A first-principles study of helium diffusion in quartz and coesite under high pressure up to 12GPa

Helium diffusion in mantle minerals is crucial for understanding mantle structure and the dynamic processes of Earth's degassing. In this paper, we report helium incorporation and the mechanism of its diffusion in perfect crystals of quartz and coesite. The diffusion pathways, activation energies (E_a), and frequency factors of helium under ambient and high pressure conditions were calculated using Density Functional Theory (DFT) and the climbing image nudged elastic band (CI-NEB) method. The calculated diffusive coefficients of He in the quartz in different orientations are:
D100=1.24×10^-6 exp. (-26.83 kJ / mol / RT) m² /s
D010=1.11×10^-6 exp. (-31.60 kJ / mol / RT) m² /s
and in the coesite:
D100=3.00×10-7 exp. (-33.79 kJ / mol / RT) m² /s
D001=2.21×10^-6 exp. (-18.33 kJ / mol / RT) m² /s
The calculated results indicate that diffusivity of helium is anisotropic in both quartz and coesite and that the degree of anisotropy is much more pronounced in coesite.
Helium diffusion behavior in coesite under high pressures was investigated. The activation energies increased with pressure: E_a100 increased from 33.79 kJ/mol to 58.36 kJ/mol, and E_a001 increased from 18.33 kJ/mol to 48.87 kJ/mol as pressure increased from 0 GPa to 12 GPa. Our calculations showed that helium is not be quantitatively retained in silica at typical surface temperatures on Earth, which is consistent with the findings from previous studies. These results have implications for discussion of the Earth's mantle evolution and for recognition thermal histories of ultra-high pressure (UHP) metamorphic terranes.