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At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Synergistic Effect of Nitrogen and Refractory Material on TiN Formation and Equiaxed Grain Structure of Ferritic Stainless Steel

The effect of nitrogen content on the formation of an equiaxed solidification structure of Fe-16Cr steel was investigated. Moreover, two different kinds of refractory materials, i.e., alumina and magnesia, were employed to control the type of oxide inclusion. The characteristics of TiN(-oxide) inclusions were quantitatively analyzed in both molten steel and solidified samples. When the melting was carried out in the alumina refractory, the grain size continuously decreased with increasing nitrogen content. However, a minimum grain size was observed at a specific nitrogen content (approx. 150 ppm) when the steel was melted in the magnesia refractory. Most of the single TiN particles had a cuboidal shape and fine irregularly shaped particles were located along the grain boundary due to the microsegregation of Ti at the grain boundary during solidification. The type of TiN-oxide hybrid inclusion was strongly affected by the refractory material where Al{sub 2}O{sub 3}-TiN and MgAl{sub 2}O{sub 4}-TiN hybrid-type inclusions were obtained in the alumina and magnesia refractory experiments, respectively. The formation of oxide inclusions was well predicted by thermochemical computations and it was commonly found that oxide particles were initially formed, followed by the nucleation and growth of TiN. When the nitrogen content increased, the number density of TiN linearly increased in the alumina refractory experiments. However, the number of TiN exhibits a maximum at about [N] = 150 ppm, at which a minimum grain size was obtained in the magnesia refractory experiments. Therefore, the larger the number density of TiN, the smaller the primary grain size after solidification. The number density of TiN in the steel melted in the magnesia refractory was greater than that in the steel melted in the alumina refractory at given Ti and N contents, which was due to the lower planar lattice disregistry of MgAl{sub 2}O{sub 4}-TiN interface rather than that of Al{sub 2}O{sub 3}-TiN interface. When ∆T{sub TiN} (= difference between the TiN precipitation temperature and the liquidus of the steel) was 20 K to 40 K, the number density of effective TiN was maximized and thus, the grain size was minimized after solidification. Finally, although most of the TiN particles were smaller than 1 μm in the molten steel samples irrespective of the nitrogen content, TiN particles larger than 10 μm were observed in the solidified samples when the nitrogen content was greater than 150 ppm. The growth of TiN particles during melting and solidification was well predicted by the combinatorial simulation of the ‘Ostwald ripening model’ based on the Lifshitz–Slyozov–Wagner theory in conjunction with the ‘Diffusion controlled model’ using Ohnaka’s microsegregation equation.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗
DOE OSTI2023

Determination of Kinetic Properties of Ni(II) Ions in Molten LiF-NaF-KF via Voltammetry

Kinetic properties of Ni(II) in eutectic LiF-NaF-KF (FLiNaK) molten salt were determined at T = 748–823 K using cyclic voltammetry (CV), square wave voltammetry (SWV), and chronoamperometry (CA) measurements using a glassy C working electrode, Ni(II)/Ni reference electrode, and Ni counter electrode. Reduction of Ni(II) to Ni(s) was determined to be a single step, two-electron transfer process. Diffusivity values were calculated using the Berzins and Delahay equation and semi-integral electroanalysis from the CV measurements as well as using the Cottrell equation from the CA measurements. Diffusivity of Ni(II) in molten FLiNaK at T = 748–823 K was determined to be 3.27 × 10 –7 –3.04 × 10 –6 cm 2 s –1 with an activation energy of 62–104 kJ mol –1 . The estimated kinetic properties varied appreciably among methodologies possibly due to inherent assumptions in theory regarding reversibility and unit activity during Ni metal deposition on the working electrode.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

A discrete model of a modified Burgers' partial differential equation

A new finite-difference scheme is constructed for a modified Burger's equation. Three special cases of the equation are considered, and the 'exact' difference schemes for the space- and time-independent forms of the equation are presented, along with the diffusion-free case of Burger's equation modeled by a difference equation. The desired difference scheme is then obtained by imposing on any difference model of the initial equation the requirement that, in the appropriate limits, its difference scheme must reduce the results of the obtained equations.

Mickens, R. E.↗
DOE OSTI2016

The Transport Equation in Optically Thick Media: Discussion of IMC and its Diffusion Limit

We discuss the limits of validity of the Implicit Monte Carlo (IMC) method for the transport of thermally emitted radiation. The weakened coupling between the radiation and material energy of the IMC method causes defects in handling problems with strong transients. We introduce an approach to asymptotic analysis for the transport equation that emphasizes the fact that the radiation and material temperatures are always different in time-dependent problems, and we use it to show that IMC does not produce the correct diffusion limit. As this is a defect of IMC in the continuous equations, no improvement to its discretization can remedy it.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Multiscale Modeling and Experimental Insights into High-Temperature Soil Biodegradation Dynamics of Semi-Crystalline Poly(Lactic Acid) Nonwoven Fabrics

This study investigates the biodegradation of semi-crystalline poly(lactic acid) (PLA) nonwovens (NWs) in soil at 58 °C using both experimental and mathematical modeling approaches. The model utilizes a system of parabolic diffusion-reaction partial differential equations (PDEs) to elucidate chemical transformations over time and in space. It accounts for phenomena such as the diffusion of water and lactic acid monomers through the polymer matrix and into the surrounding soil, along with their microbial breakdown. It also accounts for the initial PLA crystallinity and predicts its evolution in time. The model is solved numerically for a single filament, and the results were used to shed light on PLA NW transformations observed in soil over a 180-day incubation period. Various characterization techniques, including scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and Raman spectroscopy, were employed to assess morphological changes, crystallinity, and molecular changes in the NWs throughout the experiment. By comparing the experimental data with the model predictions, the hydrolysis rate coefficient was found to be 3.37 × 10 -7 s -1 , while the rate of microbial degradation of lactic acid monomers was faster, of the order of 9.63 × 10 -7 s -1 . The findings highlight the significant role of crystallinity in the biodegradation process. The PLA degradation ceases when no amorphous material remains, and the crystallinity reaches 0.8, as observed in the experiments by day 120. Furthermore, this research contributes to a deeper understanding of PLA biodegradation dynamics and offers insights for effectively managing biodegradable materials in environmental settings.

Diffusion−reaction modeling↗
NASA NTRS2005

Cosmic Ray Propagation through the Magnetic Fields of the Galaxy with Extended Halo

In this project we perform theoretical studies of 3-dimensional cosmic ray propagation in magnetic field configurations of the Galaxy with an extended halo. We employ our newly developed Markov stochastic process methods to solve the diffusive cosmic ray transport equation. We seek to understand observations of cosmic ray spectra, composition under the constraints of the observations of diffuse gamma ray and radio emission from the Galaxy. The model parameters are directly are related to properties of our Galaxy, such as the size of the Galactic halo, particle transport in Galactic magnetic fields, distribution of interstellar gas, primary cosmic ray source distribution and their confinement in the Galaxy. The core of this investigation is the development of software for cosmic ray propagation models with the Markov stochastic process approach. Values of important model parameters for the halo diffusion model are examined in comparison with observations of cosmic ray spectra, composition and the diffuse gamma-ray background. This report summarizes our achievement in the grant period at the Florida Institute of Technology. Work at the co-investigator's institution, the University of New Hampshire, under a companion grant, will be covered in detail by a separate report.

Zhang, Ming↗
DOE OSTI2015

The mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient

Numerical schemes for nonlinear parabolic equations based on the harmonic averaging of cell-centered diffusion coefficients break down when some of these coefficients go to zero or their ratio grows. To tackle this problem, we propose new mimetic finite difference schemes that use a staggered discretization of the diffusion coefficient. The primary mimetic operator approximates div (k•); the derived (dual) mimetic operator approximates - ∇(•). The new mimetic schemes preserve symmetry and positive-definiteness of the continuum problem which allows us to use algebraic solvers with optimal complexity. We perform detailed numerical analysis of the new schemes for linear elliptic problems and a specially designed linear parabolic problem that has solution dynamics typical for nonlinear problems. We also show that the new schemes are competitive with the state-of-the-art schemes for steady-state problems but provide much more accurate solution dynamics for the transient problem.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Transitions to chaos in two-dimensional double-diffusive convection

The partial differential equations governing two-dimensional thermosolutal convection in a Boussinesq fluid with free boundary conditions have been solved numerically in a regime where oscillatory solutions can be found. A systematic study of the transition from nonlinear periodic oscillations to temporal chaos has revealed sequences of period-doubling bifurcations. Overstability occurs if the ratio of the solutal to the thermal diffusivity tau is less than 1 and the solutal Rayleigh number Rs is sufficiently large. Solutions have been obtained for two representative values of tau. For tau = 0.316, R(s) = 10,000, symmetrical oscillations undergo a bifurcation to asymmetry, followed by a cascade of period-doubling bifurcations leading to aperiodicity, as the thermal Rayleigh number R(T) is increased. At higher values of R(T), the bifurcation sequence is repeated in reverse, restoring simple periodic solutions. As R(T) is further increased more period-doubling cascades, followed by chaos, can be identified. Within the chaotic regions there are narrow periodic windows, and multiple branches of oscillatory solutions coexist. Eventually the oscillatory branch ends and only steady solutions can be found. The development of chaos has been investigated for tau = 0.1 by varying R(T) for several different values of R(s). When R(s) is sufficiently small there are periodic solutions whose period becomes infinite at the end of the oscillatory branch. As R(s) is increased, chaos appears in the neighborhood of these heteroclinic orbits. At higher values of R(s), chaos is found for a broader range in R(T). A truncated fifth-order model suggest that the appearance of chaos is associated with heteroclinic bifurcations.

Knobloch, E.↗
NASA NTRS2002

Volcanic Plume Heights on Mars: Limits of Validity for Convective Models

Previous studies have overestimated volcanic plume heights on Mars. In this work, we demonstrate that volcanic plume rise models, as currently formulated, have only limited validity in any environment. These limits are easily violated in the current Mars environment and may also be violated for terrestrial and early Mars conditions. We indicate some of the shortcomings of the model with emphasis on the limited applicability to current Mars conditions. Specifically, basic model assumptions are violated when (1) vertical velocities exceed the speed of sound, (2) radial expansion rates exceed the speed of sound, (3) radial expansion rates approach or exceed the vertical velocity, or (4) plume radius grossly exceeds plume height. All of these criteria are violated for the typical Mars example given here. Solutions imply that the convective rise, model is only valid to a height of approximately 10 kilometers. The reason for the model breakdown is hat the current Mars atmosphere is not of sufficient density to satisfy the conservation equations. It is likely that diffusion and other effects governed by higher-order differential equations are important within the first few kilometers of rise. When the same criteria are applied to eruptions into a higher-density early Mars atmosphere, we find that eruption rates higher than 1.4 x 10(exp 9) kilograms per second also violate model assumptions. This implies a maximum extent of approximately 65 kilometers for convective plumes on early Mars. The estimated plume heights for both current and early Mars are significantly lower than those previously predicted in the literature. Therefore, global-scale distribution of ash seems implausible.

Glaze, Lori S.↗
DOE OSTI2015

Insights into cadmium diffusion mechanisms in two-stage diffusion profiles in solar-grade Cu(In,Ga)Se{sub 2} thin films

Cadmium diffusion experiments were performed on polished copper indium gallium diselenide (Cu(In,Ga)Se{sub 2} or CIGS) samples with resulting cadmium diffusion profiles measured by time-of-flight secondary ion mass spectroscopy. Experiments done in the annealing temperature range between 275 °C and 425 °C reveal two-stage cadmium diffusion profiles which may be indicative of multiple diffusion mechanisms. Each stage can be described by the standard solutions of Fick's second law. The slower cadmium diffusion in the first stage can be described by the Arrhenius equation D{sub 1} = 3 × 10{sup −4} exp (− 1.53 eV/k{sub B}T) cm{sup 2} s{sup −1}, possibly representing vacancy-meditated diffusion. The faster second-stage diffusion coefficients determined in these experiments match the previously reported cadmium diffusion Arrhenius equation of D{sub 2} = 4.8 × 10{sup −4} exp (−1.04 eV/k{sub B}T) cm{sup 2} s{sup −1}, suggesting an interstitial-based mechanism.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Nonlinear optimization for a tumor invasion PDE model

In this work, we introduce a methodology to approximate unknown parameters that appear on a non-linear reaction–diffusion model of tumor invasion. These equations consider that tumor-induced alteration of micro-environmental pH furnishes a mechanism for cancer invasion. A coupled system reaction–diffusion explaining this model is given by three partial differential equations for the non-dimensional spatial distribution and temporal evolution of the density of normal tissue, the neoplastic tissue growth and the excess concentration of H{sup +} ions. The tumor model parameters have a corresponding biological meaning: the reabsorption rate, the destructive influence of H{sup +} ions in the healthy tissue, the growth rate of tumor tissue and the diffusion coefficient. We propose to solve the direct problem using the Finite Element Method (FEM) and minimize an appropriate functional including both the real data (obtained via in-vitro experiments and fluorescence ratio imaging microscopy) and the numerical solution. The gradient of the functional is computed by the adjoint method.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

27 Al Pulsed Field Gradient, Diffusion–NMR Spectroscopy of Solvation Dynamics and Ion Pairing in Alkaline Aluminate Solutions

Here, pulsed field gradient nuclear magnetic resonance (PFG-NMR) measurements were successfully applied to the 27 Al (I = 5/2) nucleus in concentrated electrolytes to investigate the diffusion of aluminate ions [Al(OH) 4 – ] in simulant high-level nuclear waste (3 M NaOH) between 25 and 85 °C. The temperature-dependent diffusion coefficients obtained from 1 H, 23 Na, and 27 Al PFG-NMR were well fit by a Vogel–Fulcher–Tammann model and a power law equation. Comparison of 27 Al diffusion coefficients of 0.1 M Al(OH) 4 – in ~3 M MOH (where M = Na + , K + , (CH 3 ) 4 N + ) at room temperature varied in agreement with the expected changes in solution viscosity via Stokes–Einstein relationship, confirming that the dominant Al species at these conditions are Al(OH) 4 – monomers. This 27 Al PFG-NMR study extends an established methodology to a previously unexplored nucleus enabling this experimental technique to be leverage for exploring ion transport, speciation, and solution structure in concentrated electrolytes.

Diffusion↗
NASA NTRS1987

On the acceleration of charged particles at relativistic shock fronts

The diffusive acceleration of highly relativistic particles at a shock is reconsidered. Using the same physical assumptions as Blandford and Ostriker (1978), but dropping the restriction to nonrelativistic shock velocities, the authors find approximate solutions of the particle kinetic equation by generalizing the diffusion approximation to higher order terms in the anisotropy of the particle distribution. The general solution of the transport equation on either side of the shock is constructed, which involves the solution of an eigenvalue problem. By matching the two solutions at the shock, the spectral index of the resulting power law is found by taking into account a sufficiently large number of eigenfunctions. Low-order truncation corresponds to the standard diffusion approximation and to a somewhat more general method described by Peacock (1981). In addition to the energy spectrum, the method yields the angular distribution of the particles and its spatial dependence.

Kirk, J. G.↗
NASA NTRS1994

Microwave heating and joining of ceramic cylinders: A mathematical model

A thin cylindrical ceramic sample is placed in a single mode microwave applicator in such a way that the electric field strength is allowed to vary along its axis. The sample can either be a single rod or two rods butted together. We present a simple mathematical model which describes the microwave heating process. It is built on the assumption that the Biot number of the material is small, and that the electric field is known and uniform throughout the cylinder's cross-section. The model takes the form of a nonlinear parabolic equation of reaction-diffusion type, with a spatially varying reaction term that corresponds to the spatial variation of the electromagnetic field strength in the waveguide. The equation is analyzed and a solution is found which develops a hot spot near the center of the cylindrical sample and which then propagates outwards until it stabilizes. The propagation and stabilization phenomenon concentrates the microwave energy in a localized region about the center where elevated temperatures may be desirable.

Booty, Michael R.↗
DOE OSTI2016

A model for the compositions of non-stoichiometric intermediate phases formed by diffusion reactions, and its application to Nb 3 Sn superconductors

In this work we explore the compositions of non-stoichiometric intermediate phases formed by diffusion reactions: a mathematical framework is developed and tested against the specific case of Nb 3 Sn superconductors. In the first part, the governing equations for the bulk diffusion and interphase interface reactions during the growth of a compound are derived, numerical solutions to which give both the composition profile and growth rate of the compound layer. The analytic solutions are obtained with certain approximations made. In the second part, we explain an effect that the composition characteristics of compounds can be quite different depending on whether it is the bulk diffusion or grain boundary diffusion that dominates in the compounds, and that “frozen” bulk diffusion leads to unique composition characteristics that the bulk composition of a compound layer remains unchanged after its initial formation instead of varying with the diffusion reaction system; here the model is modified for the case of grain boundary diffusion. Lastly, we apply this model to the Nb 3 Sn superconductors and propose approaches to control their compositions.

36 MATERIALS SCIENCE↗