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DOE OSTI2017

Time-Harmonic Gaussian Beams: Exact Solutions of the Helmhotz Equation in Free Space

An exact solution of the Helmholtz equation u{sub xx} + u{sub yy} + u{sub zz} + k{sup 2}u = 0 is presented, which describes propagation of monochromatic waves in the free space. The solution has the form of a superposition of plane waves with a specific weight function dependent on a certain free parameter a. If ka→∞, the solution is localized in the Gaussian manner in a vicinity of a certain straight line and asymptotically coincides with the famous approximate solution known as the fundamental mode of a paraxial Gaussian beam. The asymptotics of the aforementioned exact solution does not include a backward wave.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Liquid-phase epitaxy of the (Si{sub 2}){sub 1−x−y}(Ge{sub 2}){sub x}(GaAs){sub y} substitutional solid solution (0 ≤ x ≤ 0.91, 0 ≤ y ≤ 0.94) and their electrophysical properties

(Si{sub 2}){sub 1−x−y}(Ge{sub 2}){sub x}(GaAs){sub y} substitutional solid solutions (0 ≤ x ≤ 0.91, 0 ≤ y ≤ 0.94) are grown by liquid-phase epitaxy from a Pb-based solution-melt on Si substrates with the (111) crystallographic orientation. The chemical composition of the epitaxial films is studied by X-rays probe microanalysis, and the distribution profile of solid solution components is determined. Spectral dependences of the photosensitivity and photoluminescence of the n-Si-p(Si{sub 2}){sub 1−x−y}(Ge{sub 2}){sub x}(GaAs){sub y} heterostructures are studied at room and liquid-nitrogen temperatures. Two maxima are found in the photoluminescence spectra of the (Si{sub 2}){sub 1−x−y}(Ge{sub 2}){sub x}(GaAs){sub y} films (0 ≤ x ≤ 0.91, 0 ≤ y ≤ 0.94) against the background of a broad emission spectrum. The fundamental maximum with an energy of 1.45 eV is caused by the band-to-band recombination of solid solution carriers, and an additional maximum with an energy of 1.33 eV is caused by the recombination of carriers with the participation of impurity levels of the Si-Si bond (Si{sub 2} is covalently coupled with the tetrahedral lattice of the solid solution host)

36 MATERIALS SCIENCE↗

DOE OSTI2019

Simulation of the NaGd(MoO{sub 4}){sub 2}–NaEu(MoO{sub 4}){sub 2} and Na{sub 2}Gd{sub 4}(MoO{sub 4}){sub 7}–Na{sub 2}Eu{sub 4}(MoO{sub 4}){sub 7} Solid Solutions by the Interatomic Potential Method

Simulation of the solid solutions in the system of double sodium–gadolinium and sodium–europium molybdates, which are promising matrices for solid state lasers and phosphors has been carried out by the method of interatomic potentials. Two types of solid solutions have been studied, one of which contains finite components corresponding to the stoichiometric NaGd(MoO{sub 4}){sub 2}–NaEu(MoO{sub 4}){sub 2} compositions with statistical distribution of cations in the crystal lattice. Another object is a cation-deficient Na{sub 2}Gd{sub 4}(MoO{sub 4}){sub 7}–Na{sub 2}Eu{sub 4}(MoO{sub 4}){sub 7} system, in which we have examined the variants of statistical distribution and partial ordering of cations over structural positions. Atomistic simulation has been performed using the GULP 4.0.1 software package (General Utility Lattice Program). It is shown that when we pass from sodium-gadolinium molybdate to sodium-europium molybdate, both of stoichiometric and cation-deficient compositions, an increase in the unit cell volume is observed, while the density of the crystal, the energy of interatomic interactions in the structure, the vibrational entropy and the heat capacity decrease along with increasing europium content. The energy of interatomic interactions in the structure for cation-deficient solid solutions is less than for stoichiometric ones. Other aforementioned characteristics for cation-deficient solid solutions have greater values than for stoichiometric ones. The role of cluster europium centers in concentration quenching in NaGd(MoO{sub 4}){sub 2}–NaEu(MoO{sub 4}){sub 2} solid solutions has been examined.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Lattice Parameter Behavior with Different Nd and O Concentrations in (U 1-y Nd y )O 2±x Solid Solution

The solid solution of (U1-yFPy)O- 2±x , has the same fluorite structure as UO 2±x lambda, and the lattice parameter is affected by dissolved fission product and oxygen concentrations. We investigated the relation between the lattice parameter and the concentrations of neodymium and oxygen in the fluorite structure of (U 1-y Nd y )O 2±x using X-ray diffraction. Moreover, the lattice parameter behavior in the (U 1-y Nd y )O 2±x , solid solution shows a linear change as a function of the oxygen-to-metal ratio and solubility of neodymium. The lattice parameter depends on the radii of ions forming the fluorite structure and also can be expressed by a particular rule (modified Vegard's law). Furthermore, the numerical analyses of the lattice parameters for the stoichiometric and nonstoichionietric solid solutions were conducted, and the lattice parameter model for the (U1-yNdy)O 2±x , solid solution was assessed. There is a very linear relationship between the lattice parameter and the Nd and O concentration for the stoichiometry and nonstoichiometry of the (U 1-y Nd y )O 2±x solid solution was verified.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Pore-Scale Study on the Positive Feedback Between Stress and Porosity Caused by Pressure Solution in Porous Media

Pressure solution is an important process in the evolution of sedimentary rocks, which provide storage space for most of our petroleum resources. It directly influences the generation, migration, and storage of petroleum fluids in subsurface sedimentary rocks. Here, in this paper, we develop a pore-scale, mechanochemical model to demonstrate a possible positive feedback between the local porosity and pore surface stress, in which a higher local porosity causes a higher local pore surface stress, thus enhancing pressure solution and consequently further increasing the local porosity. Pore surface stress represents stress on a solid grain adjacent to a pore. Specifically, the pore-scale, mechanochemical model directly simulates the stress distribution over solid and pore surfaces using a finite element model. The dissolution of solids at the solid-pore interfaces under a far-from-equilibrium condition is simulated using a first-order kinetics model that accounts for the local stress distribution. The updated pore geometry, caused by pore surface dissolution, is then used in the stress simulation in the next numerical iteration. Two types of porous media, the Oriskany sandstone and an artificial porous medium with spherical pores, were tested in the mechanochemical simulation. The positive stress-porosity feedback during pressure solution was observed in both samples. In addition, the model quantitatively illustrated the distribution of local mineral dissolution rates on all pore surfaces, as well as its relation to the effective mineral dissolution rate of the entire sample. Based on the comparison between the two porous media, the local mineral dissolution was regulated by pore space distribution, geometry, and coalescence during pressure solution. This work is the first that uses direct, pore-scale numerical simulation to demonstrate the positive stress-porosity feedback during pressure solution, which has the potential to advance the understanding of the mechanical-chemical (MC) coupling in many geological processes that are relevant to subsurface energy systems, such as the recovery of petroleum hydrocarbons and geothermal energy.

CT scanning↗

DOE OSTI2012

Oxide Melt Solution Calorimetry of Fe2+ -bearing Oxides and Application to the Magnetite - Maghemite (Fe3O4-Fe8/3O4) system

A consistent methodology for obtaining enthalpy of formation of Fe{sup 2+}-containing binary and multicomponent oxides using high temperature oxide melt solution calorimetry has been developed. The enthalpies of wuestite (FeO) and magnetite (Fe{sub 3}O{sub 4}) oxidation to hematite (Fe{sub 2}O{sub 3}) were measured using oxidative drop solution calorimetry in which the final product is dissolved ferric oxide. Two methods were applied: drop solution calorimetry at 1073 K in lead borate solvent and at 973 K in sodium molybdate, each under both oxygen flowing over and bubbling through the solvent, giving consistent results in agreement with literature values. The enthalpies of formation of all three iron oxides from the elements were obtained using a thermodynamic cycle involving the directly measured oxidative dissolution enthalpy of iron metal in sodium molybdate at 973 K and gave excellent consistency with literature data. The methodology was then applied to the magnetite - maghemite system. The enthalpy of mixing of the Fe{sub 3}O{sub 4}-Fe{sub 8/3}O{sub 4} spinel solid solution is exothermic and, 2 represented by a subregular (Margules) formalism, {Delta}H{sub mix} = x(1-x)(-63.36 {+-} 8.60(1-x) + 17.65 {+-} 6.40x) kJ/mol, where x is the mole fraction of magnetite. The entropies of mixing of the solid solution were calculated for different assumptions about the distribution of cations, charges, and vacancies in these defect spinels. The different models lead to only small differences in the entropy of mixing. Calculated free energies of mixing show no evidence for a solvus in the magnetite - maghemite system.

58 GEOSCIENCES↗

DOE OSTI2015

Experimental Results for Direct Electron Irradiation of a Uranyl Sulfate Solution: Bubble Formation and Thermal Hydraulics Studies

In support of the development of accelerator-driven production of fission product Mo-99 as proposed by SHINE Medical Technologies, a 35 MeV electron linac was used to irradiate depleted-uranium (DU) uranyl sulfate dissolved in pH 1 sulfuric acid at average power densities of 6 kW, 12 kW, and 15 kW. During these irradiations, gas bubbles were generated in the solution due to the radiolytic decomposition of water molecules in the solution. Multiple video cameras were used to record the behavior of bubble generation and transport in the solution. Seven six-channel thermocouples were used to record temperature gradients in the solution from self-heating. Measurements of hydrogen and oxygen concentrations in a helium sweep gas were recorded by a gas chromatograph to estimate production rates during irradiation. These data are being used to validate a computational fluid dynamics (CFD) model of the experiment that includes multiphase flow and a custom bubble injection model for the solution region.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2019

Tank 9H Salt Solution Supernatant Characterization in Support of Potential Operating Strategies of Tank 9H Supernatant Through the Tank Closure Cesium Removal System

Savannah River Remediation (SRR) recently initiated an ion exchange process to remove radioactive cesium from dissolved salt solution in Tank 10H, known as Tank Closure Cesium Removal (TCCR). As part of that ongoing campaign, the salt in Tank 9H will be dissolved and transferred to Tank 10H for processing through the TCCR system, and SRR requested the characterization of the dissolved salt solution in Tank 9H prior to the transfer to Tank 10H. On July 18, 2019, Savannah River Remediation Engineering (SRR-E) delivered two variable depth Tank 9H salt solution samples, identified as samples HTF-9-19-74 and HTF-9-19-75 (combined total sample volume of about 400 mL) to the Savannah River National Laboratory (SRNL) for characterization. These two Tank 9H variable depth samples (HTF-9-19-74 and HTF-9-19-75 taken at ~180” and 42”, respectively) were retrieved from Riser 7 after hydro-lancing activities were complete. Approximately 4200 gallons of water were added to the tank during this activity. This report presents the analytical characterization results for the Tank 9H salt solution variable depth samples HTF-9-19-74 and HTF-9-19-75 and contains mainly the filtrate analytical results for anions, elements, mass spectral data, total cesium characterization results and select radionuclide results, along with the X-ray diffraction characterization of the solid fractions from the liquid /solid separation of the variable depth salt solutions. Most of these analyses were performed in duplicate with the percent relative standard deviation (%RSD), a measure of the variability between each duplicate data set expressed as a percentage, used to estimate the analytical result quality for each analyte.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Design Optimization of A generic Fissile Solution for Mo99 production using Electron Beam-based Neutron Generator using MCNP+CFD

Molybdenum-99 ( 99 Mo) is a medical isotope used in 80% of all medical imaging procedures today. However, 99 Mo is not directly administered to patients for imaging; its decay product, technetium-99m ( 99 mTc), is a metastable isotope with a half-life of ~6 hours. Such a short half-life does not allow for production, separation, and application to a patient before decaying further. Therefore, the solution is to produce the precursor to 99 mTc, 99 Mo. 99 Mo has a half-life of 66 hours, long enough to produce the material and send it to the desired location before it fully decays. Under National Nuclear Security Administration’s (NNSA) highly enriched uranium (HEU) minimization mission, the Material Management and Minimization (M3) office leads the Molybdenum-99 (Mo-99) program. A major goal of the Mo-99 program is to develop methods of producing 99 Mo using low enriched uranium (LEU) opposed to the traditionally used HEU domestically in the U.S. Internationally, LEU is the new standard for use in research reactors and isotope production facility. In this study, we introduce a generic fissile solution system for 99 Mo production facility meeting the design requirement of 1) LEU usage as fissile material and 2) subcritical fissile system coupled with a horizontal electron beam (E-beam) accelerator. The focus of this research is to optimize a fissile solution configuration for maximum 99 Mo production yield using MCNP model, and ultimately implement the optimized design with computational fluid dynamics (CFD) model to understand thermal hydraulic behavior and solution convection characteristic. The report consists of two parts: 1) isotope yield calculation and criticality analysis with a wide range of parametric test matrix, and 2) thermal hydraulic analysis for solution mixing and cooling assessment.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

DC-AC Tool: Fully Automating the Acquisition of AC Power Flow Solution

DC2AC is an automated tool for achieving a converged AC power flow solution from any dispatch, e.g., determined using DC power flow model based optimal power flow. The entire process is free of human interference. It is usually encountered in practice that, even with a DC power flow solution, acquiring the solved AC power flow solution, if exists, sometimes could be a challenging task, especially during the planning stage. It is also difficult to distinguish the unsolvable cases from diverging iterations. Manual adjustments to approach the desired power flow condition has been largely relied on in the past using lots of engineering heuristics. This tool provides a systematic way to first achieve a solvable AC power flow case by modifying the power flow condition, and then try to track the AC power flow solution while gradually removing the adopted changes. If all adopted changes can be completely removed, then the original AC power flow solution is obtained. Otherwise, insights for actionable controls are derived to help operation and planning. Currently, this tool has been implemented in Python using SIEMENS PTI PSS/E as power flow solver, where only adjusting generator terminal voltage set point is considered as an available means to try to turn an unsolved power flow to a solved one. In future, more means should be considered, including the operation of tap-changing transformers, switched shunts and redispatch of active power.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Time–Concentration Superposition for Linear Viscoelasticity of Polymer Solutions

The concentration dependence of linear viscoelastic properties of polymer solutions is a well-studied topic in polymer physics. Dynamic scaling theories allow qualitative predictions of polymer solution rheology, but quantitative predictions are still limited to model polymers. Meanwhile, the scaling properties of non-model polymer solutions must be determined experimentally. In present paper, the time–concentration superposition (TCS) of experimental data is shown to be a robust procedure for studying the concentration scaling properties of binary and ternary polymer solutions. TCS can not only identify whether power law scaling may exist or not, and over which concentration range, but also unambiguously estimate the concentration scaling exponents of linear viscoelastic properties for a range of non-model polymer solutions.

42 ENGINEERING↗

DOE OSTI2012

The Method of Manufactured Solutions for RattleSnake A SN Radiation Transport Solver Inside the MOOSE Framework

The Method of Manufactured Solutions (MMS) is an accepted technique to verify that a numerical discretization for the radiation transport equation has been implemented correctly. This technique offers a few advantages over other methods such as benchmark problems or analytical solutions. The solution can be manufactured such that properties for the angular flux are either stressed or preserved. For radiation transport, these properties can include desired smoothness, positiveness and arbitrary order of anisotropy in angle. Another advantage is that the angular flux solution can be manufactured for multidimensional problems where analytical solutions are difficult to obtain in general.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Vacancy-mediated transport and segregation tendencies of solutes in FCC Ni under diffusional creep

Nickel-based alloys are known for their excellent corrosion resistance and high-temperature strength. However, at high temperatures, polycrystals experience grain boundary-stress-driven vacancy diffusion leading to diffusion-driven creep. Understanding the fundamentals of defect migration is essential to predict diffusion creep behavior. In this talk, we explore the Nabarro-Herring diffusion creep and the associated solute segregation that is likely to result from the different diffusivities of the solute and solvent elements. Density functional theory calculations are performed to determine the formation, migration and binding energies of the solute and vacancy defects in stress-free and stressed states. The dilute-limit transport coefficients are then calculated using the self-consistent mean field theory as implemented in the Kinetic Cluster Expansion (KineCluE) code. Predictions of diffusion creep strain rates and solute segregation are then presented for various solutes, stress and temperatures. This work opens research avenues for exploration of diffusion creep via characterization of elemental segregation to grain boundaries.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Convergence and asymptotical stability of numerical solutions for neutral stochastic delay differential equations driven by G-Brownian motion

There are few numerical analysis results for nonlinear neutral stochastic delay differential equations driven by G-Brownian motion (G-NSDDEs). This paper is concerned with the numerical solutions of the G-NSDDEs to fill this gap. In this paper, we first devote to show that the stochastic theta numerical solution converges to the exact solution for the G-NSDDE. We then prove that the backward Euler–Maruyama numerical solution for the G-NSDDE is asymptotically mean-square stable under suitable conditions. Moreover, a numerical example is demonstrated to illustrate the effectiveness of our obtained results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Exact analytical solution of the linear structure growth rate in {Lambda}CDM cosmology and its cosmological applications

We derive the exact analytical solution of the linear structure growth rate in {Lambda}CDM cosmology with flat or curved geometry, under the Newtonian gauge. Unlike the well known solution under the Newtonian limit [D. J. Heath, Mon. Not. R. Astron. Soc. 179, 351 (1977)], our solution takes all general relativistic corrections into account and is hence valid at both the sub- and superhorizon scales. With this exact solution, we evaluate cosmological impacts induced by these relativistic corrections. (1) General relativistic corrections alter the density growth from z=100 to z=0 by 10% at k=0.01 h/Mpc and the impact becomes stronger toward larger scales. We caution the readers that the overdensity is not gauge invariant and the above statement is restrained to the Newtonian gauge. (2) Relativistic corrections introduce a k{sup -2} scale dependence in the density fluctuation. It mimics a primordial non-Gaussianity of the local type with f{sub NL}{sup local{approx}}1. This systematical error may become non-negligible for future all sky deep galaxy surveys. (3) Cosmological simulations with box size greater than 1 Gpc are also affected by these relativistic corrections. We provide a postprocessing recipe to correct for these effects. (4) These relativistic corrections affect the redshift distortion. However, at redshifts and scales relevant to redshift distortion measurements, such effect is negligible.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Utilization of Novel (KNbO 3 ) 1− x (Ba 2 FeNbO 6 ) x ( x = 0.1, 0.2, 0.3) Solid Solutions for Efficient Photo‐Assisted Fenton Degradation of Methylene Blue Dye

Novel (KNbO 3 ) 1− x (Ba 2 FeNbO 6 ) x ( x = 0.1, 0.2, 0.3) solid solutions corresponding to K 0.82 Ba 0.18 Fe 0.09 Nb 0.91 O 3 , K 0.64 Ba 0.36 Fe 0.18 Nb 0.82 O 3 , and K 0.46 Ba 0.54 Fe 0.27 Nb 0.73 O 3 compounds have been synthesized via molten salt method. X‐ray diffraction confirms the formation of solid solutions, while transmission electron microscopy combined with energy‐dispersive spectroscopy results demonstrates a homogeneous distribution of elements. The obtained solid solutions crystallized in a cubic crystal structure, whereas the parent KNbO 3 possesses an orthorhombic structure. The wide bandgap semiconductor KNbO 3 transformed into a visible‐light‐active material, with its bandgap energy reduced from 3.56 eV to ≈2.4 eV. The substitution of K in KNbO 3 with Ba is responsible for structural modification from orthorhombic to cubic symmetry, whereas both structural modification and the substitution of Nb with Fe correlated with optical properties. The photocatalytic activities of all obtained solid solutions are improved compared with the parent KNbO 3 and Ba 2 FeNbO 6 compounds for photocatalytic degradation of methylene blue (MB) dye. Among the series of solid solutions, K 0.82 Ba 0.18 Fe 0.09 Nb 0.91 O 3 photocatalysts show the highest MB removal efficiency owing to its relatively higher surface area, suppressed charge carrier recombination, and more negative conduction band edge. Moreover, K 0.82 Ba 0.18 Fe 0.09 Nb 0.91 O 3 photocatalyst (0.1 g) combined with hydrogen peroxide (H 2 O 2 ) to form a novel photo‐Fenton system, achieving almost complete degradation of 100 mL of 10 mg L −1 MB dye in 30 min.

Avcıoğlu, Celal [Technische Universität Berlin, Fa↗

DOE OSTI2017

Sensing trace levels of molecular species in solution via zinc oxide nanoprobe Raman spectroscopy

Surface-enhanced Raman spectroscopy (SERS) has potential for unique clinical, environmental, and military applications, among many others, but it is limited by a rapid decrease in signal with distance from the sensing surface. For this reason, much study of SERS-based biosensing involves chemical or physical adsorption of analytes to an active surface. Adsorption, however, limits the types of analytes that can be detected and detection sensitivity. The three-dimensional closely packed architecture of zinc oxide (ZnO) nanowires decorated with silver nanoparticles increases SERS intensity, allowing for adsorption-free biosensing. This approach greatly expands the potential applications of Raman spectroscopy as a biosensing technique. This article demonstrates a significant SERS enhancement from silver nanoparticle-decorated ZnO nanoprobes to the Raman spectra of crystal violet, melamine, and adenine solutions. These enhancements were quantified by comparing the intensity of Raman peaks from each of the three solutions through ZnO nanowires decorated with silver nanoparticles with that through bare ZnO nanowires. Estimated enhancement of the Raman signal accounted for the volume difference between solution affected by SERS and solution sensed by the Raman system. More importantly, the detected SERS signal is from molecules in solution and unadsorbed to the sensing surfaces. This lack of adsorption was confirmed by tracking the SERS enhancement of a crystal violet Raman peak over time. This greatly enhances the value and flexibility of Raman spectroscopy as a detection technique for a wide variety of applications.

42 ENGINEERING↗

DOE OSTI2022

Efficient co-solution of time step size and independent state in simulations of fluid-driven fracture propagation with embedded meshes

Here we present an efficient time-continuation scheme for fluid-driven fracture propagation problems in the extended finite element method framework. The approach applies a monolithic solution strategy to a fully coupled and implicit approximation of hydro-mechanical systems in conjunction with simultaneous linear elastic propagation of multiple fractures. At the end of each time step, the process ensures that the weakest fracture tip is in an equilibrium propagation regime. Furthermore, the solution process provides an initialization procedure for the newly created fracture spaces and an a priori estimate of the stress intensity factor growth rate, improving simulation robustness, and efficiency. The solution process is validated using the Kristianovich-Geertsma-de Klerk analytical solution under the toughness- and viscosity-dominated regimes. It is also extended to and demonstrated on problems with multiple fractures undergoing simultaneous propagation with stress shadow interactions. Numerical examples demonstrate that the solution process can reduce the required computational cost by one order of magnitude compared to other existing methods.

42 ENGINEERING↗