Time-temperature relation of mineral isochrons: a thermodynamic model, and illustrative examples for the Rb-Sr system

Mathematics – Logic

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Scientific paper

We have developed a thermodynamic model for the determination of the closure temperature (TC) at which the minerals defining an internal isochron in Rb-Sr, or similar, geochronological system were set with a geochronological clock. It is shown that the equilibrium fractionation of 87Rb and 87Sr between a pair of minerals at TC [KD(87Rb-87Sr)C] is given by the ratio of the quantity (87Rb/86Sr) in the two minerals as measured at the present time. KD(87Rb-87Sr), which equals the element distribution coefficient KD(Rb-Sr) under equilibrium condition, can be calibrated as a function of temperature, and compared with the retrieved value of KD(87Rb-87Sr)C in a natural pair to obtain TC. The various mineral pairs defining an internal isochron will yield concordant or discordant values of TC depending on whether or not they closed simultaneously with respect to the diffusion of Rb and Sr. Both types of results are expected, and are important in the analyses of the evolutionary history of the host rocks. Preliminary analyses of the published data in the Rb-Sr system suggest a fairly wide range of TC even for the same mineral pair, reflecting differences in the cooling rates and physico-chemical environments of the host rocks.

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