Article ID Journal Published Year Pages File Type
1450571 Acta Materialia 2006 11 Pages PDF
Abstract

A new theoretical approach is developed for the derivation of self-similar grain size distributions for three-dimensional polycrystals. The method is based on representing each class of irregular NN-sided polyhedral grains in a space-filling network by the corresponding “average NN-hedron” – or topological proxy. This method allows a more rigorous statistical mechanical derivation of the theoretical grain size distribution for three-dimensional polycrystals, and provides a clearer understanding of the assumptions underlying it, as well as clarification of its predictive limitations. Our method also yields several new results, namely, the self-similar distributions of the normalized cube-root grain volumes and of the number of faces per grain. A statistical comparison of the theoretical predictions with simulation data based on Brakke’s Evolver and kinetic Monte Carlo methods is also provided.

Related Topics
Physical Sciences and Engineering Materials Science Ceramics and Composites
Authors
, ,