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:

D[100] = 1.24 × 10⁻⁶ exp. (−26.83 kJ / mol / RT) m² /s.

D[010] = 1.11 × 10⁻⁶ exp. (−31.60 kJ / mol / RT) m² /s.

and in the coesite:

D[100] = 3.00 × 10⁻⁷ exp. (−33.79 kJ / mol / RT) m² /s.

D[001] = 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_a[100] increased from 33.79 kJ/mol to 58.36 kJ/mol, and E_a[001] 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.

氦在地幔矿物中的扩散对于了解地幔结构和地球除气的动态过程至关重要。在本文中，我们报告了氦的掺入及其在石英和堇青石的完美晶体中扩散的机理。利用密度泛函理论（DFT）和爬升微动弹性带（CI-NEB）方法计算了氦在环境和高压条件下的扩散途径，活化能（E _a）和频率因子。计算得出的不同方向上He在石英中的扩散系数为：

D [100] = 1.24×10 ^-6 exp。（-26.83kJ / mol / RT） m ² / s。

D [010] = 1.11×10 ^-6 exp。（−31.60 kJ / mol / RT） m ² / s。

并在coesite中：

D [100] = 3.00×10 ^-7 exp。（-33.79 kJ / mol / RT） m ² / s。

D [001] = 2.21×10 ^-6 exp。（−18.33 kJ / mol / RT） m ² / s。

计算结果表明，氦在石英和柯石英中的扩散率都是各向异性的，并且各向异性程度在柯石英中更为明显。

研究了高压条件下氦在钴铝矿中的扩散行为。活化能随压力增加：随着压力从0 GPa增加到12 GPa，E _a [100]从33.79 kJ / mol增加到58.36 kJ / mol，E _a [001]从18.33 kJ / mol增加到48.87 kJ / mol 。我们的计算表明，在地球上典型的表面温度下，氦气不能定量保留在二氧化硅中，这与以前的研究结果是一致的。这些结果对讨论地球的地幔演化以及对超高压（UHP）变质地层的热历史的认识具有启示意义。