Modelling of Trace Element Transfer between Mantle Melt and Heterogranular Peridotite Matrix

Abstract

Small-scale inhomogeneities in trace element patterns observed in mantle rocks are interpreted as transient features produced by non-steady-state mass transfer. These heterogeneities are observed at both microscopic and macroscopic scales. At the microscopic scale, they can be observed as core-to-rim trace element profiles in minerals of sheared garnet peridotite xenoliths from kimberlites. These gradients are attributed to the interaction of the rock with an infiltrated melt, followed by rapid quenching. At the macroscopic scale, the heterogeneities have been observed in peridotites adjacent to vein conduits in orogenic massifs. They consist of a variation in the chemical composition, with bulk REE enrichment close to the vein and selective LREE enrichment further into the host. This feature is believed to result from the differential buffering of a percolating melt through a host rock. To understand these phenomena, we present a model of non-equilibrium chemical interaction between a magmatic liquid and a heterogeneous solid matrix. This model describes the exchange of trace elements between liquid and solid components at the scale of a representative elementary volume. A general solution of the diffusion-convection equation, with non-equilibrium diffusion in the solid phase, is given. The validity of this assumption is discussed in terms of relaxation times and characteristic lengths. The general solution is applied to the two geological phenomena quoted above. At the microscopic scale, we model core-to-rim diffusion patterns following a sudden invasion of a peridotitic matrix by an exotic melt. We emphasize the critical role played by neighbouring crystals in the transient concentration profile of a particular grain. This ‘matrix effect’ is strongly dependent upon grain-size and mineralogical heterogeneity of the rock. At the macroscopic scale, we use the assumption of transfer by porous flow advection of magma associated with diffusion in heterogeneous media. It is shown that REE fractionation resulting from the chromatographic effect is more effective for (1) time duration greater than the relaxation times of crystals, (2) high magma velocity, and (3) low porosity.