¹⁷⁶Lu–¹⁷⁶Hf geochronology of garnet I: experimental determination of the diffusion kinetics of Lu³⁺ and Hf⁴⁺ in garnet, closure temperatures and geochronological implications

Abstract

The ¹⁷⁶Lu–¹⁷⁶Hf and ¹⁴⁷Sm–¹⁴³Nd decay systems are routinely used to determine garnet (Grt)–whole-rock (WR) ages; however, the ¹⁷⁶Lu–¹⁷⁶Hf age of garnet is typically older than the ¹⁴⁷Sm–¹⁴³Nd age determined from the same aliquots. Here we present experimental data for Lu³⁺ and Hf⁴⁺ diffusion in garnet as functions of temperature, pressure and oxygen fugacity and show that the diffusivity of Hf⁴⁺ in almandine/spessartine garnet is significantly slower than that of Lu³⁺. The diffusive closure temperature (T _C) of Hf⁴⁺ is significantly higher than that of Nd³⁺, and although this property is partly responsible for the observed ¹⁷⁶Lu–¹⁷⁶Hf and ¹⁴⁷Sm–¹⁴³Nd Grt–WR age discrepancies, the difference between the T _C-s of Lu³⁺ and Hf⁴⁺ could lead to apparent Grt–WR ¹⁷⁶Lu–¹⁷⁶Hf ages that are skewed from the age of Hf⁴⁺ closure in garnet. In addition, the slow diffusivity of Hf⁴⁺ indicates that the bulk of metamorphic garnets retain a substantial fraction of prograde radiogenic ¹⁷⁶Hf throughout peak metamorphic conditions, a phenomenon that further complicates the interpretation of ¹⁷⁶Lu–¹⁷⁶Hf garnet ages and invalidates the use of analytical T _C expressions. We argue that the diffusion of trivalent rare earth elements in garnet becomes much faster when their concentration level falls below a few hundred ppm, as in the experiments of Tirone et al. (Geochim Cosmochim Acta 69: 2385–2398, 2005), and further argue that this low-concentration mechanism is appropriate for modeling the susceptibility of ¹⁴⁷Sm–¹⁴³Nd garnet ages to diffusive resetting.