PRESSURE GRADIENTS IN GARNETS INDUCED BY DIFFUSION RELAXATION OF MAJOR ELEMENT ZONING

Diffusive re-equilibration of zonation of bi-valent cations (Fe, Mg, Ca, Mn) in garnet is common at temperature-time paths corresponding to the upper amphibolite-facies or granulite-facies. Zoning in garnet is typically established prograde, either due to changes in fractionation factor or depletion of the element in the matrix (Rayleigh fractionation). While diffusion potentially destroys initial information on garnet formation conditions, it has been used successfully to estimate cooling history of rocks. Over the last decades, excellent experiments have calibrated diffusion coefficients for bivalent cations, and results have been compared to field studies to deduce rate of exhumation, or alternatively, field processes have been used to calibrate diffusion.

A neglected aspect of diffusion re-equilibration is the volume change due to the different molar volumes of the garnet end members. Any internal volume modification will lead to important pressure gradients within the garnet crystal, since it is well established that garnets are very rigid (e.g. coesite inclusions found in garnet require a local overpressure of more than 20 kbar.)

Assuming that garnet is perfectly rigid, the elastic properties of garnet can be readily used to calculate internal pressure. Re-equilibration of 0.1 mole fraction of Ca, Fe, Mn, or Mg will lead to several kbar pressure differences, with the largest effects observed for Ca (up to 14 kbar differential pressure). These pressure gradients force changes in chemical potential gradients, slowing diffusion and in extreme cases stabilizing or increasing compositional gradients.

The uphill diffusion observed in experiments by Vielzeuf & Saul (2010 CMP) might be due to this phenomenon. Indeed, the Mg component, which moves against its apparent chemical gradient in their experiments, behaves in such a way that the overall volume of each zone is maintained, suggesting that the significant coupling of the fluxes is mainly due to maintaining constant volume to reduce strain energy and stress.

Whether this process is important in garnets from metamorphic environments is uncertain at this time. However the effect could be responsible for atoll garnet formation, diffusion profile preservation, and uphill diffusion.