The abundance of ¹⁸O isotopes and ¹³C-¹⁸O isotopic “clumps” (measured as δ¹⁸O and Δ₄₇, respectively) in carbonate minerals have been used to infer mineral formation temperatures. An inherent requirement or assumption for these paleothermometers is mineral formation in isotopic equilibrium. Yet, apparent disequilibrium is not uncommon in biogenic and abiogenic carbonates formed in nature and in synthetic carbonates prepared under laboratory settings, as the dissolved carbonate pool (DCP) from which minerals precipitate is often out of δ¹⁸O and Δ₄₇ equilibrium. For this, a complete understanding of both equilibrium and kinetics of isotopic partitioning and ¹³C-¹⁸O clumping in DCP is crucial. To this end, we analyzed Δ₄₇ of inorganic BaCO₃ samples from Uchikawa and Zeebe (2012) (denoted as UZ12), which were quantitatively precipitated from NaHCO₃ solutions at various times over the course of isotopic equilibration at 25 °C and pH_NBS of 8.9. Our data show that, although the timescales for δ¹⁸O and Δ₄₇ equilibrium in DCP are relatively similar, their equilibration trajectories are markedly different. As opposed to a simple unidirectional and asymptotic approach toward δ¹⁸O equilibrium (first-order kinetics), Δ₄₇ equilibration initially moves away from equilibrium and then changes its course towards equilibrium. This excess Δ₄₇ disequilibrium is manifested as a characteristic “dip” in the Δ₄₇ equilibration trajectory, a feature consistent with an earlier study by Staudigel and Swart (2018) (denoted as SS18). From the numerical model of SS18, the non-first-order kinetics for Δ₄₇ equilibration can be understood as a result of the difference in the exchange rate for oxygen isotopes bound to ¹²C versus ¹³C, or an isotope effect of ∼25‰. We also developed an independent model for the Exchange and Clumping of ¹³C and ¹⁸O in DCP (ExClump38 model) to trace the evolution of singly- and doubly-substituted isotopic species (i.e., δ¹³C, δ¹⁸O and Δ₄₇). The model suggests that the dip in the Δ₄₇ equilibration trajectory is due largely to kinetic carbon isotope fractionation for hydration and hydroxylation of CO₂. We additionally examined the BaCO₃ samples prepared from NaHCO₃ solutions supplemented with carbonic anhydrase (CA), an enzyme known to facilitate δ¹⁸O equilibration in DCP by catalyzing CO₂ hydration (UZ12). These samples revealed that, while CA effectively shortens the time required for Δ₄₇ equilibrium in DCP, the overall pattern and magnitude of the dip in the Δ₄₇ equilibration trajectory remain unchanged. This suggests no additional isotope effects due to the CA enzyme within the tested CA concentrations. With the ExClump38 model, we test various physicochemical scenarios for the timescales and trajectories of isotopic equilibration in DCP and discuss their implications for the Δ₄₇ paleothermometry.

碳酸盐矿物中¹⁸ O 同位素和¹³ C- ¹⁸ O 同位素“团块”（分别测量为 δ ¹⁸ O 和 Δ ₄₇）的丰度已被用于推断矿物形成温度。这些古温度计的固有要求或假设是同位素平衡中的矿物形成。然而，在自然界形成的生物和非生物碳酸盐以及在实验室环境下制备的合成碳酸盐中，明显的不平衡并不少见，因为从中沉淀矿物的溶解碳酸盐池 (DCP) 通常脱离 δ ¹⁸ O 和 Δ ₄₇平衡。为此，全面了解同位素分配的平衡和动力学以及¹³ C- ¹⁸ O 在 DCP 中结块是至关重要的。为此，我们分析了来自 Uchikawa 和 Zeebe (2012)（表示为 UZ12）的Δ ₄₇无机 BaCO ₃样品，这些样品是在 25 °C 和 pH _NBS的同位素平衡过程中在不同时间从 NaHCO ₃溶液中定量沉淀的8.9。我们的数据表明，尽管DCP 中δ ¹⁸ O 和 Δ ₄₇平衡的时间尺度相对相似，但它们的平衡轨迹明显不同。与对 δ ¹⁸ O 平衡（一级动力学）的简单单向渐近方法相反，Δ ₄₇平衡最初远离平衡，然后转向平衡。这种过量的 Δ ₄₇不平衡表现为 Δ ₄₇平衡轨迹中的特征“下降” ，这一特征与 Staudigel 和 Swart（2018 年）（表示为 SS18）的早期研究一致。从 SS18 的数值模型中，Δ ₄₇平衡的非一级动力学可以理解为与¹² C 和¹³ C结合的氧同位素交换率不同的结果，或~25‰的同位素效应. 我们还开发了一个独立的模型，防爆变化和丛荷兰国际集团的^{1 3} C和¹DCP（ExClump38 模型）中的⁸ O 以追踪单取代和双取代同位素物种（即δ ¹³ C、δ ¹⁸ O 和 Δ ₄₇）的演化。该模型表明Δ ₄₇平衡轨迹的下降主要是由于CO _{2 的}水合和羟基化的动力学碳同位素分馏。我们另外检查了由补充有碳酸酐酶 (CA) 的NaHCO ₃溶液制备的 BaCO ₃样品，碳酸酐酶 (CA) 是一种已知通过催化 CO ₂促进DCP 中δ ¹⁸ O 平衡的酶水合作用（UZ12）。这些样品表明，虽然 CA 有效地缩短了DCP 中Δ ₄₇平衡所需的时间，但 Δ ₄₇平衡轨迹中下降的整体模式和幅度保持不变。这表明在测试的 CA 浓度中没有由于 CA 酶而产生的额外同位素效应。使用 ExClump38 模型，我们测试了 DCP 中同位素平衡的时间尺度和轨迹的各种物理化学情景，并讨论了它们对 Δ ₄₇古测温法的影响。