Rare earth diffusion kinetics in garnet: Experimental studies and applications

We determined the diffusion coefficient of Sm in almandine garnet as function of temperature at 1 bar and fO₂ corresponding that of wüstite-iron buffer, and to a limited extent, that of a few other selected rare earth elements in almandine and pyrope garnets. Both garnets were demonstrated to have metastably survived the diffusion annealing at conditions beyond their stability fields. The experimental diffusion profiles were analyzed by secondary ion mass spectrometry, and in addition, by Rutherford back scattering spectroscopy for two samples. Transmission electron microscopic study of an almandine crystal that was diffusion-annealed did not reveal any near-surface fast diffusion path. Using reasonable approximations and theoretical analysis of vacancy diffusion, the experimental data were used to develop an expression of rare earth element (REE) diffusion coefficient in garnet as a function of temperature, pressure, fO₂, ionic radius, and matrix composition. Calculation of the closure temperature for the Sm-Nd decay system in almandine garnet in a metamorphic terrain shows very good agreement with that constrained independently. Modeling of the REE evolution in melt and residual garnet suggests that for dry melting condition, the REE pattern in the melt should commonly conform closely to that expected for equilibrium melting. However, for much lower solidus temperatures that would prevail in the presence of a H₂O-CO₂ fluid, the concentration of light REE in the melt could be significantly lower than that under equilibrium melting condition. A reported core and rim differences in the REE content of a garnet crystal in a mantle xenolith in kimberlite have been reproduced by assuming that the REE zoning was a consequence of entrapment in a magma derived from an external source for ∼32,000 yr before the eruption.