Cellular Automaton Simulations of Surface Mass Transport Due to Curvature Gradients: Simulations of Sintering in 3-D.
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CELLULAR AUTOMATON SIMULATIONS OF SURFACE MASS TRANSPORT DUE TO CURVATURE GRADIENTS: SIMULATIONS OF SINTERING IN 3-D. D.P. BENTZ', P.J.P. PIMIENTA*, E.J. GARBOCZI, and W.C. CARTER" "Building Material Division and "Ceramics Division, National Institute of Standards & Technology, Gaithersburg, MD 20899. ABSTRACT A cellular automaton algorithm is described that simulates the evolution of a surface driven by the reduction of chemical potential differences on the surface. When the surface tension is isotropic, the chemical potential is proportional to the curvature at the surface. This process is important in the development of microstructure during the sintering of powders. The algorithm is implemented in two and three dimensions in a digital image mode, using discrete pixels to represent continuum objects. The heart of the algorithm is a pixel-counting-based method for computing the potential at a pixel located in a digital surface. This method gives an approximate measure of the curvature at the given surface pixel. The continuum version of this method is analytically shown to give the true curvature at a point on a continuum surface. The digital version of the curvature computation method is shown to obey the scaling laws derived for the continuum version. The evolution of the surface of a three dimensional loosely packed powder, along with the percolation characteristics of its pore space, are computed as an example of the algorithm. INTRODUCTION Theoretical calculations of microstructural development are, in general, quite difficult, especially when considering materials consisting of an originally random collection of particles that are subsequently amalgamated by a processing step. Inorganic examples include random packings of ceramic [1] or metal particles [2], which are densified by heat treatment (sintering), and random dispersions of portland cement particles in water, which are solidified by hydraulic reactions [3] to form cement-based composites. The randomness of the original particle collection and the complicated physics and chemistry that take place during the processing to achieve a final microstructure in general preclude any analytical calculations except for extremely simple particle configurations, like a single pair of particles or a periodic array of particles. In order to consider collections of many particles, computer simulations become necessary, and in particular fundamental computer simulations [4]. For the types of materials considered above, computer simulation models of microstructural development are considered to be fundamental if they directly treat the material at the particle or grain level, which is the most relevant building block of the microstructure, and realistically incorporate as much of the known physics and chemistry as possible into the growth rules. Examples exist for cement-based materials [5,6,7], sedimentation in rocks [8], grain growth in powdered metals [9,10], and ceramics [11-14]. In this paper we concentrate on the problem of microstructural development during s
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