Connectivity and percolation behaviour of grain boundary networks in three dimensions

TitleConnectivity and percolation behaviour of grain boundary networks in three dimensions
Publication TypeJournal Article
Year of Publication2005
AuthorsFrary, M, Schuh, CA
JournalPhilosophical Magazine
Volume85
Issue11
Pagination1123 - 1143
Date Published2005/04/11/
Abstract

Grain boundary networks are subject to crystallographic constraints at both triple junctions (first-order constraints) and quadruple nodes ( second-order constraints). First-order constraints are known to influence the connectivity and percolation behaviour in two-dimensional grain boundary networks, and here we extend these considerations to fully three-dimensional microstructures. De. ning a quadruple node distribution ( QND) to quantify both the composition and isomerism of quadruple nodes, we explore how the QNDs for crystallographically consistent networks differ from that expected in a randomly assembled network. Configurational entropy is used to quantify the relative strength of each type of constraint ( i.e., first- and second-order), with first- order triple junction constraints accounting for at least 75% of the nonrandom correlations in the network. As the dominant effects of constraint are captured by considering the triple junctions alone, a new analytical model is presented which allows the 3-D network connectivity to be estimated from data on 2-D microstructural sections. Finally, we show that the percolation thresholds for 3-D crystallographically consistent networks differ by as much as +/- 0.07 from those of standard percolation theory.