|Title||Connectivity and percolation behaviour of grain boundary networks in three dimensions|
|Publication Type||Journal Article|
|Year of Publication||2005|
|Authors||Frary, M, Schuh, CA|
|Pagination||1123 - 1143|
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.