Modeling of Coarsening Processes In Patterned Systems
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Modeling of Coarsening Processes In Patterned Systems M. H. Jhon, A. M. Glaeser and D. C. Chrzan1 Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, U.S.A. Materials Sciences Division, Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, U.S.A. ABSTRACT Although particle coarsening has been studied for over a century, it remains an active area of materials science research. The current work presents a theoretical analysis of the degradation of regular arrays of spherical particles through diffusional interaction. In order to understand the onset of coarsening, a linear stability analysis is performed on a simple square lattice of particles. It is predicted that particles will dissolve in a spatially ordered manner. The active transport mechanism plays a strong role in the selection of the coherent growth modes. INTRODUCTION The recent study of nanostructures has renewed interest in the stability of material features. At elevated temperatures, microstructures may evolve in order to minimize the total surface energy of a system. In particular, larger particles tend to grow at the expense of smaller ones. In many different materials systems, particles coarsen through an evaporation-condensation mechanism. This phenomenon has since become known as Ostwald ripening. Quantitative theories explaining this process were first developed by Lifshitz and Slyosov and independently by Wagner using mean-field techniques [1, 2]. This so-called LSW approach concentrates on understanding the asymptotic limit, in which the particle size distribution reaches a self-similar shape. This mean field analysis is limited: it does not take into account the local environment about each particle. Modern theories of coarsening have improved on this aspect of LSW theory using various statistical averaging methods [3–5]. Another shortcoming comes from the difficulty reaching the asymptotic regime [6]. Instead, transient effects may dominate the coarsening process. It has further been shown that in certain system geometries, the coarsening process is only approximately self-similar [7]. The present work addresses these two concerns by studying the onset of coarsening for a known particle size distribution. In this study, a model two-component system is considered in which one phase is dispersed in a matrix phase. Elastic effects are ignored. A linear stability analysis is applied to a regular, 2-dimensional array of spherical particles. This model system is chosen because of the existence of lithographic techniques to pattern regular arrays of features at a grain-boundary [8]. Further, examining regular lattices may allow us to better understand materials processes in which spatial patterns persist during coarsening, such as spinodal decomposition [9] and Liesegang patterning [10]. 1 [email protected]
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THEORY In order to analyze the coarsening of the particle lattice, it is necessary to solve the microscopic diffusion problem. There are a v
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