Percolation and conduction on the 3D Voronoi and regular networks: a second case study in topological disorder

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Abstract
To assess the effect of random coordination percolation properties of the three-dimensional (3D) Voronoi network and the body-centred cubic with second-nearest-neighbour bonding (BCC2) are calculated by Monte Carlo simulation and compared. The accessible fraction, backbone fraction and effective conductivity of the Voronoi network and regular networks are qualitatively the same. Moreover, when enough bonds are removed from the Voronoi network to make the average coordination match that of the BCC2 network the difference between the conductivities of the two networks is less than 0.002. Finite-size scaling theory is used to estimate percolation thresholds and critical exponents. The bond percolation thresholds of the Voronoi and BCC2 networks are 0.082 and 0.0991, whereas the site percolation thresholds are 0.145 and 0.169. The correlation length, backbone and conductivity exponents of the Voronoi network are v=0.88, beta '=1.06 and t=2.02, in good agreement with the values accepted for regular 3D networks. The effective conductivity of the network derived from a crude finite-element approximation to the Voronoi tessellation is only slightly different from that of the same network with the conductances redistributed at random.