Grain-Size Distribution for Certain Metamorphic Minerals in Relation to Nucleation and Growth

Abstract

True grain-size measurements are reported for garnet and biotite in schist from a metamorphic aureole and for phlogopite, pyroxene, and sphene in marble from a regional metamorphic terrain. One of the size distributions (garnet 1) is bimodal, while the remainder are unimodal and positively skewed. One of the unimodal distributions (garnet 2) lies between an arithmetic-normal and a log-normal distribution, while the remainder are log normal. The spacial distribution of garnet grains in a specimen of schist is random, and the size attained by any garnet grain is unrelated to the distance to its nearest neighbor. The form of the unimodal size distributions indicates that the nucleation rate for the corresponding minerals increased with time and then declined. Equations are derived for the rate of nucleation of garnet, phlogopite, and sphene on the assumption of a constant rate of linear growth. The form of these equations is: garnet: power law; phlogopite: exponential law; sphene: exponent of exponential law. The size of crystal grains in metamorphic rocks is determined by the rate of nucleation relative to the rate of crystal growth.