Rapid and precise measurement of carbonate clumped isotopes using laser spectroscopy

Abstract

Carbonate clumped isotope abundance is an important paleothermometer, but measurement is difficult, slow, and subject to cardinal mass (m/z) interferences using isotope ratio mass spectrometry (IRMS). Here, we describe an optical spectroscopic measurement of carbonate clumped isotopes. We have adapted a tunable infrared laser differential absorption spectrometer (TILDAS) system to measure the abundances of four CO₂ isotopologues used for clumped isotope thermometry. TILDAS achieves the same precision (0.01‰ SE) as IRMS measurements rapidly (∼50 min per carbonate analysis) and using small samples (<2 mg of calcite), without making assumptions about ¹⁷O abundance in the sample. A temperature calibration based on 406 analyses of CO₂ produced by digestion of 51 synthetic carbonates equilibrated at 6° to 1100°C is consistent with results for natural carbonates and previous calibrations. Our system results were indistinguishable from IRMS systems after replicating the InterCarb interlaboratory calibration. Measurement by TILDAS could change the landscape for clumped isotope analysis.

A fast, automated, high-throughput spectroscopic system is implemented for carbonate clumped isotope thermometry.

INTRODUCTION

In recent years, measurement of rare isotopologues with more than one heavy isotope has been a subject of growing interest. Perhaps the most ubiquitous application of this “clumped isotope” research is carbonate clumped isotope thermometry. With this method, the relative abundance of multiply-substituted isotopologues containing ¹⁸O-¹³C bonds is used to estimate the formation temperature of carbonate minerals (1, 2). The key advantage of this method is that no knowledge of the water isotopic composition from which the mineral was precipitated is required, also allowing one to calculate the δ¹⁸O composition of the parent water using a conventional oxygen isotope fractionation relationship.

The field of carbonate clumped isotope geochemistry has advanced rapidly since it was first demonstrated as a practical paleothermometer by (3). Interlaboratory standardization efforts have greatly improved reproducibility (4, 5), discrepancies between empirical temperature-clumping calibrations have been markedly reduced (6, 7), and automation and development of new isotope ratio mass spectrometry (IRMS) techniques have shortened analysis times and decreased the sample size required for analysis (8–10). Despite these substantial improvements, the low natural abundance of clumped isotopologues and their nonunique mass continue to hinder IRMS clumped isotope measurements. Measurement remains difficult and costly and requires ¹⁷O corrections that introduce significant uncertainty (11, 12). Because of these limitations, the method is underused compared to conventional stable isotope methods, with a relatively small number of laboratories producing reliable data.

To address these issues, we developed a tunable infrared (IR) laser differential absorption spectrometer (TILDAS) for clumped isotope analysis of CO₂. It has been previously demonstrated that this spectrometer is capable of accurately and precisely (0.01‰ SE) measuring clumping in CO₂ gas in 20 to 25 min per analysis and with sample sizes of 1.9 mg calcite equivalent (13). By using mid-IR absorption instead of mass to measure the relative abundance of isotopologues, the TILDAS system determines clumping more directly than IRMS because it measures the molecular species rather than the cardinal mass (m/z) and hence does not require, for example, a ¹⁷O correction for mass interference or removal of contaminant isobaric molecules (13). However, in previous work, only CO₂ samples from gas cylinders were analyzed, not gas derived from acid digestion of carbonate mineral samples. This additional step is required for a direct comparison to IRMS systems and to demonstrate the applicability of TILDAS clumped isotope analysis to carbonates. Spectroscopic clumped isotope measurements of carbonate-derived CO₂ have been previously reported by other researchers (14). However, (14) and (13) were proof-of-concept papers by design and did not attempt to compare performance to IRMS using carbonates.

Here, we report the results from a new, fully automated carbonate clumped isotope analyzer system that extends previously published TILDAS instrument capabilities to measure carbonates. We present results from 1678 analyses performed over a 61-day period. Using this dataset, we establish an empirical temperature versus clumping calibration based on a set of carbonates synthesized or equilibrated in the laboratory. The calibration is validated using natural samples that have known formation temperatures. The synthetic samples are also used to establish a temperature versus calcite-water oxygen isotope fractionation (α_{calcite-water}) relationship. In addition, we compare TILDAS-derived data to IRMS data using a series of CO₂ gases equilibrated with waters at different temperatures [carbon dioxide equilibrium scale (CDES)] and a carbonate-based method [InterCarb-CDES (I-CDES)] for projecting raw data into an interlaboratory reference frame. Clumping values of seven interlaboratory standards are compared to accepted values measured using IRMS systems. We demonstrate that the TILDAS system reliably produces clumped isotope data that are competitive in quality with the best IRMS systems but with a much higher sample throughput and small sample size.

Notation

IRMS-based carbonate clumped isotope thermometry involves defining a measurable temperature-dependent clumping Δ₄₇ value for CO₂ (1) derived from carbonate. In this study, we adopt the analogous TILDAS-based measure of clumping in CO₂ of (13). This laser-specific notation is based on the Air Force Geophysics Laboratory shorthand notation, which has been used in the spectroscopic high-resolution transmission (HITRAN) database for decades (15). In this notation, ¹⁶O¹²C¹⁶O, ¹⁶O¹³C¹⁶O, ¹⁶O¹²C¹⁸O, and ¹⁶O¹³C¹⁸O are referred to as 626, 636, 628, and 638, respectively. Isotopologues are identified by the second digit of the atoms’ atomic mass. We define the composition of isotopologue i as

$${\mathrm{\delta }}_{i=}(\frac{\frac{[i_{\text{sample}}]}{[{626}_{\text{sample}}]}}{\frac{[i_{\text{standard}}]}{[{626}_{\text{standard}}]}}-1)\times 1000$$ (1)

The molecular ratios δ₆₃₆ and δ₆₂₈ are good approximations of the atomic isotopic composition [see (16) for definitions of “molecular” and “atomic”], δ¹³C and δ¹⁸O, respectively, whereas δ₆₃₈ is approximately equal to (δ₆₃₆ + δ₆₂₈) and thus to (δ¹³C + δ¹⁸O) and is used in place of IRMS δ₄₇ (δ₄₇ = [(R_47,sample/R_{47,working reference gas}) − 1] × 1000) (17). R₄₇ is the abundance ratio of mass-47 CO₂ to the isotopically normal isotopologue, ¹⁶O¹²C¹⁶O. These ratios are expected to be nearly equal to the atomic isotopic composition because the 636 and 628 isotopologues are naturally three and two orders of magnitude more abundant than the next most common isotopologues with ¹³C and ¹⁸O, respectively (18). Given that the differences between the atomic and molecular ratios are expected to be negligible (16) and that projection into the Vienna Pee Dee Belemnite (VPDB) reference frame using International Atomic Energy Agency (IAEA) values for carbonate standards effectively eliminates minor discrepancies, all results given in the VPDB reference frame are reported as δ¹⁸O and δ¹³C to avoid introduction of additional and potentially confusing notation. This assumption is in fact shown to be valid in this study. Only raw values (defined below) are reported as δ₆₂₈ or δ₆₃₆.

The following isotope exchange reaction is referred to in the clumped isotope calculation

$${}^{16}\mathrm{O}{}^{12}\mathrm{C}{}^{16}\mathrm{O}+{}^{16}\mathrm{O}{}^{13}\mathrm{C}{}^{18}\mathrm{O}\leftrightarrow {}^{16}\mathrm{O}{}^{13}\mathrm{C}{}^{16}\mathrm{O}+{}^{16}\mathrm{O}{}^{12}\mathrm{C}{}^{18}\mathrm{O}$$ (2)

The equilibrium constant of isotope exchange reaction (Eq. 2) can be written as

$$K_{\text{eq}}=\frac{[{}^{16}\mathrm{O}{}^{13}\mathrm{C}{}^{16}\mathrm{O}]\times [{}^{16}\mathrm{O}{}^{12}\mathrm{C}{}^{18}\mathrm{O}]}{[{}^{16}\mathrm{O}{}^{12}\mathrm{C}{}^{16}\mathrm{O}]\times [{}^{16}\mathrm{O}{}^{13}\mathrm{C}{}^{18}\mathrm{O}]}$$ (3)

The abundance of isotopologue i relative to that expected if all isotopes were randomly distributed (stochastic distribution) among all isotopologues is defined as

$${\mathrm{\Delta }}_i=(\frac{R_i}{R_i^{\ast }}-1)\times 1000$$ (4)

where R_i is the abundance of isotopologue i relative to the nonsubstituted isotopologue and the * in $R_i^{\ast }$ stands for the random distribution condition. A previous study (1) derived the approximation

$$\begin{array}{cc}\hfill {\mathrm{\Delta }}_{{}^{16}\mathrm{O}{}^{13}\mathrm{C}{}^{18}\mathrm{O}}\approx & -1000\text{ln}\left(\frac{K_{\text{eq}}}{K_{\text{eq}}^{*}}\right)=\hfill \\ & -1000\text{ln}\left(\frac{[{}^{16}\mathrm{O}{}^{13}\mathrm{C}{}^{16}\mathrm{O}]\times [{}^{16}\mathrm{O}{}^{12}\mathrm{C}{}^{18}\mathrm{O}]}{[{}^{16}\mathrm{O}{}^{12}\mathrm{C}{}^{16}\mathrm{O}]\times [{}^{16}\mathrm{O}{}^{13}\mathrm{C}{}^{18}\mathrm{O}]}\right)\hfill \end{array}$$ (5)

where $K_{\text{eq}}^{*}$ is the equilibrium constant for the fully randomized stochastic distribution and, in the case of Eq. 2, $K_{\text{eq}}^{*}$ = 1. We therefore denote the CO₂ clumping relative to stochastic distribution as measured by TILDAS as Δ_638. While similar to the Δ₄₇ notation used by the IRMS community, Δ₆₃₈ is different because (i) its measurement does not involve (nor necessitate) a correction for isobaric interferences and (ii) Δ₆₃₈ includes only the isotopologues in Eq. 3. In contrast, Δ₄₇ includes contributions from all m/z-47 isotopologues (1), although the ¹⁶O¹³C¹⁸O isotopologue contributes roughly 97% of the 47 mass (18), so differences between Δ₆₃₈ and Δ₄₇ are expected to be minor with respect to analytical precision. A “raw” subscript (e.g., δ_628raw) indicates that values are reported relative to a working reference (WR) gas. Following analogous conventions for IRMS-based clumped isotope measurements, values presented as “CDES” are projected into an interlaboratory reference frame using equilibrated/heated gas anchors (4, 13). Values presented as “I-CDES” are projected into an interlaboratory reference frame using ETH carbonate standards (Materials and Methods) (5). We follow the definitions of (19) for “sample,” “analysis,” and “anchor.”

RESULTS

Sample size and analytical throughput

The automated carbonate clumped isotope analyzer system is composed of an autosampling carousel for carbonate digestion in phosphoric acid, a CO₂ extraction and purification line, a bellows pressure-control system, and the TILDAS instrument previously described by (13) (Fig. 1) (Materials and Methods). The analytical setup does not require a gas chromatographic or equivalent cleanup step and can process up to 36 carbonate powders in a single fully automated run. However, this would require more than 24 hours, so we chose to load roughly 25 carbonate powder samples (standards and unknowns) per 24-hour period, in addition to three water-equilibrated or heated gas CO₂ samples that were analyzed daily. Using this procedure, we ran approximately 28 analyses total every 24 hours, including the time required to reload the carousel.

Fig. 1. System schematic.

A diagram of the fully automated carbonate clumped isotope analyzer. The system is composed of a CO₂ extraction and cleanup section, a sample collection, mixing and delivery system, and an inlet and spectroscopic analysis component. P sensor, pressure sensor; LN₂, liquid nitrogen Dewar; N₂, nitrogen gas; WR, working reference gas; concentric circles, critical orifice. See Materials and Methods for a detailed description of the analysis protocol.

The carbonate samples analyzed included 45 synthetic carbonates we precipitated at known temperature from water of known δ¹⁸O composition, analyzed 5 to 11 times each; 8 carbonates re-equilibrated to temperatures of 450°C to 1100°C, analyzed 3 to 10 times each; and 17 natural carbonates formed at known temperature, analyzed 3 to 21 times each. We also typically analyzed six different carbonate standards, four interlaboratory ETH standards and two intralaboratory standards, in each carousel run. The MK standard (Mallinckrodt AR analytical reagent, a synthetic calcium carbonate powder) was analyzed roughly twice in each run (n = 130), and the others approximately once per run (n_ETH-1 = 40, n_ETH-2 = 41, n_ETH3 = 41, n_ETH-4 = 41, n_car-2 = 82). Car-2 is a Carrera marble. In addition, commercially available primary IAEA standards NBS-18, NBS-19, IAEA-CO-8, IAEA-603, and LSVEC were analyzed 4 to 10 times each to establish VPDB values for car-2 and MK. Last, we analyzed a set of carbonate standards used in the InterCarb project (5) and distributed to the University of Washington (UW) IsoLab, ETH-1, ETH-2, ETH-3, ETH-4, IAEA-C1, IAEA-C2, and MERCK (n = 6) (table S4).

During the analytical session that produced the data reported in this study, we performed 1678 analyses in 61 days, averaging 27.5 analyses per day (including downtime). Of these, 1563 analyses are presented here, including 318 gas sample analyses and 1245 carbonate analyses (data S1). To our knowledge, this sample throughput is a major improvement on the capabilities of current IRMS systems. The TILDAS system performs an entire analysis, including acid digestion, in ∼50 min, while the newest IRMS systems require 6 to 10 hours to achieve comparable precision. The minimum sample size required for a single analysis (Δ₆₃₈ or Δ₄₇ 0.01‰ SE) is 1.9 mg of pure carbonate, competitive with modern automated clumped IRMS systems. This amount of carbonate produces sufficient CO₂ for a measurement at 60 torr and a CO₂/N₂ mixing ratio of 0.35%.

Dependence of Δ₆₃₈ on δ₆₂₈ and projection of raw Δ₆₃₈ values into an interlaboratory reference frame

An important step in clumped isotope analysis is the projection of raw Δ₄₇ or Δ₆₃₈ values for CO₂, measured relative to a specific WR gas, into an interlaboratory reference frame. For IRMS systems, this requires a bulk isotope correction that accounts for the dependence of Δ₄₇ on δ₄₇. This dependence is due to pressure baseline signals in the Faraday cups of the smaller ion beams (20, 21) and scrambling of ions during ionization in the instrument source (17). As the TILDAS system does not ionize the CO₂ gas, there is no reason to expect a similar dependence of Δ_638raw on δ_638raw. To test for bulk dependence and project our raw data into an interlaboratory reference frame, we prepared and analyzed a set of CO₂ gases with different δ₆₃₆ and δ₆₂₈ compositions equilibrated at different temperatures (Materials and Methods). As expected, measurements of CO₂ gas samples with different δ₆₃₆ compositions equilibrated at the same temperature show a δ_636raw dependence indistinguishable from zero for gases equilibrated at 6°C and 23°C (0.0003 ± 0.0005 Δ_638raw/1‰ δ_636raw and −0.0003 ± 0.0004 Δ_638raw/1‰ δ_636raw, respectively) but display a weak dependence for gases equilibrated at 60°C (−0.0011 ± 0.0004 Δ_638raw/1‰ δ_636raw) (Fig. 2A). Although the common slope of all gas samples combined is statistically distinguishable from zero (−0.00062‰ ± 0.00005 Δ_638raw/1‰ δ_636raw), we did not apply a δ₆₃₆ correction because the magnitude of this dependence is very small, is inconsistent between equilibration temperatures, and is more likely to introduce noise (by adding a poorly quantified correction factor) than to improve the accuracy of the results. However, measurements of gas samples equilibrated at the same temperature but with different δ_628raw compositions demonstrate that the TILDAS system has a linear dependence of measured Δ_638raw on the δ_628raw composition of the sample (0.0034‰ Δ_638raw/1‰ δ_628raw) (Fig. 2B). The possible causes of the dependence of Δ_638raw on δ_628raw are discussed below (Discussion).

Fig. 2. Bulk isotope dependence.

The empirical relationship between ∆_638raw and δ_636raw (A) and between ∆_638raw and δ_628raw (B) in the equilibrated and heated gases. Symbols: individual measurement (four sample-WR comparisons); vertical and horizontal error bars: 1 SD uncertainty in ∆_638raw, δ_636raw, and δ_628raw measurements; r: Pearson correlation coefficient. In (A), only samples with equal δ_628raw composition and different δ_636raw composition are shown. In (B), only samples with equal δ_636raw composition and different δ_628raw composition are shown.

We adopted the method used in IRMS studies (4, 17) for monitoring the δ₆₂₈ dependence by regularly measuring equilibrated and heated CO₂ gases that bracket a range of 77.1‰ in δ₆₂₈ space and a temperature range of 6° to 1000°C, bracketing the compositions of all the carbonate-derived CO₂ analyzed. Although the magnitude of the δ₆₂₈ dependence can vary over time [note lack of dependence in (13)], it remained stable enough for the duration of this calibration effort (22 July 2021 to 2 November 2021) such that a single average correction was sufficient for the entire carbonate dataset.

From theoretical considerations, the more a sample differs from the WR gas in its δ₆₂₈ composition, the more susceptible it is to this dependence and to potential shifts in the dependence magnitude. For example, a change in δ₆₂₈ dependence from 0.0034‰ Δ_638raw/1‰ δ_628raw to 0.0024‰ Δ_638raw/1‰ δ_628raw would induce an apparent shift of 0.02‰ in Δ₆₃₈ for a sample with a δ_628raw value of 20‰ versus WR but would only cause a 0.0005‰ shift in Δ₆₃₈ for a sample with a δ_628raw value of 5‰ versus WR. Therefore, to minimize the impact of this dependence, we selected a WR gas that has a bulk isotope composition similar to CO₂ derived from most of the carbonates analyzed (δ¹³C = −4.701 ± 0.0178‰ VPDB and δ¹⁸O = −1.707 ± 0.012‰ VPDB). In this way, the δ₆₂₈ dependence correction (with its associated uncertainty) was multiplied by a smaller δ_628raw factor.

We projected the sample Δ₆₃₈ data into the interlaboratory CDES reference frame using as anchors (i) only equilibrated CO₂ gas measurements (4), which are referenced to theoretical clumping values for Δ₆₃₈, and (ii) only ETH carbonate standards, which necessitate a direct comparison of IRMS-derived Δ₄₇ values to TILDAS-derived Δ₆₃₈ values (Materials and Methods) (5). The results demonstrate that such a comparison is valid (Fig. 3). Our mathematical approach is that of (12) and takes the form

$${{\mathrm{\Delta }}^{\text{raw}}}_{47}=a\times {\mathrm{\Delta }}_{47}+b\times {\mathrm{\delta }}_{47}+c$$ (6)

or in our system

$${\mathrm{\Delta }}_{638\text{raw}}=a\times {\mathrm{\Delta }}_{638}+b\times {\mathrm{\delta }}_{628}+c$$ (7)

where δ₆₂₈ is used in place of δ₆₃₈ because the TILDAS system Δ₆₃₈ values only depend on δ₆₂₈ (Fig. 2). Using the equilibrated CO₂ approach (a = 1.0069 ± 0.0748; b = 0.0034 ± 0.000008; c = −0.9434 ± 0.0575), the “a” factor is close to unity, indicating excellent agreement between the theoretical and observed Δ₆₃₈ values of the gas anchors, with a very slightly expanded scale for the TILDAS system, similar to (13). Using ETH carbonate standards as anchors (a = 1.0648 ± 0.2204; b = 0.0030 ± 0.00005; c = −0.9668 ± 0.0404) produces a larger “a” factor, indicating a more expanded scale using carbonate anchors compared to the gas anchor reference frame, but this difference is statistically insignificant given the uncertainties. The smaller δ₆₂₈ dependence (b = 0.0034 ± 0.000008 versus 0.0030 ± 0.00005) may be due to the much narrower range in δ₆₂₈ that is bracketed by the ETH standards (17.3‰) compared to the gas samples (77.1‰), although the dependence appears to be linear for the entire range (Fig. 2). Notably, the uncertainties in Δ₆₃₈ and ultimately in temperature are larger using ETH anchors because they bracket a smaller range in δ₆₂₈ and in Δ₆₃₈ space (tables S3 and S4 and data S1) similar to the effect of bracketing a smaller range in δ₄₇ for IRMS systems (5).

Fig. 3. InterCarb standards comparison.

Δ₄₇ and Δ₆₃₈ results from IRMS and TILDAS measurements of seven Interlaboratory standards: ETH-1, ETH-2, ETH-3, ETH-4, IAEA-C1, IAEA-C2, and MERCK. IRMS results are from the InterCarb study (5). In (A) to (D), raw data are projected into the CDES reference frame using equilibrated and heated gases as anchors. IRMS results are ordered from left to right in the order of laboratories A to J as reported in table 1 of (5) with regular intervals. Each circle represents the mean value for a standard reported by a single laboratory. The blue line represents the weighted mean value for all IRMS laboratories. Red diamonds represent TILDAS mean values for each standard for powders received in March 2019, analyzed 40 times for ETH-1 and 41 times for ETH-2,3,4. Purple diamonds are TILDAS mean values for the same standards but for the exact powders distributed to UW IsoLab for the InterCarb study, analyzed six times each. Error bars are ±1 SE. In (E) to (G), results are projected into the I-CDES reference frame using carbonate standards ETH-1,2,3 for IRMS results and ETH-1,2,3,4 for TILDAS results. The results from IRMS instruments 1 to 26 as reported in table 3 of (5) are ordered from left to right. Note that not all mass spectrometers 1 to 26 reported data for all three standards. In all panels, IRMS values are corrected to 70°C acid digestion by adding a factor of 0.022‰.

System stability

The ability of the TILDAS system to consistently produce accurate results can be assessed by regular measurement of homogeneous standard materials. To evaluate the stability and reproducibility of the system, we analyzed six homogeneous carbonates on a near-daily basis during the analytical session (Fig. 4). The SDs of Δ₆₃₈ for the carbonate standards (n_MK = 130, n_ETH-1 = 40, n_ETH-2 = 41, n_ETH3 = 41, n_ETH-4 = 41, n_car-2 = 82) ranged from 0.019 to 0.035‰. The “pooled reproducibility” is 0.023‰, calculated as described by (19) using all homogeneous carbonates, standards, and unknowns analyzed at least five times. For comparison, the SD of the WR gas measured against itself is 0.0154‰. This represents the expected reproducibility limit for the TILDAS system, as WR versus WR comparisons involve no acid digestion and do not go through the CO₂ purification line, both of which could potentially add noise.

Fig. 4. Carbonate standards stability.

(A) Repeated analyses of intralaboratory (car-2, MK) and interlaboratory (ETH) carbonate standards between 22 July 2021 and 2 November 2021. Clumped isotope values are projected into CDES using equilibrated and heated gases. Carbonates are digested in 70°C acid, and Δ_638CDES values are not corrected to 25°C. Error bars are ±1 SD of individual analyses. Number of analyses: car-2, 82; MK, 130; ETH-1, 40; ETH-2, 41; ETH-2, 41; ETH-4, 41. (B) Deviation from the mean value of each standard for the same analyses as (A). Error bars removed for clarity.

We used a homogeneous carbonate that has a δ_628raw value close to that of the WR gas to assess the amount of noise contributed from acid digestion and CO₂ purification. The Δ₆₃₈ value of such a carbonate is minimally affected by the bulk correction, as explained above. Intralaboratory standard C64 has an SD of 0.0160‰ (n = 21), only 0.0006‰ larger than the WR gas, likely because its δ_628raw composition is only −5.70‰ (table S4 and data S1) versus the working gas. Although the number of analyses is smaller for C64 than for other standards, this suggests that the acid digestion and gas cleanup steps have only a minor impact on the overall reproducibility of the system. For conventional stable isotope composition, the pooled reproducibility for δ¹³C is 0.0305‰ and for δ¹⁸O is 0.0367‰, both competitive with IRMS systems.

Comparison of interlaboratory standards to accepted IRMS values

A key question regarding the TILDAS system is whether the Δ₆₃₈, δ₆₂₈, and δ₆₃₆ values it generates can be directly compared to IRMS Δ₄₇, δ¹⁸O, and δ¹³C values, respectively. Because the TILDAS system measures molecular ratios, while IRMS systems measure atomic ratios, there could be inherent differences between the values produced by the two methods.

The recent InterCarb clumped isotope community project (5) provides an excellent dataset for comparison with TILDAS results, as it demonstrates the interlaboratory reproducibility of carbonate standards between IRMS systems and provides consensus values for seven standards (ETH-1, ETH-2, ETH-3, ETH-4, IAEA-C1, IAEA-C2, and MERCK). To compare TILDAS results to IRMS values, we analyzed four of these standards (ETH-1,2,3,4), received in March 2019, 40 to 41 times each, and separately analyzed the full set of InterCarb standards, using the exact same powders distributed to UW IsoLab, six times each. After correcting InterCarb values to a 70°C acid digestion temperature by adding a factor of 0.022‰ (5), the difference between TILDAS Δ_638CDES and mean IRMS Δ_47CDES values for the ETH standards ranges between −0.012 and +0.017‰, with an average absolute difference of 0.0095‰ (Fig. 3).

Three more standards, IAEA-C1, IAEA-C2, and MERCK, were analyzed in the InterCarb project and projected into the I-CDES reference frame using ETH standards as anchors. Since our Δ_638CDES values of the ETH standards are comparable to IRMS values, we applied the same methodology using the InterCarb consensus values for ETH standards corrected to a 70°C acid temperature as anchors. It should be noted that the InterCarb IRMS laboratories used ETH-1, ETH-2, and ETH-3 as anchors and treated ETH-4 as an unknown, while we used all four ETH standards as anchors. After projecting the IAEA-C1, IAEA-C2, and MERCK results into the I-CDES reference frame, the differences between the mean IRMS Δ_47,I-CDES from all InterCarb instruments and the TILDAS Δ_638,I-CDES values for IAEA-C1, IAEA-C2, and MERCK were 0.0025, 0.0000, and −0.0174‰, respectively. As with the gas anchor method, these differences are smaller than those observed between IRMS laboratories (Fig. 3) and do not appear to be systematic, implying that a direct comparison of TILDAS CDES or I-CDES values to IRMS CDES or I-CDES values, respectively, is as valid as a comparison of results from different IRMS instruments.

TILDAS raw δ₆₂₈ and δ₆₃₆ values were projected into the VPDB scale using carbonate standards with consensus δ¹⁸O and δ¹³C values (Materials and Methods). Again, using the InterCarb dataset, we find that TILDAS δ₆₃₆ and δ₆₂₈ VPDB values are within the range of IRMS δ¹³C and δ¹⁸O VPDB values for the standards measured (fig. S3). A single exception is the δ₆₃₆ value of MERCK, which is 0.14‰ lower than the lowest mean value for any InterCarb IRMS instrument. The MERCK standard has the most extreme δ₆₃₆ value, −42.21‰ VPDB, so its abnormal value compared to IRMS could be a result of a slight inaccuracy in the measured VPDB value of our MK secondary standard, which anchors the low end of our δ₆₃₆ scale. Alternatively, it could be a result of an inherent difference between δ₆₃₆ and δ¹³C that is only manifested at extreme compositions. The current dataset does not allow us to resolve the issue, as more standards with low δ₆₃₆ composition are required. In either case, these results indicate that comparing TILDAS δ₆₂₈ values to IRMS δ¹⁸O values is equivalent to comparing δ¹⁸O values from different IRMS instruments. The same is true for TILDAS δ₆₃₆ and IRMS δ¹³C for all but extremely low δ₆₃₆ values. Although the TILDAS system measures δ₆₃₆ and δ₆₂₈, the normalization of these ratios to IAEA standards with assigned δ¹⁸O and δ¹³C values results in equivalent values. We therefore suggest that singly substituted carbonate isotope ratios can be reported using the traditional δ¹³C and δ¹⁸O VPDB notation.

Empirical temperature calibration

A fundamental tool in low-temperature isotope geochemistry and paleoclimate studies is the temperature dependence of oxygen fractionation between carbonate minerals and the water they precipitate from. To establish an empirical calibration based on TILDAS δ¹⁸O measurements of calcite, we precipitated 44 carbonate powders under controlled conditions at temperatures of 6.3° to 69.7°C (Materials and Methods and the Supplementary Materials). One sample was 3% aragonite and 97% calcite, and the rest were 100% calcite (data S2). By measuring the oxygen isotope composition of the carbonates and the water, we constructed a rigorous calcite-water fractionation-temperature calibration, resulting in the following relationship

$$\begin{array}{c}1000\text{ln}{\mathrm{\alpha }}_{\text{calite-water}}=18.0508\pm 0.0875\times \left(\frac{1000}{T}\right)-\\ 32.1996\pm 0.2850R^2=0.996\end{array}$$ (8)

This relationship is indistinguishable in slope and intercept from the widely cited IRMS calibration of (22) (Fig. 5) and improves on most low-temperature calibrations in the number of samples, mineralogic homogeneity, and temperature range and arguably in the method of carbonate precipitation. The experimental setup used for this series of precipitations (fig. S1) has advantages over most previous studies in that it resulted in highly reproducible experiments (fig. S2) at low calcite saturation indexes (table S1) in well-mixed solutions and with temperature control better than 0.2°C. Furthermore, solution chemistry (pH, electrical conductivity, and temperature) was tracked continuously throughout the experiments, allowing a better understanding of the precipitation process as opposed to only knowing the start and end conditions (Materials and Methods and the Supplementary Materials). This calibration can be coupled to the clumped isotope-temperature calibration below to calculate the δ¹⁸O value of the parent water of a carbonate of interest, with adjustments for noncalcite mineralogy. Although TILDAS δ¹⁸O values appear to be comparable to IRMS δ¹⁸O values (see above), we also measured the δ¹⁸O composition of the carbonates using conventional IRMS (Materials and Methods) to produce a purely IRMS-based calibration, which may be preferable for IRMS users. The resulting relationship is

$$\begin{array}{c}1000\text{ln}{\mathrm{\alpha }}_{\mathit{\text{calcite-water}}}=18.0972\pm 0.0870\times \left(\frac{1000}{T}\right)-\\ 32.0952\pm 0.2851R^2=0.994\end{array}$$ (9)

Fig. 5. Conventional calcite-water ¹⁸O fractionation-temperature calibration.

Black circles are 1000lnα_{calcite-water} values based on mean δ¹⁸O values of 41 synthetic calcite samples prepared for this study and the δ¹⁸O values of the water they precipitated from. Calcite powders were analyzed 5 to 11 times each. Horizontal and vertical error bars are smaller than markers. The red line is a linear regression based on TILDAS δ¹⁸O values of the carbonates. The brown line is the regression based on IRMS δ¹⁸O values of the same samples. Blue diamonds are data points from (22). The blue line is the linear regression of (22).

Both relationships are within error of each other in slope and intercept (Fig. 5).

We used the same set of 44 synthetic calcites to construct a Δ_638CDES-temperature calibration, analyzing each sample 5 to 11 times for a total of 359 clumped isotope analyses. The resulting relationship is

$$\begin{array}{c}{\mathrm{\Delta }}_{638\text{CDES}}=0.405\pm 0.0006\times \left(\frac{{10}^6}{T^2}\right)+0.1822\pm 0.0061\\ R^2=0.985\end{array}$$ (10)

An additional set of seven carbonates reequilibrated to temperatures of 450° to 1100°C (Materials and Methods) was added to expand the range of the calibration to temperatures relevant to diagenetic and metamorphic processes. These were analyzed 4 to 10 times for a total of 47 analyses. It should be noted that the high-temperature (>70°C) part of the calibration is less robust than the low-temperature segment. There is a large sampling gap between 70° and 450°C and a second large gap between 600° and 1100°C. In addition, the solid-state reordering method used to equilibrate samples in the 450° to 600°C range was less reproducible, making it difficult to ascertain that the samples fully equilibrated to the desired temperature. We therefore regard the high-temperature end of the calibration with caution. The 1100°C sample, prepared using a piston cylinder apparatus, is more robust because this high-temperature, high-pressure experimental setup very likely induced complete recrystallization (Materials and Methods). The temperature-clumping relationship calculated using the full set of samples is given by the equation

$$\begin{array}{cc}\hfill {\mathrm{\Delta }}_{638\mathit{\text{CDES}}}& =0.0409\pm 0.0003\times \left(\frac{{10}^6}{T^2}\right)+0.1776\pm 0.0031\hfill \\ \hfill R^2& =0.997\hfill \end{array}$$ (11)

Despite the shortcomings of the high-temperature segment of the calibration, the expanded range relationship is within the uncertainty of the low-temperature calibration. The two overlap in the 6° to 70°C range and only diverge slightly at the high-temperature end (Fig. 6), suggesting that the high-temperature carbonates are near equilibrium or, possibly, at the same disequilibrium as the low-temperature samples. The key difference is the much smaller uncertainty in slope and intercept in the full-range calibration, a result of the two data clusters (6° to 70°C and 450° to 1100°C) forming a pseudo–two-point regression. The reduced uncertainty using the full-range calibration propagates to temperature uncertainties that are roughly 1°C smaller for unknown samples formed at Earth surface temperatures (table S3). Both the low-temperature and full-range relationships are not within the uncertainty of a recent IRMS calibration compilation (6) (Fig. 6), but the difference between the TILDAS and IRMS relationships is no larger than the discrepancies observed between previous IRMS calibrations. Because IRMS Δ₄₇ measurements include contributions from the ¹⁷O¹³C¹⁷O and ¹⁷O¹²C¹⁸O isotopologues, which have a stronger temperature dependence than the ¹⁶O¹³C¹⁸O isotopologue measured separately by TILDAS, the Δ₄₇-reciprocal-temperature relationship should, in theory, have a slightly lower slope compared to Δ₆₃₈ (1, 6), consistent with our result. However, the theoretical differences are too small to fully explain the discrepancies between the calibrations.

Fig. 6. Empirical temperature calibration.

(A) The black circles are mean Δ₆₃₈ CDES values of synthetic calcite prepared for this study, plotted against their precipitation/reequilibration temperatures. Uncertainties in Δ₆₃₈ and in temperatures are smaller than circles. The red line is a weighted linear regression based on the synthetic samples precipitated between 6° and 70°C, as shown in main figure. The dashed brown line is a regression based on both the low-temperature samples and samples reequilibrated at 450° to 1100°C, shown in the bottom left of the inset. The colored symbols are mean Δ₆₃₈ values of natural carbonates plotted against their known formation temperatures. Vertical error bars are smaller than symbols, and horizontal error bars represent uncertainties in formation temperatures. The blue line is the IRMS calibration of (6) with the intercept adjusted to 70°C acid digestion temperature. (B) Same as (A) but samples are projected into the I-CDES reference frame using ETH anchors. The blue line is the calibration of (7).

Recent work has shown that using ETH carbonate anchors instead of gas anchors results in better agreement between temperature-clumping calibrations produced by different laboratories (7). Our results indicate that the same approach can be applied to project Δ_638raw values into the I-CDES. Using this method, the temperature-clumping relationship based on only the low-temperature synthetic carbonates becomes

$$\begin{array}{c}{\mathrm{\Delta }}_{638\text{I-CDES}}=0.0395\pm 0.0007\times \left(\frac{{10}^6}{T^2}\right)+0.1800\pm 0.0074\\ R^2=0.986\end{array}$$ (12)

Expanding the calibration to include the 450° to 1100°C samples yields the following relationship

$$\begin{array}{c}{\mathrm{\Delta }}_{638\text{I-CDES}}=0.0386\pm 0.0002\times \left(\frac{{10}^6}{T^2}\right)+0.1902\pm 0.0025\\ R^2=0.996\end{array}$$ (13)

The low-temperature calibration is within the uncertainty of the IRMS calibration of (7). The full-range calibration slope is within the uncertainty of the calibration of (7) slope, and the intercept is slightly higher (Fig. 6). It is likely that the shallower slope in the carbonate anchor relationship compared to the gas anchor relationship is a result of the larger-scale compression introduced by projection into the I-CDES compared to projection into the CDES (larger “a” parameter in the conversion). Ultimately, both methods produce indistinguishable temperatures for the carbonates analyzed in this dataset, but temperature uncertainty is ∼0.5° to 1°C larger using the carbonate anchors (table S3 and data S1).

Natural samples

To test the ability of the calibration to predict the formation temperatures of natural carbonates, we analyzed 17 natural samples with known formation temperatures ranging from 7.8° to 39°C (Materials and Methods). These include 4 inorganic and 13 biogenic carbonates and a mix of calcite and aragonite (table S2). Using the low-temperature gas anchor calibration, the temperature predicted by the calibration and the measured Δ_638CDES value of 13 of the samples is within the uncertainty of the known formation temperature (table S3). Temperature uncertainties are calculated on the basis of the 95% confidence interval (1.96 SE) of Δ₆₃₈ values using full error propagation (19) also propagating the uncertainties in the Δ₆₃₈-temperature calibration slope and intercept. The largest offset between predicted and known temperatures (39° ± 4°C and 33°C, respectively) is for the spring tufa sample. Spring tufas formed in similar settings have been shown to deviate from expected clumped composition (23), although not in all cases (24). In addition, the sample in question was collected from a shallow stream in Ash Meadows National Wildlife Refuge, Nevada, which may reach higher temperatures during the summer months compared to those measured when the sample was collected in January. However, the sample was collected directly upstream of a pool that has only a 2°C annual temperature cycle based on temperature logger data (fig. S4), so stream temperature fluctuations are likely limited. Another sample not within the uncertainty of predicted temperature is the Laghetto Basso calcite. This material was initially thought to deviate significantly from empirical clumping-temperature calibrations (25), but a recent calibration appears to have resolved the discrepancy (7). In either case, the known temperature is only 0.4°C outside of the predicted temperature range. Two other outliers are aquatic gastropods. The reason for their deviation is unclear because other samples of the same species collected at different springs and other species collected from the same springs did not deviate beyond uncertainty from expected temperatures. In total, the average absolute offset between predicted and measured values was 2.3 ± 1.7°C (1 SD) including all natural samples and 2.1 ± 1.3°C excluding the biggest outlier, the tufa sample (table S3).

Using the extended temperature range calibration produces at most a 0.2°C difference in expected temperatures of the natural samples but a roughly 1°C smaller uncertainty. While appealing, the smaller uncertainty means that four more samples have known temperatures that are not within the uncertainty of predicted values, so the smaller uncertainty may be statistically true but unrealistic. Using ETH carbonate anchors increases the average offset between predicted and measured values to 2.6° ± 1.9°C (2.3 ± 1.7°C excluding the tufa outlier), so it appears to be slightly less accurate based on the limited number of natural samples analyzed in this study. However, because of the larger temperature uncertainty, only 3 of 17 samples have known temperatures not within the uncertainty of the predicted temperatures based on the low-temperature calibration (table S3).

DISCUSSION

This study describes an analytical approach, an operational routine, and a data analysis method that produce precise clumped isotope data using the TILDAS instrument with a high sample throughput and small sample sizes. It also establishes temperature-clumping and temperature-oxygen isotope fractionation calibrations validated using natural samples. Although the system is performing well, a lingering issue is the bulk isotope dependence. The system has a linear dependence of Δ₆₃₈ on δ₆₂₈ and no dependence of Δ₆₃₈ on δ₆₃₆ (Fig. 2). Although seemingly similar to IRMS bulk dependence, the TILDAS instrument’s nonlinearity effects are driven by different mechanisms. In this TILDAS dual laser instrument, laser 1 is tuned to 2250.2 cm⁻¹ to measure the absorbance of the ¹⁶O¹³C¹⁶O and ¹⁶O¹³C¹⁸O isotopologues, and laser 2 is tuned to 2285.1 cm⁻¹ to measure the ¹⁶O¹²C¹⁶O and ¹⁶O¹²C¹⁸O absorbance peaks [see figure 1 in (13)]. Therefore, the spectral fitting, whose basis functions are laser intensity baseline forms and absorption line shapes, is conducted separately for each laser. The deviation of baseline fitting from “true baseline” is a possible explanation of the nonlinearity and its different magnitude in δ_636raw and δ_628raw. A better understanding of this bulk dependence could lead to its elimination and even better precision, as seen by the SDs of carbonate standards with small δ_628raw values. Until a better solution is found, the method presented in this study is effective in monitoring and correcting for this dependence.

Both the equilibrated CO₂ gas and carbonate standard approaches tested for projection of raw data into an interlaboratory reference frame work well. On the basis of a comparison to the InterCarb dataset, using either gas anchors or ETH carbonate anchors, both resulted in Δ₆₃₈ values that are within the range of IRMS Δ₄₇ values for the carbonate standards tested, meaning that a direct comparison of TILDAS and IRMS datasets is as accurate as comparing datasets from two IRMS instruments.

The advantages and disadvantages of each approach for IRMS analysis are discussed in detail in (5). Specifically for the TILDAS system (and as with select IRMS systems), the carbonate anchor approach has a distinct advantage because carbonate processing is entirely automated, allowing one to easily run more anchors, while gas samples have to be manually introduced into the gas purification line. The calibration based on carbonate anchors is also in better agreement with the most recent IRMS calibration (7) than the gas-based calibration is with the latest equivalent IRMS calibration (6), although this improved agreement may be a product of forcing the Δ₆₃₈ values of ETH anchors to exactly match IRMS consensus values. Although based on theory (1, 6) we do expect a slight difference between the temperature dependence of Δ₆₃₈ and Δ₄₇, this theoretical difference is too small to fully explain the discrepancies between the gas anchor calibrations. However, using gas anchors reduces the analytical uncertainty in Δ₆₃₈ and ultimately the temperature uncertainties. Moreover, ETH anchors cannot be used to monitor (or correct) for a potential future dependence of Δ_638raw on δ_636raw because they do not provide two carbonates with identical clumped temperatures and identical δ_628raw compositions that bracket a wide range in δ₆₃₆ space. We have not observed a significant δ₆₃₆ dependence, but until the bulk dependence issue is better understood, the ability to check for changes in this dependence is important and necessitates the use of some gas anchors.

There are several limitations to the results presented in this study. While spectroscopic systems do not suffer from mass interferences, optical interferences can occur. An unrecognized absorbance peak overlapping one of the peaks used for our Δ₆₃₈ measurement could potentially result in an erroneous value. We are not aware of any common gases that absorb in our narrow measured spectral region and have not observed these peaks, but optical interferences are possible for the TILDAS system. If these gases were produced by acid reaction with some natural samples, a gas chromatographic or equivalent purification step may become necessary, but presently no such purification seems to be required. A second limitation of the system is the need to thoroughly mix CO₂ samples with nitrogen before measurement, a step that is time-consuming and makes it difficult to recapture a gas sample for repeated analyses. The mixing ratio of CO₂ to nitrogen in the sample must closely match that of the WR gas for best performance. While this is relatively simple to do for the bulk CO₂/N₂ ratio, individual isotopologues can have very different mixing ratios from the WR gas depending on the bulk composition and clumping of the sample. This could be a source of measurement error or bias. As discussed above, the TILDAS system also requires a δ₆₂₈ correction, the underlying causes of which are still not fully understood. Last, the conversion of δ_636raw and δ_628raw data into the VPDB reference frame may be improved by establishing more accurate VPDB values for our secondary standards. This could also resolve the discrepancy between TILDAS and IRMS δ¹³C VPDB values observed for the MERCK sample.

The results presented in this study open the door to exciting potential future applications. The high analytical throughput of the TILDAS system and the small sample size required can quickly produce large robust datasets with increased sample replication. This will allow higher resolution sampling of materials, critical to paleoclimatic reconstructions, and could expand the use of clumped isotope geochemistry to new users and fields. Future plans to couple the system to an additional single-laser spectrometer capable of high-precision ¹⁷O measurements could produce conventional, clumped, and triple oxygen data with a simple rapid analysis and a sample size of only <2 mg calcite equivalent (∼15 μmol CO₂). Dual clumped isotope analyses, which have recently been shown to resolve kinetic effects in certain natural carbonates (26, 27), could conceivably be done using an additional dual-laser or single-laser spectrometer in a separate optical box with a different spectral range. With the TILDAS system, measurements would not be limited to isotopologue pairs with different masses (e.g., Δ₄₇ and Δ₄₈), as is the case with IRMS, and could focus on Δ₆₃₈ and Δ₈₂₈ directly.

In conclusion, the TILDAS system described in this study is comparable in sample size to the best IRMS systems and improves on IRMS systems in analysis time, sample throughput, and simplicity, as it does not require a gas chromatographic or equivalent CO₂ purification step. In addition, it is capable of measuring individual isotopologues directly, regardless of their mass, eliminating the need for ¹⁷O corrections. On the basis of these results, the TILDAS system is now set to substantially advance the field of carbonate clumped isotope research and low-temperature geochemistry as a whole.

MATERIALS AND METHODS

Experimental design

The objectives of this study are to (i) evaluate the long-term reproducibility and stability of the TILDAS instrument for clumped isotope analysis, (ii) evaluate the projection of raw data into an interlaboratory reference frame using gas and carbonate anchors, (iii) determine whether clumped and conventional isotope data produced by the TILDAS system are directly comparable to IRMS data, (iv) construct an empirical temperature-clumping calibration, and (v) test the system’s ability to reconstruct formation temperatures of natural samples. We took the following steps to meet these objectives:

1) To test long-term reproducibility, we regularly analyzed a set of six homogeneous carbonates for the duration of the study. Reproducibility is assessed on the basis of the SD of all analyses for each sample and on observed variations in analysis results over time. The pooled reproducibility of all carbonates analyzed at least five times is also considered.

2) A set of gas anchors and carbonate anchors was routinely analyzed during the study, allowing us to use both to project data into interlaboratory reference frames. The methods are evaluated on the basis of the analytical uncertainty they produce for unknown samples, the technical ease of use for each method, and the interlaboratory reproducibility achieved with each method.

3) Once data are projected into an interlaboratory reference frame, results from seven interlaboratory standards are compared to a large dataset of IRMS analyses of the same standards. The difference between mean IRMS values and TILDAS values is compared to the variability of results between different IRMS laboratories.

4) Fifty-one carbonates are precipitated at or reequilibrated to controlled temperatures between 6.3° and 1100°C and analyzed. The results are used to construct a temperature-clumping calibration.

5) Seventeen natural samples with known formation temperatures are also analyzed. The results of the natural sample analyses are applied to the temperature-clumping calibration to calculate predicted temperatures for the natural samples. A comparison of the predicted temperatures to known temperatures is used to test the empirical calibration.

Gas extraction/cleanup line and laser system description

The fully automated carbonate clumped isotope analyzer has three parts: (i) gas extraction/dehydration line, (ii) CO₂ sample mixing and delivery system, and (iii) TILDAS dual-laser instrument (Fig. 1). The gas extraction line follows common methods for carbonate-phosphoric acid reaction and cryogenic purification of the CO₂ gas. The reaction is conducted at 70°C in a temperature-controlled container, in which an autosampler carousel enables up to 36 samples to be processed in unattended operation. This gas extraction/dehydration procedure takes ca. 20 min. The sample mixing and delivery system thoroughly mixes CO₂ gas with N₂ gas in a stainless steel bellows and loads the mixture into the TILDAS instrument for the CO₂ isotopologue suite measurement. By diluting the CO₂ in a buffer gas, the spectral lines are broadened, which improves the precision of the spectral fitting in the data processing software and reduces the impact of the laser jitter noise. As a result, the repeatability of the analysis is improved. The gas-mixing procedure takes ca. 20 min. The TILDAS dual laser instrument, described in (13), directly and simultaneously measures four CO₂ isotopologues (¹⁶O¹²C¹⁶O, ¹⁶O¹³C¹⁶O, ¹⁶O¹²C¹⁸O, and ¹⁶O¹³C¹⁸O) in the mid-IR spectral regions of 2250.2 cm⁻¹ and 2285.1 cm⁻¹. Isotopologues associated with ¹⁷O are not present in the absorption peaks measured for the clumped isotope calculation. The automated sampler, gas extraction line, and the sample mixing apparatus were constructed in-house at the University of Arizona, whereas the TILDAS instrument was custom-built for this project by Aerodyne Research (Billerica, MA) based on existing laser designs. A detailed, step-by-step protocol for operating the system is given in the Supplementary Materials.

Equilibrated and heated gas samples

A set of gas anchors was used to project raw data into CDES. Equilibrated gases were prepared at the University of Arizona. Pyrex tubes with 10 μl of water were evacuated on a high vacuum line by first freezing the water with an ethanol/LN₂ slurry. After evacuation, the ethanol/LN₂ slurry was replaced by LN₂ and sufficient CO₂ for a single clumped isotope analysis was frozen into the tube, after which the tube was flame-sealed. The gas was then allowed to equilibrate at 6°, 23°, or 60°C for at least 2 weeks before measurement. Temperature was tracked using HOBO loggers at 1-hour intervals. To maximize the bulk composition range, we used one gas with δ¹³C = ∼−4‰ VPDB and δ¹⁸O = ∼−7‰ VPDB and a second gas with δ¹³C = ∼−40‰ VPDB and δ¹⁸O = ∼−20‰ VPDB. These were equilibrated with either Vostok water (δ¹⁸O = ∼−31‰ VPDB) or evaporated water (δ¹⁸O = ∼+32‰ VPDB), resulting in four gas types with bulk compositions spanning 36‰ in δ¹³C space and 77‰ in δ¹⁸O space. To verify the linearity of the bulk dependence, we prepared 12 samples with intermediate δ¹⁸O compositions (−15‰, +2‰, +6‰, and +9‰ VPDB), all equilibrated at 23°C.

Heated gases were prepared using the same procedure but without water and replacing Pyrex tubes with quartz tubes. The samples were heated to 1000°C for at least 24 hours before analysis.

Synthetic samples

We used carbonate samples prepared in the laboratory to establish temperature calibrations. Carbonates were precipitated at controlled temperatures using a custom-built apparatus composed of a reaction vessel, two reagent vessels, a peristaltic pump, a water chiller/heater circulator, and a pH/electric conductivity (EC)/temperature meter with probes (fig. S1). Each experiment began with pure water in the reaction vessel and 20 mM solutions of NaHCO₃ and CaCl₂ in the reagent vessels. The solutions were equilibrated at the desired temperatures by circulating water through the water-jacketed vessels. After equilibration, reagent solutions were slowly dosed into the reaction vessel and solution was removed from the reaction vessel at an equal rate using the peristaltic pump. In this way, the concentrations of Ca²⁺ and HCO₃⁻ in the reaction vessel gradually increased while maintaining a constant water volume until supersaturation was reached and carbonate was precipitated. When sufficient carbonate had precipitated for clumped isotope and x-ray diffraction (XRD) analyses, the experiments were ended and the carbonate was scraped off the vessel walls, filtered from the solution, dried, and stored for analysis. The pH, EC, and temperature in the reaction vessel were logged at 1-min intervals. The resulting pH/EC curves show that the experiments are highly reproducible (fig. S2) and that carbonate was precipitated at a low saturation state and therefore likely near equilibrium. On the basis of XRD analyses performed at the University of Arizona Department of Chemistry, all but one sample were 100% calcite. One sample contained trace amounts (∼3%) of aragonite. See the Supplementary Materials for a detailed description of the precipitation apparatus and the experiments.

High-temperature samples

To extend the range of the clumping-temperature calibration, carbonate samples were equilibrated at 450°, 500°, 550°, and 600°C by solid-state reordering. For each sample, sufficient calcite for multiple clumped isotope analyses was inserted into a quartz tube. The tube was evacuated and filled with enough CO₂ gas for a single TILDAS analysis (2 mg calcite equivalent) before the tube was flame-sealed. Samples were then heated to the desired temperature for 21, 9, 13, and 4 days (for 450°, 500°, 550°, and 600°C, respectively) for solid-state reequilibration, following (28). After heating, the tubes were cracked, and the water vapor and CO₂ pressure were measured to detect decarbonation of the calcite. In some cases, the isotope composition of gas was also measured for the same purpose. After extracting the gas, the carbonate was removed and stored for analysis. Our intralaboratory standards, car-2 and MK, as well as BB (vein calcite spar from Barrancas Blancas, northern Chile), were used as starting material because they have different grain sizes and initial clumped and bulk isotope values. In this way, we could test whether samples had equilibrated to the desired temperature. In several samples, including all samples with MK as a starting material, the heated powder was heterogenous with respect to clumping (differences of ∼0.1‰ between replicate analysis) likely due to incomplete resetting. These samples were not used in the calibration. A single sample prepared with car-2 as the starting material and heated to 700°C for 5 days produced a homogeneous powder but was a clear outlier in the temperature calibration. Adding it to the calibration substantially degraded the regression fit and the accuracy with which the calibration predicted the temperatures of natural samples, so it was omitted from the calibration.

One sample was recrystallized at 1100°C using a high-temperature, high-pressure system at the University of Arizona Experimental Petrology Laboratory. The sample was pressurized to 1 GPa and heated to 1100°C using a half-inch assembly in a piston cylinder apparatus. Twenty milligrams of reagent-grade calcite (Alfa Aesar, 11403; CaCO₃ 5 μm powder, minimum 95% purity) was placed in a 2-mm-diameter, 7.07-mm-high Au75-Pd25 capsule, surrounded by a MgO sleeve. A four-hole Al₂O₃ sleeve as thermocouple insulator, type C thermocouple, graphite furnace for heating, and BaCO₃ pressure medium were used. The sample was pressurized to 1 GPa, and then the temperature was increased to 1100°C at a rate of 50°C/min. It was then allowed to equilibrate for 48 hours. At the end of the experiment, the sample was rapidly quenched to room temperature by shutting off power, reaching <50°C within 31 s.

IRMS analysis

Mass spectrometric measurements were used to determine the δ¹⁸O composition of the waters that the synthetic samples precipitated from and to calculate an oxygen fractionation–temperature calibration that is entirely IRMS-based. Water δ¹⁸O was measured on an automated gas-source isotope ratio mass spectrometer (Finnigan Delta S) at the University of Arizona Environmental Isotope Laboratory. Samples were equilibrated with CO₂ gas at approximately 15°C in an automated equilibration device coupled to the mass spectrometer. Standardization is based on international reference materials Vienna Standard Mean Ocean Water (VSMOW) and Standard Light Antarctic Precipitation (SLAP). Analytical precision (1σ) is 0.1‰ or better for δ¹⁸O on the basis of repeated intralaboratory standards. Carbonate δ¹³C and δ¹⁸O values were measured using an automated carbonate preparation device (KIEL-III) coupled to a gas-ratio mass spectrometer (Finnigan MAT 252). Powdered samples were reacted with dehydrated phosphoric acid under vacuum at 70°C. The isotope ratio measurement is calibrated on the basis of repeated measurements of NBS-19 and NBS-18, and precision is ±0.10‰ for δ¹⁸O and ±0.08‰ for δ¹³C (1σ).

Natural samples

A set of natural samples with known formation temperatures was used to validate the temperature-clumping calibration. These included a ~13,000-year-old ostrich egg shell from Gona, Ethiopia [∼39° ± 1°C (29)] and a large freshwater bivalve collected in 1998 from Lake Tanganyika in central Africa. The shell was collected from a spit of land just south of Kigoma, Tanzania, latitude 4.912°S, 24° to 27°C (30); subaqueous mammillary calcite precipitated on the walls of the Devil’s Hole cave system [33.7°C (25, 31)]; subaqueous calcite coating formed at the bottom of Laghetto Basso, a small lake in Corchia Cave, Italy [7.9°C (25)]; aquatic gastropods and spring tufa collected in January 2020 from warm, high discharge springs in Ash Meadows National Wildlife Refuge, Nevada (32) (28° to 33°C; fig. S4); and modern non-encrusted deep mixed-layer dwelling planktic foraminifera Globorotalia truncatulinoides (dextral) that flourish during January and February (mean temperature = 18°C) picked from the topmost sediments in core 2010-GB2-MCC raised in the Garrison Basin, Western Gulf of Mexico (33–35). More details are provided in table S2.

Statistical analysis

Bivariate linear regressions used for calculating the temperature calibrations, including uncertainties in slope and intercept, were performed using the method of (36), implemented by the MATLAB code of (37). For the Δ₆₃₈-clumping calibration, the mean values of replicate analyses of each sample were used as single data points, with the 95% confidence interval, calculated as described below, used as uncertainty. Each point in the regression was weighted using the inverse square of the Δ₆₃₈ uncertainty (1.96 SE) and the inverse square of the temperature uncertainty taken as either the temperature variation (SD) during sample preparation or the analytical uncertainty of the temperature probe, whichever was larger. For the oxygen isotope fractionation calibration, points were weighted by the inverse square of the uncertainty in 1000lnα propagated from the SD in δ¹⁸O values of replicate analyses of each sample.

The parameters used to project raw data into the CDES and I-CDES reference frames were calculated using the method of (19), adjusted to our system. Because our Δ₆₃₈ values are only dependent on δ₆₂₈, we replaced δ₄₇ with δ₆₂₈ in the calculation and Δ₄₇ was replaced with Δ₆₃₈. To calculate conversion parameters for the CDES reference frame, equilibrated and heated gas anchors are used. The theoretical Δ₆₃₈ values for the gases at the equilibration temperatures (6.2°, 22.8°, 63.5°, and 1000°C) were calculated using a seventh-order polynomial fit to the calculated Δ₆₃₈ values from (6), in which the International Union of Pure and Applied Chemistry (IUPAC) parameters were used (6, 38). For the I-CDES conversion, the InterCarb consensus Δ₄₇ values for ETH-1,2,3,4 anchors are used (5), adjusted to 70°C acid digestion by adding a factor of 0.022‰. This method includes full error propagation of the uncertainties in the parameters of the transfer function and the analytical reproducibility of the system. We used a “pooled reproducibility” approach to calculate the reproducibility of Δ₆₃₈, δ₆₂₈, and δ₆₃₆ as described by (19). All carbonates that were analyzed at least five times are included in the calculation. This method was implemented using a MATLAB script based in part on that used by (11) and in part on the “ClumpyCrunch” Python code from (19).

Clumped isotope (Δ₆₃₈) uncertainties presented in this study for each sample are 95% confidence intervals calculated as 1.96 SE of the CDES or I-CDES value of the sample. The mean value of replicate analyses of the sample and the external pooled reproducibility are used. These uncertainties and the uncertainties of the slope and intercept of the temperature-clumping calibration are propagated to calculate the temperature uncertainty of the sample.

The VPDB values of our secondary standards, car-2 and MK, were determined by comparison to primary IAEA standards NBS-18, NBS-19, IAEA-CO-8, IAEA-603, and LSVEC (LSVEC was only used as a δ¹³C standard) analyzed on the same day. The conversion of δ_628raw and δ_636raw values to VPDB for unknown samples was done using a moving window approach with our secondary standards, car-2 (δ¹⁸O = −1.593 and δ¹³C = 1.969‰) and MK (δ¹⁸O = −22.608 and δ¹³C = −43.244‰). For each analysis, all car-2 and MK results in the previous 25 analyses and the next 25 analyses (51 analyses window centered around the analysis of interest) in the dataset are used to establish conversion factors to VPDB values. This window width typically corresponded to 2 to 3 days of analyses and two to four MK and car-2 analyses. For example, for analysis 100 in the dataset, the average δ_628raw and δ_636raw values for all MK and car-2 samples in the analysis range 75 to 125 are calculated. Then, a conversion function to VPDB, specific to analysis 100, is calculated on the basis of the raw δ₆₂₈ and δ₆₃₆ and established δ¹⁸O and δ¹³C VPDB values of the two standards; this is then applied to analysis 100. Expanding the window width or centering it asymmetrically (for example, previous 40 analyses and following 10 analyses) resulted in a degradation of the pooled reproducibility of δ¹⁸O and δ¹³C. Narrowing the window width resulted in some windows that had no MK or no car-2 analyses, so a VPDB conversion function could not be calculated.

An abrupt change in δ_628raw and particularly in δ_636raw values occurred after routine pump maintenance on 29 October 2021 (analysis 1595 of 1679 in the dataset). To account for this change, we used a cutoff in the moving window analysis such that windows for analyses before 1595 did not include MK or car-2 data after analysis 1595 and windows for analysis after 1595 did not include MK or car-2 data from before 1595.

Correction (2 December 2022): The previous version of Figure 1 inadvertently included a typo, with the label “TILDAS” displaying incorrectly. This has now been corrected. In addition, the red equation in Figure 6B has been corrected. This equation previously included typos and has been corrected to match Equation 12 as intended.

Supplementary Materials

This PDF file includes:

Supplementary Text

Figs. S1 to S5

Tables S1 to S4

References

Other Supplementary Material for this manuscript includes the following:

Data S1 to S4