Diffusion of helium, hydrogen and deuterium in diamond: Experiment, theory and geochemical applications

Diffusivities of helium, deuterium and hydrogen have been characterized in diamond. Polished CVD diamond was implanted with either ³He, ²H, or ¹H. Implanted samples were sealed under vacuum in silica glass capsules, and annealed in 1-atm furnaces. ³He, ²H and ¹H distributions were measured with Nuclear Reaction Analysis. We obtain these Arrhenius relations D_He = 4.00 × 10⁻¹⁵ exp(−138 ± 14 kJ mol⁻¹/RT) m² s⁻¹. D_2H = 1.02 × 10⁻⁴ exp(−262 ± 17 kJ mol⁻¹/RT) m² s⁻¹. D_1H = 2.60 × 10⁻⁴ exp(−267 ± 15 kJ mol⁻¹/RT) m² s⁻¹. Diffusivities of ¹H and ²H agree within experimental uncertainties, indicating little diffusive mass fractionation of hydrogen in diamond. To complement the experimental measurements, we performed calculations using a first-principles quantum mechanical description of diffusion in diamond within the Density Functional Theory (DFT). Differences in ¹H and ²H diffusivities from calculations are found to be ∼4.5%, reflected in differences in the pre-exponential factor. This small difference in diffusivities, despite the large relative mass difference between these isotopes, is due to the fact that the atomistic process involved in the transition along the diffusion pathway is dictated by local changes to the diamond structures rather than to vibrations involving ¹H/²H. This finding is consistent with the experimental results given experimental uncertainties. In contrast, calculations for helium diffusion in diamond indicate a difference of 15% between diffusivities of ³He and ⁴He. Calculations of diffusion distances for hydrogen using our data yield a distance of 50 μm in diamond in 300,000 years at 500 °C and ∼30 min at 1400 °C. Diffusion distances for He in diamond are shorter than for H at all temperatures above ∼350 °C, but differences increase dramatically with temperature because of the higher activation energy for H diffusion. For example, a 50 μm diffusion distance for He would be attained in ∼40 Myr at 500 °C and 400 yr at 1400 °C. For comparison, a 50 μm diffusion distance for N in diamond would require nearly 1 billion years at 1400 °C. The experimental data indicate that diamonds equilibrate with ambient H and He in the mantle on timescales brief relative to most geological processes and events. However, He diffusion in diamond is slower than in any other mineral measured to date, including other kimberlite-hosted minerals. Under some circumstances, diamond may provide information about mantle He not recoverable from other minerals. One possibility is diamonds entrained in kimberlites. Since the ascent of kimberlite from the mantle to near-surface is very rapid, entrained diamonds may retain most or all of the H and He acquired in mantle environments. Calculations using reasonable ascent rates and T-t paths indicate that He diffusive loss from kimberlite-hosted diamonds is negligible for grains of 1.0–0.2 mm radius, with fractional losses <0.15% for all ascent rates considered. If the host kimberlite magma is effectively quenched in the near-surface (or is erupted), diamonds should contain a faithful record of [He] and He isotopes from the mantle source region. Preservation of H in kimberlite-hosted diamonds is less clear-cut, with model outcomes depending critically upon rates of ascent and cooling.