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.

中文翻译：

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针铁矿中的氖扩散，α-FeO​​(OH)：多尺度理论研究

针铁矿中的氖扩散行为已被研究用于地质 (U-Th)/Ne 测年，因为与自然 U 和 Th α 衰变相关的成核反应在针铁矿中产生的 Ne 可以扩散出晶体。根据之前的工作，结合原子尺度的密度泛函理论研究和宏观尺度的动力学蒙特卡罗模拟的多尺度计算方法已被用于确定针铁矿中的 Ne 扩散行为。已进行周期性 DFT 计算以研究针铁矿的结构、电子和磁特性，从而确定纯无缺陷针铁矿以及含有铁铝取代的针铁矿和含有晶体缺陷的针铁矿中的 Ne 插入位点，获得最接近天然针铁矿晶体的晶体结构。轻推弹性带方法用于定义相邻间隙位点之间 Ne 迁移的最小能量路径。采用 Climbing Image Nudged Elastic Band 方法来获得更准确的过渡状态。使用动力学蒙特卡罗方法模拟间隙位点之间 Ne 跳跃的 3 维随机游走。我们发现一个 Ne 原子沿着针铁矿的未占据通道沿着锯齿形路径在纯无缺陷针铁矿中扩散，有效活化能为 Ea = 0.50 eV，指数前因子为 D0 = 6.38 × 10–4 cm2 s−1。此外，铁铝取代引起未占据通道的小体积收缩，这将 Ne 扩散的能垒增加到 0.66 eV。尽管如此，该能垒仍然不足以在表面温度下将 Ne 原子保留在针铁矿结构中。然而，晶体缺陷会强烈影响针铁矿中的 Ne 扩散率。在肖特基缺陷的情况下，即大空位，Ne 原子保留在由空位产生的新稳定位点。在水合 Fe 空位的情况下，空间约束仍然是抑制 Ne 在两个相邻未占据通道之间跳跃的障碍。