FORWARD AND INVERSE MODELING OF IGNEOUS CRYSTALLIZATION TO CONSTRAIN KINETIC INFORMATION OBTAINABLE FROM ROCKS

The theory for relating rates of crystal nucleation and growth to a crystal size distribution (CSD) requires that the crystals grow freely in a mother liquid or magma with fixed aspect ratios or shapes (the forward problem). Of special interest to petrology, however, is the inverse problem of extracting quantitative kinetic information from the CSD of an igneous rock in which grain-to-grain impingements have inhibited the free growth of crystals and modified their aspect ratios. Further complicating the inverse problem is that the rock CSD is usually estimated from 2-dimensional grain sizes measured in thin sections, and these data are converted by stereological methods to the 3-dimensional CSD. Computer modeling is an ideal way to conduct fundamental studies on forward and inverse crystallization problems since direct experimental methods are lacking. The forward model performs the crystallization using an exponential function for nucleation, a constant rate of crystal growth and constant aspect ratios, and this produces a simple linear CSD similar to that reported in some igneous rocks. The inverse problem then consists of measuring grain sizes in computer generated thin slices, and these data are converted to the 3-dimensional CSD the slope of which is used to extract the ratio of the nucleation constant/growth constant. Our results indicate that the difference between the forward predicted ratio and that obtained by the inverse method is primarily due to the impingement effects and secondarily to the stereological conversion methods. These results constitute one level of constraints in estimating the kinetics of crystallization from the texture of any polycrystalline solid.