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Results for “Diffusion model”
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Understanding copper diffusion in CuInSe 2 with first-principles based atomistic and continuum models
We investigate the diffusion of copper in CuInSe 2 using thermodynamic and kinetic models based on density functional theory calculations, attempting to reconcile large differences in reported experimental diffusivities. We find that observations of rapid chemical diffusion can be explained by large thermodynamic factors, which we calculate using a compositionally constrained model of intrinsic point defect formation. We further characterize how copper diffusion coefficients depend on material synthesis conditions and exhibit their variation across the CuInSe 2 secondary phase diagram. In doing so, we identify stable off-stoichiometries that are dominated by either vacancy- or interstitial-mediated diffusion mechanisms. These results are employed in the development of a continuum reaction–diffusion model, which we use to simulate experimental depth profiles.
Bayesian uncertainty quantification of tristructural isotropic particle fuel silver release: Decomposing model inadequacy plus experimental noise and parametric uncertainties
Tristructural isotropic (TRISO) particle fuel is one of the most promising fuel concepts enabling high temperature and high burnup reactor operation. One dominant source of radioactivity released from the TRISO particles is silver (Ag), which is subject to a high release fraction and long decay life compared to other fission products. Previous modeling efforts using the fuel performance code BISON indicated nonnegligible uncertainties in modeling the diffusion process of fission products in TRISO compared to the Advanced Gas Reactor experiments. The overall uncertainties observed when modeling the fission product diffusion can result from uncertainties in model parameters, noisy experimental measurements, and deficiencies in the developed models. The three types of underlying uncertainties have not yet been properly quantified in open literature. Here, this paper presents the Bayesian uncertainty quantification (UQ) using massively parallelizable Markov chain Monte Carlo samplers. The uncertainties due to model parameters, model inadequacy, and experimental measurement noise are quantified, with the σ term used to represent the sum of the model inadequacy and measurement noise uncertainties. It is worth noting that this is the first time the σ term is inferred for nuclear fuel experiments, as compared to using prescribed values for uncertainty quantification in previous work. The parallelizable Markov chain Monte Carlo samplers efficiently infer the model parameters and the σ term, giving insight into physical parameters like diffusion coefficients and the combined model discrepancy and measurement noise. A subsequent forward uncertainty quantification (UQ) is also performed based on the calibration results to generate more accurate predictions of the Ag release. The model inadequacy plus experimental noise is the most dominant source of uncertainty compared to the parametric uncertainty. All the UQ analyses presented in this work are based on the second series of the irradiation experiments in the Advanced Gas Reactor program.
Analysis of transient fission gas behaviour in oxide fuel using BISON and TRANSURANUS
The modelling of fission gas behaviour is a crucial aspect of nuclear fuel analysis in view of the related effects on the thermo-mechanical performance of the fuel rod, which can be particularly significant during transients. Experimental observations indicate that substantial fission gas release (FGR) can occur on a small time scale during transients (burst release). To accurately reproduce the rapid kinetics of burst release in fuel performance calculations, a model that accounts for non-diffusional mechanisms such as fuel micro-cracking is needed. In this work, we present and assess a model for transient fission gas behaviour in oxide fuel, which is applied as an extension of diffusion-based models to allow for the burst release effect. The concept and governing equations of the model are presented, and the effect of the newly introduced parameters is evaluated through an analytic sensitivity analysis. Then, the model is assessed for application to integral fuel rod analysis. The approach that we take for model assessment involves implementation in two structurally different fuel performance codes, namely, BISON (multi-dimensional finite element code) and TRANSURANUS (1.5D semi-analytic code). The model is validated against 19 Light Water Reactor fuel rod irradiation experiments from the OECD/NEA IFPE (International Fuel Performance Experiments) database, all of which are simulated with both codes. The results point out an improvement in both the qualitative representation of the FGR kinetics and the quantitative predictions of integral fuel rod FGR, relative to the canonical, purely diffusion-based models, with both codes. The overall quantitative improvement of the FGR predictions in the two codes is comparable. Furthermore, calculated radial profiles of xenon concentration are investigated and compared to experimental data, demonstrating the representation of the underlying mechanisms of burst release by the new model.
Diffusive deposition of aerosols in Phebus containment during FPT-2 test
At present the lumped-parameter codes is the main tool to investigate the complex response of the containment of Nuclear Power Plant in case of an accident. Continuous development and validation of the codes is required to perform realistic investigation of the processes that determine the possible source term of radioactive products to the environment. Validation of the codes is based on the comparison of the calculated results with the measurements performed in experimental facilities. The most extensive experimental program to investigate fission product release from the molten fuel, transport through the cooling circuit and deposition in the containment is performed in PHEBUS test facility. Test FPT-2 performed in this facility is considered for analysis of processes taking place in containment. Earlier performed investigations using COCOSYS code showed that the code could be successfully used for analysis of thermal-hydraulic processes and deposition of aerosols, but there was also noticed that diffusive deposition on the vertical walls does not fit well with the measured results. In the CPA module of ASTEC code there is implemented different model for diffusive deposition, therefore the PHEBUS containment model was transferred from COCOSYS code to ASTEC-CPA to investigate the influence of the diffusive deposition modelling. Analysis was performed using PHEBUS containment model of 16 nodes. The calculated thermal-hydraulic parameters are in good agreement with measured results, which gives basis for realistic simulation of aerosol transport and deposition processes. Performed investigations showed that diffusive deposition model has influence on the aerosol deposition distribution on different surfaces in the test facility. (authors)
BF{sub 3} PIII modeling: Implantation, amorphisation and diffusion
In the race for highly doped ultra-shallow junctions (USJs) in complementary metal oxide semi-conductor (CMOS) technologies, plasma immersion ion implantation (PIII) is a promising alternative to traditional beamline implantation. Currently, no commercial technology computer aided design (TCAD) process simulator allows modeling the complete USJ fabrication process by PIII, including as-implanted dopant profiles, damage formation, dopant diffusion and activation. In this work, a full simulation of a p-type BF{sub 3} PIII USJ has been carried out. In order to investigate the various physical phenomena mentioned above, process conditions included a high energy/high dose case (10 kV, 5 Multiplication-Sign 10{sup 15} cm{sup -2}), specifically designed to increase damage formation, as well as more technology relevant implant conditions (0.5 kV) for comparison. All implanted samples were annealed at different temperatures and times. As implanted profiles for both boron and fluorine in BF{sub 3} implants were modeled and compared to Secondary Ion Mass Spectrometry (SIMS) measurements. Amorphous/crystalline (a/c) interface depths were measured by transmission electron microscopy (TEM) and successfully simulated. Diffused profiles simulations agreed with SIMS data at low thermal budgets. A boron peak behind the a/c interface was observed in all annealed SIMS profiles for the 10 kV case, indicating boron trapping from EOR defects in this region even after high thermal budgets. TEM measurements on the annealed samples showed an end of range (EOR) defects survival behind the a/c interface, including large dislocation loops (DLs) lying on (001) plane parallel to the surface. In the last part of this work, activation simulations were compared to Hall measurements and confirmed the need to develop a (001) large BICs model.
A fully coupled 3D transport model in SPH for multi-species reaction-diffusion systems
Abstract—In this paper we present a fully generalized transport model for multiple species in complex two and threedimensional geometries. Based on previous work [1] we have extended our interfacial reaction-diffusion model to handle arbitrary numbers of species allowing for coupled reaction models. Each species is tracked independently and we consider different physics of a species with respect to the bulk phases in contact. We use our SPH model to simulate the reaction-diffusion problem on a pore-scale level of a solid oxide fuel cell (SOFC) with special emphasize on the effect of surface diffusion.
Detailed numerical investigation of the Bohm limit in cosmic ray diffusion theory
A standard model in cosmic ray diffusion theory is the so-called Bohm limit in which the particle mean free path is assumed to be equal to the Larmor radius. This type of diffusion is often employed to model the propagation and acceleration of energetic particles. However, recent analytical and numerical work has shown that standard Bohm diffusion is not realistic. In the present paper, we perform test-particle simulations to explore particle diffusion in the strong turbulence limit in which the wave field is much stronger than the mean magnetic field. We show that there is indeed a lower limit of the particle mean free path along the mean field. In this limit, the mean free path is directly proportional to the unperturbed Larmor radius like in the traditional Bohm limit, but it is reduced by the factor δB/B {sub 0} where B {sub 0} is the mean field and δB the turbulent field. Although we focus on parallel diffusion, we also explore diffusion across the mean field in the strong turbulence limit.
A Robust Numerical Treatment of Solid-Phase Diffusion in Pseudo Two-Dimensional Lithium-Ion Battery Models
Solid-phase diffusion in active materials of lithium-ion batteries significantly affects charging and safety-related behavior of lithium-ion batteries. Therefore, it is essential to develop an efficient and robust numerical algorithm for solving solid-phase diffusion equations in physics-based battery models. In this work, we discuss the origins of numerical instabilities that can occur when solving the solid-phase diffusion equations using iterative methods. Then, in order to resolve such issues, we propose a simple numerical treatment to the surface flux term of discretized solid-phase diffusion equations. To demonstrate its numerical robustness, the proposed method is implemented into a pseudo two-dimensional (P2D) physics-based battery model and simulations are conducted at wide ranges of operating conditions. Even with extremely poor initial guesses for the Li+ concentrations of the active materials, computations using the proposed method do not diverge and the their computational speeds are comparable to those with conventional initial guesses. Comprehensive tests of the proposed method are also performed with a dynamic current profile based on US06 driving profile and a multi-stage charging profile with very high initial C-rate (12C).
Predicting Effective Diffusion Coefficients in Mudrocks Using a Fractal Model and Small-Angle Neutron Scattering Measurements
The determination of effective diffusion coefficients of gases or solutes in the water–saturated pore space of mudrocks is time consuming and technically challenging. Yet, reliable values of effective diffusion coefficients are important to predict migration of hydrocarbon gases in unconventional reservoirs, dissipation of (explosive) gases through clay barriers in radioactive waste repositories, mineral alteration of seals to geological CO 2 storage reservoirs and contaminant migration through aquitards. In this study, small angle and very small angle neutron scattering techniques have been utilized to determine a range of transport properties in mudrocks, including porosity, pore size distributions and surface and volume fractal dimensions of pores and grains, from which diffusive transport parameters can be estimated. Using a fractal model derived from Archie's Law, we calculate effective diffusion coefficients from these parameters and compare them to laboratory–derived effective diffusion coefficients for CO 2 , H 2 , CH 4 and HTO on either the same or related mudrock samples. The samples include Opalinus Shale from the underground laboratory in Mont Terri, Switzerland; Boom Clay from a core drilled in Mol, Belgium and a marine claystone cored in Utah, USA. The predicted values were compared to laboratory diffusion measurements. The measured and modeled diffusion coefficients show good agreement, differing generally by less than factor 5. Furthermore, neutron or X–ray scattering analysis is therefore proposed as a novel method for fast, accurate estimation of effective diffusion coefficients in mudrocks, together with simultaneous measurement of multiple transport parameters including porosity, pore size distributions and surface areas, important for (reactive) transport modelling.
Cascade annealing simulations of bcc iron using object kinetic Monte Carlo
Simulations of displacement cascade annealing were carried out using object kinetic Monte Carlo based on an extensive MD database including various primary knock-on atom energies and directions. The sensitivity of the results to a broad range of material and model parameters was examined. The diffusion mechanism of interstitial clusters has been identified to have the most significant impact on the fraction of stable interstitials that escape the cascade region. The maximum level of recombination was observed for the limiting case in which all interstitial clusters exhibit 3D random walk diffusion. The OKMC model was parameterized using two alternative sets of defect migration and binding energies, one from ab initio calculations and the second from an empirical potential. The two sets of data predict essentially the same fraction of surviving defects but different times associated with the defect escape processes. This study provides a comprehensive picture of the first phase of long-term defect evolution in bcc iron and generates information that can be used as input data for mean field rate theory (MFRT) to predict the microstructure evolution of materials under irradiation. In addition, the limitations of the current OKMC model are discussed and a potential way to overcome these limitations is outlined.
The influence of hydrothermal temperature and time toward crystallinity of zeolite X supported on glass wool for CO{sub 2} adsorption
In this study, the influence of hydrothermal temperature and time at zeolite X supported on glasswool were investigated. The results of characterization using XRD showed that a single phase zeolite X with highest crystallinity was obtained when hydrothermal temperature and time at 100°C during 24 hours (ZXF100-24H). The CO{sub 2} adsorption capacity of ZXF100-24H has reached up to 10.15 wt. %. Kinetics of CO{sub 2} adsorption onto zeolite X supported on glasswool was investigated using pseudo-first-order, pseudo-second-order and intra-particle diffusion kinetic models. After evaluating three kinetic models for CO{sub 2} adsorption at adsorption temperatures of 30°C, 40°C and 50°C, it was found that intra-particle diffusion kinetic model provided the best fitting for the adsorption data. Furthermore, the thermodynamic parameters of CO{sub 2} adsorption were obtained as follows, Gibbs free energy change (ΔG°) are −0.409 kJ/mol at 30°C, −0.274 kJ/mol at 40°C and −0.138 kJ/mol at 50 °C, whereas the enthalpy change (ΔH°) is −4.53 kJ/mol and the entropy change (ΔS°) is −0.0135 kJ/(mol K).
Assessment of model assumptions and budget terms of the unsteady flamelet equations for a turbulent reacting jet-in-cross-flow
An a priori analysis of the flamelet model for diffusion flames is conducted to systematically assess model assumptions that are associated with the asymptotic expansion, the omission of higher-order expansion terms, the consideration of preferential diffusion effects, and the one-dimensional flamelet representation. For this, a recent direct numerical simulation database of a reacting hydrogen/air jet-in-cross-flow (JICF) by Grout et al. [15,16] is used. The full flamelet equation for temperature, exact to the order of the Eulerian transport equation and general to different definitions of the mixture fraction, is derived. Analysis of mixture fraction conditioned profiles of temperature and scalar dissipation rate along the jet trajectory identified different ignition and flame stabilization scenarios on the windward and leeward sides of the reacting JICF. A balance analysis of the temperature flamelet equation is conducted to quantify contributions in flame-aligned and flame-orthogonal directions. Consistent with the flamelet assumption, it is shown that terms arising from scalar diffusion, heat-release, and species-diffusion-induced enthalpy flux are the dominant contributions, while the flame-aligned preferential diffusion promotes entrainment of heat into the flamelet structure. Finally, for the current JICF-configuration, it is found that contributions along the flame-orthogonal direction are on average negligible.
Using a coupled dispersion model to estimate depletion of a tritium oxide plume by a forest
Tritium processing facilities may release tritium oxide (HTO) to the atmosphere which poses potential health risks to exposed co-located workers and to offsite individuals. Most radiological consequence analyses determine HTO dose by applying Gaussian plume models to simulate the transport of HTO. Within these models, deposition velocity is used to assess the sum of all deposition processes acting on the plume. While this may account for vegetative and soil uptake or respiration processes, it may currently lack inclusion of the complex interactions within heterogeneous forested environments. In this complex morphology, dispersion patterns are significantly altered by changing flow regimes above and below the forest canopy and by the transfer of plume material across the canopy boundary. To determine the effects of a heterogeneous forest canopy on an airborne HTO plume, a Gaussian plume model coupled with an advection-diffusion plume model was applied to estimate transport in the free atmosphere above the forest and within the forest canopy and understory. During 2012, wind speed and wind direction measurements taken at 5 heights, ranging from 2-m to 28-m, on an instrumented meteorological tower located in a loblolly pine forest at the Department of Energy (DOE) Savannah River Site (SRS), near Aiken, SC. From these measurements, model predictions were made over a full spectrum of meteorological conditions. Deposition and resuspension velocities were calculated based on the model-predicted flux of plume material across the top of the forest canopy. Additionally, net deposition velocity of the plume material was calculated as the difference between the deposition and resuspension velocities. The 1st and 5th percentile net deposition velocities were estimated to be 0.7 cm s-1 and 1.2 cm s-1, respectively.
Modeling of a 43 GHz microplasma within a photonic crystal
The electron density (n e ) and argon metastable density (1 s 5 ) of a 43GHz microplasma are obtained using the zero-dimensional plasma kinetics solver (ZDPlasKin®) for an incident power of 160 and 1000mW and argon pressures of 10–600Torr (1.3 ×10 3 to 8.0 × 10 4 Pa). These simulations are compared with previously published experimental data. To determine the self-consistent electric field in the modeled plasma, the three-dimensional millimeter wave fields are computed as a function of electron density using ANSYS EM19.2, HFSS®. This electromagnetic field model is coupled to ZDPlasKin such that any increase in the simulated plasma density correctly attenuates the simulated electric field within the microplasma. The electron density is found to be sensitive to argon gas temperature, so a two-zone temperature model was needed to obtain agreement with experimental measurements. The temperature in the central core of the microplasma was determined by a previous experimental study. That temperature was used as an input to the model for the simulation of volume recombination losses. The outer regions of the microplasma are assumed to be in equilibrium with the walls (300K). This second temperature was used in the model to determine diffusion losses. The modeled electron and metastable densities are of the order 10 20 and 10 18 m –3 , respectively. This is in good agreement with those measured experimentally as long as the two-zone temperature model is used. In the absence of a hot gas core, the modeled three-body recombination rates are excessive and the simulation severely under-predicts the electron density and over-estimates the metastable density. We conclude that the millimeter wave microplasma has a hot core (2500K at 600 Torr) that rarifies the argon gas and effectively reduces three-body recombination. Furthermore, this allows one to achieve high electron density on the order of 10 20 m –3 with only 100mW of wave power.
Ag Transport Through Non-Irradiated and Irradiated SiC
Silicon carbide is the main barrier to diffusion of fission products in the current design of TRistuctural ISOtropic (TRISO) coated fuel particles, and Ag is one of the few fission products that have been shown to escape through this barrier. Because the SiC coating in TRISO is exposed to radiation throughout the lifetime of the fuel, understanding of how radiation changes the transport of the fission products is essential for the safety of the reactor. The goals of this project are: (i) to determine whether observed variation in integral release measurements of Ag through SiC can be explained by differences in grain size and grain boundary (GB) types among the samples; (2) to identify the effects of irradiation on diffusion of Ag through SiC; (3) to discover phenomena responsible for significant solubility of Ag in polycrystalline SiC. To address these goals, we combined experimental analysis of SiC diffusion couples with modeling studies of diffusion mechanisms through bulk and GBs of this material. Comparison between results obtained for pristine and irradiated samples brings in insights into the effects of radiation on Ag transport.
Modeling of fission gas diffusion and release for Gd 2 O 3 doped UO 2
Uranium dioxide (UO 2 ) is the primary nuclear fuel in light water reactors, and its excess neutronic reactivity can be controlled by adding burnable absorbers, such as Gd 2 O 3 . This burnable absorber has a large neutron absorption cross-section, lowering the high reactivity of the reactor's initial fuel load. However, there needs to be more understanding of how added Gd 2 O 3 influences the properties of UO 2 under irradiation. To understand the behavior of defects and fission gas in the UO 2 /Gd 2 O 3 system under irradiation, we use cluster dynamics modeling supported by density functional theory calculations. First, we calculate the formation energies of Gd point and cluster defects, and evaluate the temperature-dependent defect concentrations using the defect formation energies and entropies. We show that Gd is soluble in UO 2 , introducing a negative charge in the system. Using this information, we adapted the cluster dynamics code Centipede to model the influence of Gd on U self-diffusion and Xe diffusion in UO 2 with 10 wt% Gd 2 O 3 . Also, we analyzed the Xe diffusion as a function of Gd 2 O 3 concentration, showing that the Xe diffusivity is decreased, which means that the athermal diffusivity due to electronic stopping persists at higher temperatures. In conclusion, the decrease in Xe diffusion means that more Xe stays in the matrix, decreasing the Xe release, and lowering its influence of fission gas release on the thermomechanical properties of UO 2 .
Pathologic Validation of a Model Based on Diffusion-Weighted Imaging and Dynamic Contrast-Enhanced Magnetic Resonance Imaging for Tumor Delineation in the Prostate Peripheral Zone
Purpose: For focal boost strategies in the prostate, the robustness of magnetic resonance imaging-based tumor delineations needs to be improved. To this end we developed a statistical model that predicts tumor presence on a voxel level (2.5 Multiplication-Sign 2.5 Multiplication-Sign 2.5 mm3) inside the peripheral zone. Furthermore, we show how this model can be used to derive a valuable input for radiotherapy treatment planning. Methods and Materials: The model was created on 87 radiotherapy patients. For the validation of the voxelwise performance of the model, an independent group of 12 prostatectomy patients was used. After model validation, the model was stratified to create three different risk levels for tumor presence: gross tumor volume (GTV), high-risk clinical target volume (CTV), and low-risk CTV. Results: The model gave an area under the receiver operating characteristic curve of 0.70 for the prediction of tumor presence in the prostatectomy group. When the registration error between magnetic resonance images and pathologic delineation was taken into account, the area under the curve further improved to 0.89. We propose that model outcome values with a high positive predictive value can be used to define the GTV. Model outcome values with a high negative predictive value can be used to define low-risk CTV regions. The intermediate outcome values can be used to define a high-risk CTV. Conclusions: We developed a logistic regression with a high diagnostic performance for voxelwise prediction of tumor presence. The model output can be used to define different risk levels for tumor presence, which in turn could serve as an input for dose planning. In this way the robustness of tumor delineations for focal boost therapy can be greatly improved.