Morphometry of Quartz Aggregates in Granites: Fractal Images Referring to Nucleation and Growth Processes

Abstract

Knowledge of mineral aggregate morphologies is of importance to analyze characteristic differences in rock-forming features. For quantifying these differences, the fractal geometry of quartz aggregate cuts digitized from polish sections of different types of granites has been studied. As an approach to measure fractal dimension (D), a power-law dependence of square of aggregate cuts on their linear size has been used. The D values thus calculated mainly increase from 1.48–1.62 for amazonite granites to 1.63–1.70 for alaskite granites and 1.75–1.81 for standard granites. To account for the data of morphometry, the model of nucleation and growth as applied to silicate melt freezing has been considered. For comparison between the nature and model textures, the fractal properties of cluster cuts in the system of overlapping spheres randomly distributed with random radii have been investigated through computer simulation. It has been demonstrated that the distributions of quartz aggregates in granites may be simulated by homogeneous or heterogeneous Poisson models, and both order of crystallization and metamorphic recrystallization should be taken for explaining textural variability. The results of the simulation have enabled the granitic texture to be discussed with respect to the random configuration of the spatial percolation cluster.