A grain boundary model of garnet growth

Abstract

Numerical models for the growth of garnet are presented to evaluate the relative significance of reaction-limited growth and diffusion-limited growth following garnet nucleation after significant overstepping of the equilibrium garnet-in reaction. Reactions are only permitted among phases that are adjacent across grain boundaries and the extent of reaction at a given reaction site is scaled to the local amount of chemical affinity available to the two or three reactant phases relative to the grain boundary composition. This local affinity is dissipated as the local reaction proceeds, which changes the composition of the adjacent grain boundary “phase” and sets up chemical gradients that drive diffusion along the grain boundaries. Reactions proceed until all affinity is exhausted at which point the rock is essentially at equilibrium. Two extremes are modeled. Reaction-limited growth is modeled as infinitely rapid grain boundary diffusion whereas diffusion-limited growth is modeled by assuming that reactions proceed infinitely fast such that the supply of nutrients and removal of waste products from a reaction site is restricted by the rate of diffusion. Models are presented with model assemblages chlorite + quartz + garnet and chlorite + quartz + muscovite + biotite + plagioclase + garnet. Reaction-limited models result in garnets displaying well-formed “bell-shaped” Mn zoning profiles with all garnet crystals showing similar amounts of growth and zoning profiles. Diffusion-limited models result in mineral growth or consumption that is texture-sensitive such that the amount of consumption or production of a phase depends on the location of the crystal in the sample and the proximity of other phases. For example, the total amount of garnet continues to increase for the duration of diffusion-limited models although locally an individual garnet crystal may first grow and then be consumed. Mn zoning in models with short diffusion times display distinct “peaks” in the central garnet cores, in contrast to the bell-shaped profiles in reaction-limited models. With increasing diffusion times, these Mn zoning profiles evolve towards bell-shapes. These models demonstrate that diffusion-limited growth of garnet porphyroblasts may result in textural and compositional complexities that are not encapsulated by bulk-rock thermodynamic modeling.