Statistical properties of ideal rock textures: Relationship between crystal size distribution and spatial correlation of minerals

The concept of an ideal rock texture, in which crystals are distributed randomly in space, is proposed for use in general analysis of rock textures. The spatial correlation function far the ideal rock texture was examined and the sigma function, a specific kind of spatial correlation function, is related to crystal size distribution and to some extent to crystal boundaries. The sigma function is unity at distance zero, and monotonically decreases with increasing distance for the ideal texture. This behavior of the sigma function is observed for any size distribution. In on ideal texture, the sigma function is directly related to crystal size distribution and crystal shape. It is important in stereology because the crystal size distribution in three dimensions may be deduced from analyzing a sigma function that is obtained from analyzing two-dimensional section images. Crystal shape is also related to the sigma function. If crystals are concave in shape, or have inclusions of other phases, the sigma function may show a hump or plateau when plotted against distance. However, the crystal shape effect cannot produce a values smaller than zero. If sigma values become negative, the texture is no longer considered ideal. The ideal textures for two model size distributions - step and delta functions - are considered. The rate of decrease of sigma values is more strongly dependent on size distribution than on system dimension.