A 3-D crystal growth-disorder model with cubic symmetry

Abstract A three-dimensional model of crystal growth-disorder is described. It is shown that imposition of m3m symmetry on the model results in the same reduction to essentially one dimensional properties, as occurs in pre­viously described work in two dimensions. The probability parameter space is subject to more stringent restrictions than for the corresponding two dimensional model and only realizations with nearest-neighbour two-point correlations less than √2 -1 can occur. For zero two-point corre­lation a considerable degree of variation in multi-point properties is possible. The three-dimensional distributions are shown to have Markov chains embedded in them.