Modeling of crystal size distributions (CSDs) in sills

Abstract

A new model for the generation of crystal size distributions (CSDs) in igneous rocks is presented here. Synthetic or numerically simulated CSDs are generated with a growth rate that is proportional to the amount of precipitating solids and inversely related to the second moment of the CSD (total surface area) and with the log(nucleation rate, I) vs. log(cooling rate) relationship of Cashman [Cashman, K.V., (1993). Relationship between plagioclase crystallization and cooling rate in basaltic melts. Contrib. Mineral. Petrol., v. 113, pp. 126–142.] for crystal nucleation. The resultant CSDs resemble those observed in natural rocks. In the new model, growth rate is constrained by a mass balance and crystal population systematics; it is not calculated as a function of cooling rate or undercooling. The development of the numerical model was motivated in part by the failure of analytical modeling of crystal populations based solely on cooling rate to generate CSDs similar to those observed naturally. The new model is used to create a suite of CSDs from various positions within a sill; cooling and solidification of the sill are calculated numerically. The model reproduces many features observed in the CSDs of natural rocks such as linear CSDs in plots of ln(population density) vs. crystal size, ‘D’-shaped mean crystal size profiles and decreasing CSD intercept and slope magnitude (i.e., |slope|) with distance from the sill/wallrock contact, and the CSD intercept vs. slope relationship. The model suggests the use of inversion to more accurately determine residence time from a natural CSD.