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

Abstract

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.