The /D/ matrix for multicomponent diffusion
Multicomponent diffusion process calculation using eigenvalues of Onsager diffusion matrix
Cooper, A. R., Jr.↗
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Progress in Solving the Elusive Ag Transport Mechanism in TRISO Coated Particles: What is new?
The TRISO particle for HTRs has been developed to an advanced state where the coating withstands internal gas pressures and retains fission products during irradiation and under postulated accidents. However, one exception is Ag that has been found to be released from high quality TRISO coated particles when irradiated and can also during high temperature accident heating tests. Although out- of- pile laboratory tests have never hither to been able to demonstrate a diffusion process of Ag in SiC, effective diffusion coefficients have been derived to successfully reproduce measured Ag-110m releases from irradiated HTR fuel elements, compacts and TRISO particles It was found that silver transport through SiC does not proceed via bulk volume diffusion. Presently grain boundary diffusion that may be irradiation enhanced either by neutron bombardment or by the presence of fission products such as Pd, are being investigated. Recent studies of irradiated AGR-1 TRISO fuel using scanning transmission electron microscopy (STEM), transmission kukuchi diffraction (TKD) patterns and high resolution transmission electron microscopy (HRTEM) have been used to further the understanding of Ag transport through TRISO particles. No silver was observed in SiC grains, but Ag was identified at triple-points and grain boundaries of the SiC layer in the TRISO particle. Cadmium was also found in some of the very same triple junctions, but this could be related to silver behavior as Ag-110m decays to Cd-110. Palladium was identified as the main constituent of micron-sized precipitates present at the SiC grain boundaries and in most SiC grain boundaries and the potential role of Pd in the transport of Ag will be discussed.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Ab Initio Thermodynamics and Kinetics for Coalescence of Two-Dimensional Nanoislands and Nanopits on Metal (100) Surfaces
Postdeposition coalescence or sintering of pairs of lowstrain two-dimensional nanoislands and nanopits on unreconstructed metal (100) surfaces is typically mediated by diffusion along step edges, and is highly sensitive to the associated kinetics. Thus, for selected systems, we provide an ab initio density functional theory (DFT) level description of both system thermodynamics and kinetics. Specifically, we assess lateral pair and trio interactions both conventionally with adatoms at 4-fold hollow adsorption sites, and unconventionally with one adatom at the bridge-site transition state for hopping. Rather than use standard cluster expansion algorithms, these interactions are determined subject to the constraint that key step-edge properties are recovered exactly. Together, both classes of interactions determine barriers for edge diffusion processes for any local step configuration, including diffusion along close-packed $\langle$110$\rangle$ edges, kink rounding, meandering processes at kinked $\langle$100$\rangle$ steps, and extraction processes at pit corners. Our formalism applies for homoepitaxial systems, and also for several lattice-matched heteroepitaxial systems. The barriers provide input for stochastic models of nanocluster evolution, which are analyzed by kinetic Monte Carlo simulation. Such modeling with DFT energetics from the PBEsol functional recovers extensive experimental observations of both the time scale and the island-size dependence for sintering of Ag islands on Ag(100). In conclusion, description of pit sintering on Ag(100) is more delicate, being sensitive to specific unconventional trio interactions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Stochastic Schrödinger evolution over piecewise enlarged filtrations
This paper constructs a nonlinear filtering framework that admits appearances of new information processes at random times by introducing piecewise enlargements of filtrations and proposes a new energy-based Schrodinger evolution expressed as a stochastic differential equation on a complex Hilbert space. Each information process is modeled as the sum of a random variable taking the eigenvalues of a Hamiltonian and an independent Brownian bridge noise. It is shown that under a piecewise enlarged filtration, the wave function is a jump-diffusion process until it collapses at some terminal time. In between discontinuities, the dynamics of the state vector are governed by different Wiener processes and diffusion coefficients. This motivates the introduction of an inclusive chain of Kolmogorov probability spaces or a *-isomorphic chain of commutative von Neumann probability spaces, on which the quantum system evolves differently based on the number of active information processes. The expectation of the Hamiltonian at a given state is the solution of a second-order nonlinear differential equation determined by one of the possible regimes that the quantum system belongs to. It is shown that the collapse rate is a submartingale with positive jumps and the Shannon entropy process is a supermartingale with expected negative jumps when passing to higher-order probability spaces. The framework is extended to the case when the Hamiltonian is modeled as a function of a set of commutative operators, where each operator is associated with a different piecewise enlarged filtration.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Prediction and evaluation of eddy-viscosity models for free mixing
Analysis for the turbulent mixing of free jets is presented in this paper and compared to recent experimental results. A turbulent mass diffusion model is presented and is based on the concentration potential core. The model yielded good results when compared with the experimental results except for low-speed flows where few experimental data are available. A review of recent experimental results verifies again that the three diffusion processes in turbulent mixing are interrelated; however, no single diffusion model may be used for all three processes. This is especially true when pressure gradients are present in the flow field. It is shown that even though momentum diffusion is significantly affected by pressure gradients, mass diffusion is not. It is further indicated that the mass diffusion model has been derived and is based on the accurate correlations of experimental results obtained for the concentration potential core. Similar techniques may be used in deriving an expression for the momentum and thermal diffusion coefficients. These expressions would be more complicated since they would have to take care of the boundary layer at the start of the mixing region. Finally, a comparison of the analyses, using this particular model and Ferri's model, with available experimental results is made.
Zakkay, V.↗
Understanding the Mechanism of Electronic Defect Suppression Enabled by Nonidealities in Atomic Layer Deposition
Silicon germanium (SiGe) is a multifunctional material considered for quantum computing, neuromorphic devices, and CMOS transistors. However, implementation of SiGe in nanoscale electronic devices necessitates suppression of surface states dominating the electronic properties. The absence of a stable and passive surface oxide for SiGe results in the formation of charge traps at the SiGe-oxide interface induced by GeOx. In an ideal ALD process in which oxide is grown layer by layer, the GeO x formation should be prevented with selective surface oxidation (i.e., formation of an SiO x interface) by controlling the oxidant dose in the first few ALD cycles of the oxide deposition on SiGe. However, in a real ALD process, the interface evolves during the entire ALD oxide deposition due to diffusion of reactant species through the gate oxide. In this work, this diffusion process in nonideal ALD is investigated and exploited: the diffusion through the oxide during ALD is utilized to passivate the interfacial defects by employing ozone as a secondary oxidant. Periodic ozone exposure during gate oxide ALD on SiGe is shown to reduce the integrated trap density (D it ) across the band gap by nearly 1 order of magnitude in Al 2 O 3 (<6 × 10 10 cm -2 ) and in HfO 2 (<3.9 × 10 11 cm -2 ) by forming a SiO x -rich interface on SiGe. Depletion of Ge from the interfacial layer (IL) by enhancement of volatile GeO x formation and consequent desorption from the SiGe with ozone insertion during the ALD growth process is confirmed by electron energy loss spectroscopy (STEM-EELS) and hypothesized to be the mechanism for reduction of the interfacial defects. In this work, the nanoscale mechanism for defect suppression at the SiGe-oxide interface is demonstrated, which is engineering of diffusion species in the ALD process due to facile diffusion of reactant species in nonideal ALD.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Bayesian Static Parameter Estimation for Partially Observed Diffusions via Multilevel Monte Carlo
In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for instance, using the Euler--Maruyama method. Given this assumption, we show how one can use Markov chain Monte Carlo (MCMC) and particularly particle MCMC [C. Andrieu, A. Doucet, and R. Holenstein, J. R. Stat. Soc. Ser. B Stat. Methodol., 72 (2010), 269--342] to implement a new approximation of the multilevel (ML) Monte Carlo (MC) collapsing sum identity. Our approach comprises constructing an approximate coupling of the posterior density of the joint distribution over parameter and hidden variables at two different discretization levels and then correcting by an importance sampling method. The variance of the weights are independent of the length of the observed data set. The utility of such a method is that, for a prescribed level of mean square error, the cost of this MLMC method is provably less than i.i.d. sampling from the posterior associated to the most precise discretization. However the method here comprises using only known and efficient simulation methodologies. Finally, the theoretical results are illustrated by inference of the parameters of two prototypical processes given noisy partial observations of the process: the first is an Ornstein--Uhlenbeck process and the second is a more general Langevin equation.
97 MATHEMATICS AND COMPUTING↗
New insights on the formation of supersaturated Cu-Nb solid solution prepared by mechanical alloying
The deformation-driven alloying mechanisms in the immiscible Cu-Nb system during mechanical alloying (MA) process have been studied by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and high-resolution TEM (HRTEM) observations. It is found that the dominating alloying mechanism changes at the different stages of milling. Initially, the alloying process is mainly governed by interfaces and dislocations, which supply fast diffusion channels between phases. In the intermediate stage, Nb particles with sizes below 8 nm undergo a bcc to fcc allotropic transformation, and the interdiffusion between fcc-Nb and fcc-Cu is promoted due to the similarity of lattice structures. Further milling generates disclination defects, which contribute to the formation of fragments or subgrains with sizes below 5 nm. The introduction of such defects and fragments benefits the formation of a complete Cu-Nb solid solution. The formation kinetics of solid solution is analyzed by Johnson-Mehl-Avrami equation, which suggests that the speed of the diffusion of Nb atoms into Cu is very slow. - Highlights: •The bcc to fcc transformation in Nb nanoparticles promotes diffusion process. •The formation of fragments with sizes below 5 nm is attributed to the disclination defects. •Defect-assisted diffusion is responsible for the alloying process.
36 MATERIALS SCIENCE↗
Quantification of the internal quantum efficiency in GaN via analysis of the heat generated by non-radiative recombination processes
The internal quantum efficiency (IQE) in a GaN epilayer is quantified using transient lens (TL) spectroscopy and numerical simulations. TL spectroscopy can optically detect temperature and carrier changes induced in a photo-pumped GaN layer, and the observed temperature change is closely associated with non-radiative recombination processes that create heat. Then numerically solving diffusion equations, which represent the diffusion processes of the photo-generated heat and carriers, provide the spatiotemporal distributions. These distributions are subsequently converted into the refractive index distributions, which act as transient convex or concave lenses. Finally, ray-tracing simulations predict the TL signals. Comparing the experimentally obtained and simulated TL signals quantifies the generated heat and the IQE without the often-adopted assumption that non-radiative recombination processes are negligible at low temperatures.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Chemistry and Formation of the Beilby Layer During Polishing of Fused Silica Glass
The chemical characteristics and the proposed formation mechanisms of the modified surface layer (called the Beilby layer) on polished fused silica glasses are described. Fused silica glass samples were polished using different slurries, polyurethane pads, and at different rotation rates. The concentration profiles of several key contaminants, such as Ce, K, and H, were measured in the near surface layer of the polished samples using Secondary Ion Mass Spectroscopy (SIMS). The penetration of K, originating from KOH used for pH control during polishing, decreased with increase in polishing material removal rate. In contrast, penetration of the Ce and H increased with increase in polishing removal rate. In addition, Ce penetration was largely independent of the other polishing parameters (e.g., particle size distribution and the properties of the polishing pad). The resulting K concentration depth profiles are described using a two-step diffusion process: (1) steady-state moving boundary diffusion (due to material removal during polishing) followed by (2) simple diffusion during ambient postpolishing storage. Using known alkali metal diffusion coefficients in fused silica glass, this diffusion model predicts concentration profiles that are consistent with the measured data at various polishing material removal rates. On the other hand, the observed Ce profiles are inconsistent with diffusion based transport. Rather we propose that Ce penetration is governed by the ratio of Ce–O–Si and Si–O–Si hydrolysis rates; where this ratio increases with interface temperature (which increases with polishing material removal rate) resulting in greater Ce penetration into the Beilby layer. Calculated Ce surface concentrations using this mechanism are in good agreement to the observed change in measured Ce surface concentrations with polishing material removal rate. In conclusion, these new insights into the chemistry of the Beilby layer, combined together with details of the single particle removal function during polishing, are used to develop a more detailed and quantitative picture of the polishing process and the formation of the Beilby layer.
36 MATERIALS SCIENCE↗
Modeling fission product diffusion in TRISO fuel particles with BISON
Diffusion of fission products in intact TRISO particles depends on particle geometry, fission product source rates, time, temperature, and temperature-dependent diffusion coefficients. Simulating this diffusion process requires models for source rates and diffusion coefficients, plus computation of the temperature field if not prescribed. In addition, simulation quality depends on discretization of the geometry, appropriate time stepping, and the accuracy of the solution method. In this paper, we explore the simulation of fission product diffusion in TRISO fuel particles using the finite element method via the fuel performance code Bison. Recent material model development has occurred in Bison for each material present in tri-structural isotropic (TRISO) fuel particles: the buffer, inner pyrolytic carbon, silicon carbide, and outer pyrolytic carbon layers, as well as the fuel kernel. Also, new mesh generation and fission product release fraction capabilities have been added. Diffusion capabilities are shown to converge to the correct solution via formal verification tests. A large number of code benchmarking problems are also given, with good results, showing that Bison’s computed release fractions closely match those of other software tools. Finally, a significant validation effort is detailed in which fission product release, measured as part of the AGR-1 capsule experiments, is compared to Bison outputs. Bison outputs compare very well to the experimental data and to PARFUME results.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
The leaching kinetics of cadmium from hazardous Cu-Cd zinc plant residues
Highlights: • A cleaner cadmium, zinc and copper recovery method from zinc plant waste residues was investigated. • The mechanisms and kinetics of cadmium recovery were discussed. • The effects of leaching variables were discussed. •The XRD and morphology analysis of raw residue and leaching residue were conducted. - Abstract: A large amount of Cu-Cd zinc plant residues (CZPR) are produced from the hydrometallurgical zinc plant operations. Since these residues contain substantial amount of heavy metals including Cd, Zn and Cu, therefore, they are considered as hazardous wastes. In order to realize decontamination treatment and efficient extraction of the valuable metals from the CZPR, a comprehensive recovery process using sulfuric acid as the leaching reagent and air as the oxidizing reagent has been proposed. The effect of temperature, sulfuric acid concentration, particle size, solid/liquid ratio and stirring speed on the cadmium extraction efficiency was investigated. The leaching kinetics of cadmium was also studied. It was concluded that the cadmium leaching process was controlled by the solid film diffusion process. Moreover, the order of the reaction rate constant versus H{sub 2}SO{sub 4} concentration, particle size, solid/liquid ratio and stirring speed was calculated. The XRD and SEM-EDS analysis results showed that the main phases of the secondary sulfuric acid leaching residues were lead sulfate and calcium sulfate.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Physical electronics and surface physics
Current analytical and experimental investigations of the influence of surface processes on the rate of permeation of gases through solids are summarized. A brief description is presented of an analytical model that provides an approximate prediction of the dependence of the permeation rate on the rates of surface processes relative to the rate of the diffusion process. Results of experiments indicate that the desorption process of hydrogen from various materials is influenced by surface impurities to the degree that substantial changes in the spatial distribution of the desorbed molecules are observed when the impurities are varied. Except possibly for H-Nb, the permeation measurements indicate that the desorption process is not influenced to the degree that detectable changes in the permeation rates are observed when the impurities and temperatures are varied. On the basis of analysis, it is unlikely that the desorption process will be the rate-controlling step under the conditions of the present experiments.
Stickney, R. E.↗
Baffle aperture design study of hollow cathode equipped ion thrusters
A simple theoretical model which can be used as an aid in the design of the baffle aperture region of a hollow cathode equipped ion thruster was developed. An analysis of the ion and electron currents in both the main and cathode discharge chambers is presented. From this analysis a model of current flow through the aperture, which is required as an input to the design model, was developed. This model was verified experimentally. The dominant force driving electrons through the aperture was the force due to the electrical potential gradient. The diffusion process was modeled according to the Bolm diffusion theory. A number of simplifications were made to limit the amount of detailed plasma information required as input to the model to facilitate the use of the model in thruster design. This simplified model gave remarkably consistant results with experimental results obtained with a given thruster geometry over substantial changes in operating conditions. The model was uncertain to about a factor of two for different thruster cathode region geometries. The design usefulness was limited by this factor of two uncertainty and by the accuracy to which the plasma parameters required as inputs to the model were specified.
Brophy, J. R., Jr.↗
Coupled low-energy - ring current plasma diffusion in the Jovian magnetosphere
The outwardly diffusing Iogenic plasma and the simultaneously inwardly diffusing ring current plasma in the Jovian magnetosphere are described using a coupled diffusion model which incorporates the effects of the pressure gradient of the ring current into the cross-L diffusion coefficient. The coupled diffusion coefficient is derived by calculating the total energy available to drive the diffusion process. The condition is imposed that the diffusion coefficient takes on a local minimum value at some point in the region L = 7-8, at which point the gradient of the Io plasma density is specified as ramp value given by Siscoe et al. (1981). The hypothesis that the pressure gradient of the ring current causes the diminution of radial plasma transport is tested, and solution profiles for the Iogenic and ring current plasma densities are obtained which imply that the Io plasma ramp is caused by a high-density, low-energy component of the ring current hitherto unobserved directly.
Summers, D.↗
Diffusion mechanisms in Ir-coated Re for high-temperature, radiation-cooled rocket thrusters
Materials used for radiation-cooled rocket thrusters must be capable of surviving under extreme conditions of high temperatures and oxidizing environments. Thruster chambers were developed using chemical-vapor-deposited (CVD) Re coated with CVD Ir on the inside surface which is exposed to hot combustion gases. Ir serves as an oxidation barrier protecting the Re which maintains structural integrity at high temperatures. In order to predict and extend the performance limits of these Ir-coated Re thrusters, the diffusion kinetics of CVD materials at temperature are studied. Thruster end ring sections were examined using electron microprobe analysis both before and after exposure to high temperature vacuum environments. The resulting elemental maps for Re, Ir, and Mo in the near-surface region allow identification of diffusion mechanisms operating at these temperatures. Line scans for Ir and Re were fit using a diffusion model to extract relevant diffusion constants. The fastest diffusion process is seen to be grain boundary diffusion with Re diffusing down grain boundaries in the Ir overlayer. The measured dependence of the diffusion rate on temperature will allow prediction of operating lifetimes for these thrusters.
Hamilton, J. C.↗
Relativistic electron precipitation enhancements near the outer edge of the radiation belt
Characteristics of relativistic electron precipitation bursts observed by the Heavy Ion Large Telescope (HILT) experiment onboard the Solar, Anomalous, and Magnetospheric Partical Explorer (SAMPEX) satellite were examined. Relatively narrow, persitent, latitudinal bands of precipitation with time scales of 10 to approximately 30 sec near the outer edge of the radiation belt which develop and decay with a time scale of a few hours are reported. Acceleration processes more effective than the usual radial diffusion process or scattering process would be needed to explain this strong precipitation band phenomenon. Another prominent signature is microbursts with a time scale down to a few hundred milliseconds. It is suggested that these microbursts are due to wave-particle interaction involving a relaxation-oscillator type of mechanism.
Nakamura, R.↗
Effects of Experiment Location and Orbiter Attitude on the Residual Acceleration On-Board STS-73 (USML-2)
A knowledge of the quasi-steady acceleration environment on the NASA Space Shuttle Orbiter is of particular importance for materials processing experiments which are limited by slow diffusive processes. The quasi-steady (less than 1 HZ) acceleration environment on STS-73 (USML-2) was measured using the Orbital Acceleration Research Experiment (OARE) accelerometer. One of the facilities flown on USML-2 was the Crystal Growth Furnace (CGF), which was used by several Principal Investigators (PIS) to grow crystals. In this paper the OARE data mapped to the sample melt location within this furnace is presented. The ratio of the axial to radial components of the quasi-steady acceleration at the melt site is presented. Effects of Orbiter attitude on the acceleration data is discussed.
Hakimzadeh, Roshanak↗