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Causal electric charge diffusion and balance functions in relativistic heavy-ion collisions
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Quantal diffusion description of multinucleon transfers in heavy-ion collisions
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Diffuse Growth of Plant Cell Walls
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On the Diffuse Structure of the Toluene-Water Interface
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Temperature-dependent diffuse reflectance spectroscopy of plasma-sprayed Cr-doped α-alumina using supercontinuum laser illumination and CO_2 laser heating
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Supercontinuum-laser diffuse reflectance spectroscopy in conjunction with an extended Kubelka–Munk model—a methodology for determination of temperature-dependent quantum efficiency in highly scattering and fluorescent media
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Development of Planar PyC/SiC Diffusion Couples to Investigate Irradiation Effects and Microstructural Variation on Fission Product Diffusion
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3D-printed electrode, gas diffusion electrode (GDE) and gas diffusion layer (GDL) for fuel cell applications
An electrocatalytically active ink composition is used with an additive manufacturing process, such as 3D printing, to produce electrodes having consistent, adaptable, and high surface area structures. The electrocatalytically active ink composition includes a mixed powdered precursor and a polymer matrix. The mixed powdered precursor includes a carbon source, a dopant source, and/or a metal-containing catalyst. The material and electrochemical properties of the ink composition may facilitate 3D printing of electrochemically active electrodes for energy conversion and storage devices, and may allow fine-tuning of macro- and microstructures to develop electrodes having improved activity and efficiency.
Kinetic Monte Carlo Simulation of Hydrogen Diffusion in Tungsten
Nuclear fusion is considered as the most promising sustainable energy source. If achieved, it could provide electricity to the mankind for millions of years. During the reaction, the fusion ash is continuously removed from the magnetic gap, the divertor region, and the divertor facing component is subjected to intense plasma bombardment. It is proposed to use tungsten as the divertor facing material, because it has low physical sputtering yield and superior thermomechanical properties. However, the high mobility of hydrogen in tungsten and the high bombardment flux bring the hydrogen isotopes deep into the tungsten tile. The presence of hydrogen in tungsten tends to weaken the gram boundaries and produce surface blistering. The ejection of tungsten particulates into the plasma core will cool the reaction and cease the fusion reactions. Therefore, it is important to have a detailed understanding of the hydrogen diffusion in tungsten bulk. The KMC method is a stochastic computer simulation to predict the time evolution of a certain system. Typically, at a given time, the system will evolve through a few possible paths with known probabilities. In each step, the KMC method analyzes the entire system and randomly determines the system evolving events based on all transition rates of all possible events and advance the physical time. This process is repeated till the simulation of the entire physical time is completed. In previous work, the authors developed a kinetic Monte Carlo (KMC) algorithm and program to simulate hydrogen diffusion process on tungsten reconstructed surface. In this article, this KMC method is extended to model the hydrogen diffusion in tungsten bulk. The diffusion coefficients are calculated and fitted to the Arrhenius equation. The result matches the experiment measurement very well. KMC diffusion simulation needs the locations of the hydrogen trapping sites, diffusion paths and the corresponding diffusion energy barriers. The hydrogen interstitial sites in tungsten crystal have been thoroughly studied by density function theory (DFT) and molecular dynamics (MD). Johnson and Carter used DFT to determine the preferred location of the hydrogen interstitial sites m tungsten crystal, which are the tetrahedral sites (T-sites) in body-centered-cubic (bcc) lattice surfaces. All T-sites are located on the surfaces of a lattice cell. There are four T-sites per surface and twelve T-sites per lattice cell. The hydrogen atoms diffuse by traveling from one T-site to one of its nearest four T-site neighbors. Thus, each T-site is surrounded by two neighbors on the same surface, and one neighbor on each of the two adjacent surfaces perpendicular to the surface holding the center T-site. The diffusion barrier between two neighboring T-sites was calculated to be 0.38 eV. Knowing the diffusion path, energy barrier, and the crystal structure, the KMC simulation is readily to be performed. Based on other researchers' DFT calculations, the hydrogen stable interstitial site in tungsten bulk is determined as the tetrahedral site on the surface of the bee lattice. Each T-site has 4 neighbors and the energy barrier between two adjacent T-sites are estimated to be 0.38 eV. Based on those facts and the KMC theory, a MATLAB program is developed to model the hydrogen diffusion in tungsten bulk. In the MATLAB program, substrate temperature, hydrogen concentration, physical time to be simulated, and the number of cycles are all customizable. To compare the KMC determined diffusion coefficients with experiment results in the literature, the simulations are performed for temperature 300 K - 2500 K and low hydrogen concentration (0.1%), mimicking the experiment condition. The calculated diffusion coefficients match the reference values measured by the experiment under low hydrogen concentration condition. The results are also fitted to the Arrhenius equation. The pre-exponential factor and the average activation energy in Arrhenius equation are obtained. The good agreement between simulation and experiment proves that the developed KMC algorithm truly reflect the well-established theory of interstitial hydrogens in tungsten. The developed program could easily be used to model the diffusion process and predict the diffusion coefficients under other concentrations and temperatures. This work is part of the ongoing development of hydrogen diffusion in tungsten integrating surface diffusion (previous work), bulk diffusion (this work), and adsorption/desorption on surface (future work)
Modified Closures in Monte Carlo Algorithms for Diffusive Binary Stochastic Media Transport Problems
In a stochastic medium, the material properties at a given spatial location are known only statistically. The most common approach to solving particle transport problems involving binary stochastic media (BSM) is to use the atomic mix approximation in which the transport problem is solved using homogenized (volume-averaged) material properties. A common deterministic model developed for solving BSM particle transport problems is the Levermore-Pomraning (LP) model. Zimmerman and Adams proposed a Monte Carlo algorithm (Algorithm A) that solves the LP equations and another Monte Carlo algorithm (Algorithm B) that locally preserves the sampled material realization; we refer to these Monte Carlo algorithms as the LP and LPLRP (LP local realization preserving) algorithms, respectively. One-dimensional (1D) planar geometry benchmark studies have shown that the LPLRP algorithm is often significantly more accurate than the LP algorithm for problems with an incident angular flux as well as for problems with an interior source. The LPLRP algorithm implementation in these benchmark comparisons made explicit use of the one-dimensional nature of the problem. The LP model is derived by assuming an 'upwind' closure in the coupling term relating the two materials in a binary stochastic medium. Su and Pomraning developed a modified form of this closure by considering the small correlation length limit and requiring the modified closure to produce the correct exponential decay for a source-free half-line albedo problem in rod geometry. They concluded that the modified closure is generally not inferior to the LP closure and in some cases is significantly better. Brantley investigated the use of the Su-Pomraning (SP) closure in the Monte Carlo LP algorithm (LP-SP) for the suite of benchmark problems and concluded that 1) the LP-SP algorithm was somewhat more accurate overall than the LP algorithm and somewhat less accurate overall than the LPLRP algorithm for an incident angular flux benchmark suite, and 2) the LP-SP algorithm was generally the least accurate of the algorithms for an interior source benchmark suite. Larsen et al. performed an asymptotic analysis of the transport equation in 1D planar geometry for the situation in which the physical system is 1) a random binary stochastic medium with material macroscopic total cross sections and mean slab width values of O(1) or smaller and 2) optically thick with weak absorption and sources at each spatial point and therefore globally diffusive. The asymptotic analysis demonstrates that, under these assumptions, the transport equation limits to the conventional diffusion equation with atomically-mixed (volume-averaged) material properties. Larsen et al. also demonstrate that, under these same assumptions, the LP equations asymptotically limit to an atomically-mixed diffusion equation with a diffusion coefficient that is too large, leading to an unphysical flattening of the ensemble-averaged scalar flux distribution. Vasques and Yadav recently performed an asymptotic analysis of an adjusted Levermore-Pomraning closure in which the Markovian transition functions are rescaled such that the equations asymptotically limit to the correct atomically-mixed diffusion equation; we refer to this model as LP-VY. In this paper, we demonstrate that the adjusted LP closure proposed by Vasques and Yadav is a special case of the SP closure obtained by assuming that the absorption cross sections in the two materials are equal. We further demonstrate that the Su-Pomraning closure has the correct asymptotic limit for the diffusive physical system and is therefore an appropriate closure for these problems. We also describe how to incorporate these various closures into the Monte Carlo LP and LPLRP particle transport algorithms, and we present numerical results comparing the accuracy of the Monte Carlo LP, LP-VY, LP-SP, LPLRP, and LPLRP-SP algorithms for the set of diffusive benchmark problems. We demonstrated that the SP closure has the correct asymptotic limit for the diffusive physical system under investigation in this paper and that the VY closure is a special case of the SP closure obtained by assuming equal absorption in the two materials. Both of these closures are readily implemented in the Monte Carlo LP and LPLRP algorithms for particle transport in BSM. Through numerical comparisons to a diffusive benchmark suite, we confirmed that 1) the LP and LPLRP algorithms do not limit to the appropriate diffusion solution and 2) the LP-VY, LP-SP, and LPLRP-SP algorithms limit to the appropriate diffusion solution and are of comparable accuracy. The LPLRP algorithm has been shown to be generally more accurate than the LP algorithm for non-diffusive problems. However, the numerical results in this paper indicate that the LPLRP algorithm does not limit to the correct diffusion equation for the asymptotic limit under consideration. The work in this paper demonstrates that the SP algorithm does limit to the correct diffusion equation for the asymptotic limit considered. Future work will investigate the possibility of whether the LPLRP-SP algorithm is accurate for both diffusive and non-diffusive problems.
Computational determination of a primary diffusion mode in γ U-10Mo under irradiation
Low enriched uranium (< 20 % 235 U)-molybdenum (U-Mo) monolithic fuel is the primary candidate for high performance research and test reactors, and is in the process of being qualified to replace highly enriched uranium (≥ 20 % 23 5U) fuel. As part of the qualification process, it is critical to understand and predict the behavior of fission gas bubbles under irradiation, which affects fuel swelling and fuel failure. Mechanistic fuel models are being developed that can both reproduce the existing experimental data for fuel swelling, and be further applied to irradiation conditions beyond the experimental scope. Diffusion of species under irradiation conditions is an important parameter in the mechanistic fuel models; however, no temperature-relevant experimental diffusion data exists. In the present work, radiation-enhanced diffusion coefficients of U, Mo, and Xe in λU-10wt.%Mo were calculated in the temperature range between 300 K and 1400 K via rate-theory models and molecular dynamics simulations with an embedded-atom method interatomic potential for the U-Mo-Xe system. Accordingly, total diffusion coefficients under relevant irradiation conditions are determined using previously obtained intrinsic thermal diffusion and radiation-driven diffusion coefficients, as well as the newly calculated radiation-enhanced diffusion coefficients presented herein. Radiation-enhanced diffusion of U and Mo was dominant in the intermediate temperature range, whereas radiation-enhanced diffusion of Xe did not significantly contribute to total diffusion of Xe at the relevant fission rate densities. Radiation-enhanced diffusion of Xe became faster than both intrinsic thermal diffusion and radiation-driven diffusion at a fission rate density of 5 x 10 22 fissions/m 3 /s, which is higher than the typical fission rate density range in research reactors. The temperature regime that radiation-enhanced diffusion of each element dominated was dependent on the fission rate density. Finally, the total diffusion coefficients of U, Mo, and Xe, updated in this work, will be utilized as parameters in the mechanistic fuel models to help predict the behavior of fission gas bubbles under irradiation more accurately.
Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking
Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated nitrogen atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. Furthermore, these results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.
A First-Principles Density Function Theory Study of Tritium Diffusion in Li 2 ZrO 3 : Application for Producing Tritium
The ceramic material Li 2 ZrO 3 has superior thermo-physical and thermo-chemical properties and is highly compatible with other blanket materials used in nuclear reactors. Like LiAlO 2 , it could be used in the form of an annular pellet in tritium-producing burnable absorber rods (TPBARs) to produce tritium( 3 H) upon thermal neutron irradiation of lithium isotope ( 6 Li). The radiation damaged pellet crystal contains vacancies, defects of its constituent elements, and several other trapping sites which hinder the 3 H diffusion process and releasing behavior. In this study, we investigate the diffusion mechanisms of 3 H and O 3 H species in Li 2 ZrO 3 ceramic pellet in order to understand the effects on diffusion barriers and diffusion coefficients due to the presence of interstitial and substitutional Li defects, hydroxide (O– 3 H) vacancy defect, and of the interactions of 3 H with O-vacancies in the radiation damaged Li 2 ZrO 3 crystal. We consider several possible diffusion pathways of interstitial and substitutional 3 H and its species in a defective supercell and calculate the activation energy barrier profiles. We find that the smallest activation energy barrier is 0.3 eV and corresponding diffusion coefficient at 600 K is 1.93 × 10 –9 m 2 /s for 3 H substitutional diffusion. The smallest 3 H interstitial diffusion barrier and diffusion coefficient are found to be 0.34 eV and 3.25 × 10 –9 m 2 /s. By examining several channels for diffusion, our results show the most likely diffusion mechanism of 3 H migration is occurring along the c-direction by exchange of 3 H within and between different Li sites. Here, our calculated results reveal that the smallest energy barrier for O 3 H diffusion is 0.75 eV which is when O 3 H is diffusing to the O–Li vacancy pair and the corresponding diffusion coefficient is 6.31 × 10 –13 m 2 /s. In terms of 3 H diffusion, the obtained results indicate that the performance of Li 2 ZrO 3 could be better than γ-LiAlO 2 , a widely used ceramic material in TPBAR for producing 3 H.
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)