Simulated garnet-clinopyroxene geothermometry of eclogites

The Fe-Mg thermometer widely used to infer the "equilibration" temperature of garnet-clinopyroxene assemblages of eclogites records the progressive bl ocking of diffusion-limited exchanges between coexisting mineral phases. It is argued that equilibrium is achieved through the fast grain boundary mod el in which Fe and Mg circulate in an interstitial medium fast enough for t he rate-limiting step to be the volume diffusion in each mineral phase. A s emi-analytic solution is found and the influence of the cooling history, gr ain size distribution, and rock composition on the temperature at which the Fe-Mg exchange between garnet and clinopyroxene is frozen in are quantitat ively evaluated. In particular, the model simulates the temperatures that w ould be obtained from the concentration of Fe and Mg in the rim of adjacent garnet and clinopyroxene crystals such as those commonly obtained by elect ron probe. For eclogites, the simulations show that correct peak temperatur es are retrieved as long as the temperature of the metamorphic climax does not exceed 650 degrees C. At higher climax temperatures, rim-rim temperatur es underestimate the peak temperature and cluster around 650 degrees C. Fas t cooling, however, strongly limits diffusive equilibration. In crustal-typ e eclogites, cooling rates of a few degrees per million years at 700 degree s C and of a few tens of degrees at 800 degrees C preserve the record of th e peak temperature. It is shown that these results are largely independent of the chemical composition of the garnet and clinopyroxene. On the contrar y, the mineral grain size and the respective proportions of garnet and clin opyroxene have a major effect on retrogressive diffusion. For eclogites for med at a temperature of 800 degrees C and under conditions of slow cooling, the record of the climax temperature is preserved by crystal rims as long as the volume of clinopyroxene is smaller than that of garnet and crystal s ize is at least millimetric. The choice of a particular set of experimental data for the diffusion coefficients is found to be immaterial. We suggest that the temperature of the metamorphic climax of eclogites is best estimat ed from the composition of clinopyroxene rims combined with that of the inn er edge of the diffusion boundary layer fringing the coexisting garnet grai ns.