Fractal (Scaling) Clusters in Thin Gold Films near the Percolation Threshold

Transmission electron micrographs of thin evaporated gold films were analyzed by computer. For length scales above 10 nm, the irregular connected clusters show a perimeter linearly proportional to area. Near the percolation threshold the large-scale power-law correlations and area distributions are consistent with the scaling theory of second-order phase transitions. Geometrically, the boundary of all clusters is a fractal of dimension D=2 while individual boundaries are of fractal dimension D₂1. 9.