“Clumped-isotope” thermometry is an emerging tool to probe the temperature history of surface and subsurface environments based on measurements of the proportion of ¹³C and ¹⁸O isotopes bound to each other within carbonate minerals in ¹³C¹⁸O¹⁶O₂^2- groups (heavy isotope “clumps”). Although most clumped isotope geothermometry implicitly presumes carbonate crystals have attained lattice equilibrium (i.e., thermodynamic equilibrium for a mineral, which is independent of solution chemistry), several factors other than temperature, including dissolved inorganic carbon (DIC) speciation may influence mineral isotopic signatures. Therefore we used a combination of approaches to understand the potential influence of different variables on the clumped isotope (and oxygen isotope) composition of minerals.

We conducted witherite precipitation experiments at a single temperature and at varied pH to empirically determine ¹³C-¹⁸O bond ordering (Δ₄₇) and δ¹⁸O of CO₃^2- and HCO₃^- molecules at a 25 °C equilibrium. Ab initio cluster models based on density functional theory were used to predict equilibrium ¹³C-¹⁸O bond abundances and δ¹⁸O of different DIC species and minerals as a function of temperature. Experiments and theory indicate Δ₄₇ and δ¹⁸O compositions of CO₃^2- and HCO_3- ions are significantly different from each other. Experiments constrain the Δ_47-δ¹⁸O slope for a pH effect (0.011 ± 0.001; 12 ⩾ pH ⩾ 7). Rapidly-growing temperate corals exhibit disequilibrium mineral isotopic signatures with a Δ_47-δ¹⁸O slope of 0.011 ± 0.003, consistent with a pH effect.

Our theoretical calculations for carbonate minerals indicate equilibrium lattice calcite values for Δ₄₇ and δ¹⁸O are intermediate between HCO₃⁻ and CO₃²⁻. We analyzed synthetic calcites grown at temperatures ranging from 0.5 to 50 °C with and without the enzyme carbonic anhydrase present. This enzyme catalyzes oxygen isotopic exchange between DIC species and is present in many natural systems. The two types of experiments yielded statistically indistinguishable results, and these measurements yield a calibration that overlaps with our theoretical predictions for calcite at equilibrium. The slow-growing Devils Hole calcite exhibits Δ₄₇ and δ¹⁸O values consistent with lattice equilibrium.

Factors influencing DIC speciation (pH, salinity) and the timescale for DIC equilibration, as well as reactions at the mineral–solution interface, have the potential to influence clumped-isotope signatures and the δ¹⁸O of carbonate minerals. In fast-growing carbonate minerals, solution chemistry may be an important factor, particularly over extremes of pH and salinity. If a crystal grows too rapidly to reach an internal equilibrium (i.e., achieve the value for the temperature-dependent mineral lattice equilibrium), it may record the clumped-isotope signature of a DIC species (e.g., the temperature-dependent equilibrium of HCO₃⁻) or a mixture of DIC species, and hence record a disequilibrium mineral composition. For extremely slow-growing crystals, and for rapidly-grown samples grown at a pH where HCO₃^- dominates the DIC pool at equilibrium, effects of solution chemistry are likely to be relatively small or negligible. In summary, growth environment, solution chemistry, surface equilibria, and precipitation rate may all play a role in dictating whether a crystal achieves equilibrium or disequilibrium clumped-isotope signatures.