Physics of Surface, Interface and Cluster Catalysis reviews the fundamental physics of catalysis from simple surface models through to complex cluster and catalytic structures.

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Physics of Surface, Interface and Cluster Catalysis

Estimating permeability in shales and other heterogeneous porous media: Deterministic vs. stochastic investigations

This chapter contains basic concepts and applications of wide-angle X-ray diffraction (XRD) and small-angle X-ray scattering (SAXS) to studies of nanostructured materials. The first part includes an introduction to the technique of X-ray powder diffraction (XPD), which is commonly applied to phase identification of powdered materials, characterization of unit cells, determinations of lattice parameters and, in some cases, also coordinates of atoms inside the unit cells. The main aspect described here is the analysis of the shape of X-ray diffraction peak profiles, which allows one to determine additional and also valuable structural information of nanomaterials, such as average crystallite sizes and crystallite microstrains. Detailed deductions of the equations used for different applications of X-ray diffraction and basic concepts of crystallography (such as those related to symmetries, Bravais and reciprocal lattices, etc.) are not described. The second part presents the basic equations related to the SAXS method and their applications to several biological systems (proteins in solution). Classical SAXS is an experimental procedure that is employed in transmission mode and is also applied to the study of many nanostructured inorganic materials. The third part includes two variants of the classical SAXS procedure, namely grazing incidence small-angle X-ray scattering (GISAXS) and anomalous small-angle X-ray scattering (ASAXS). The basic concepts of the GISAXS method and several applications to studies of nanostructured materials deposited on flat substrates and buried nanostructures are presented. The basic concepts of the ASAXS method are described, together with its applications to complex materials that cannot be properly studied using the classical SAXS technique, such as, for example, materials modeled by three phases with different electron densities. Most of the experiments described in this chapter were performed by the authors using X-ray beam lines of the National Synchrotron Light Laboratory (LNLS), Campinas, Brazil.

X-Ray Diffraction and Scattering by Nanomaterials

On-lattice kinetic Monte Carlo (KMC) is a computational method used to simulate (among others) physicochemical processes on catalytic surfaces. The KMC algorithm propagates the system through discrete configurations by selecting (with the use of random numbers) the next elementary process to be simulated, e.g., adsorption, desorption, diffusion, or reaction. An implementation of such a selection procedure is the first-reaction method in which all realizable elementary processes are identified and assigned a random occurrence time based on their rate constant. The next event to be executed will then be the one with the minimum interarrival time. Thus, a fast and efficient algorithm for selecting the most imminent process and performing all of the necessary updates on the list of realizable processes post execution is of great importance. In the current work, we implement five data-structures to handle the elementary process queue during a KMC run: an unsorted list, a binary heap, a pairing heap, a one-way skip list, and finally, a novel two-way skip list with a mapping array specialized for KMC simulations. We also investigate the effect of compiler optimizations on the performance of these data-structures on three benchmark models, capturing CO oxidation, a simplified water gas shift mechanism, and a temperature-programmed desorption run. Excluding the least efficient and impractical for large-problems unsorted list, we observe a 3× speedup of the binary or pairing heaps (most efficient) compared to the one-way skip list (least efficient). Compiler optimizations deliver a speedup of up to 1.8×. These benchmarks provide valuable insight into the importance of, often-overlooked, implementation-related aspects of KMC simulations, such as the queueing data-structures. Our results could be particularly useful in guiding the choice of data-structures and algorithms that would minimize the computational cost of large-scale simulations.

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Physics of Surface, Interface and Cluster Catalysis

Citations

Estimating permeability in shales and other heterogeneous porous media: Deterministic vs. stochastic investigations

X-Ray Diffraction and Scattering by Nanomaterials

Comparison of Queueing Data-Structures for Kinetic Monte Carlo Simulations of Heterogeneous Catalysts.

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