Open Access

Xin Zhong, Felix Höfling, Timm John

• Garnet has been widely used to decipher the pressure-temperature-time history of rocks, but its physical properties such as elasticity and diffusion are strongly affected by trace amounts of hydrogen. Experimental measurements of H diffusion in garnet are limited to room pressure. We use atomistic simulations to study H diffusion in perfect and defective garnet lattices, focusing on protonation defects at the Si and Mg sites, which are shown to be energetically favored. The ab-initio simulation of H diffusion is computationally challenging due to a transient trapping of H, which is overcome with machine learning techniques by training a deep neural network that encodes the interatomic potential. Our results show high mobility of hydrogen in defect free garnet lattices, whereas H diffusivity is significantly diminished in defective lattices. Tracer simulation focusing on H alone highlights the vital role of atomic vibrations of heavier atoms like Mg in the untrapping of H atoms. Two regimes of H diffusion are identified: a diffuser-dominated regime at high hydrogen content with low activation energies, due to saturation of vacancies by hydrogen, and a vacancy-dominated regime at low hydrogen content with high activation energies, due to trapping of H atoms at vacancy sites. These regimes account for experimental observations, such as a H-concentration dependent diffusivity and the discrepancy in activation energy between deprotonation and D-H exchange experiments. This study underpins the crucial role of vacancies in H diffusion and demonstrates the utility of machine-learned interatomic potentials in studying kinetic processes in the Earth's interior.