A new calibration of radiation damage control on He diffusivity in apatite: implications for (U-Th)/He thermochronology
Authors: Derycke Alexis , Gallagher Kerry , Gautheron Cécile 
Published: February 2023

In low temperature thermochronology, reliable interpretation of (U-Th)/He data is controlled by our understanding of helium diffusion in a crystal. The diffusion kinetics can be simulated through the classic Arrhenius-type equation, with parameters frequency factor Do and activation energy Ea (Farley, 2000). For apatite, it has been demonstrated that accumulated radiation damage perturbed the Arrhenius-type equation and exerts a strong control on He diffusion. Two models have been developed to parameterise the evolution of diffusion kinetics in apatite in terms of accumulated radiation damage: one based on the physical phenomenon (Gautheron et al., 2009) and the other calibrated on empirical observations (Flowers et al., 2009). As the amount of radiation damage depends on both time (U and Th decay producing damage) and temperature (annealing of radiation damage), both of these models are routinely used to interpret apatite (U-Th)/He data in terms of thermal histories. However, results obtained from inverse thermal history modelling with these two models can differ and be inconsistent with other low thermochronological data (e.g., apatite fission tracks). In this contribution we present a new radiation damage-based diffusion model that combines the approaches of both the Gautheron et al. and Flowers et al. models.Our new model is based on the theoretical diffusion model proposed by Gerin et al. (2017) but incorporates a new calibration from the available He diffusion experiment results. The Gerin et al. model is built on a theoretical understanding of the fundamental physical processes and predicts diffusion parameters for different levels of crystal lattice damage, using quantum calculus. We recalibrated this model through an empirical law based on real crystal mesh damage calculated from available experimental data. To test the reliability of the revised model and to compare it to the existing models, it was implemented in the modelling software, QTQt (Gallagher, 2012). Here we present results of both forward and inverse modelling to highlight the benefits of the new model. The results are assessed in terms of the impact for &#8220;deep time&#8221; (>500 Ma) thermochronology, in which accumulated radiation damage can have a significant control on the inferred thermal history models.&#160;Farley, K.A., 2000. Helium diffusion from apatite: General behavior as illustrated by Durango fluorapatite. J. Geophys. Res. 105, 2903&#8211;2914. https://doi.org/10.1029/1999JB900348Flowers, R.M., Ketcham, R.A., Shuster, D.L., Farley, K.A., 2009. Apatite (U&#8211;Th)/He thermochronometry using a radiation damage accumulation and annealing model. Geochimica et Cosmochimica Acta 73, 2347&#8211;2365. https://doi.org/10.1016/j.gca.2009.01.015Gallagher, K., 2012. Transdimensional inverse thermal history modeling for quantitative thermochronology. Journal of Geophysical Research: Solid Earth 117, n/a-n/a. https://doi.org/10.1029/2011JB008825Gautheron, C., Tassan-Got, L., Barbarand, J., Pagel, M., 2009. Effect of alpha-damage annealing on apatite (U&#8211;Th)/He thermochronology. Chemical Geology 266, 157&#8211;170. https://doi.org/10.1016/j.chemgeo.2009.06.001Gerin, C., Gautheron, C., Oliviero, E., Bachelet, C., Mbongo Djimbi, D., Seydoux-Guillaume, A.-M., Tassan-Got, L., Sarda, P., Roques, J., Garrido, F., 2017. Influence of vacancy damage on He diffusion in apatite, investigated at atomic to mineralogical scales. Geochimica et Cosmochimica Acta 197, 87&#8211;103. https://doi.org/10.1016/j.gca.2016.10.018