A crystal-chemical basis for Pb retention and fission-track annealing systematics in U-bearing minerals, with implications for geochronology

This study develops an empirical crystal-chemical framework for systematizing the kinetics of Pb loss and fission-track annealing in U-bearing minerals. Ionic porosity, Z (the fraction of a mineral's unit-cell volume not occupied by ions) potentially accounts for kinetic behavior by monitoring mean metal-oxygen bond length/strength. Various tests of a general kinetics-porosity relationship are presented, based upon diverse mineral data including: (1) Pb diffusion parameters; (2) measured closure temperatures (T_C) for fission-track annealing and (3) retentivities of both Pb and fission tracks, from apparent-age data. Every kinetic parameter (including T_C and mineral age for both the U/Pb and fission-track systems) is inversely correlated with Z within the sub-assemblage: zircon (Z ≈ 29%), titanite ( 34%) and apatite ( 38%). Assuming a diffusional closure model, Pb isotopic transport phenomena are described by a T_C-Z scale “calibrated” with field-based T_C data for titanite (≥ 680 ± 20°C) and apatite ( 500°C). Extrapolation of this scale yields T_C estimates for the following minerals: staurolite (T_C ≥ 1060°C, Z ≈ 25%); garnet (≥ 1010°C, 26.5%); zircon (≥900°C); monazite, xenotime, and epidote (≥ 750°C, 32%); and Ca-clinopyroxene (≥ 670 ± 30°C, 34 ± 1%, depending on composition). These empirical results imply that a (U/)Pb/Pb date for staurolite or garnet records the time of mineral growth, not post-growth isotopic closure, as also concluded in recent field studies. Because Z systematizes fission-track annealing, this recrystallization process, like volume-diffusion, must also be rate-limited by the strength of chemical bonds. The extent to which other recrystallization processes are likewise rate-limited is important to U/Pb geochronology because they potentially compete with diffusion as mechanisms for Pb-isotopic resetting in nature.