Numerical Modelling of Radiogenic Ingrowth and Diffusion of Pb in Apatite Inclusions with Variable Shape and U-Th Zonation

The fundamental premise of apatite U-Th-Pb thermochronology is that radiogenic Pb is redistributed by volume diffusion. In practice, it is often additionally assumed that crystals (1) lose radiogenic Pb to an infinite reservoir, (2) have a simple geometry and (3) are chemically homogeneous. Here we explore the significance of the latter three assumptions by numerical modelling of Pb radiogenic ingrowth and diffusion in apatite inclusions within other minerals. Our results indicate that the host minerals are likely to hamper diffusive Pb loss from the apatite inclusions by limiting the Pb flux across their boundaries, and thus the thermal histories that are reconstructed assuming a fully open boundary may be significantly inaccurate, precluding a meaningful interpretation. We also find that when apatite boundaries are flux-limited, heterogeneities in U and Th concertation within apatite have subordinate effect on bulk-grain U-Th-Pb dates and can cause intra-grain U-Th-Pb dates to increase towards the boundaries. Finally, we show that it is important to correctly account for crystal geometry when modelling intra-grain U-Th-Pb dates. We suggest that the effect of surrounding minerals on diffusive Pb loss from apatite (and loss of other radiogenic isotopes from other minerals) should be examined more closely in future research.