Empirical determination of diffusion coefficients and geospeedometry

Geospeedometry allows to estimate the cooling rate (sinit) of metamorphic rocks at the beginning of the cooling history using diffusion data. But the choice of a diffusion activation energy (E) and a preexponential factor (D0) from experimental results can be difficult. We propose a method to obtain E directly from the rock itself by studying the variation of the average concentration of elements or isotopes (〈C〉) as a function of mineral grain size (d). An appropriate value of D0 can then be estimated using an existing compensation rule, a linear relationship between log D0 and E. Consequently, uncertainties on sinit are markedly reduced. All parameters of this analytical model and their sensitivity on sinit can be estimated from 〈C〉 of the mineral grains under study. As a test we apply our model to a study by Edwards and Valley (1998)**** on 18O/16O fractionation between diopside and calcite in Adirondacks marbles, and find a cooling rate in agreement with previous works, without choosing experimental values for E and D0.