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

Abstract

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 reequilibration 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 i...

Modeling the effects of diagenesis on carbonate clumped-isotope values in deep- and shallow-water settings

“…A common explanation for some of these elevated temperatures is that they are the result of dissolutionreprecipitation reactions occurring during sedimentary burial at elevated temperatures. Additionally, solid-state isotope-exchange reactions can also result in changes in  47 values for samples that reach burial temperatures greater than ~100°C for calcite (Passey and Henkes, 2012;Henkes et al, 2014;Stolper and Eiler, 2015;Shenton et al, 2015). In this section, we explore the predictions of the model developed for deep-sea sediments for shallow-water systems.…”

“…At this temperature, calcite  47 values are expected to begin changing on geological timescales due to solid-state isotope-exchange reactions. For example, the model of Stolper and Eiler (2015) predicts that a sample formed at 25°C and held at 100°C for 100 million years will have  47 -based temperatures to increase by 25°C. Importantly, the most deeply buried samples (below 3.2 km) are dolomite which, empirically, appear not to undergo measureable solid state reordering reactions in nature until burial temperatures exceed at least ~200 °C (Bonifacie et al, 2013;Lloyd et al, 2017).…”

“…We show the output of the model to depths of 3 km, i.e., to burial temperatures of ~100°C. We choose this temperature cut off as, for calcite, the influence of solid-state isotope-exchange reactions on clumped-isotope compositions becomes increasingly important to consider at burial temperatures above 100°C (Passey and Henkes, 2012;Henkes et al, 2014;Stolper and Eiler, 2015;Shenton et al, 2015). For this calculation, we used the  47 vs. temperature calibration constrained from 1-1650°C (Fig.…”

“…The equation is  47 = 0.00173 x (10 6 /T 2 ) 2 + 0.0203 x 10 6 /T 2 + 0.261 where T is the temperature in Kelvin. Data used in this calibration comes only from measurement made at the Caltech laboratories Ghosh et al, 2007;Came et al, 2007;Guo et al, 2009;Tripati et al, 2010;Eagle et al, 2010;Thiagarajan et al, 2011;Dennis et al, 2011;Stolper and Eiler, 2015;Eagle et al, 2015;Spooner et al, 2016;Bonifacie et al, 2017). …”

Experimental calibration of clumped isotope reordering in dolomite

“…As with previous heating experiments using calcite and apatite, dolomite ∆47 exhibited complex reordering behavior inadequately described by first-order Arrhenian-style models. Instead, we fit the data using two published models for clumped isotope reordering: the transient defect/equilibrium defect model of Henkes et al (2014), and the exchange-diffusion model of Stolper and Eiler (2015). For both models, we found optimal reordering parameters by using global leastsquares minimization algorithms and estimated uncertainties on these fits with a Monte Carlo scheme that resampled individual ∆47 measurements and re-fit the dataset of these new mean values.…”