Impact of boundary nucleation on product grain size distribution
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Impact of boundary nucleation on product grain size distribution W. S. Tong, J. M. Rickman, and K. Barmak Department of Materials Science and Engineering, Lehigh University, Bethlehem, Pennsylvania 18015 (Received 9 August 1996; accepted 19 February 1997)
We examine quantitatively the impact of boundary nucleation on the size distribution of product grains in a computer simulation of a two-dimensional phase transformation. This is accomplished by determining the probability distribution of product grain areas under different nucleation conditions. Specifically, a comparison of the moments of normalized area distributions of product grains arising from site-biased nuclei with the corresponding moments of the area distribution of Voronoi grains reveals those spatial features of the collection of catalytic sites which most affect product microstructure. The impact of other relevant length scales, including the square root of the inverse nucleation site density, the lattice parameter, and the system size, on microstructure is also discussed.
I. INTRODUCTION
An analysis of the product microstructure resulting from a phase transformation can yield information on both the transformation kinetics and the distribution of any catalytic sites. For example, the grain structure of a metal solidified in a mold is critically dependent on the mold wall temperature and the presence of impurities which promote heterogeneous nucleation. Further, in many systems it has been found that the time dependence of the nucleation rate correlates with rather sharp, straight phase boundaries separating Voronoi polygons in the case of a burst of nuclei at some initial time (the so-called cell model), while a more rounded phase morphology is associated with a constant nucleation rate (the Johnson–Mehl model).1 More recently, a study of the kinetics and product microstructure resulting from boundary nucleated reactions suggested that, under some conditions, product grains are nonequiaxed due to the detailed shape of underlying grain boundaries.2 While a number of metrics exist for the characterization of a given product microstructure, an analytic expression for the probability distribution of grain areas is generally not known, even for many idealized cases. In the aforementioned cell model, for example, an exact analytical description of the areas of generated Voronoi polyhedra is still lacking, although it has been possible to obtain the exact distribution variance1 and an approximate functional form for the distribution.3 Given the difficulty of completely characterizing microstructures resulting from spatially random transformations, it is expected that a similar analysis of microstructures resulting from boundary nucleation will be problematic. Nevertheless, it is reasonable to assume that the locations of underlying catalytic sites will effectively determine J. Mater. Res., Vol. 12, No. 6, Jun 1997
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both the sizes and shapes of product gr
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