Element and isotope equilibration between minerals: Thermodynamic and kinetic controls of geothermometry and isochron dating

With respect to mineral Sm-Nd and Rb-Sr isochron dating of igneous and metamorphic rocks, a critical premise is that the chronometric system of mineral isochrones has achieved isotopic equilibrium during a given metamorphic event and the equilibrium has not changed afterwards. An analogue to mineral chronometry is O isotope geothermometry, so that this provides a mutual constraint on validity of the two methods. Because the rates of Sm-Nd, Sr and O diffusion in igneous and metamorphic minerals are comparable under nominally anhydrous conditions, the state of O isotope equilibrium between high-T minerals can provide a test for the validity of mineral Sm-Nd and Rb-Sr chronometers. Applicability of this principle is illustrated for ultrahigh-pressure metamorphic rocks from the Dabie-Sulu orogenic belt in east-central China. When mineral Sm-Nd isochrones do not always give consistent Triassic ages for eclogitefacies metamorphism, mineral O isotope geothermometry do not yields concordant temperatures either. There is a direct correspondence in equilibrium or disequilibrium state between the O and Sm-Nd isotopic systems of metamorphic minerals. Sonic omphacite-garnet pairs from the eclogites exhibit O isotope equilibrium fractionations at eclogite-facies conditions and mineral Sm-Nd isochrones give meaningful Triassic ages. In contrast, some of the omphacite-garnet pairs show 0 isotope disequilibrium fractionations, and mineral Sm-Nd isochrones give geologically meaningless non-Triassic ages. While the mineral with relatively slower diffusivity of the element has exerted the primary control on the homogenization rate of initial isotope ratios among isochron minerals during retrograde metamorphism, the mineral with high parent/daughter ratio has exerted the principal control on the determined age. Valid mineral isochrones can be expected to date the timing of metamorphism only if the mineral with high parent/daughter ratio has a fast rate of radiogenic isotope diffusion during the metamorphism. Based on the differences of element diffusivity in different minerals, it is possible to quantitatively estimate the timescale of eclogite-facies metamorphism during continental collision. Oxygen isotope fractionation factors and element diffusion Arrhenius parameters for all solid minerals can be theoretically calculated by the increment method and the empirical model of ionic porosity, respectively. The results can be used to quantitatively estimate the relative O-18-enrichment in coexisting minerals at thermodynamical equilibrium and the relative rates of element diffusion in various minerals under the same conditions.