Helium diffusion in pure hematite ($\alpha$-Fe$_2$O$_3$) for thermochronometric applications: A theoretical multi-scale study

International audienceHe diffusion coefficient in iron oxide alpha-hematite crystal has been determined using computational multi scale approach in the purpose of geological dating as He is produced during U-Th-Sm decay in this mineral. Natural hematite samples are generally made of nanometric to micrometric scale crystals leading to the difficulty to determine the total He diffusion behavior. A multi-scale theoretical approach will so bring new information on the He diffusion coefficient in 3D. Investigations, at microscopic scale, of helium insertion and atomic jumps into hematite crystal have been performed by DFT and transition state theory. The minimum path energy of helium migration between interstitial sites and its position at transition state are determined by the climbing image-Nudged Elastic Band method. Based on the microscopic results the 3D random walk of helium, in the hematite crystal, has been simulated by the Kinetic Monte Carlo method. The diffusion coefficient has been determined: D-3D (cm(2)/s) = 9.32 x 10(-3) e(-163 ev/kg(-1)). The calculated activation energy, for a perfect crystal, is in very good agreement with experiment data showing that He diffusion in hematite is controlled only by the crystal structure. These results give the 3D He diffusion and permit to determine that He is highly retain in crystal at surface temperature, with closure temperature of 83 and 154 degrees C for grain size of 0.1 and 10 mu m respectively. These diffusion coefficient data can so be used in the future for a better interpretation of geological ages