Crystal Size Distributions and Scaling Laws in the Quantification of Igneous Textures

Abstract

This study demonstrates the value of the combined use of scaling analysis and crystal size distribution (CSD) measurements in the interpretation of igneous textures and outlines applications of these methods to other fundamentally important problems. Theoretical calculations and measurements of natural samples are used to characterize the relationship between igneous texture and cooling history. The total number (NT) and mean length (L̄) of crystals in a sample are correlated through a scaling relationship of the form NT−1/3 ∝ L̄. This proportionality depends on the mineralogy of the rock, and so a modal normalization factor (C) is introduced. The CSD slope, S, and intercept, ln(n°), are uniquely related to each other through the equation ln(n°) = 4ln(S) − ln(C), where S = L̄−1. This overall relationship allows the texture of a rock to be related to the local duration of cooling through an arbitrary crystal growth model. Quantification of the link between the texture of a rock and its cooling history makes it possible to predict spatial variations in texture. We show an example of this method using the Sudbury Igneous Complex, Canada. Additional applications include relating the textures of volcanic rocks to spatial and temporal variations in the magma chamber and extracting kinetic parameters from suites of comagmatic rocks.