Verification of ideal semi-logarithmic, lognormal or fractal crystal size distributions from 2D datasets

Crystal size distributions can follow any function, provided the total crystal content is less than 100%. However, many theories suggest that they approximate a number of ideal distribution models. The most widely adopted model for igneous rocks produces a straight line on a ‘classic’ CSD diagram of ln (population density) versus size. Lognormal by size distributions have been proposed for igneous and metamorphic rocks and materials that crystallise at low temperatures. Lognormal models are difficult to prove with simple linear frequency histograms or on a classic CSD diagram. Instead, it is better to use a normalized cumulative distribution function diagram, which gives a straight line for lognormal distributions. Similarly, fractal size distributions can best be verified simply by using a bi-logarithmic diagram. Statistical measures can be used to invalidate a null hypothesis, but with much caution for real data, especially those derived from two-dimensional measurements and with a limited range in sizes. These methods are applied to CSDs of plagioclase in three igneous rock samples to illustrate the pitfalls of model fitting. A simple nomenclature is proposed for ideal CSD shapes.