Computer Simulation of Grain Growth in Polycrystalline Aggregates
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CCMPUTER SIMULATION OF GRAIN GRCWTH IN POLYCRYSTALLINE AGGREGATES
M. P. Anderson, D. J. Srolovitz, G. S. Grest and P. S. Sahni Exxon Research and Engineering Company P.O. Box 45 Linden, New Jersey 07036 I.
INTRODUCTION
The physical and chemical properties of materials are determined in part by microstructure. Grain orientation and size in polycrystalline aggregates affect, for example, yield strength, catalytic efficiency, chemisorption, physisorption, fracture and a host of other properties. The final grain morphology is often determined by thermal processing, addition of a second phase, deformation, etc. However, in order to effectively tailor the microstructure for specific applications, the mechanisn and kinetics of grain growth must be known. Unfortunately, present theories predict grain growth kinetics (1-3) which often differ from experimental observation, have little predictive ability with respect to microstructure and are not easily generalized to account for experimentally controllable factors. Most of the existing grain growth theories (1,2) implicitly assume that grains can be described as spherical, and that growth occurs in an average environment. This, however, ignores the fact that adjacent grains share common boundaries, resulting in a microstructure that is topologically connected. These theories (1-3) predict long time growth kinetics of the form
S=
(1)
ktn
where T is the mean grain radius, t is time, k is constant, and n = 1/2. Since grain growth experiments in general yield an exponent, n, less than 1/2, the discrepancy may be a consequence of neglecting topological constraints and the detailed environment. In this paper we review the application of Monte Carlo computer simulation techniques to the grain growth problem (4-8). Employing this technique, we have treated the next level of complexity by including grain boundary topology and detailed local environments. This paper summarizes the evolution of a two dimensional, connected assembly of mutually interacting grains. A simulation of the evolution of a single circular grain embedded in an infinite matrix (4,5) is used to demonstrate the validity of the Mbnte Carlo technique and the near isotropy of the model. The model is shown to reproduce the classical kinetics (n = 1/2) only under very limited conditions which are inappropriate for grain growth. In addition, the grain topology, grain size distribution and curvature are analyzed. II.
SIMULATION PROCEDURE
The microstructure is mapped onto a triangular lattice containing 40,000 lattice sites (Fig. 1). Each lattice site is assigned a number which corresponds to the orientation of the grain in which it is embedded. A large number of grain orientations is employed so that domains of like orientations rarely impinge. Lattice sites which are adjacent to neighboring sites having different grain orientations are regarded as being part of the grain boundary, while a site surrounded by sites with the same
Mat. Res. Soc.
Symp. Proc. Vol.
21 (1984) OElsevier Science Publishing Co.,
Inc.
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