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DOE OSTI2016

Charge Carrier Diffusion Length Determination in 4H-SiC Schottky Alpha Detectors

When developing semiconductor radiation detectors detailed characterization of the detector behavior is required. The ability of a semiconductor radiation detector to collect the charge liberated by incident ionizing radiation is a critical characteristic. Several factors influence the charge collection efficiency of a semiconductor radiation detector, including electron-hole trapping, applied electric field strength, and dopant concentrations and dimensions of low doped regions. Applying a reverse bias electric potential to a low doped semiconductor region creates a free charge carrier depleted region and establishes an electric field which can remove subsequently freed charge in the form of an electrical signal. When ionizing radiation is incident upon a semiconductor electron-hole pairs are generated. These charge carriers are created along the path of the ionizing radiation regardless of the doping concentration. However, only the charge freed in the low doped epitaxial region of a detector will be collected as a result of the applied electric field. When the electric field is insufficient to develop a depleted region equal to or larger than the range of the ionizing radiation in the detector material some charge freed by the ionizing radiation outside of the sensitive region will be lost, thus potentially resulting in less than complete charge collection. The incomplete collection of charge complicates the analysis of the incident particle energy spectrum. Charge freed in the highly doped bulk region beyond the low doped epitaxial region may diffuse back into the low doped depleted region and be subsequently included in the integral pulse. The amount of charge collected as a result of this diffusion mechanism is dependent upon the diffusion length of the charge carriers in the material. The diffusion length is subsequently dependent on the material properties of the detector including the number of defects, trapping centers, and temperature. In order to fully characterize the properties of 4H-SiC as a radiation detector the diffusion length was calculated by adjusting the theoretical diffusion length value used in the calculation of the charge collection efficiency to agree with empirically observed charge collection efficiencies. The discrepancy between the observed and theoretical charge collection efficiency at 50 to 150 volts applied bias indicates an unexplained charge collection phenomenon which is contributing to the larger than predicted charge collection efficiency of the detectors. This voltage range corresponds to an intermediate applied bias, indicating that either the theoretical depletion width is too short, the diffusion length varies with the composition of the region that the charge carriers are diffusing through, or some other phenomenon is involved. If the charge carrier diffusion length varies depending on whether or not the diffusing charge is freed in unbiased epitaxy or bulk layer, then a function describing the variation of the diffusion layer could be determined by measuring the diffusion length at the applied voltages used previously, but over a range of epitaxial layer thicknesses. Future work includes the characterization of the effects of high temperature operation on the diffusion length of 4H-SiC in addition to measuring the effects of varying energy alpha emitter electrodeposition on the observed diffusion length. Additional Schottky barrier contacts, namely those with a nickel-platinum contact, will be tested in various sizes which have been developed in order to eliminate certain failure mechanisms and explore the potential effects of Schottky contact size on charge collection efficiency. (authors)

36 MATERIALS SCIENCE↗

DOE OSTI2017

Comparison of Experimental Methods for Estimating Matrix Diffusion Coefficients for Contaminant Transport Modeling

Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2018

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

Here, diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Density functional theory calculations of self- and Xe diffusion in U 3 Si 2

Uranium silicide, U 3 Si 2 , has been proposed as an advanced nuclear fuel to be used in light water reactors (LWRs). Development of this alternative to the predominant current fuel, UO 2 , is motivated by enhanced accident tolerance as a result of higher thermal conductivity as well as improved fuel cycle economics through increased uranium density. In order to accurately model the fuel performance of U 3 Si 2 , the diffusion rate of point defects, which is related to self-diffusion, and of fission gas atoms must be determined. DFT calculations are used to predict the U and Si point defect concentrations, the corresponding self-diffusivities, the preferred Xe trap site and the Xe diffusivity. Effects of irradiation are not considered. A low defect formation energy and a high entropy for Si interstitials give rise to Si-rich non-stoichiometry at elevated temperatures. Both U and Si self-diffusion and Xe diffusion are anisotropic as a consequence of the tetragonal crystal structure of U 3 Si 2 . Si diffusion occurs by interstitial mechanisms in both the a-b plane and along the c axis, while the U c axis diffusion rate is controlled by a vacancy mechanism. Interstitial diffusion of U is very fast in the a-b plane of the U 3 Si 2 crystal structure. Xe atoms prefer to occupy U vacancy trap sites. The highest Xe diffusion rate occurs by a vacancy mechanism in both the a-b plane and along the c axis. The diffusion rate is similar in the a-b plane and along the c axis. U and Si self-diffusion and Xe diffusion are all faster in U3Si2 than intrinsic U and Xe diffusion in conventional UO 2 nuclear fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Seismic Diffusivity and the Influence of Heterogeneity on Injection‐Induced Seismicity

Abstract The spatiotemporal patterns of injection‐induced seismicity (IIS) are commonly interpreted with the concept of a triggering front, which propagates in a diffusion‐like manner with an associated diffusivity parameter. Here, we refer to this diffusivity as the “seismic diffusivity.” Several previous studies implicitly assume that seismic diffusivity is equivalent to the effective hydraulic diffusivity of the subsurface, which describes the behavior of the mean pressure field in heterogeneous porous media. Seismicity‐based approaches for hydraulic characterization or simulations of IIS using domains of homogeneous equivalent porous media are implicitly based on this assumed equivalence. However, seismicity is expected to propagate with the threshold triggering pressure, and thus not be controlled by the evolution of the mean pressure field. We present numerical simulations of fluid injection to compare the seismic and effective hydraulic diffusivities in heterogeneous formations (including fractured rock). The numerical model combines uncoupled, linear pressure diffusion with the Mohr‐Coulomb failure criterion to simulate IIS. We demonstrate that connected pathways of relatively high hydraulic diffusivity in heterogeneous media (particularly in fractured rock domains) allow the threshold triggering pressure to propagate more rapidly than predicted by the effective hydraulic diffusivity. As a result, the seismic diffusivity is greater than the effective hydraulic diffusivity in heterogeneous porous media, possibly by an order of magnitude or more. Additionally, we present a case study of IIS near Soultz‐sous‐Forêts where seismic diffusivity is found to be at least one order of magnitude larger than the effective hydraulic diffusivity.

Haagenson, Ryan↗

DOE OSTI2022

Oxygen diffusion in garnet: Experimental calibration and implications for timescales of metamorphic processes and retention of primary O isotopic signatures

Knowledge of oxygen diffusion in garnet is crucial for a correct interpretation of oxygen isotope signatures in natural samples. A series of experiments was undertaken to determine the diffusivity of oxygen in garnet, which remains poorly constrained. The first suite included high-pressure (HP), nominally dry experiments performed in piston-cylinder apparatus at: (1) T = 1050–1600 °C and P = 1.5 GPa and (2) T = 1500 °C and P = 2.5 GPa using yttrium aluminum garnet (YAG; Y3Al5O12) cubes. Second, HP H2O-saturated experiments were conducted at T = 900 °C and P = 1.0–1.5 GPa, wherein YAG crystals were packed into a YAG + Corundum powder, along with 18O-enriched H2O. Third, 1 atm experiments with YAG cubes were performed in a gas-mixing furnace at T = 1500–1600 °C under Ar flux. Finally, an experiment at T = 900 °C and P = 1.0 GPa was done using a pyrope cube embedded into pyrope powder and 18O-enriched H2O. Experiments using grossular were not successful. Profiles of 18O/(18O+16O) in the experimental charges were analyzed with three different secondary ion mass spectrometers (SIMS): sensitive high-resolution ion microprobe (SHRIMP II and SI), CAMECA IMS-1280, and NanoSIMS. Considering only the measured length of 18O diffusion profiles, similar results were obtained for YAG and pyrope annealed at 900 °C, suggesting limited effects of chemical composition on oxygen diffusivity. However, in both garnet types, several profiles deviate from the error function geometry, suggesting that the behavior of O in garnet cannot be fully described as simple concentration-independent diffusion, certainly in YAG and likely in natural pyrope as well. The experimental results are better described by invoking O diffusion via two distinct pathways with an inter-site reaction allowing O to move between these pathways. Modeling this process yields two diffusion coefficients (D values) for O, one of which is approximately two orders of magnitude higher than the other. Taken together, Arrhenius relationships are:logDm2s-1=-7.2(±1.3)+(-321(±32)kJmol-12.303RT) for the slow pathway, andlogDm2s-1=-5.4(±0.7)+(-321(±20)kJmol-12.303RT) for the fast pathway. We interpret the two pathways as representing diffusion following vacancy and inter-stitial mechanisms, respectively. Regardless, our new data suggest that the slow mechanism is prevalent in garnet with natural compositions, and thus is likely to control the retentivity of oxygen isotopic signatures in natural samples. The diffusivity of oxygen is similar to Fe-Mn diffusivity in garnet at 1000–1100 °C and Ca diffusivity at 850 °C. However, the activation energy for O diffusion is larger, leading to lower diffusivities at P-T conditions characterizing crustal metamorphism. Therefore, original O isotopic signatures can be retained in garnets showing major element zoning partially re-equilibrated by diffusion, with the uncertainty caveat of extrapolating the experimental data to lower temperature conditions.

Geochemistry & Geophysics↗

DOE OSTI2022

Effect of charge and anisotropic diffusivity on ion exchange kinetics in nuclear waste form materials

Motifs of radionuclide absorption particles (absorbers or fillers) for the nuclear waste treatment usually have crystal structures with nano-sized tunnels for fast ion diffusion. On the other hand, the accumulation of ions generates an electric field which affects the ion diffusion. Therefore, the strong anisotropic kinetic properties and the electric field affect ion exchange kinetics, especially in an assembly of these particles which may block the fast diffusion tunnels for each other. In this work, we developed a mesoscale model to describe the effect of anisotropic kinetic properties and electric field on ion exchange kinetics. With the model we simulated the effect of anisotropic diffusivity, electrochemical potential, particle morphology, size and aggregation on ion exchange kinetics during batch experiments. Here, tt is found that 1) ion exchange results in charge accumulation inside the particle because different ions have different diffusivities and different diffusion driving forces. The electric neutrality is not preserved; 2) the electric field speeds up the slower diffusion ions (either uptake or release) and slows down the faster diffusion ions to reduce charge accumulation and maintains charge neutrality; 3) the ion exchange becomes very slow at the later stages because a) diffusion driving force (electrochemical gradient, Cs + concentration in the solution and Na + inside the particle) continuously decreases, as observed in batch experiments; and b) the diffusivity decreases due to the Cs + concentration dependence of ion diffusivity. This can explain the observed experimental phenomena that the radionuclide capacity usually cannot be reached; 4) for needle-like particle and their clusters, both surface area and diffusion distance along the direction with the fastest diffusivities have significant impact on the ion exchange kinetics.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2016

Perturbative thermal diffusivity from partial sawtooth crashes in Alcator C-Mod

Perturbative thermal diffusivity has been measured on Alcator C-Mod via the use of the extended-time-to-peak method on heat pulses generated by partial sawtooth crashes. Perturbative thermal diffusivity governs the propagation of heat pulses through a plasma. It differs from power balance thermal diffusivity, which governs steady state thermal transport. Heat pulses generated by sawtooth crashes have been used extensively in the past to study heat pulse thermal diffusivity, but the details of the sawtooth event typically lead to non-diffusive 'ballistic' transport, making them an unreliable measure of perturbative diffusivity on many tokamaks. Partial sawteeth are common on numerous tokamaks, and generate a heat pulse without the 'ballistic' transport that often accompanies full sawteeth. This is the first application of the extended-time-to-peak method of diffusivity calculation to partial sawtooth crashes. Furthermore, this analysis was applied to over 50 C-Mod shots containing both L- and I-Mode. Results indicate correlations between perturbative diffusivity and confinement regime (L- versus I-mode), as well as correlations with local temperature, density, the associated gradients, and gradient scale lengths (a/L Te and a/L n ). In addition, diffusivities calculated from partial sawteeth are compared to perturbative diffusivities calculated with the nonlinear gyrokinetic code GYRO. We find that standard ion-scale simulations (ITG/TEM turbulence) under-predict the perturbative thermal diffusivity, but new multi-scale (ITG/TEM coupled with ETG) simulations can match the experimental perturbative diffusivity within error bars for an Alcator C-Mod L-mode plasma. Perturbative diffusivities extracted from heat pulses due to partial sawteeth provide a new constraint that can be used to validate gyrokinetic simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Diffusion of aromatic hydrocarbons in hierarchical mesoporous H-ZSM-5 zeolite

Hierarchical mesoporous zeolites exhibit higher catalytic activities and longer lifetime compared to the traditional microporous zeolites due to improved diffusivity of substrate molecules and their enhanced access to the zeolite active sites. Understanding diffusion of biomass pyrolysis vapors and their upgraded products in such materials is fundamentally important during catalytic fast pyrolysis (CFP) of lignocellulosic biomass, since diffusion makes major contribution to determine shape selectivity and product distribution. However, diffusivities of biomass relevant species in hierarchical mesoporous zeolites are poorly characterized, primarily due to the limitations of the available experimental technology. In this work, molecular dynamics (MD) simulations are utilized to investigate the diffusivities of several selected coke precursor molecules, benzene, naphthalene, and anthracene, in hierarchical mesoporous H-ZSM-5 zeolite. The effects of temperature and size of mesopores on the diffusivity of the chosen model compounds are examined. The simulation results demonstrate that diffusion within the microspores as well as on the external surface of mesoporous H-ZSM-5 dominates only at low temperature. At pyrolysis relevant temperatures, mass transfer is essentially conducted via diffusion along the mesopores. Furthermore, the results illustrate the heuristic diffusion model, such as the extensively used Knudsen diffusion, overestimates the diffusion of bulky molecules in the mesopores, thus making MD simulation a powerful and compulsory approach to explore diffusion in zeolites.

09 BIOMASS FUELS↗

DOE OSTI2017

Computing eddy-driven effective diffusivity using Lagrangian particles

A novel method to derive effective diffusivity from Lagrangian particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from Lagrangian particles. We compute the effective diffusivity by first performing scalar transport on Lagrangian control areas using stored trajectories computed from online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the Lagrangian scalar transport scheme is compared against an Eulerian scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based Eulerian and Lagrangian effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The Eulerian and Lagrangian effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

Fast self-diffusion of ions in CH 3 NH 3 PbI 3 : the interstiticaly mechanism versus vacancy-assisted mechanism

The stability of organic-inorganic halide perovskites is a major challenge for their applications and has been extensively studied. Among the possible underlying reasons, ion self-diffusion has been inferred to play important roles. While theoretical studies congruously support that iodine is more mobile, experimental studies only observe the direct diffusion of the MA ion and possible diffusion of iodine. The discrepancy may result from the incomplete understanding of ion diffusion mechanisms. With the help of first-principles calculations, we studied ion diffusion in CH3NH3PbI3 (MAPbI3) through not only the vacancy-assisted mechanisms presumed in previous theoretical studies, but also the neglected interstiticaly mechanisms. We found that compared to the diffusion through the vacancy-assisted mechanism, MA ion diffusion through the interstiticaly mechanism has a much smaller barrier which could explain experimental observations. For iodine diffusion, both mechanisms can yield relatively small barriers. Depending on the growth conditions, defect densities of vacancies and interstitials can vary and so do the diffusion species as well as diffusion mechanisms. Our work thus supports that both MA and iodine ion diffusion could contribute to the performance instability of MAPbI3. While being congruous with experimental results, our work fills the research gap by providing a full understanding of ion diffusion in halide perovskites.

14 SOLAR ENERGY↗

DOE OSTI2016

METAL DIFFUSION IN SMOOTHED PARTICLE HYDRODYNAMICS SIMULATIONS OF DWARF GALAXIES

We perform a series of smoothed particle hydrodynamics simulations of isolated dwarf galaxies to compare different metal mixing models. In particular, we examine the role of diffusion in the production of enriched outflows and in determining the metallicity distributions of gas and stars. We investigate different diffusion strengths by changing the pre-factor of the diffusion coefficient, by varying how the diffusion coefficient is calculated from the local velocity distribution, and by varying whether the speed of sound is included as a velocity term. Stronger diffusion produces a tighter [O/Fe]–[Fe/H] distribution in the gas and cuts off the gas metallicity distribution function at lower metallicities. Diffusion suppresses the formation of low-metallicity stars, even with weak diffusion, and also strips metals from enriched outflows. This produces a remarkably tight correlation between “metal mass-loading” (mean metal outflow rate divided by mean metal production rate) and the strength of diffusion, even when the diffusion coefficient is calculated in different ways. The effectiveness of outflows at removing metals from dwarf galaxies and the metal distribution of the gas is thus dependent on the strength of diffusion. By contrast, we show that the metallicities of stars are not strongly dependent on the strength of diffusion, provided that some diffusion is present.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Methane Diffusion and Adsorption in Shale Rocks: A Numerical Study Using the Dusty Gas Model in TOUGH2/EOS7C-ECBM

Gas production from shale gas reservoirs plays a significant role in satisfying increasing energy demands. Compared with conventional sandstone and carbonate reservoirs, shale gas reservoirs are characterized by extremely low porosity, ultra-low permeability and high clay content. Slip flow, diffusion, adsorption and desorption are the primary gas transport processes in shale matrix, while Darcy flow is restricted to fractures. Understanding methane diffusion and adsorption, and gas flow and equilibrium in the low-permeability matrix of shale is crucial for shale formation evaluation and for predicting gas production. Modeling of diffusion in low-permeability shale rocks requires use of the Dusty gas model (DGM) rather than Fick’s law. The DGM is incorporated in the TOUGH2 module EOS7C-ECBM, a modified version of EOS7C that simulates multicomponent gas mixture transport in porous media. Also included in EOS7C-ECBM is the extended Langmuir model for adsorption and desorption of gases. In this study, a column shale model was constructed to simulate methane diffusion and adsorption through shale rocks. The process of binary CH 4 - N 2 diffusion and adsorption was analyzed. A sensitivity study was performed to investigate the effects of pressure, temperature and permeability on diffusion and adsorption in shale rocks. The results show that methane gas diffusion and adsorption in shale is a slow process of dynamic equilibrium, which can be illustrated by the slope of a curve in CH4mass variation. The amount of adsorption increases with the pressure increase at the low pressure, and the mass change by gas diffusion will decrease due to the decrease in the compressibility factor of the gas. With the elevated temperature, the gas molecules move faster and then the greater gas diffusion rates make the process duration shorter. The gas diffusion rate decreases with the permeability decrease, and there is a limit of gas diffusion if the permeability is less than 1.0×10 -15 m 2 . In conclusion, the results can provide insights for a better understanding of methane diffusion and adsorption in the shale rocks so as to optimize gas production performance of shale gas reservoirs.

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2016

Dissociative diffusion mechanism in vacancy-rich materials according to mass action kinetics

We conducted two sets of diffusion-reaction numerical simulations using a finite difference method (FDM) in order to investigate fast impurity diffusion via interstitial sites in vacancy-rich materials such as Cu(In,Ga)Se 2 (CIGS) and Cu 2 ZnSn(S, Se) 4 (CZTSSe or CZTS) via the dissociative diffusion mechanism where the interstitial diffuser ultimately reacts with a vacancy to produce a substitutional. The first set of simulations extends the standard interstitial-limited dissociative diffusion theory to vacancy-rich material conditions where vacancies are annihilated in large amounts, introducing non-equilibrium vacancy concentration profiles. The second simulation set explores the vacancy-limited dissociative diffusion where impurity incorporation increases the equilibrium vacancy concentration. In addition to diffusion profiles of varying concentrations and shapes that were obtained in all simulations, some of the profiles can be fitted with the constant- and limited-source solutions of Fick’s second law despite the non-equilibrium condition induced by the interstitial-vacancy reaction. The first set of simulations reveals that the dissociative diffusion coefficient in vacancy-rich materials is inversely proportional to the initial vacancy concentration. In the second set of numerical simulations, impurity-induced changes in the vacancy concentration lead to distinctive diffusion profile shapes. The simulation results are also compared with published data of impurity diffusion in CIGS. And according to the characteristic properties of diffusion profiles from the two set of simulations, experimental detection of the dissociative diffusion mechanism in vacancy-rich materials may be possible.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Simulation of fission gas diffusion in UO{sub 2} by vacancy clusters

The low solubility of fission gas in nuclear fuel leads to inter- and intra-granular bubbles. These bubbles affect performance of the fuel rod and increase the fuel temperature through the increase of porosity in the fuel pellets and decreased thermal conductivity across the pellet-clad gap as gas is released into the plenum. The nucleation, growth, and inter-connectivity of the fission gas bubbles ultimately depend on the diffusivity of gas atoms through the fuel matrix. Using mechanisms and data previously established from density functional theory (DFT) and empirical potential calculations, diffusion and reaction models have been derived for xenon atoms, uranium atoms, and vacancies in the substitutional and interstitial locations. Although similar to previous models, the diffusion and reaction rates have been re-derived in a more robust manner. Previous studies have under-predicted the experimentally observed diffusivity of xenon atoms in UO{sub 2}, however it has been previously shown that by including xenon atoms bound to two vacancies, the calculated diffusivity approaches the measured data. The derived model for species diffusion and inter-species reactions has been implemented in the MARMOT phase-field code in a modular structure so as to capture the enhanced diffusion of xenon due to bound gas + vacancy-cluster movement. The MARMOT code allows for the diffusion, reaction, and source rates to be solved simultaneously, resulting in steady state or transient concentrations of each species, and ultimately the diffusion behavior of xenon atoms. By including the diffusion of clusters of different combinations of xenon and vacancies, the calculated diffusivity more closely captures the measured diffusivity of xenon when using preliminary parameters. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

Diffusion and Flow of CO{sub 2} in Carbon Anode for Aluminium Smelting

Using a well-made carbon anode with the right porosity characteristics is essential to the successful operation of a Hall–Héroult cell. Bubble generation at this carbon anode and its contribution to the overall voltage drop in aluminum production holds significant potential for reducing overpotential and improving energy savings. This voltage drop is believed to be greatly influenced by the gas diffusion in the anode carbon, for which there are a limited number of measurements to correlate with the carbon anode properties. In the present study, the CO{sub 2} gas diffusion characteristics were first investigated via measuring anode porosity using mercury intrusion porosimetry (MIP) for different samples with different permeability. Second, diffusion experiments were conducted by flowing CO{sub 2} gas into the anode sample at elevated temperatures (up to 960 °C). The impact of temperature, average pore size, and permeability on the diffusion coefficient was investigated. The diffusion coefficient was consequently calculated by curve fitting using diffusion theories. The value obtained varied from 1.38 × 10{sup −6} to 7.89 × 10{sup −6} m{sup 2}/s. A high diffusion coefficient was measured in the carbon sample with larger average pore size and higher permeability. It was found that anomalous diffusion behavior in the temperature range 600 °C to 960 °C was caused by convective flow effects, different diffusion mechanisms, and the Boudouard reaction for these carbon anode samples. Furthermore, by plotting the measured diffusion coefficient against average pore size and permeability, an increasing trend of diffusivity with an increase in pore size and permeability was observed.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Diffusion coefficients of transition metals in fcc cobalt

Using first-principles density functional theory (DFT), we calculate the diffusivities of 32 different solute elements—all transition metals, together with Al and Si—in fcc cobalt within the formalism of the five-frequency model. For self-diffusion in fcc cobalt, we compare the accuracy of various approximations to the exchange-correlation energy functional of DFT in estimating the activation energy, and find that only the Perdew-Burke-Ernzerhof (PBE) approximation agrees well with experimental reports and all other functionals largely overestimate it. Our calculations also show that an accurate estimation of the self-diffusion coefficient requires explicit calculation of the effective jump frequency and vacancy formation entropy via phonons. Using accurate self-diffusion data and scaling all solute-related attempt frequencies with respect to the attempt frequency for self-diffusion using a simple relation involving the atomic mass and melting temperature of the solute yields solute diffusivities in excellent agreement with experiments, where such data is available. Additionally, we find that large solutes spontaneously relax toward the nearest neighbor vacancy to relieve the misfit strain, and the extent of this relaxation correlates negatively with the migration energy. Thus, in general, larger solutes have lower migration energies and diffuse faster than smaller solutes in fcc cobalt. However, extremely large solutes, e.g., group III elements Sc, Y, Lu, tend to be trapped in an energy valley located halfway toward the vacancy, and monovacancy mediated diffusion may no longer be valid in such cases. Finally, for all the solutes considered, we systematically tabulate the diffusion-related quantities calculated—diffusion prefactors, migration and activation energies—constructing an extensive and accurate first-principles database for solute diffusion in fcc cobalt.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Hydrogen Diffusion in Slit Pores: Role of Temperature, Pressure, Confinement, and Roughness

Diffusion of hydrogen (H 2 ) is important to understand the leakage risk and transport behavior for H 2 geologic storage. We applied molecular dynamics simulations to investigate the influencing factors of H2 diffusion in the slit pores of calcite, hematite, and quartz, owing to their abundance. It is revealed that the H2 self-diffusion coefficient increases with the temperature, regardless of the type of pore minerals. The diffusion of H 2 in the 20 nm slit pores falls into the bulk diffusion regime when the pressure is 10 MPa. The self-diffusion of H 2 decreases with pressure in all three types of slit pores, following a power law model with the exponents ranging from -0.825 to -0.964. Furthermore, the impact of confinement on H 2 diffusion is more pronounced for the slit pores with stronger interactions with H 2 -like calcite. The role of surface roughness in H 2 diffusion depends on the slit aperture. The rough surface enhances H 2 diffusion in the larger slit pores due to the enlarged effective pore space, whereas it weakens H 2 diffusion in the small slit pores due to stronger adsorption. These findings will fill the knowledge gap on the coupling effect of different factors influencing H 2 diffusion.

08 HYDROGEN↗