First-principles calculation of H/D isotopic fractionation between hydrous minerals and water

Hydrogen fractionation laws between selected hydrous minerals (brucite, kaolinite, lizardite, and gibbsite) and perfect water gas have been computed from first-principles quantum-mechanical calculations. The β-factor of each phase was calculated using the harmonic phonon dispersion curves obtained within density functional theory. All the fractionation laws show the same shape, with a minimum between 200 °C (brucite) and 500 °C (gibbsite). At low temperatures, the mineral/liquid water fractionation laws have been obtained using the experimental gas/liquid water fractionation laws. The resulting fractionation laws systematically overestimate measurements by 15‰ at low temperatures to 8‰ at ≈400 °C. Based on this general agreement, all calculated laws were empirically corrected with reference to brucite/water data. These considerations suggest that the experimental or natural calibrations by Xu and Zheng (1999) and Horita et al. (2002) (brucite/water), Gilg and Sheppard (1996) (kaolinite/water), Wenner and Taylor (1973) (lizardite/water), and in some extents Vitali et al. (2001) (gibbsite/water) are representative of equilibrium fractionations. Besides, internal isotopic fractionation of hydrogen between inner-surface and inner hydroxyl groups has been computed for kaolinite and lizardite. The obtained fractionation is large, of opposite sign for the two systems (respectively, −23‰ and +63‰ at 25 °C) and is linear in T^-2. Internal fractionation of hydrogen in TO phyllosilicates might thus be used in geothermometry.