¹⁷⁶Lu–¹⁷⁶Hf geochronology of garnet II: numerical simulations of the development of garnet–whole-rock ¹⁷⁶Lu–¹⁷⁶Hf isochrons and a new method for constraining the thermal history of metamorphic rocks

We present numerical modeling results for the development of ¹⁷⁶Lu–¹⁷⁶Hf and ¹⁴⁷Sm–¹⁴³Nd garnet–whole-rock (WR) isochrons and show that the ¹⁷⁶Lu–¹⁷⁶Hf system can sometimes produce spurious garnet ages due to the faster diffusion of Lu³⁺ relative to Hf⁴⁺ in garnet, and resulting preferential retention of ¹⁷⁶Hf relative to ¹⁷⁶Lu. It is found that when ¹⁷⁶Lu–¹⁷⁶Hf garnet–WR ages are compromised by diffusion, the corresponding ages generally tend to pre- and post-date garnet growth in metapelites and metabasites, respectively. ¹⁴⁷Sm–¹⁴³Nd garnet ages are not compromised by preferential retention of the daughter product, due to the nearly identical diffusion kinetic properties of the parent and daughter nuclides. Garnet Hf isotopes are rarely re-equilibrated with those of the surrounding matrix phase(s) via diffusion at peak temperature; as a consequence, unlike ages determined from the ¹⁴⁷Sm–¹⁴³Nd system, garnet ¹⁷⁶Lu–¹⁷⁶Hf ages seldom represent cooling ages. When ¹⁷⁶Lu–¹⁷⁶Hf garnet ages are spurious due to preferential retention of the daughter product, it is still possible to use these ages to constrain the prograde thermal history of the host rocks, provided the peak P–T conditions and cooling rate are independently constrained. This technique has been exemplified by modeling the grain-size-dependent ¹⁷⁶Lu–¹⁷⁶Hf and ¹⁴⁷Sm–¹⁴³Nd garnet ages of metapelites from the Pikwitonei granulite domain, Canada. Although this study focuses on the ¹⁷⁶Lu–¹⁷⁶Hf decay system in garnet, preferential retention of the daughter product could potentially impact any geochronological system in which the parent nuclide diffuses significantly faster than the daughter isotope.