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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

3D simulations of spinlike flames in Co/Al multilayers with enhanced conduction losses

Reactive Co/Al multilayers are uniformly structured materials that may be ignited to produce rapid and localized heating. Prior studies varying the bilayer thickness (i.e., sum of two individual layers of Co and Al) have revealed different types of flame morphologies, including: (a) steady/planar, (b) wavy/periodic, and (c) transverse bands, originating in the flame front. These instabilities resemble the “spin waves” first observed in the early studies of solid combustion (i.e., Ti cylinder in a N 2 atmosphere), and are likewise thought to be due to the balance of heat released by reaction and heat conduction forward into the unreacted multilayer. However, the multilayer geometry and three-dimensional (3D) edge effects are relatively unexplored. In this work, a new diffusion-limited reaction model for Co/Al multilayers was implemented in large, novel 3D finite element analysis (FEA) simulations, in order to study the origins of these spinlike flames. This reaction model builds upon previous work by introducing three new phase-dependent property models for: (1) the diffusion coefficient, (2) anisotropic thermal conductivity tensor, and (3) bulk heat capacity, as well as one additional model for the bilayer-dependent heat of reaction. These novel 3D simulations are the first to predict both steady and unsteady flames in Co/Al multilayers. Moreover, two unsteady modes of flame propagation are identified, which depend on the enhanced conduction losses with slower flames, as well as flame propagation around notched edges. Finally, future work will consider the generality of the current modeling approach and also seek to define a more generalized set of stability criteria for additional multilayer systems.

42 ENGINEERING↗
DOE OSTI2020

Fast Proton Transfer and Hydrogen Evolution Reactivity Mediated by [Co 13 C 2 (CO) 24 ] 4–

A common approach to speeding up proton transfer (PT) by molecular catalysts is manipulation of the secondary coordina-tion sphere with proton relays and these enhance overall reaction rates by orders of magnitude. In contrast, heterogenous electrocatalysts have band structures that promote facile PT concerted with electron transfer (ET), known as the Volmer mechanism. Here in this paper, we show that [Co 13 C 2 (CO) 24 ] 4– , containing multiple Co-Co bonds to statistically enhance observed rates of PT, promotes PT on the order of 2.3 × 10 9 M -1 s -1 which suggests a diffusion-limited rate. The fast ET and PT chemistry is at-tributed to the delocalized electronic structure of [Co 13 C 2 (CO) 24 ] 4– . Electrochemical characterization of [Co 13 C 2 (CO) 24 ] 4– in the presence and absence of protons reveals ET kinetics and diffusion behavior similar to other small clusters such as nano-materials and fullerenes.

08 HYDROGEN↗
DOE OSTI2022

Circumventing thermodynamics to synthesize highly metastable perovskites: nano eggshells of SnHfO 3

Sn(II)-based perovskite oxides, being the subject of longstanding theoretical interest for the past two decades, have been synthesized for the first time in the form of nano eggshell particle morphologies. All past reported synthetic attempts have been unsuccessful owing to their metastable nature, i.e., by their thermodynamic instability towards decomposition to their constituent oxides. A new approach was discovered that finally provides an effective solution to surmounting this intractable synthetic barrier and which can be the key to unlocking the door to many other predicted metastable oxides. A low-melting KSn 2 Cl 5 salt was utilized to achieve a soft topotactic exchange of Sn(II) cations into a Ba-containing perovskite, i.e., BaHfO 3 with particle sizes of ~350 nm, at a low reaction temperature of 200 °C. The resulting particles exhibit nanoshell-over-nanoshell morphologies, i.e., with SnHfO 3 forming as ~20 nm thick shells over the surfaces of the BaHfO 3 eggshell particles. Formation of the metastable SnHfO 3 is found to be thermodynamically driven by the co-production of the highly stable BaCl 2 and KCl side products. Despite this, total energy calculations show that Sn(II) distorts from the A-site asymmetrically and randomly and the interdiffusion has a negligible impact on the energy of the system (i.e., layered vs. solid solution). Additionally, nano eggshell particle morphologies of BaHfO 3 were found to yield highly pure SnHfO 3 for the first time, thus circumventing the intrinsic ion-diffusion limits occurring at this low reaction temperature. In summary, these results demonstrate that the metastability of many theoretically predicted Sn(II)-perovskites can be overcome by leveraging the high cohesive energies of the reactants, the exothermic formation of a stable salt side product, and a shortened diffusion pathway for the Sn(II) cations.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Mechanism of Stoichiometrically Governed Titanium Oxide Brownian Tree Formation on Stepped Au(111)

Previously observed formation of substoichiometric titanium oxide dendritic structures across terraces of Au(111) is computationally studied and shown to follow the classical fractal formation mechanism of diffusion-limited aggregation (DLA). Globally optimized gas-phase oxide cluster structures are sampled in a variety of landing formations on gold surfaces and shown to favor isomers driving polymerization to Brownian tree fractal structures. Mobility of Ti 3 O 5 monomers is shown to be extremely high, with diffusion barriers of 0.21 eV or less. Through bonding stabilization, polymerization of these monomers is energetically favorable and irreversible on the 111 terrace but geometrically impossible to propagate along the step edge. Simulated scanning tunneling microscopy (STM) images show strong similarity to experiment. By contrast, observation of Ti 3 O 6 aggregating as wires along step edges is explained by the affinity of oxygen to step edges and statistical arguments for aggregation entropy at the step, in addition to low barriers for monomer diffusion and polymerization.

36 MATERIALS SCIENCE↗
NASA NTRS2003

Evolution of Local Microstructures: Spatial and Temporal Correlation in Clusters Undergoing 2-Dimensional Diffusion

Diffusion-limited, capillarity-driven, coarsening of precipitates is an important and intensively studied phenomenon. Coarsening can occur among several microstructural constituents ranging from the primary phases to widely dispersed precipitates. Moreover, coarsening of three-dimensional (3-D) phase domains, occurring via mass transport through a two-dimensional (2-D) diffusion field (called mixed-dimensional phase coarsening) is a cooperative phenomenon that is of practical importance, especially in thin film technologies and catalysis. A primary objective of our current work is to focus on the details of evolving microstructures through a study of 'island' formation in heteroepitaxial film/substrate systems. Whereas this work has been designed for space-based coarsening studies, which require long-duration quality microgravity to observe 3-D Ostwald ripening, a significant amount of work has been performed during ground-based studies to observe diffusional coarsening in a liquid-liquid two-phase system. We have performed the experiment at an isopycnic point to maximize exclusion of gravity-based system disturbance. This has allowed observations of 3-D droplets, immobilized by container wall contact, undergoing coarsening by 2-D diffusion for the required long times (approximately 4 months) using a holographic imaging technique. Although such systems may not be as reliant on long-duration microgravity processing as 3-D systems are, they are of direct relevance to so-called mixed-dimensional coarsening and to the study of heterostructures grown by thin-film technique

Curreri, Peter A.↗
NASA NTRS2003

Evolution of Local Microstructures: Spatial Instabilities in Coarsening Clusters

Diffusion-limited capillarity-driven coarsening of precipitates is an important and intensively studied phenomenon. The classic coarsening theory developed by Lifshitz and Syozov and Wagner (LSW theory) is limited to infinitesimally small volume fractions, V(sub nu), therefore neglects all direct interparticle interactions. This work uses modeling and holographic imaging to compare coarsening rates in "high" volume fraction versus low volume fraction microstructures by observing mixed-dimensional droplets (spherical caps on a surface coarsening by two-dimensional diffusion) during ground-based investigations. The method involves filling a cell with selected homogeneous parent phase, and cooling below the consolute temperature to the isopycnic temperature in the two-phase region of a monotectic system. A microgravity holographic experiment is required for three-dimensional observations to minimize sedimentation during long-term coarsening. Determination of sizes and positions of the many droplets in the holographic images requires automation. We have developed software for automated data analysis, and demonstrated good agreement between regenerated maps and scaled photographs of the original holograms for mixed dimensional coarsening. The results of these experiments were presented in a formal microgravity Science Concept Review (SCR) on December 18, 2000.

Source record↗
NASA NTRS1971

Mechanism of the oxidation of titanium disilicide.

Study of the oxidation of TiSi2 at temperatures of 300 to 1300 C. Wafers prepared using the techniques of powder metallurgy had densities of 95 to 98% of the theoretical value. On oxidation at temperatures up to 600 C, the polished wafers formed a protective, titania-silica glass. The rate data indicate a complex surface and diffusion-limited mechanism. Above 600 deg C, the oxide consisted of an amorphous SiO2 film with crystalline islands of TiO2 (rutile). From 1000 to 1300 C, parabolic kinetics with an activation energy of 21.3 kcal/mole were observed. These data are consistent with a model in which the rate-determining step is the diffusion of oxygen through the silica film with the simultaneous diffusion of titanium from the substrate to the islands of rutile growing on top of the amorphous silica.

Schwettmann, F. N.↗
DOE OSTI2025

Annihilation-limited long-range exciton transport in high-mobility conjugated copolymer films

A combination of ultrafast, long-range, and low-loss excitation energy transfer from the photoreceptor location to a functionally active site is essential for cost-effective polymeric semiconductors. Delocalized electronic wavefunctions along π-conjugated polymer (CP) backbone can enable efficient intrachain transport, while interchain transport is generally thought slow and lossy due to weak chain–chain interactions. In contrast to the conventional strategy of mitigating structural disorder, amorphous layers of rigid CPs, exemplified by highly planar poly(indacenodithiophene-co-benzothiadiazole) (IDT-BT) donor-accepter copolymer, exhibit trap-free transistor performance and charge-carrier mobilities similar to amorphous silicon. Here, we report long-range exciton transport in HJ -aggregated IDTBT thin-film, in which the competing exciton transport and exciton–exciton annihilation (EEA) dynamics are spectroscopically separated using a phase-cycling-based scheme and shown to depart from the classical diffusion-limited and strong-coupling regime. In the thin film, we find an annihilation-limited mechanism with ≪100% per-encounter annihilation probability, facilitating the minimization of EEA-induced excitation losses. In contrast, excitons on isolated IDTBT chains diffuse over 350 nm with 0.56 cm 2 s −1 diffusivity, before eventually annihilating with unit probability on first contact. We complement the pump–probe studies with temperature-dependent photocurrent and EEA measurements from 295 K to 77 K and find a remarkable correspondence of annihilation rate and photocurrent activation energies in the 140 K to 295 K temperature range.

Shi, Yuping (ORCID:0000000318289415)↗
DOE OSTI2020

Predicting cell-to-cell failure propagation and limits of propagation in lithium-ion cell stacks

Thermal runaway of lithium-ion batteries is a risk that is magnified when stacks of lithium-ion cells are used for large scale energy storage. When limits of propagation can be identified so that systems can be designed to prevent large scale cascading failure even if a failure does occur, these systems will be safer. This work addresses the prediction of cell-to-cell failure propagation and the propagation limits in lithium-ion cell stacks to better understand and identify safe designs. A thermal-runaway model is presented based on recent developments in thermochemical source terms. It is noted that propagating failure is characterized by temperatures above which calorimetry data is available. Results show high temperature propagating failure predictions are too rapid unless an intra-particle diffusion limit is included, introducing a Damköhler number limiter into the rate expression. This new model form is evaluated against cell-to-cell failure propagation where the end cell of a stack is forced into thermal runaway through a nail-induced short circuit. Limits of propagation for this configuration are identified. Results show cell-to-cell propagation predictions are consistent with measurements over a range of cell states of charge and with the introduction of metal plates between cells to add system heat capacity representative of structural members. This consistency extends from scenarios where propagation occurs through scenarios where propagation is prevented.

25 ENERGY STORAGE↗
DOE OSTI2024

Understanding particle size effect on fast-charging behavior of graphite anode using ultra-thin-layer electrodes

Extreme fast charging (≤ 15 min) of lithium-ion batteries is highly desirable to accelerate mass-market adoption of electric vehicles. However, significant capacity fading, as well as safety issues due to the lithium plating caused by the fast charging rate, limit its implementation. In this study, we investigated the fast-charging capability of graphite materials with various particle sizes. To eliminate the Li + ion concentration gradient effect across the thickness of the electrode, ultra-thin-layer graphite electrodes were developed to investigate the "real" fast-charging capability of graphite at the particle level. Electrochemical assessments as well as microscopic characterizations revealed that smaller particles exhibited superior fast-charging performance, featuring enhanced capacity reversibility, faster charging rate, and less lithium plating under the same fast-charging conditions. It is shown that small-particle graphite (mean radius of 3.3 μm) could withstand a 4C charge (to 80 % state-of-charge) without plating, with minimal plating occurring at 6C. Thicker particles exhibited plating at lower C-rates. Since the experimental data could not directly explain whether intra-particle diffusion limitations or interfacial reaction limitations dominated the plating mechanism, the pseudo-2-dimensional model was used to evaluate the most likely plating mechanism. The model suggested that particle-level diffusion is the dominant mechanism contributing to plating at high rates. Finally, this work provides comprehensive insights into the particle size effects on fast-charging capability, offering a better understanding of fast-charging behavior and valuable guidance for designing optimal electrode architecture for high-rate lithium-ion batteries.

25 ENERGY STORAGE↗
NASA NTRS1996

Non-linear resonance of fluids in a crystal growth cavity

In the microgravity environment, the effect of gravity on fluid motion is much reduced. Hence, secondary effects such as vibrations, jitters, surface tension, capillary effects, and electromagnetic forces become the dominant mechanism of fluid convection. Numerous studies have been conducted to investigate fluid behavior in microgravity with the ultimate goal of developing processes with minimal influence from convection. Industrial applications such as crystal growth from solidification of melt and protein growth for pharmatheutical application are just a few examples of the vast potential benefit that can be reaped from material processing in space. However, a space laboratory is not immune from all undesirable disturbances and it is imperative that such disturbances be well understood, quantifiable, and controlled. Non-uniform and transient accelerations such as vibrations, jitters, and impulsive accelerations exist as a result of crew activities, space vehicle maneuvering, and the operations of on-board equipment. Measurements conducted on-board a U.S. Spacelab showed the existence of vibrations in the frequency range of 1 to 100 Hz with a dominant mode of 17 Hz and harmonics of 54 Hz. The observed vibration is not limited to any coordinate plane but exists in all directions. Similar situation exists on-board the Russian MIR space station. Due to the large structure of its design, the future International Space Station will have its own characteristic vibration spectrum. It is well known that vibration can exert substantial influence on heat and mass transfer processes, thus hindering any attempts to achieve a diffusion-limited process. Experiments on vibration convection for a liquid-filled enclosure under one-g environment showed the existence of different flow regimes as vibration frequency and intensity changes. Results showed the existence of a resonant frequency, near which the enhancement is the strongest, and the existence of a high frequency asymptote. Numerical simulations of vibration convection have been conducted by Yurkov, Fu and Shieh, and by Wang. These analyses considered a two-dimensional air-filled cell under weightlessness condition and showed results similar to those of the experiments. It is not yet known whether resonance convection can be triggered by jitter alone or whether it requires the interaction of jitter with other convective forces in low gravity. An order of magnitude analysis, however, can be used to show the dependence of the resonance frequency on the fluid Prandtl number. Even though the onset of resonance convection may depend on other factors, results indicates that fluids with low Prandtl numbers are more susceptible to resonance than those with high Prandtl numbers. The current study is aimed at gaining additional insights to this problem using germanium as working fluid. Germanium was chosen for this analysis because of its common usage in solidification process and its relatively low Prandtl number (Pr = 0.02).

Wang, Francis C.↗
NASA NTRS1976

Theoretical study of reactive and nonreactive turbulent coaxial jets

The hydrodynamic properties and the reaction kinetics of axisymmetric coaxial turbulent jets having steady mean quantities are investigated. From the analysis, limited to free turbulent boundary layer mixing of such jets, it is found that the two-equation model of turbulence is adequate for most nonreactive flows. For the reactive flows, where an allowance must be made for second order correlations of concentration fluctuations in the finite rate chemistry for initially inhomogeneous mixture, an equation similar to the concentration fluctuation equation of a related model is suggested. For diffusion limited reactions, the eddy breakup model based on concentration fluctuations is found satisfactory and simple to use. The theoretical results obtained from these various models are compared with some of the available experimental data.

Gupta, R. N.↗
NASA NTRS1999

Control of Meridional Flow in Circular Cylinders by a Travelling Axial Magnetic Field

Convective flow in a Bridgman or float zone configuration significantly affects the interface shape and segregation phenomena. While the primary causative factor for this flow is buoyancy induced convection in an enclosed Bridgman melt, the presence of a free surface gives rise to surface tension driven flows in the floating zone processing of melts. It is of interest to curtail these flows in order to realize near quiescent growth conditions that have shown to result in crystals with good longitudinal and radial homogeneity and thereby of better overall quality. While buoyancy effects can be reduced by careful processing in a low gravity (space) environment, the reduction of Marangoni flows due to surface tension variations is not that straight forward. Attempts have been made with some limited success with the use of external fields to affect the melt thermo-fluid behavior. The use of a static magnetic field that reduces convective contamination through the effects of a non-intrusively induced, dissipative Lorentz force in an electrically conducting melt is one such approach. Experiments have shown that axial fields of the order of 5 Tesla can significantly eliminate convection and yield close to diffusion limited crystal growth conditions. The generation and use of such high magnetic fields require substantial hardware and incur significant costs for its operation. Lately, the use of rotating magnetic fields has been tested in semiconductor crystal growth. The method is fairly well known and commonly used in metal processing but its adaptation to crystal growth of semiconductors is fairly recent. The elegance of the technique rests in its low power requirement (typically 10-20 milli-Tesla at 50-400 Hz) and its efficacy in curtailing deleterious temperature fluctuations in the melt. A rotating magnetic field imposes a rotational force and thereby induces a circulation within the melt that tends to dominate other sporadic convective effects. Thus a known low level of convective flow is introduced into the system. A new novel variation of the Lorentz force mechanism is proposed and investigated in this study. Since one of the desired process conditions in melt crystal growth is the minimization of convective effects, this investigation examines the use of an external field of magnetic origin to counteract existing convective flow within the melt. This is accomplished by utilizing a running or traveling axial magnetic wave in the system. The concept is similar to the use of vibrational means in order to induce streaming flows that oppose buoyant or surface tension driven convection in the system. The rotation direction as well as the magnitude (strength) of this circulation can be easily controlled by external inputs thus affording a direct means of controlling the developing shape of the crystallizing front (interface). The theoretical model of this technique is fully developed and presented in this paper. Results from the solution of the developed governing equations and boundary conditions are also presented. An experimental demonstration of the concept is presented through the suppression of natural convective flow in a mercury column. Implications to crystal growth systems will be fully explored in the final manuscript.

Mazuruk, K.↗
DOE OSTI2026

Thermodynamic Control of Interface Directs MnO 2 Nucleation Chemistry for Dense and Conformal Electrodeposition

Manganese dioxide (MnO 2 ) is widely recognized as a promising material for high-energy-density energy storage systems due to its broad applicability and facile electrodeposition. However, achieving uniform, thin, and high-mass-loading MnO 2 coatings on high-surface-area electrodes remains a significant challenge. Conventional electrodeposition methods typically yield nonuniform, thick layers with poor conductivity and limited material utilization, restricting their practical use. Here, we uncover a thermodynamically engineered vanadyl/pervanadyl (VO 2+ /VO 2 + ) interface that fundamentally reshapes MnO 2 electrodeposition chemistry, enabling highly uniform and dense coatings. Here, combining in situ AFM measurement, Classical Nucleation Theory, and Johnson–Mehl–Avrami–Kolmogorov modeling, we show that this interface reduces early-stage detectable MnO 2 island size by 35-fold and shifts the MnO 2 growth from diffusion-limited to reaction-limited progressive nucleation. This thermodynamically controlled interface yields highly dense and conformal MnO 2 films with record-high mass loading of 241 mg cm –2 (1607 mg cm –3 ) on 3D-printed graphene aerogels, without compromising porosity or inducing thickness gradient. As a prototype demonstration, the resulting MnO 2 electrodes deliver record-setting volumetric performance in both capacitors (106 F cm –3 ) and Zn//MnO 2 pouch cells (162 mAh cm –3 ). Beyond energy storage, our findings demonstrate the significance of thermodynamic interface control in MnO 2 nucleation chemistry for achieving dense and uniform coatings on various substrates, with implications for electrocatalysis, semiconductor processing, and advanced materials manufacturing.

Batteries↗
DOE OSTI2023

Interpreting inorganic compositional depth profiles to understand the rate-limiting step in vapor phase infiltration processes

Vapor phase infiltration (VPI) is a post-polymerization modification technique that infuses inorganics into polymers to create organic–inorganic hybrid materials with new properties. Much is yet to be understood about the chemical kinetics underlying the VPI process. The aim of this study is to create a greater understanding of the process kinetics that govern the infiltration of trimethyl aluminum (TMA) and TiCl 4 into PMMA to form inorganic-PMMA hybrid materials. To gain insight, this paper initially examines the predicted results for the spatiotemporal concentrations of inorganics computed from a recently posited reaction–diffusion model for VPI. This model provides insight on how the Damköhler number (reaction versus diffusion rates) and non-Fickian diffusional processes (hindering) that result from the material transforming from a polymer to a hybrid can affect the evolution of inorganic concentration depth profiles with time. Subsequently, experimental XPS depth profiles are collected for TMA and TiCl 4 infiltrated PMMA films at 90 °C and 135 °C. The functional behavior of these depth profiles at varying infiltration times are qualitatively compared to various computed predictions and conclusions are drawn about the mechanisms of each of these processes. TMA infiltration into PMMA appears to transition from a diffusion-limited process at low temperatures (90 °C) to a reaction-limited process at high temperatures (135 °C) for the film thicknesses investigated here (200 nm). While TMA appears to fully infiltrate these 200 nm PMMA films within a few hours, TiCl 4 infiltration into PMMA is considerably slower, with full saturation not occurring even after 2 days of precursor exposure. Infiltration at 90 °C is so slow that no clear conclusions about mechanism can be drawn; however, at 135 °C, the TiCl 4 infiltration into PMMA is clearly a reaction-limited process, with TiCl 4 permeating the entire thickness (at low concentrations) within only a few minutes, but inorganic loading continuously increasing in a uniform manner over a course of 2 days. Near-surface deviations from the uniform-loading expected for a reaction-limited process also suggest that diffusional hindering is high for TiCl 4 infiltration into PMMA. In conclusion, these results demonstrate a new, ex situ analysis approach for investigating the rate-limiting process mechanisms for vapor phase infiltration.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Dynamic Metal–Support Interaction Dictates Cu Nanoparticle Sintering on Al 2 O 3 Surfaces

Nanoparticle sintering remains a critical challenge in heterogeneous catalysis. In this work, we present a unified deep potential (DP) model based on the Perdew–Burke–Ernzerhof approximation of density functional theory for Cu nanoparticles on three Al 2 O 3 surfaces (γ-Al 2 O 3 (100), γ-Al 2 O 3 (110), and α-Al 2 O 3 (0001)). Using DP-accelerated simulations, we reveal that the nanoparticle size-mobility relationship strongly depends on the supporting surface. The diffusion of nanoparticles on the two γ-Al 2 O 3 surfaces is almost independent of the size of the nanoparticle, while the diffusion on α-Al 2 O 3 (0001) decreases rapidly with increasing size. Interestingly, nanoparticles with fewer than 55 atoms diffuse several times faster on α-Al 2 O 3 (0001) than on γ-Al 2 O 3 (100) at 800 K while expected to be more sluggish based on their larger binding energy at 0 K. The diffusion on α-Al 2 O 3 (0001) is facilitated by dynamic metal–support interaction (MSI), where Al atoms move out of the surface plane to optimize contact with the nanoparticle and relax back to the plane as the nanoparticle moves away. In contrast, the MSI on γ-Al 2 O 3 (100) and on γ-Al 2 O 3 (110) is dominated by more stable and directional Cu–O bonds, consistent with the limited diffusion observed on these surfaces. Our extended MD simulations provide insight into the sintering processes, showing that the dispersity of the nanoparticles strongly influences the coalescence driven by nanoparticle diffusion. We observed that the coalescence of Cu 13 nanoparticles on α-Al 2 O 3 (0001) can occur in a short time (10 ns) at 800 K even with an initial internanoparticle distance increased to 3 nm, while the coalescence on the two γ-Al 2 O 3 surfaces are inhibited significantly by increasing the initial internanoparticle distance. These findings demonstrate that the dynamics of the supporting surface is crucial to understanding the sintering mechanism and offer guidance for designing sinter-resistant catalysts by engineering the support morphology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1986

Smoothing and the second law

The technique of obtaining second order, oscillation free, total variation diminishing (TVD), scalar difference schemes by adding a limited diffusion flux (smoothing) to a second order centered scheme is explored. It is shown that such schemes do not always converge to the correct physical answer. The approach presented here is to construct schemes that numerically satisfy the second law of thermodynamics on a cell by cell basis. Such schemes can only converge to the correct physical solution and in some cases can be shown to be TVD. An explicit scheme with this property and second order spatial accuracy was found to have an extremely restrictive time step limitation (Delta t less than Delta x squared). Switching to an implicit scheme removed the time step limitation.

Merriam, Marshal L.↗