COOLING RATE HISTORIES FROM GARNET PLUS BIOTITE EQUILIBRIUM

Dodson's (1986) solution of the temperature-dependent diffusion equati on may be used to determine cooling histories from geothermometrically inferred closure temperatures. If a mineral pair such as garnet + bio tite equilibrated at the start of cooling and continued to equilibrate during cooling, then such closure temperatures, T(c), are a strong fu nction of grain size and cooling rate (s). Thus garnet grains of diffe rent sizes that equilibrated with biotite within one rock or thin sect ion will close at different temperatures and thus should record differ ent stages of the thermal history. The application of Dodson's equatio n in the deduction of thermal histories is straightforward if the posi tion of the cut through a garnet grain is known. Unfortunately, the po sition of the section is normally unknown. However, with the use of a single garnet grain cut at an unknown position, an apparent closure te mperature can be determined from an exchange geothermometer, and an ap parent cooling rate can be calculated from the observed radius. From t his apparent closure temperature and apparent cooling rate, a family o f solutions of possible actual closure temperatures and cooling rates can be calculated for a family of assumed actual grain radii. This fam ily of solutions forms a locus on a In s vs. T(c) diagram. With many a nalyses of garnet grain centers in one thin section, garnets of a part icular size that give higher closure temperatures normally are cut clo ser to their centers. Using this practice, the cooling history of a ro ck may be determined. This approach was tested with a Monte Carlo simu lation. The calculated cooling histories provide potentially important constraints on the tectonic evolution of metamorphic terrains.