Closure temperature in cooling bi-mineralic systems: I. Definition and with application to REE-in-two-pyroxene thermometer

Abstract

Closure temperature is an important concept to many diffusion related problems involving cooling. The basic idea and formulation were outlined in the seminal work of Dodson for cooling mono-mineralic systems. The Dodson’s equation has been widely used to calculate closure temperatures for igneous and metamorphic rocks that contain more than one mineral. The purpose of this study is to examine closure temperatures in cooling bi-mineralic systems and to investigate the physical meaning of temperatures calculated using the REE-in-two-pyroxene thermometer. We conduct numerical simulations of diffusive redistribution of trace elements between two coexisting minerals under prescribed cooling using temperature-dependent diffusion coefficients and mineral–mineral partition coefficients. Following Dodson’s treatment, the closure temperature in bi-mineralic systems can be defined by the evolution of either average trace element concentrations in the two minerals or their ratio. The latter defines an effective partition coefficient. Closure temperatures calculated based on the two definitions are compared for a range of cooling rates, grain sizes, mineral proportions, and temperature-dependent partition coefficients and diffusion coefficients. Temperatures defined by the effective partition coefficient are recommended. Application to diffusive redistribution of rare earth elements (REE) in orthopyroxene–clinopyroxene systems demonstrates that closure temperature differences among REE are small and hence their average value may be used as the closure temperature for the cooling two-pyroxene system. The average closure temperature of REE in the two-pyroxene system is essentially the same as the temperature calculated using the REE-in-two-pyroxene thermometer and practically independent of pyroxene modal abundance in the system. Differences in temperatures calculated using the REE- and major element-based two-pyroxene thermometers can be used to infer cooling rate of two-pyroxene bearing mafic and ultramafic rocks.