Connectivity and percolation behaviour of grain boundary networks in three dimensions Export

@article{citeulike:912048, 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. Defining 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 non-random 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.}, author = {Frary}, citeulike-article-id = {912048}, citeulike-linkout-0 = {http://www.journalsonline.tandf.co.uk/media/n1dr7rryql1jng77tmdq/contributions/k/n/q/p/knqpyga2eqa33w78_html/fulltext.html}, journal = {Philosophical Magazine}, keywords = {characterisation, grain-boundary}, number = {11}, pages = {1123--1143}, posted-at = {2006-10-24 23:48:02}, priority = {2}, title = {Connectivity and percolation behaviour of grain boundary networks in three dimensions}, url = {http://www.journalsonline.tandf.co.uk/media/n1dr7rryql1jng77tmdq/contributions/k/n/q/p/knqpyga2eqa33w78_html/fulltext.html}, volume = {85}, year = {2005} }

TY - JOUR ID - citeulike:912048 L3 - citeulike-article-id:912048 N2 - 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. Defining 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 non-random 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. IS - 11 JF - Philosophical Magazine EP - 1143 TI - Connectivity and percolation behaviour of grain boundary networks in three dimensions VL - 85 SP - 1123 KW - characterisation KW - grain-boundary AU - Frary PY - 2005/// UR - http://www.journalsonline.tandf.co.uk/media/n1dr7rryql1jng77tmdq/contributions/k/n/q/p/knqpyga2eqa33w78_html/fulltext.html ER -