Diffusion is a fundamental mass transfer process in magmatic and metamorphic systems. Simple recipes for evaluating time scales for diffusive re-equilibration of a trace element in bi-
mineralic
aggregates with and without the presence of intergranular fluid or melt are obtained through approximate solutions to diffusion equations. Diffusive re-equilibration times for the trace element depend on average grain sizes of the two
minerals, diffusion coefficients and partition coefficients for the element in the two
minerals, and volume fractions or volume fluxes of the
minerals and fluid or melt in the system. There are two time scales for diffusive re-equilibration in fluid-bearing bi-
mineralic systems. The fast time scale is proportional to fluid fraction and dominated by the
mineral that has a faster diffusion rate. The slow time scale is bounded by the time scales of diffusion in the two
minerals and determines the overall time scale of diffusive re-equilibration for the system. Presence of small amount of fluid or melt does not lead to a reduction in the time scale of diffusive re-equilibration for the bi-
mineralic aggregate. Percolation of fluid or melt drives the system further away from equilibrium and increases the length and time scales for diffusive re-equilibration in the system. The time scales for subsolidus re-equilibration in bi-
mineralic
aggregates are determined by the minor’s rule: the
mineral that contains a lesser amount of the trace element of interest in the system contributes more to the overall diffusive time.
Applications to REE redistribution between clinopyroxene and orthopyroxene and between plagioclase and orthopyroxene highlight the importance of REE diffusion and partitioning in pyroxene and plagioclase. The time scales for subsolidus re-equilibration of REE in noritic rocks are dominated by light REE diffusion in orthopyroxene and by middle and heavy REE diffusion in plagioclase. The time scales for subsolidus re-equilibration of REE in two-pyroxene bearing rocks are controlled primarily by REE diffusion in orthopyroxene. The time scales for diffusive re-equilibration of REE in melt-bearing two-pyroxene aggregates are determined by diffusion in clinopyroxene for light REE and by diffusion in orthopyroxene for middle to heavy REE. Presence of melt flow further expands the role of clinopyroxene. This contrasting behavior in diffusive time scale may provide a simple explanation for the ubiquitous chemical disequilibrium in light REE between clinopyroxene and orthopyroxene observed in mantle peridotites from a wide range of tectonic settings.
