Effect of heterogeneity on the diffusion of Pb in apatite for petrochronological applications: A multiscale approach to characterizing the influence of apatite chemistry and anisotropy on Pb diffusion

The investigation of various factors effecting the Lead (Pb) diffusion in phosphate minerals such as apatite is still challenging in the interpretation of (U[sbnd]Th)/Pb geochronology. For (U[sbnd]Th)/Pb system, apatite minerals have closure temperatures in the range of 375 to 600 °C and therefore can be used for the investigation of mid-temperature thermochronological and/or petrochronological questions i.e., the reconstruction of thermal events in Earth's crust. There is still uncertainty whether Pb diffusion in apatite is characterized by thermally activated volume and/or anisotropic diffusion profiles or is instead impacted by novel growth processes and recrystallization (chemical substitutions). As the apatite structure support extensive compositional variability, including partial or total substitution of both the cationic and anionic sites and forms solid solutions therefore, it necessitates a thorough examination of these effects and anisotropy on Pb diffusivity and (U[sbnd]Th)/Pb geochronometric system. For this, a multi-scale study is carried out to examine the effects of chemical composition, anisotropy, and growth structure on the diffusion of Pb in order to better understand the behaviour of Pb diffusion in apatite. This study employed computational techniques like Density Functional Theory (DFT) and Transition State Theory (TST) at the atomic level and integrates it with the Kinetic Monte Carlo (KMC) simulations at the macroscopic level. Models of this study shows that Pb diffusion is completely anisotropic along the preferred z-axis or [001] direction and Pb readily escapes faster from Na-substituted apatite when compared to pure F-apatite and Cl-substituted apatite. Because of this anisotropy and chemical substitutions, Pb diffusivity in apatite either increases by opening of diffusion channels or decreases by blocking the diffusion channels depending on the site and type of chemical substitution. Further, in case of blocking effect the Pb diffusion occurs through workaround pathways and approaches towards the isotropic diffusion. For Na-substituted apatite, the impact of Na occupation on anisotropic Pb diffusion is significantly greater while in case of Cl-substituted apatite the Cl occupation mostly leads towards isotropic diffusion by opening the diffusion paths along other directions (mostly along the in-plane direction). Furthermore, the high closure temperatures (Tc) (e.g., ∼1370 °C) of the modelled apatites (except the perfect Na-substituted apatite e.g., ∼500 °C) of this study when compared to the Tc of Durango apatite obtained experimentally for the effective grain size of 100 μm and cooling rates of 10 °C/Ma indicate that the effective closure temperature dominantly depends on the degree and types of chemical substitutions and play a crucial role for the closure or opening of Pb diffusion/loss in apatites.