THE SPATIAL DISTRIBUTION OF GRAINS AND CRYSTALS IN ROCKS

Abstract

Characterisation and analysis of the spatial distribution pattern (SDP) of grains or crystals in rocks is potentially a powerful technique which can be used to constrain the processes which operate in the formation of rocks. A method to quantify the SDP of grains in thin section is presented. The distance betwen the centre of a grain and the centre of its nearest neighbour is calculated for all the grains in the sample area to produce a distribution of distances that characterises the spatial pattern of grains in the rock. This distribution is then normalised to a random distribution of points with the same population density to give a descriptive value, R. Values of R for rock samples are plotted against porosity (modal abundance of other phases in igneous and metamorphic rocks) to characterise the SDP. The SDP of randomly packed distributions of equal size spheres varies systematically with porosity, producing a line on a porosity versus R plot, termed the random sphere distribution line (RSDL). Rocks which plot above the RSDL have an ordered SDP and those that plot below, a clustered SDP. The effects of variation in grain packing order, grain sorting, compaction and random crystallisation (overgrowth) on determined R values were investigated using a combination of 3-D sphere models and 2-D texture models. The maximum possible value of R is 2.148, corresponding to a perfect section through hexagonal/cubic close packing of grains. The minimum value of R is dependent on the proportion of grains in the sample volume and may be as low as 1.2, for a sample volume with 30% grains which are clustered. Variations in size sorting can cause R to vary by approximately 0.25. Mechanical compaction of a loose framework of grains results in a higher packing order and an increase in R. Continued compaction creates a fabric in the texture and R decreases as cluster patterns are developed perpendicular to the principal stress. The overgrowth of grains in a touching framework alters the location of the geometric grain centre as the crystal shape changes, leading to an increase in R as porosity decreases. Results reveal that grain sorting, compaction and grain overgrowth produce different R versus porosity relationships which can be identified in, and therefore used to constrain, the relative importance of these processes in rock samples.