Controls on the nucleation and growth of porphyroblasts: Kinetics from natural textures and numerical models

Quantitative textural analysis of garnetiferous rocks from diverse metamorphic environments has demonstrated that diffusionally influenced nucleation and thermally accelerated diffusion-controlled growth are commonly among the dominant controls on porphyroblast crystallization. A new numerical model of diffusion-controlled nucleation and growth that incorporates time as an explicit variable is capable of replicating the essential features of many of these natural porphyroblastic textures using geologically reasonable values for the kinetic parameters governing crystallization. This model has been used to interpret quantitative textural data from four rocks in which garnet grew during prograde regional metamorphism, by assuming constant heating rates and by accepting a previously published estimate for the activation energy for intergranular diffusion. From fits of the model to natural textures, estimates have been extracted for three previously undetermined kinetic quantities that control the nucleation and growth of garnet porphyroblasts, namely the activation energy for nucleation and the pre-exponential rate constants for nucleation and intergranular diffusion. The uncertainty in derived values for the pre-exponential rate constant for intergranular diffusion is probably not much larger than a factor of two because it is proportional to the uncertainty in prograde heating rates, given a defined temperature interval over which crystallization occurs. The uncertainty in estimates of the activation energy and pre-exponential rate constant for nucleation is larger, perhaps a factor of ten, because values for these quantities are derived from fits of the model to natural crystal size distributions; the precision of these estimates appears to be limited by the fact that the crystal size distributions are affected by factors not encompassed within the model (probably variable heating rates and inhomogeneity in the distribution of nutrients in the rock's precursor).