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Calculation of radiation heat fluxes in an enclosure of plane, gray surfaces with an arbitrary number of specularly reflecting and diffusely reflecting area
Radiation heat fluxes in an enclosure of plane gray surfaces with an arbitrary number of specularly reflecting and diffusely reflecting areas
Coarsening and degradation phenomena in metals have largely focused on thermally driven processes, such as bulk and surface diffusion. However, dramatic coarsening has been reported in high-surface-area, nanometer-sized Pt-based catalysts during potential cycling in an electrolyte at room temperature─a temperature too low for the process to be explained purely by surface mobility values measured in both vacuum and electrolytes (∼10 –22 and ∼10 –18 cm 2 /s, respectively). This morphological evolution must be due to a different mechanism for mass transport that is sensitive to electrochemical conditions (e.g., electrolyte composition, potential limits, and scan rate). However, there have been no notable studies of electrochemically induced coarsening in nanometer-sized electrocatalysts. Here, we unveil the origins of coarsening in an electrolyte through coupled in situ experiments and atomistic kinetic Monte Carlo (kMC) simulations. Our work demonstrates electrochemical coarsening is driven by two concurrent mechanisms that can be explained at the atomistic level: (i) dissolution/redeposition during the reduction of an oxidized species and (ii) rapid surface diffusion of undercoordinated atoms.
A viable alternative to the net exchange method of radiative analysis which is equally applicable to diffuse and diffuse-specular enclosures is presented. It is particularly more advantageous to use than the net exchange method in the case of a transient thermal analysis involving conduction and storage of energy as well as radiative exchange. A new quantity, called the distribution factor is defined which replaces the angle factor and the configuration factor. Once obtained, the array of distribution factors for an ensemble of surface elements which define an enclosure permits the instantaneous net radiative heat fluxes to all of the surfaces to be computed directly in terms of the known surface temperatures at that instant. The formulation of the thermal model is described, as is the determination of distribution factors by application of a Monte Carlo analysis. The results show that when fewer than 10,000 packets are emitted, an unsatisfactory approximation for the distribution factors is obtained, but that 10,000 packets is sufficient.
Coarse-grained molecular dynamics simulations are used to study the diffusion of thin nanorods in entangled polymer melts for varying nanorod length and roughness. While prior studies observed a nanorod parallel diffusion constant scaling inversely with rod length D ∥ ~ l –1 , here, we show that this scaling is not universal and depends sensitively on the nanorod surface roughness. We observe D ∥ ~ l –k , where k < 1 and decreases with decreasing surface roughness. The weaker scaling is driven by the non-Gaussian diffusion of nanorods due to the emergence of an intermittent hopping process that becomes more pronounced with decreasing roughness at the monomer scale. Analysis shows that the mean hop size grows for smoother rods but shows little to no variation with rod length. The mean hopping frequency shows no dependence on either rod length or roughness, suggesting it originates from the polymer melt environment. Further, our results show that the small-scale features of the nanorod surface strongly influence the large-scale and long-time transport of nanorods in polymer matrices, creating new material design opportunities for precisely engineered nanocomposites.
For chemisorption and oxidation on Pt/HOPG (highly-orientated pyrolytic) graphite, reflectance Fourier Transform Infrared (FTIR)-microspectrometry reveals a variable state and reactivity for CO. Even for model surface science systems, where surface heterogeneity is minimal, surface diffusion may be too slow relative to the reaction rate to avoid segregation of reactants into surface islands under steady-state conditions. Thus in CO oxidation on Pt (where the relevant surface diffusion coefficients are such that D sub O less than D sub CO) then reactant CO islands exists at the perimeters of which the surface reaction is thought to occur. Furthermore CO can chemisorb on metals in linear and bridge forms to extents which vary with precise faces predominantly exposed coverage, etc. Infrared has long been used to probe the nature of adsorbed CO on model film and heterogeneous surfaces, but it may now be that FTIR-microspectrometry will allow the state of this adsorbate and reactant to be investigated with a spatial resolution of 4.4 microns on model (and real) catalytic surfaces.
The corrosion dealloying behavior of cold-worked (CW) Ni20Cr alloy (wt%) was studied in molten LiF-NaF-KF (or FLiNaK) salts at 600 °C, equal to a homologous temperature (TH) of 0.52. Alloys were cold-rolled to achieve reductions of thickness of 10%, 30%, and 50% introducing plastic deformation and a high density of dislocations. Potentiostatic holds (Eapplied) were applied in two different electrode potential regimes. At 1.75VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, Cr dealloying to Cr(II) and Cr(III) is predominant, while at 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, both Ni and Cr are oxidized in molten FLiNaK at 600 °C. In these potential regimes, dealloyed Ni20Cr displayed bicontinuous porosity within the grain interior and at grain boundaries, driven by the high driving force for Cr dissolution and sustained by defect mediated outward solid state diffusion of Cr in parallel with surface diffusion of Ni. The bicontinuous porous structure developed was observed to undergo further coarsening and densification of the Ni-rich ligaments at a higher electrode potential. The main effect of CW observed is the introduction of plastic deformation and dislocation substructures that serve as short-circuit paths for Cr solid state diffusion to surfaces exposed to FLiNaK. This modified the evolution of the bicontinuous porous structure which increased with CW substantially. Kinetic analysis reveals that the Cr dealloying at +1.75 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$ and 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$ is initially charge transfer controlled, except for the 50% CW condition at 1.90 VK+/K$${\text{V}}_{{\text{K}}^{+}/{\text{K}}}$$, where the process becomes limited by slow Cr defect mediated bulk diffusion. The rate determining factors are explored and compared to experimental results.
Measurements were made of the kinetics of thermal grooving at the intersection of rhombohedral twin boundaries with the (1 0 -1 0) plane in alumina, at temperatures from 1773 to 2273 K. An analysis of the values obtained on the basis of the model of Mullins (1957) indicated that surface diffusion was the dominant mass transport mechanism. Comparisons are made with the results of other investigations of alumina, and an equation is derived for the surface diffusion value.
Dissociative adsorption onto a surface introduces dynamic correlations between neighboring sites not found in non-dissociative absorption. We study surface coverage dynamics where reversible dissociative adsorption of dimers occurs on a finite linear lattice. We derive analytic expressions for the equilibrium surface coverage as a function of the number of reactive sites, N, and the ratio of the adsorption and desorption rates. Using these results, we characterize the finite size effect on the equilibrium surface coverage. For comparable N’s, the finite size effect is significantly larger when N is even than when N is odd. Moreover, as N increases, the size effect decays more slowly in the even case than in the odd case. The finite-size effect becomes significant when adsorption and desorption rates are considerably different. These finite-size effects are related to the number of accessible configurations in a finite system where the odd-even dependence arises from the limited number of accessible configurations in the even case. We confirm our analytical results with kinetic Monte Carlo simulations. We also analyze the surface-diffusion case where adsorbed atoms can hop into neighboring sites. As expected, the odd-even dependence disappears because more configurations are accessible in the even case due to surface diffusion.
In shale gas production, gas composition may vary over time. To understand this phenomenon, we use molecular dynamics simulations to study the permeation of CH 4 , C 2 H 6 and their mixture from a source container through a pyrophyllite nanopore driven by a pressure gradient. For a pure gas, the flow rate of CH 4 is always higher than that of C 2 H 6 , regardless of pore size. For a 1:1 C 2 H 6 : CH 4 mixture, however, C 2 H 6 :CH 4 flow rate ratio is higher than the compositional ratio in the container (i.e., 1:1) when the pore size is smaller than ~1.8 nm. The selective transport is caused by the competitive adsorption of C 2 H 6 over CH 4 in the nanopore. The selectivity is also determined by the interplay between the surface diffusion of the adsorbed molecules and the viscous flow in the center of the pore, and it diminishes as the viscous flow becomes to dominate the surface diffusion when the pore size becomes larger than 1.8 nm. Our work shows that compositional differentiation of shale gas in production is a consequence of nanopore confinement and therefore a key characteristic of an unconventional reservoir. Finally, the related compositional information can potentially be used for monitoring the status of a production well such as its recovery rate.
This is the final report documenting the results of the polarization testing of near-planar objects with various reflectance properties. The purpose of this investigation was to determine the portion of the reflected signal which is polarized for materials commonly used in space applications. Tests were conducted on several samples, with surface characteristics ranging from highly reflective to relatively dark. The measurements were obtained by suspending the test object in a beam of collimated light. The amount of light falling on the sample was controlled by a circular aperture placed in the light field. The polarized reflectance at various phase angles was then measured. A nonlinear least squares fitting program was used for analysis. For the specular test objects, the reflected signals were measured in one degree increments near the specular point. Otherwise, measurements were taken every five degrees in phase angle. Generally, the more diffuse surfaces had lower polarized reflectances than their more specular counterparts. The reflected signals for the more diffuse surfaces were spread over a larger phase angle range, while the signals from the more specular samples were reflected almost entirely within five degrees of angular deviation from the specular point. The method used to test all the surfaces is presented. The results of this study will be used to support the NASA Orbital Debris Optical Signature Tests. These tests are intended to help better understand the reflectance properties of materials often used in space applications. This data will then be used to improve the capabilities for identification and tracking of space debris.
Some recent work in surface microtecturing by ion beam sputtering is described. The texturing is accomplished by deposition of an impurity onto a substrate while simultaneously bombarding it with an ion beam. A summary of the theory regarding surface diffusion of impurities and the initiation of cone formation is provided. A detailed experimental study of the time-development of individual sputter cones is described. A quasi-liquid coating was observed that apparently reduces the sputter rate of the body of a cone compared to the bulk material. Experimental measurements of surface diffusion activation energies are presented for a variety of substrate-seed combinations and range from about 0.3 eV to 1.2 eV. Observations of apparent crystal structure in sputter cones are discussed. Measurements of the critical temperature for cone formation are also given along with a correlation of critical temperature with substrate sputter rate.
Highly refined capabilities of the shape-controlled solution-phase synthesis of metal nanocrystals (NCs) allow the generation of NCs with faceted nonequilibrium shapes, which optimize properties for target applications such as catalysis and plasmonics. Often, for such applications and also for TEM analysis, the NCs are removed from the solution-phase environment. We explore the postsynthesis evolution of these metastable NCs in a high-vacuum TEM environment. Specifically, here we analyze their reshaping toward the equilibrium Wulff shapes mediated by surface diffusion, where such reshaping degrades the above-mentioned optimized properties. Typical sizes for these NCs range from 5 to 30 nm or 10 3 –10 6 atoms, and reshaping often occurs on the time scale of minutes for temperatures around, say, 400 °C. We discuss the development of predictive stochastic atomistic-level models for NC evolution with a realistic description of surface diffusion. These models, in contrast to Molecular Dynamics, can naturally address the relevant time and length scales for these systems. KMC simulation results for the stochastic models are described, focusing on the reshaping of slightly elongated nanorods and of mildly truncated octahedra and nanocubes. In addition, we review appropriate theoretical formulations for reshaping, which involves the nucleation and growth on 2D islands or layers on outer facets of the NC. We note the limitations of classical nucleation theory in some scenarios and demonstrate the successes of a more fundamental and general master equation-based analysis.
Heterogeneous bimetallic nanocrystals featuring explicit spatial configurations and abundant twin defects can simultaneously enable geometric and ligand effects to enhance catalytic and photonic applications. Herein, we report two growth patterns of Au atoms on penta-twinned Pd decahedra, involving twin proliferation to generate asymmetric Pd–Au Janus icosahedra and twin elongation to produce anisotropic Pd@Au core–shell starfishes, respectively. Mechanistic analysis indicates that the injection rate determines the lower-limit number (n low ) of Au(III) ions in the steady state and thus controls the growth pattern. When n low ≤ 5.5, the kinetic rate is slow enough to initiate asymmetrical one-side growth but fast enough to outpace surface diffusion; Au tetrahedral subunits are successively proliferated along the axial $\langle$110$\rangle$ direction of Pd decahedra to form Pd–Au Janus icosahedra. Composed of five Pd and 15 Au tetrahedral subunits, such a heterogeneous icosahedron supports high (2.2 GPa) tensile strain and high strain difference up to +21.9%. In contrast, when n low > 5.5, the fast reduction kinetics promotes symmetric growth with inadequate surface diffusion. As such, Au atoms are laterally deposited along five high-indexed $\langle$211$\rangle$ ridges of Pd decahedra to generate concave Pd@Au core–shell starfishes with tunable sizes (28–40 nm), twin elongation ratios (33.82–162.08%), and lattice expansion ratios (8.82–20.10%).
The synthesis of graphene nanoribbons (GNRs) can be realized via CH4 chemical vapor deposition (CVD) on substrates such as Ge(001) that promote highly anisotropic growth kinetics. Small polycyclic aromatic hydrocarbons (PAHs) are first sublimed onto Ge near room temperature to form graphene-like seeds that subsequently initiate GNR growth with CH4 exposure at 1173 K. The behaviors of PAHs in the time in between their sublimation onto Ge and GNR growth are unclear. Here, we study an archetypical PAH, perylene-3,4,9,10-tetracarboxyl acid dianhydride (PTCDA), on Ge(001) using both scanning tunneling microscopy (STM) and density functional theory (DFT) to characterize PAH conformation, surface diffusivity, and clustering, versus temperature. PTCDA becomes mobile above 673 K (consistent with a DFT calculated diffusion barrier of 2.01 eV). The mobile PTCDA molecules meet, cluster, and fuse at Ge step edges. These clusters have an apparent height of 0.4 nm, similar to small graphene islands, and grow laterally with increasing temperature – reaching 1.2 – 2.1 nm in width at 1173 K, consistent with the seed size extrapolated from CVD experiments. These results provide a plausible picture for how PTCDA forms seeds for anisotropic GNR CVD and show that PAHs with reduced surface diffusivity and inter-molecular reactivity are needed to enable more monodisperse PAH-seeded GNR synthesis.
The interaction of gas diffusion with surface reaction in porous solids is discussed and applied specifically to heterogeneous rate measurements in flow-tube reactors. External diffusion to the outer surface of a reactive solid, internal diffusion within the pores, surface reaction, and laminar flow are considered. A procedure is developed to correct observed surface rate constants for the interaction of these processes. Measured surface areas and bulk densities are used to construct a semiempirical model for porous diffusion in vapor-formed HNO3-H2O ices which are used to simulate polar stratospheric cloud surfaces. The model is tested experimentally by varying the thickness of these ices from about 15 to 120 microns. The results are consistent with the model predictions and show that the HNO3-H2O ices used are highly porous, and the internal surface must be considered in calculating kinetic parameters from observed loss rates. The best fit of the data yields a tortuosity factor of 3.3 +/-1.1 for the ice substrates.
Metallic nanocrystals (NCs) can be synthesized with tailored nonequilibrium shapes to enhance desired properties, e.g., octahedral fcc metal NCs optimize catalytic activity associated with {111} facets. However, maintenance of optimized properties requires stability against thermal reshaping. Thus, we analyze the reshaping of truncated fcc metal octahedra mediated by surface diffusion using a stochastic atomistic-level model with energetic input parameters for Pd. Furthermore, the model describes NC thermodynamics by an effective nearest-neighbor interaction and includes a realistic treatment of diffusive hopping for undercoordinated surface atoms. Kinetic Monte Carlo simulation reveals that the effective barrier, E eff , for the initial stage of reshaping is strongly tied to the degree of truncation of the vertices in the synthesized initial octahedral shapes. This feature is elucidated via exact analytic determination of the energy variation along the optimal reshaping pathway at low-temperature (T), which involves transfer of atoms from truncated {100} vertex facets to form new layers on {111} side facets. Deviations from predictions of the low-T analysis due to entropic effects are more prominent for higher T and larger NC sizes.
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