Abstract
Carbonate clumped isotopes (∆47) have become a widely applied method for
paleothermometry, with applications spanning many environmental settings
over hundreds of millions of years. However, ∆47-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 have
constrained this phenomenon by heating well-characterized materials at
various temperatures, observing temporal ∆47 evolution, and fitting
results to kinetic models with prescribed C–O bond reordering
mechanisms. While informative, these models are inflexible regarding the
nature of isotope exchange, leading to potential uncertainties when
extrapolated to geologic timescales. Here, we instead propose that
observed reordering rates arise naturally from random-walk 18O diffusion
through the carbonate lattice, and we develop a “disordered” kinetic
framework that treats C–O bond reordering as a continuum of first-order
processes occurring in parallel at different rates. We show
theoretically that all previous models are specific cases of disordered
kinetics; thus, our approach reconciles the transient defect/equilibrium
defect and paired reaction-diffusion models. We estimate the rate
coefficient distributions from published heating experiment data by
finding a regularized inverse solution that best fits each ∆47
timeseries without assuming a particular functional form a priori.
Resulting distributions are well-approximated as lognormal for all
experiments on calcite or dolomite; aragonite experiments require more
complex distributions that are consistent with a change in oxygen
bonding environment during the transition to calcite. Presuming
lognormal rate coefficient distributions and Arrhenius-like temperature
dependence yields an underlying activation energy, E, distribution that
is Gaussian with a mean value of μE = 224.3 ± 27.6 kJ mol−1 and a
standard deviation of σE = 17.4 ± 0.7 kJ mol−1 (±1σ uncertainty; n = 24)
for calcite and μE = 230.3 ± 47.7 kJ mol−1 and σE = 14.8 ± 2.2 kJ mol−1
(n = 4) for dolomite. These model results are adaptable to other
minerals and may provide a basis for future experiments whereby the
nature of carbonate C–O bonds is altered (e.g., by inducing mechanical
strain or cation substitution). Finally, we apply our results to
geologically relevant heating/cooling histories and suggest that
previous models underestimate low-temperature alteration but
overestimate ∆47 blocking temperatures.