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Propagation Failure in Discrete Inhomogeneous Media Using a Caricature of the Cubic
Title
Propagation Failure in Discrete Inhomogeneous Media Using a Caricature of the Cubic.
Creator
Lydon, Elizabeth, Moore, Brian, Choudhury, Sudipto, Kaup, David, University of Central Florida
Abstract / Description
Spatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle- rosis. We construct steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison formula we de- rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain...
Show moreSpatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle- rosis. We construct steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison formula we de- rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain conditions outlined in their construction. The range of parameter values that satisfy these conditions constitutes the interval of propagation failure, determining under what circumstances a front becomes pinned in the media. Our exact solutions represent a very specific solution to the spatially discrete Nagumo equation. For example, we only consider inhomogeneous media with one defect present. We created an original script in MATLAB which algorithmically solves more general cases of the equation, including the case for multiple defects. The algorithmic solutions are then compared to known exact solutions to determine their validity.
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Date Issued
2015
Identifier
CFE0005831, ucf:50903
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005831
Diffusion and reaction in selected uranium alloy system
Title
Diffusion and reaction in selected uranium alloy system.
Creator
Huang, Ke, Sohn, Yongho, An, Linan, Xu, Chengying, Coffey, Kevin, Heinrich, Helge, University of Central Florida
Abstract / Description
U-Mo metallic fuels with Al alloys as the matrix/cladding are being developed as low enriched uranium fuels under the Reduced Enrichment for Research and Test Reactor (RERTR) program. Significant interactions have been observed to occur between the U-Mo fuel and the Al alloy during fuel processing and irradiation. U-Zr metallic fuels with stainless steel claddings have been developed for the generation IV sodium fast reactor (SFR). The fuel cladding chemical interaction (FCCI) induced by the...
Show moreU-Mo metallic fuels with Al alloys as the matrix/cladding are being developed as low enriched uranium fuels under the Reduced Enrichment for Research and Test Reactor (RERTR) program. Significant interactions have been observed to occur between the U-Mo fuel and the Al alloy during fuel processing and irradiation. U-Zr metallic fuels with stainless steel claddings have been developed for the generation IV sodium fast reactor (SFR). The fuel cladding chemical interaction (FCCI) induced by the interdiffusion of components was also observed. These interactions induce deleterious effects on the fuel system, such as thinning of the cladding layer, formation of phases with undesirable properties, and thermal cracking due to thermal expansion mismatches and changes in molar volume. The interaction between the fuel and the cladding involves multi-component interdiffusion. To determine the ternary interdiffusion coefficients using a single diffusion couple, a new method based on regression via the matrix transformation approach is proposed in this study. This new method is clear in physical meaning and simple in mathematical calculation. The reliability and accuracy of this method have been evaluated through application to three case studies: a basic asymptotic concentration profile, a concentration profile with extrema and a smoothed concentration profile with noise. Generally, this new method works well in all three cases.In order to investigate the interdiffusion behavior in U-Mo alloys, U vs. Mo diffusion couples were assembled and annealed in the temperature range of 650 to 1000(&)deg;C. The interdiffusion microstructures and concentration profiles were examined via scanning electron microscopy (SEM) and electron probe microanalysis (EPMA), respectively. Interdiffusion coefficients and activation energies were calculated as functions of temperature and Mo composition. The intrinsic diffusion coefficients of U and Mo at the marker composition were also determined. The activity of U and the thermodynamic factor of the U-Mo alloy have been calculated using the ideal solution, the regular solution, and the subregular solution models based on the molar excess Gibbs free energy of the U-Mo alloy. The calculated intrinsic diffusivities of U and Mo along with the thermodynamic factor of the U-Mo alloy were employed to estimate the atomic mobilities and the vacancy wind effects of U and Mo according to Manning's description.To explore potential diffusion barrier materials for reducing the fuel cladding chemical interaction between the U-Mo fuel and the Al alloy matrix/cladding, the interdiffusion behavior between U-Mo alloys and Mo, Zr, Nb and Mg were systematically studied. U-10wt.%Mo vs. Mo, Zr and Nb diffusion couples were annealed in the temperature range from 600 to 1000(&)deg;C. A diffusion couple between U-7wt.%Mo and Mg was annealed at 550(&)deg;C for 96 hours. SEM and transmission electron microscopy (TEM) were applied to characterize the microstructure of the interdiffusion zone. X-ray energy dispersive spectroscopy (XEDS) and EPMA were utilized to examine the concentration redistribution and the phase constituents. For the U-Mo vs. Mo diffusion couples, the interdiffusion coefficients at high Mo concentrations ranging from 22 to 32 at.%Mo were determined for the first time. In the U-Mo vs. Zr diffusion couples, the Mo2Zr phase was found at the interface. The diffusion paths were estimated and investigated according to the Mo-U-Zr ternary phase diagram. Thermal cracks and pure U precipitates were found within the diffusion zone in the U-Mo vs. Nb system. The growth rate of the interdiffusion zone was found to be lower by about 103 times for Zr, 105 times for Mo and 106 times for Nb compared to those observed in the U-10wt.%Mo vs. Al or Al-Si systems. For the diffusion couple of U-Mo vs. Mg, the U-Mo was bonded very well to the Mg and there was negligible diffusion observed even after 96 hours annealing at 550(&)deg;C.For a more fundamental understanding of the complex diffusion behavior between U-Zr fuels and their stainless steel claddings, U vs. Fe, Fe-15wt.%Cr and Fe-15wt.%Cr-15wt.%Ni diffusion couples were examined to investigate the interdiffusion behaviors between U and Fe and the effects of the alloying elements Cr and Ni. The diffusion couples were annealed in the temperature range from 580 to 700(&)deg;C for various times. Two intermetallic phases, U6Fe and UFe2, developed in all of the diffusion couples with the U6Fe layer growing faster than the UFe2 layer. For the diffusion couples of U vs. Fe, extrinsic growth constants, intrinsic growth constants, integrated interdiffusion coefficients and activation energies in each phase were calculated. The results suggest that U6Fe impeded the growth of UFe2, and the boundary condition change caused by the allotropic transformation of U played a role in the growth of the U6Fe and UFe2 layers. The reasons why U6Fe grew much faster than UFe2 are also discussed. The additions of Cr and Ni into Fe affected the growth rates of U6Fe and UFe2. The solubility of Cr and Ni in U6Fe and UFe2 were determined, and it was found that Cr diffused into U more slowly than Fe or Ni.
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Date Issued
2012
Identifier
CFE0004548, ucf:49238
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004548
Theoretical And Computational Studies Of Diffusion Of Adatom Islands And Reactions Of Molecules On Surfaces
Title
Theoretical And Computational Studies Of Diffusion Of Adatom Islands And Reactions Of Molecules On Surfaces.
Creator
Shah, Syed Islamuddin, Rahman, Talat, Kara, Abdelkader, Schelling, Patrick, Coffey, Kevin, University of Central Florida
Abstract / Description
The work presented in this dissertation focuses on the study of post deposition spatial and temporal evolution of adatom islands and molecules on surfaces using ab initio and semiemperical methods. It is a microscopic study of the phenomena of diffusion and reaction on nanostructured surfaces for which we have developed appropriate computational tools,as well as implemented others that are available. To map out the potential energy surface on which the adatom islands and molecules move, we...
Show moreThe work presented in this dissertation focuses on the study of post deposition spatial and temporal evolution of adatom islands and molecules on surfaces using ab initio and semiemperical methods. It is a microscopic study of the phenomena of diffusion and reaction on nanostructured surfaces for which we have developed appropriate computational tools,as well as implemented others that are available. To map out the potential energy surface on which the adatom islands and molecules move, we have carried out ab initio electronic structure calculations based on density functional theory (DFT) for selected systems. For others, we have relied on semiempirical interatomic potentials derived from the embedded atom method. To calculate the activation energy barriers, we have employed the (")drag(") method in most cases and verified its reliability by employing the more accurate nudged elastic band method for selected systems. Temporal and spatial evolution of the systems of interest have been calculated using the kinetic Monte Carlo (KMC), or the more accurate (complete) Self Learning kinetic Monte Carlo (SLKMC) method in the majority of cases, and ab initio molecular dynamics simulations in others. We have significantly enhanced the range of applicability of the SLKMC method by introducing a new pattern recognitionscheme which by allowing occupancy of the (")fcc(") and (")hcp(") sites (and inclusion of (")top(") site in the pattern recognition as well) is capable of simulating the morphological evolution of three dimensional adatom islands, a feature not feasible via the earlier - proposed SLKMC method. Using SLKMC (which allows only fcc site occupancy on fcc(111) surface), our results of the coarsening of Ag islands on the Ag(111) surface show that during early stages, coarsening proceeds as a sequence of selected island sizes, creating peaks and valleys in the island-size distribution. This island size selectivity is independent of initial conditions andresults from the formation of kinetically stable islands for certain sizes as dictated by the relative energetics of edge atom detachment/attachment processes together with the large activation barrier for kink detachment.On applying the new method, SLKMC-II, to examine the self diffusion of smalladatom islands (1-10 atoms) of Cu on Cu(111), Ag on Ag(111) and Ni on Ni(111), wefind that for the case of Cu and Ni islands, diffusion is dominated by concerted processes(motion of island as a whole), whereas in the case of Ag, islands of size 2-9 atoms diffusethrough concerted motion whereas the 10-atom island diffuses through single atom processes.Effective energy barriers for the self diffusion of these small Cu islands is 0.045 eV/atom,for Ni it is 0.060 eV/atom and for Ag it is 0.049 eV/atom, increasing almost linearly withisland size.Application of DFT based techniques have allowed us to address a few issues stemmingfrom experimental observations on the effect of adsorbates such as CO on the structure and stability of bimetallic systems (nanoparticles and surfaces). Total energy calculationsof Ni-Au nanoparticles show Ni atoms to prefer to be in the interior of the nanoparticle.CO molecules, however, prefer to bind to a Ni atom if present on the surface. Using abinitio molecular dynamics simulations, we confirm that the presence of CO molecule induces diffusion of Ni atom from the core of the Ni-Au nanoparticle to its surface, making the nanoparticle more reactive. These results which help explain a set of experimental data are rationalized through charge transfer analysis.Similar to the case of Ni-Au system, it is found that methoxy (CH$_{3}$O) may also induce diffusion of inner atoms to the surface on bimetallic Au-Pt systems. Our total energy DFT calculations show that it is more favorable for methoxy to bind to a Pt atom in the top Au layer than to a Au atom in Au-Pt system thereby explaining experimental observations.To understand questions related to the dependence of product selectivity on ambientpressure for ammonia decomposition on RuO2(110), we have carried out an extensivecalculation of the reaction pathways and energy barriers for a large number of intermediate products. On combining the reaction energetics from DFT, with KMC simulations, we showthat under UHV conditions, selectivity switches from N2 ( ? 100 % selectivity) at T = 373Kto NO at T = 630K, whereas under ambient conditions, N2 is still the dominant productbut maximum selectivity is only 60%. An analysis based on thermodynamics alone shows a contradiction between experimental data at UHV with those under ambient pressure. Ourcalculations of the reaction rates which are essential for KMC simulations removes this apparentinconsistency and stresses the need to incorporate kinetics of processes in order toextract information on reaction selectivity.
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Date Issued
2013
Identifier
CFE0005254, ucf:50584
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005254
From Excited Charge Dynamics to Cluster Diffusion: Development and Application of Techniques Beyond DFT and KMC
Title
From Excited Charge Dynamics to Cluster Diffusion: Development and Application of Techniques Beyond DFT and KMC.
Creator
Acharya, Shree Ram, Rahman, Talat, Chow, Lee, Stolbov, Sergey, Wu, Annie, University of Central Florida
Abstract / Description
This dissertation focuses on developing reliable and accurate computational techniques which enable the examination of static and dynamic properties of various activated phenomena using deterministic and stochastic approaches. To explore ultrafast electron dynamics in materials with strong electron-electron correlation, under the influence of a laser pulse, an ab initio electronic structure method based on time-dependent density functional theory (TDDFT) in combination with dynamical mean...
Show moreThis dissertation focuses on developing reliable and accurate computational techniques which enable the examination of static and dynamic properties of various activated phenomena using deterministic and stochastic approaches. To explore ultrafast electron dynamics in materials with strong electron-electron correlation, under the influence of a laser pulse, an ab initio electronic structure method based on time-dependent density functional theory (TDDFT) in combination with dynamical mean field theory (DMFT) is developed and applied to: 1) single-band Hubbard model; 2) multi-band metal Ni; and 3) multi-band insulator MnO. The ultrafast demagnetization in Ni reveal the importance of memory and correlation effects, leading to much better agreement with experimental data than previously obtained, while for MnO the main channels of charge response are identified. Furthermore, an analytical form of the exchange-correlation kernel is obtained for future applications, saving tremendous computational cost. In another project, size-dependent temporal and spatial evolution of homo- and hetero-epitaxial adatom islands on fcc(111) transition metals surfaces are investigated using the self-learning kinetic Monte Carlo (SLKMC) method that explores long-time dynamics unbiased by apriori selected diffusion processes. Novel multi-atom diffusion processes are revealed. Trends in the diffusion coefficients point to the relative role of adatom lateral interaction and island-substrate binding energy in determining island diffusivity. Moreover, analysis of the large data-base of the activation energy barriers generated for multitude of diffusion processes for variety of systems allows extraction of a set of descriptors that in turn generate predictive models for energy barrier evaluation. Finally, the kinetics of the industrially important methanol partial oxidation reaction on a model nanocatalyst is explored using KMC supplemented by DFT energetics. Calculated thermodynamics explores the active surface sites for reaction components including different intermediates and energetics of competing probable reaction pathways, while kinetic study attends to the selectivity of products and its variation with external factors.
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Date Issued
2018
Identifier
CFE0006965, ucf:52910
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0006965
INTERDIFFUSION BEHAVIOR OF U-MO ALLOYS IN CONTACT WITH AL AND AL-SI ALLOYS
Title
INTERDIFFUSION BEHAVIOR OF U-MO ALLOYS IN CONTACT WITH AL AND AL-SI ALLOYS.
Creator
Perez, Emmanuel, Sohn, Yong-Ho, University of Central Florida
Abstract / Description
U-Mo dispersion and monolithic fuels embedded in Al-alloy matrix are under development to fulfill the requirements of research reactors to use low-enriched molybdenum stabilized uranium alloys as fuels. The system under consideration in this study consisted of body centered cubic (gamma) U-Mo alloys embedded in an Al structural matrix. Significant interaction has been observed to take place between the U-Mo fuel and the Al matrix during manufacturing of the fuel-plate system assembly and...
Show moreU-Mo dispersion and monolithic fuels embedded in Al-alloy matrix are under development to fulfill the requirements of research reactors to use low-enriched molybdenum stabilized uranium alloys as fuels. The system under consideration in this study consisted of body centered cubic (gamma) U-Mo alloys embedded in an Al structural matrix. Significant interaction has been observed to take place between the U-Mo fuel and the Al matrix during manufacturing of the fuel-plate system assembly and during irradiation in reactors. These interactions produce Al-rich phases with physical and thermal properties that adversely affect the performance of the fuel system and can lead to premature failure. In this study, interdiffusion and microstructural development in the U-Mo vs. Al system was examined using solid-to-solid diffusion couples consisting of U-7wt.%Mo, U-10wt.%Mo and U-12wt.%Mo vs. pure Al, annealed at 600°C for 24 hours. The influence of Si alloying addition (up to 5 wt.%) in Al on the interdiffusion microstructural development was also examined using solid-to-solid diffusion couples consisting of U-7wt.%Mo, U-10wt.%Mo and U-12wt.%Mo vs. pure Al, Al-2wt.%Si, and Al-5wt.%Si annealed at 550°C for 1, 5 and 20 hours. To further clarify the diffusional behavior in the U-Mo-Al and U-Mo-Al-Si systems, Al-rich 85.7Al-11.44U-2.86Mo, 87.5Al-10U-2.5Mo, 56.1Al-18.9Si-21.9U-3.1Mo and 69.3Al-11.9Si-18.8U (at.%) alloys were cast and homogenized at 500°C to determine the equilibrium phases of the system. Scanning electron microscopy (SEM), transmission electron microscopy (TEM) and electron probe microanalysis (EPMA) and X-ray diffraction (XRD) were employed to examine the phase development in the diffusion couples and the cast alloys. In ternary U-Mo-Al diffusion couples annealed at 600°C for 24 hours, the interdiffusion microstructure consisted of finely dispersed UAl3, UAl4, U6Mo4Al43, and UMo2Al20 phases while the average composition throughout the interdiffusion zone remained constant at approximately 80 at.% Al. The interdiffusion microstructures observed by EPMA, SEM and TEM analyses were correlated to explain the observed morphological development in the interdiffusion zones. The concept of thermodynamic degrees of freedom was used to justify that, although deviations are apparent, the interdiffusion zones did not significantly deviate from an equilibrium condition in order for the observed microstructures to develop. Selected diffusion couples developed periodic bands within the interdiffusion zone as sub-layers in the three-phase regions. Observation of periodic banding was utilized to augment the hypothesis that internal stresses play a significant role in the phase development and evolution of U-Mo vs. pure Al diffusion couples. The addition of Si (up to 5 wt.%) to the Al significantly reduced the growth rate of the interdiffusion zone. The constituent phases and composition within the interdiffusion zone were also modified. When Si was present in the Al terminal alloys, the interdiffusion zones developed layered morphologies with fine distributions of the (U,Mo)(Al,Si)3 and UMo2Al20 phases. The U6Mo4Al43 phase was observed scarcely in Si depleted regions within the interdiffusion zone. The phase development and evolution of the interdiffusion zone was described in terms of thermodynamic degrees of freedom with minimal deviations from equilibrium.
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Date Issued
2011
Identifier
CFE0003747, ucf:48778
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0003747