Lattice-based structures for studying percolation in two-dimensional grain networks
نویسندگان
چکیده
The applicability of standard lattice percolation models to a random two-dimensional grain structure is explored. A random network based on the triangle lattice is proposed as a more appropriate model, and results in a higher percolation threshold (0.711 compared with 0.653 for the standard hexagonal lattice). The triple junction constraint inherent in grain boundary structures is subsequently applied to the new network. This results in a lowering of the percolation threshold to 0.686; this is opposite to its effect on the standard hexagonal lattice. The effect of varying the network’s ‘grain shape’ distribution on the percolation threshold is also considered. 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
منابع مشابه
Correlations Beyond the Nearest-Neighbor Level in Grain Boundary Networks
Correlations among ‘special’ and ‘general’ grain boundaries are studied on two-dimensional networks, by examining the configurational entropy of boundary structures as well as percolation thresholds. Consideration of crystallographic constraints at various length scales reveals that higher-order constraints play a role in boundary connectivity and network structure. Implications for grain bound...
متن کاملTwo-dimensional grain boundary percolation in alloy 304 stainless steel
An experimentally-obtained percolation threshold for high-angle random grain boundary networks in alloy 304 stainless steel is compared to thresholds predicted by percolation theory. A discrepancy occurs in the two values (0.46 experimental and 0.65 theoretical). Possible reasons for the discrepancy are explored. The grain boundary network appears to be composed of two distinct sub-networks, wi...
متن کاملPercolation of spatially constraint networks
We study how spatial constraints are reflected in the percolation properties of networks embedded in one-dimensional chains and two-dimensional lattices. We assume longrange connections between sites on the lattice where two sites at distance r are chosen to be linked with probability p(r)∼ r−δ. Similar distributions have been found in spatially embedded real networks such as social and airline...
متن کاملTwo-dimensional polymer networks near percolation
We report an extensive finite-size study of polymer networks near the percolation threshold, using numerical techniques. The polymers are modeled by random walks occupying the bonds of a two-dimensional square lattice. We measure the percolation threshold and critical exponents of the networks for various polymer lengths. We find that the critical occupation probability is a decreasing function...
متن کاملExplosive growth in biased dynamic percolation on two-dimensional regular lattice networks.
The growth of two-dimensional lattice bond percolation clusters through a cooperative Achlioptas type of process, where the choice of which bond to occupy next depends upon the masses of the clusters it connects, is shown to go through an explosive, first-order kinetic phase transition with a sharp jump in the mass of the largest cluster as the number of bonds is increased. The critical behavio...
متن کامل