Neon diffusion in goethite, α-FeO(OH): a theoretical multi-scale study

Abstract

The neon diffusion behavior in goethite has been investigated for the purpose of geological (U-Th)/Ne dating, as Ne produced in goethite by nucleogenic reactions related to natural U and Th alpha decay can diffuse out of the crystal. According to previous works, a multi-scale computational approach combining Density Functional Theory studies at the atomic scale and Kinetic Monte Carlo simulations at the macroscopic scale has been used to determine Ne diffusion behavior in goethite. Periodic-DFT calculations have been performed to study the structural, electronic, and magnetic properties of goethite, and therefore to identify the Ne insertion sites in pure defect-free goethite as well as in goethite containing iron-aluminum substitution and goethite containing crystallographic defects, to obtain a crystal structure closest to a natural goethite crystal. The Nudged Elastic Band method was used to define the minimum energy pathway for Ne migration, between neighboring interstitial sites. The Climbing Image Nudged Elastic Band method was adopted to obtain more accuracy on the transition state. The 3-dimensional random walk of Ne jumps between interstitial sites was simulated using the Kinetic Monte Carlo method. We found that a Ne atom diffuses in pure defect-free goethite following a zig-zag pathway along the unoccupied channel of goethite, with an effective activation energy of Ea = 0.50 eV and a pre-exponential factor of D0 = 6.38 × 10–4 cm2 s−1. Moreover, the iron-aluminum substitution induces a small volume contraction of the unoccupied channel, which increases the energy barrier of Ne diffusion to 0.66 eV. Nevertheless, this energy barrier remains insufficient to retain Ne atom in the goethite structure at surface temperature. However, crystallographic defects impact strongly Ne diffusivity in goethite. In the case of a Schottky defect, i.e. a large vacancy, the Ne atom is retained in the new stable site generated by the vacancy. In the case of a hydrated Fe vacancy, steric constraints remain a barrier that inhibit the Ne jumping between two adjacent unoccupied channels.