Numerical simulation of the crystallization of multicomponent melts in thin dikes or sills: 2. Effects of heterocatalytic nucleation and composition

Abstract

A kinetic model is presented for the crystallization of two‐component melts in thin dikes or sills specifically providing for the nucleation of one crystalline phase on the surface of another crystalline phase during simultaneous crystallization. This process is termed heterocatalytic nucleation. It is assumed that the activation energy for heterocatalytic nucleation is reduced by a factor F from the activation energy for ordinary nonheterocatalytic nucleation. The impediment of crystal growth of crystals growing on each others' surfaces is specifically accounted for. The resulting nucleation and growth rate functions are temperature and concentration dependent. The crystallization time was found to be almost independent of the strength of the heterocatalytic nucleation, but the crystallization paths deviate increasingly less from thermodynamic equilibrium with increasing rate of heterocatalytic nucleation. Crystal sizes for heterocatalytic nucleation are typically found to be about an order of magnitude smaller than for nonheterocatalytic nucleation. For initial compositions significantly different from the eutectic composition, two modes are observed for the crystal size distributions of the liquidus phase. The primary modes of the liquidus phase distributions are attributed to nonheterocatalytic nucleation, while the secondary modes are caused by heterocatalytic nucleation. The secondary modes may become the prominent modes in terms of amplitude for sufficiently small values of F. The bimodal crystal size frequency distributions offer an explanation for porphyritic textures of igneous rock in small‐scale intrusions by a one‐stage cooling history. The fine‐grained groundmass is the result of heterocatalytic nucleation, while the phenocrysts nucleated nonheterocatalytically. A strong coupling via a thermostat effect between undercooling and crystallization rate causes the longest part of the melt volume to crystallize at small and nearly constant rates of undercooling. The degree of crystallinity of the liquidus phase close to the margin of the intrusion may vary between 10% and 100% as a consequence of small changes of the initial composition of the melt. The latter two results are almost independent of the value of F. The suppression of the crystallization of the liquidus phase can be explained by the strong metastable crystallization of the solidus phase. This result shows that the degree of crystallinity close to the margin cannot be taken as a simple indicator of the cooling rate of an intrusion but is a complex function of kinetic parameters, cooling rate, and melt composition.