The kinetics of solid-state isotope-exchange reactions for clumped isotopes: A study of inorganic calcites and apatites from natural and experimental samples

Carbonate clumped-isotope geothermometry is a tool used to reconstruct formation or (re)equilibration temperatures of carbonate bearing minerals, including carbonate groups substituted into apatite. It is based on the preference for isotopologues with multiple heavy isotopes (for example, ^(13)C^(16)O_2^(18)O^(2−) groups) to be more abundant at equilibrium than would be expected if all isotopes were randomly distributed amongst all carbonate groups. Because this preference is only a function of temperature, excesses of multiply substituted species can be used to calculate formation temperatures without knowledge of the isotopic composition of water from which the mineral precipitated or other phases with which it may have equilibrated. However, the measured temperature could be modified after mineral growth if exchange of isotopes amongst carbonate groups within the mineral has occurred through internal isotope-exchange reactions. Because these exchange reactions occur through thermally activated processes, their rates depend on temperature and increase at higher temperatures. Thus internal isotope-exchange reactions could lead to effective re-equilibration at high temperatures, overprinting the original temperatures recorded during mineral growth. We measured clumped-isotope temperatures in carbonate bearing minerals (including apatites) from several carbonatites to constrain the kinetics of these internal isotope-exchange reactions. We observe two key trends for clumped-isotope temperatures in carbonatites: (i) clumped-isotope temperatures of apatites and carbonate-bearing minerals decrease with increasing intrusion depth and (ii) apatites record lower clumped-isotope temperatures than carbonate minerals from the same intrusion. We additionally conducted heating experiments at different temperatures to derive the temperature dependence for the rate constants that describe the alteration of clumped-isotope temperatures with time in calcites and apatites. We find that calcites exhibit complex kinetics as has been seen in previous studies. To quantify these results, we constructed a model that incorporates both diffusion of isotopes through the crystal lattice and isotope-exchange reactions between adjacent carbonate groups. We tested this model through comparison to previous measurements of optical calcites and brachiopods and to samples with known cooling histories and find that the model is able to reasonably capture kinetic data from previous experiments and the observed clumped-isotope temperatures of calcites assuming geologically reasonable cooling rates. A similar model for apatite over-predicts the observed clumped-isotope temperatures found in natural samples; we hypothesize this discrepancy is the result of annealing of radiation damage in our experiments, which lowers the diffusivity and rate of isotope exchange of carbonate groups compared to damaged natural samples. Finally, we constructed models to explore how heating can alter recorded clumped-isotope temperatures. Our model predicts that samples change in clumped-isotope temperatures in two stages. The first stage changes the recorded clumped isotope temperatures by <1 °C if held at 75 °C for 100 million years and by up to ∼40 °C if held at 120 °C, but the clumped-isotope temperatures does not reach ambient values through this low-temperature mechanism. A second, slower change becomes effective at temperatures above 150 °C and can take the measured clumped-isotope temperature up to the true ambient temperature. This result implies that old (hundreds of million years) samples that have only experienced mild (<100-125 °C) thermal histories could exhibit small but measurable (order 10 °C) changes in their clumped-isotope temperatures. We compared this heating model to clumped-isotope measurements from paleosol samples from the Siwalik Basin in Nepal, which were buried up to 5 km and then rapidly exhumed to the surface; these samples often do not give reasonable surface temperatures. The modeled temperatures agree with measured temperatures of these samples, suggesting that partial re-equilibration during shallow crustal burial is responsible for their elevated clumped-isotope temperatures.