Increasing the accuracy of (U-Th(-Sm))/He dating with 3D grain modelling

Abstract

Conventional (U-Th(-Sm))/He thermochronology requires accurate determination of the grain shape and dimension for calculation of 4He loss by alpha particle ejection and diffusion. In routine practice, calculations of 4He loss and diffusion are calculated assuming that measured grains approximate symmetric grain shapes with perfectly smooth crystal surfaces. This may introduce uncertainties that are virtually impossible to quantify if grains that do not pass the latter criteria are used. Alternatively, this leads to a selection bias for the analyses of detrital minerals if only grains with perfect crystal surfaces are measured. To address this limitation, we introduce a flexible, open-source numerical approach in Matlab™ to accurately determine the three-dimensional grain shape and numerically model He loss by alpha ejection and diffusion on individual grains. The three-dimensional surface of a mineral grain is interpolated from photomicrographs taken orthogonal to the principal grain axes. He ejection and diffusion is simulated using a coupled Monte Carlo and Brownian motion algorithm. Comparing our approach to high-resolution X-ray microtomography, we demonstrate that our “3D-He” approach improves the accuracy of He loss corrections when mineral grains do not approximate perfect crystal shapes by avoiding constraints inherent to standard manual-analytical approaches. Importantly, this method mitigates any bias introduced by user-dependent grain selection, measurements and assigning grains to a mineral shape for which analytical solutions of He production have been derived. In routine practice, we find that our 3D-He approach improves the accuracy of geometric measures (volume and surface area) and associated sphere-equivalent radii (SER) significantly, reducing the average deviation from true values from ~7–8% (manual-analytical approach) to ~2.5% (3D-He approach). The difference in SER significantly impacts the resulting apatite (U-Th-Sm)/He ages, which may deviate up to 40% when long held at temperatures where He production roughly matches diffusive loss of He. Using the 3D-He approach, the average deviation and overall spread of He loss corrections due to alpha ejection (FT factors) could be reduced from 1.6 ± 4.6% to 0.6 ± 0.8%. In summary, our 3D-He approach is a significant refinement to (U-Th(-Sm))/He age calculation considering relatively low analytical uncertainty in U, Th, Sm and He measurement (~2%). Importantly, our 3D-He approach should mitigate the selection bias introduced through manual grain selection. Toward this end, we discuss additional advantages of our numerical approach to handling broken grains or grains with known parent isotope zonation.