Rate and mechanism in prograde metamorphism

For a given rate of heat input into a prograde metamorphic sequence the extent of overstep of reaction temperature (disequilibrium) depends on the slowest of three sequential steps: (a) surface detachment of reactant minerals, (b) transport of material to the site of mineral growth, and (c) nucleation and growth of the product mineral. We have developed analytical expressions which enable determination of the rates of mineral dissolution and growth and of advective and diffusive mass transport during metamorphism. The dissolution and growth steps are linear functions of the driving force (– G) of the overall reaction while diffusion may take place either through a grain boundary fluid film or through the disorganized grain boundary itself.While little is known about heterogeneous nucleation, we argue from field observations that the rate of nucleation is not in general rate limiting. Additionally, if a fluid phase is present true grain boundary diffusion cannot be the mechanism which transports material over the mm to cm distances observed between reactant and product minerals.Simple models of contact (200° C temperature rise in 10,000 years) and regional (10° C per million years) metamorphic events lead to several conclusions concerning the rate determining step. Firstly, growth and dissolution are extremely rapid, dehydration reactions at 500° C going to completion in 2×10² years (contact) and 1×10⁴ years (regional), if all solutes are readily transported. Secondly, the effect of substantial fracture flow of fluid is to divert the transporting medium away from the grain boundary region and hence to retard the transport step. Under most such circumstances it appears that diffusive transport of aqueous SiO₂ or Mg species will be rate controlling. Despite this retardation of reaction rates, the extent of disequilibrium is rarely more than a few degrees C. Extensive disequilibrium (40° C) can only occur for reactions such as the andalusite sillimanite transformation which have very small entropy changes and which occur in rapid metamorphic events.