A disordered kinetic model for clumped isotope bond reordering in carbonates

Carbonate clumped isotopes (Δ47) have become a widely applied method for paleothermometry, with applications spanning many environmental settings over hundreds of millions years. However, Δ47-based paleothermometry can be complicated by closure temperature-like behavior whereby C–O bonds are reset at elevated diagenetic or metamorphic temperatures, sometimes without obvious mineral alteration. Laboratory studies constrained this phenomenon heating well-characterized materials various observing temporal Δ47 evolution, and fitting results to kinetic models prescribed bond reordering mechanisms. While informative, these inflexible regarding the nature isotope exchange, leading potential uncertainties when extrapolated geologic timescales. Here, we instead propose that observed rates arise naturally from random-walk O18 diffusion through carbonate lattice, develop “disordered” framework treats as continuum first-order processes occurring in parallel different rates. We show theoretically all previous specific cases disordered kinetics; thus, our approach reconciles transient defect/equilibrium defect paired reaction-diffusion models. estimate rate coefficient distributions published experiment data finding regularized inverse solution best fits each timeseries assuming particular functional form priori. Resulting well-approximated lognormal experiments on calcite dolomite; aragonite require more complex consistent change oxygen bonding environment during transition calcite. Presuming Arrhenius-like temperature dependence yields an underlying activation energy, E, distribution is Gaussian mean value μE=224.3±27.6 kJ mol−1 standard deviation σE=17.4±0.7 (±1σ uncertainty; n=24) μE=230.3±47.7 σE=14.8±2.2 (n=4) dolomite. These model adaptable other minerals may provide basis future altered (e.g., inducing mechanical strain cation substitution). Finally, apply geologically relevant heating/cooling histories suggest underestimate low-temperature alteration but overestimate blocking temperatures.