Generating microstructures with specified correlation functions

A stochastic optimization technique has recently been developed that can reconstruct or construct random heterogeneous materials with specified statistical correlation functions. We demonstrate how this technique can be used to reconstruct a digitized image of an interpenetrating, isotropic ceramic-metal composite. In this case, the two-point probability function displays no short-range order and the image is reconstructed by optimizing in two orthogonal directions only. However, this technique results in artificial anisotropy in the unoptimized directions when one (re)constructs an image in which the isotropic two-point probability function exhibits appreciable short-range order. We show that by optimizing in more than two directions, one can effectively eliminate the artificial anisotropic effects for a system possessing significant short-range order. This is done by optimizing in three directions on a hexagonal grid and by optimizing in four directions on a square grid. Finally, an aspect of the nonuniqueness of the resulting structures is quantitatively examined.