Diffusion closure temperature and age of a mineral with arbitrary extent of diffusion: Theoretical formulation and applications

The commonly used expression of the closure temperature, T(C), of a diffusing species in a mineral, as derived by M.H. Dodson [Contrib. Mineral. Petrol. 40 (1973) 259-264], is applicable only to systems which have undergone sufficient diffusion so that even the composition at the center of individual grains is significantly removed from that established at the onset of cooling. We have extended Dodson's formulation to include cases with arbitrarily small amount of diffusion, and applied it to calculate T(C) and age profiles, which would develop in single crystals of different geometries. These results permit evaluation of the extent of resetting of mineral age and of ion exchange geothermometers during cooling. The measured age profile of a mineral can also be used to constrain its cooling rate. These applications have been illustrated for the cases of garnet-biotite Fe-Mg exchange geothermometer, and the cooling age and closure temperatures of the Sm-Nd and Lu-Hf decay systems in garnet.