field strength across the catalyst particle suggested by continuum electrostatic simulations. Substantial atomic interdiffusion between the core and shell was ruled out by X-ray absorption spectroscopy, X-ray photoelectron spectroscopy, and diffuse reflectance optical measurements. However, the optimal mass loading of catalyst was roughly 1 order of magnitude higher for the conductive and high dielectric core materials than for the low dielectric insulating cores. These findings are consistent with the hypothesis that electric field screening within the core material focuses the electric field drop between particles such that larger film thicknesses can be tolerated. Collectively, these data support the idea that it is the local electric field at the molecular level that controls proton-transfer rates and that the metal core/dielectric-shell constructs introduced here modulate that field. Further materials and synthetic design may enable optimization of the electric field strength across the proton-transfer trajectory at the material surface.

Sarma, Prasad V↗

Convective-diffusive transport in vapor growth ampoules

Theoretical and experimental work on heat and mass transport in crystal growth by closed ampoule vapor transport is reviewed. It is shown that double-diffusive phenomena, together with the three-dimensional boundary conditions of real systems lead to a complexity of the transport modes that are beyond the reach of the simplifying models currently used in the materials preparation literature. Consequences of the new insights for earth-bound vapor transport and for optimization of future space experiments are discussed.

Rosenberger, F.↗

Crystal growth of compound semiconductors in a low-gravity environment (InGaAs crystals) (M-22)

Compound semiconductor crystals, such as gallium arsenide and indium phosphide crystals, have many interesting properties that silicon crystals lack, and they are expected to be used as materials for optic and/or electro-optic integrated devices. Generally speaking, alloy semiconductors, which consist of more than three elements, demonstrate new functions. For example, values of important parameters, such as lattice constant and emission wavelength, can be chosen independently. However, as it is easy for macroscopic and/or microscopic fluctuations of composition to occur in alloy semiconductor crystals, it is difficult to obtain crystals having homogeneous properties. Macroscopic change of composition in a crystal is caused by the segregation phenomenon. This phenomenon is due to a continuous change in the concentration of constituent elements at the solid-liquid interfacing during solidification. On Earth, attempts were made to obtain a crystal with homogeneous composition by maintaining a constant melt composition near the solid-liquid interface, through suppression of the convection flow of the melt by applying a magnetic field. However, the attempt was not completely successful. Convective flow does not occur in microgravity because the gravity in space is from four to six orders of magnitude less than that on Earth. In such a case, mass transfer in the melt is dominated by the diffusion phenomenon. So, if crystal growth is carried out at a rate that is higher than the rate of mass transfer due to this phenomenon, it is expected that crystals having a homogeneous composition will be obtained. In addition, it is also possible that microscopic composition fluctuations (striation) may disappear because microscopic fluctuations diminish in the absence of convection. We are going to grow a bulk-indium gallium arsenide (InGaAs) crystal using the gradient heating furnace (GHF) in the first material processing test (FMPT). The structure of the sample is shown where InGaAs polycrystals in a crucible are doubly sealed in two quartz tubes for safety. The GHF consists of two zones, namely, high temperature and low temperature zones, which results in a large temperature gradient at the interface. Crystal growth is performed by moving the furnace (i.e. the temperature profile) from the left to right at a definite rate. Thus, we will grow crystals both on Earth and in space under the same conditions. As previously described, it is possible to obtain good quality crystals which are homogeneous in composition both macroscopically and microscopically due to the lack of convection in space. We are planning to study the effects of convection on crystal growth from a melt by comparing and characterizing the properties of crystals grown on Earth with those grown in space.

Tatsumi, Masami↗

Diffusion of Hydrophilic to Hydrophobic Forms of Nile Red in Aqueous C 12 EO 10 Gels by Variable Area Fluorescence Correlation Spectroscopy

In this work, solute diffusion within lyotropic liquid crystal gels prepared from a series of water and decaethylene glycol monododecyl ether (C 12 EO 10 ) mixtures was explored by variable area fluorescence correlation spectroscopy. Aqueous C 12 EO 10 gels were prepared in concentrations ranging from 55:45 to 70:30 wt% of surfactant and water. Small angle X-ray scattering revealed that these gels comprise hexagonal mesophases of cylindrical micelles. Micelle spacing was found to decrease with increasing C 12 EO 10 concentration. Three different Nile red (NR) dyes were employed as model solutes and were separately doped into the gels at nanomolar levels. These include a hydrophilic form of NR incorporating an anionic sulfonate group (NRSO 3 - ), a hydrophobic form incorporating a fourteen-carbon alkane tail (NRC 14 ), and commercial NR as an intermediate case. FCS data acquired from the gels revealed that NRSO 3 - diffused primarily in 3D. Its diffusion coefficient exhibited a monotonic decrease with increasing gel concentration and micelle packing density, consistent with confinement of its motions as a result of its exclusion from the micelle cores. NRC 14 exhibited the smallest diffusion coefficient, most likely due to its larger size and enhanced interactions with the micelle cores. NR yielded an intermediate diffusion coefficient and the most anomalous behavior of the three dyes, attributable to its facile partitioning between core and corona regions, and greater participation by 1D diffusion. The results of these studies afford an improved understanding of molecular mass transport through soft-matter nanomaterials like those being developed for use in drug delivery and membrane based chemical separations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Relevance of cosmic gamma rays to the mass of gas in the galaxy

The bulk of the diffuse gamma-ray flux comes from cosmic ray interactions in the interstellar medium. A knowledge of the large scale spatial distribution of the Galactic gamma-rays and the cosmic rays enables the distribution of the target gas to be examined. An approach of this type is used here to estimate the total mass of the molecular gas in the galaxy. It is shown to be much less than that previously derived, viz., approximately 6 x 10 to the 8th power solar masses within the solar radius as against approximately 3 x 10 to the 9th power based on 2.6 mm CO measurements.

Bhat, C. L.↗

Product selectivity and mass transport in levulinic acid transfer hydrogenation by monolithic MIL-100, MIL-88B and ZIF-8@Pd MOFs

The diffusion processes between adsorbent and adsorbate naturally play a significant role in the efficiency and selectivity of the heterogenous catalytic process. This paper considers the importance of diffusion processes in the transfer hydrogenation reaction of levulinic acid to γ-valerolactone by MIL-88B, MIL-100, and ZIF8@Pd monolithic catalysts. Over a period of five catalytic cycles, it was shown that the Fe-based catalysts can achieve similar conversions to the ZIF-8 supported Pd, with the only current limitation being the lower aqueous stability of these MOFs. Diffusion constants were calculated using the ZLC method, with micropore diffusion limitation found for ZIF-8 and MIL-100 monolithic frameworks at 2.7 x 10 -8 and 4.6 x 10 -8 cm 2 s -1 respectively. This diffusion limitation was also confirmed by IR spectroscopy with an increasing concentration of C—H bands on the MOF substrate post-reaction. Mass transfer coefficients, also calculated by ZLC, revealed increased mass transport for the hydrophobic ZIF-8 framework, which perhaps aids in the γ-valerolactone selectivity over side products that are produced in the absence of catalytic material, as seen for MIL-88B and MIL-100 after multiple uses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analysis techniques for tracer studies of oxidation

Analysis techniques to obtain quantitative diffusion data from tracer concentration profiles were developed. Mass balance ideas were applied to determine the mechanism of oxide growth and to separate the fraction of inward and outward growth of oxide scales. The process of inward oxygen diffusion with exchange was theoretically modelled and the effect of lattice diffusivity, grain boundary diffusivity and grain size on the tracer concentration profile was studied. The development of the tracer concentration profile in a growing oxide scale was simulated. The double oxidation technique was applied to a FeCrAl-Zr alloy using 0-18 as a tracer. SIMS was used to obtain the tracer concentration profile. The formation of lacey oxide on the alloy was discussed. Careful consideration was given to the quality of data required to obtain quantitative information.

Basu, S. N.↗

Biofilm Study Under Simulated Microgravity

The goal of this study was to understand biofilm formation under microgravity (µg), in support of biofilm mitigation efforts in exploration water recovery systems. The technical approach was to conduct a mass transfer and bacterial culture study under both simulated µg and ambient gravity. The aim was to correlate nutrient consumption to gene expression to better understand biofilm formation. A representative species of bacteria that is commonly cultured from the International Space Station (ISS) Water Processor Assembly (WPA) was cultured in a WPA influent water ersatz formulation that is tailored for microbiology studies. A mass transfer rate study was carried out using the ersatz WPA influent water by introducing a water-soluble dye to represent dissolved nutrients and nutrient particles. Imaging of dye diffusion over time allowed for the comparison of mass transport rates under a series of rotation per minute (RPM) speeds for the High Aspect Ratio Vessels (HARVs) on a Rotating Wall Vessel (RWV). This was done to determine the speed that will most accurately simulate the low convective rates experienced under actual µg conditions. Three biological replicates of the Burkholderia contaminans (B. contaminans) microbe were cultured under simulated µg with a rotating (R) control in the horizontal plane at the determined optimal RPM of 15, along with a stationary (S) reference culture. At T=0, and then at T=1,2,3 (in exponential phase) and T=4 (in S phase), the bacterial culture and ersatz were harvested for transcriptomic and nutrient content analysis, respectively. The experimental results illustrated that phosphate is a limiting nutrient in the WPA ersatz formula. Nutrient analysis illustrated that the µg treatment culture took up essential nutrients more rapidly than the R and S control cultures, yet non-essential nutrients remained higher in the µg treatment than in the controls at later timepoints. The rapid uptake and subsequent starvation of phosphate in the culture under µg conditions is further illustrated in the transcriptomic response when compared to that of the R control condition. The subsequent starvation response may serve as one element to explain a moderate enhancement of biofilm formation in the µg treatment. One implication of this work is that biofilm mitigation in the ISS environment could be supported by ensuring a steady flow of water as a vehicle for phosphate within the WPA to avoid complete phosphate consumption, which occurs in times of no flow and leads to undesired biofilm formation.

Aubrie O’Rourke↗

Transport mechanisms at the magnetopause

Convection and diffusion are discussed as possible mechanisms of mass, momentum, and energy transfer across the magnetopause. For the case of a vanishing magnetic field component normal to the boundary, convective flow does not appear possible unless substantial electric fields occur parallel to the magnetic field. The case of a nonvanishing magnetic field constant includes exactly field-aligned flows as well as magnetic field reconnection. It is shown that the efficiency of the diffusive and the convective transfer should have a strong dependence on the angle between the magnetospheric and the magnetosheath magnetic fields.

Sonnerup, B. U. O.↗

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook, Subramaniam et al., and Adler and Lele, in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a four-equation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases. The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer–Meshkov instability of a copper–aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. In conclusion, this is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

97 MATHEMATICS AND COMPUTING↗

A coupled DEM-IMB-LBM model for simulating methane hydrate exploitation involving particle dissolution

The coupled discrete element and lattice Boltzmann method using an immersed moving boundary scheme was extended to simulate methane hydrate exploitation involving mass transport and particle dissolution. In this coupled DEM-IMB-LBM model, a new Dirichlet-type thermal boundary condition is extended to simulate moving curved boundaries with constant concentration. A novel periodic boundary including an efficient searching algorithm for particle contact is proposed to reduce the computational cost and boundary effect. So, this model is validated by two numerical examples: a circular particle with concentration convection-diffusion moving in a horizontal channel and mass transport from a cylinder particle in a simple shear flow. The numerical results obtained from the proposed model agree well with previous studies. To further demonstrate the capacity of the proposed model, simulations of methane hydrate exploitation including two formations in marine sediments are carried out. The numerical results indicate that the coupled DEM-IMB-LBM is not only capable of simulating the dissolution of hydrate particles at the grain level, but also recover the sand erosion and migration process in a fundamental perspective during the methane hydrate exploitation process.

42 ENGINEERING↗

Escape and ionization of atomic oxygen from Io

Model calculations of the neutral O cloud of Io, based on atom-electron-impact excitation and ionization processes in the plasma torus, are presented. The model is quantitatively anchored to the 6300-A O I emission intensity observations of Brown (1981), and uses a plasma temperature and density structure based on Voyager 1 and 2 and EUV data. Parameters predicted by the model include satellite emission flux = 1.5 x 10 to the 9th/sq cm sec, ion-loading rate = 6.2 x 10 to the 26th ions/sec, O mass-loading rate = 16.6 kg/sec, and O ion-energy input rate = 2.7 x 10 to the 10th W. The spatial morphologies of the parameters are shown. Rough estimates obtained by accounting for a neutral S cloud and plasma-torus charge-exchange reactions include O source flux = 1.2 x 10 to the 10th/sq cm sec, ion-loading rate = 4.0 x 10 to the 27th ions/sec, ion-diffusive-loss time = 200 days, plasma mass-loading rate = 150 kg/sec, satellite mass-loss rate = 270 kg/sec, and maximum ion-energy input = 4 x 10 to the 11th W.

Smyth, W. H.↗

Impact of phase state and non-ideal mixing on equilibration timescales of secondary organic aerosol partitioning

Abstract. Evidence has accumulated that secondary organic aerosols (SOAs) exhibit complex morphologies with multiple phases that can adopt amorphous semisolid or glassy phase states. However, experimental analysis and numerical modeling on the formation and evolution of SOA still often employ equilibrium partitioning with an ideal mixing assumption in the particle phase. Here we apply the kinetic multilayer model of gas–particle partitioning (KM-GAP) to simulate condensation of semi-volatile species into a core–shell phase-separated particle to evaluate equilibration timescales of SOA partitioning. By varying bulk diffusivity and the activity coefficient of the condensing species in the shell, we probe the complex interplay of mass transfer kinetics and the thermodynamics of partitioning. We found that the interplay of non-ideality and phase state can impact SOA partitioning kinetics significantly. The effect of non-ideality on SOA partitioning is slight for liquid particles but becomes prominent in semisolid or solid particles. If the condensing species is miscible with a low activity coefficient in the viscous shell phase, the particle can reach equilibrium with the gas phase long before the dissolution of concentration gradients in the particle bulk. For the condensation of immiscible species with a high activity coefficient in the semisolid shell, the mass concentration in the shell may become higher or overshoot its equilibrium concentration due to slow bulk diffusion through the viscous shell for excess mass to be transferred to the core phase. Equilibration timescales are shorter for the condensation of lower-volatility species into semisolid shell; as the volatility increases, re-evaporation becomes significant as desorption is faster for volatile species than bulk diffusion in a semisolid matrix, leading to an increase in equilibration timescale. We also show that the equilibration timescale is longer in an open system relative to a closed system especially for partitioning of miscible species; hence, caution should be exercised when interpreting and extrapolating closed-system chamber experimental results to atmosphere conditions. Our results provide a possible explanation for discrepancies between experimental observations of fast particle–particle mixing and predictions of long mixing timescales in viscous particles and provide useful insights into description and treatment of SOA in aerosol models.

54 ENVIRONMENTAL SCIENCES↗

Mechanisms of Retention and Transport of Fission Products in Virgin and Irradiated Nuclear Graphite

To fulfill the design and licensing requirements for advanced reactors, the U.S. Department of Energy (DOE) is specifically interested in targeted research to quantify the mechanisms of fission product transport and retention in graphitic grades that will likely be used in next-generation very/high temperature reactors, fluoride salt-cooled high temperature reactors and molten salt reactors. We have examined an integrated experimental-computational approach to determine the diffusivities of selected fission products – ruthenium (Ru) and silver (Ag) in five nuclear graphite grades – POCO AXF-5Q, POCO ZXF-5Q, PCEA, IG110, and NBG-18. Experimental investigation for diffusion of other fission products (iodine, cesium, and krypton) in graphite could not be carried out due to extreme evaporation due to high vapor pressure, despite several attempts incorporating various experimental schemes. Experimental investigation with irradiated graphite could not be carried out because necessary approval to transport irradiated graphite could not be obtained due to procedural reasons at ORNL and national policy change in UK. An effort was made to “produce” by ion sputtering, but it was discontinued because the outcome did not adequately represent irradiated graphite. Thin film and “cup-and-cap” methods were employed to deposit fission products, diffusion annealed were carried out in an argon atmosphere, and concentration profiles were determined by dynamic secondary ion mass spectroscopy depth profiling technique. Regardless of graphite type, anomalous diffusion behavior of Ru (i.e., lower than expected based on Arrhenius temperature dependence) at an intermediate temperature, around 600 to 700 °C, was observed. Diffusion behavior of silver on the other hand agreed well to the Arrhenius temperature dependence although the excessive evaporation of silver hampered the accurate determination of diffusivities at temperature higher than 900 °C. In general, silver was observed to diffuse faster than Ru in the temperature range compared from 500 to 900 °C, had consistently had higher pre-exponential factor corresponding to higher jump frequency. To understand the abnormal diffusional behavior of Ru in graphite in intermediate temperature range, a detailed microstructural analysis was carried out. Clustering of Ru into particles on the surface of graphite was observed around 700 °C corresponding to de-wetting and spheroidization. This change would influence the boundary condition of diffusion, although features of clustering was much smaller (<1 mm) than the SIMS raster size (120 x 120 mm). Raman spectroscopy also demonstrated that Raman peak intensity for Ru decreased significantly for samples annealed higher than 700 °C and presence of Ru in graphite altered the crystallinity of graphite. To further elucidate the abnormal diffusion behavior observed in intermediate temperature investigated, the vibrational properties of graphene, bilayer graphene and Kr atoms in bilayer graphene were investigated with molecular dynamics. Krypton, which is a fission product, was introduced between a bilayer graphene system to evaluate (i) whether the phonon dispersion curves change with high temperature in bilayer graphene (ii) whether the addition of Kr atoms between the bilayer introduces any significant change in the vibrational properties, and (iii) whether any change in the vibrational properties can be correlated to the diffusive behavior of Kr atoms. The results show that the Kr atoms indeed exhibit an anomalous diffusive behavior at 550°C. Phonon analysis shows that a few phonon frequencies are enhanced as much as 20 to 30 % with the addition of just 0.2 at.% Kr. So, this may explain the unexpected self-diffusivity of fission products.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗