Standard stable isotopes, isotopologues and clumped isotopes
Standard isotopes are concerned with “bulk” isotopic composition of a sample (in our case, carbonates), and expressed as a difference (delta, or δ) between the sample and an international standard (mainly VPDB, or “Vienna Peebee Formation Belemnite” for carbonates). Both standard isotopes (δ18O, δ13C) and clumped isotopes (Δ47) are disciplines in the field of stable isotopes (i.e. isotopes that are stable and do not decay). Both methods also mainly deal with measuring isotopes of carbon (mainly 13C and 12C) and oxygen (mainly 18O, 16O, and to a lesser extent, 17O). The main difference between standard isotopes and clumped isotopes resides in what is measured.
The result is expressed in permil, or ‰, and reflects how far the 18O/16O ratio of the sample is from the 18O/16O ratio of the standard. Standard stable isotopes do not, however, tell us anything about how the various isotopes are organised within the lattice of the carbonate crystal.
The relatively new field of clumped isotopes goes one step further and is concerned with how the various isotopes of carbon and oxygen are distributed in the lattice of the carbonate crystal. In other words, clumped isotopes are concerned with distinguishing “isotopologues”, i.e. molecules of similar chemical composition but different isotopic composition. The table on the left, from Eiler (2007), illustrates the various isotopologues of N2, O2 and CO2.
Zero-point energy. Even at zero degree kelvin, molecules still have some energy linked to rotation of the molecule and vibration of the inter-atomic bond. It is this vibrational energy that is the subject of clumped isotopes, as it turns out that heavier isotopologues have a lower zero-point energy, and thus are more stable at low-temperatures.
When carbonates are reacted with othophosphoric acid, they produce a CO2 gas in isotopic equilibrium (but with a constant offset linked to acid temperature) with the original carbonate. The field of clumped isotopes is concerned with measuring an isotopologue of CO2 gas with a mass of 47, i.e. where the two “heavy” rare isotopes (13C and 18O) are substituted in the CO2 molecule. This is representative of the amount of “clumping” of the heavy isotopes in the crystal lattice of the carbonate measure.
Thermodynamics dictate that the clumping of heavy isotopes is favorable for the stability of a given molecule, i.e. the zero energy point of a molecule with heavy isotopes substituted in the molecule is lower than for a standard molecule (see Figure on the right, example with hydrogene, HD, and deuterium, Eiler 2007).
The Clumped Isotope Paleothermometer
The significance of measuring Δ47 resides in the fact that the amount of clumping at a known temperature can be determined thanks to the laws of thermodynamics alluded to in the previous section. The ordering of isotopes within a crystal structure (or preferential clumping of heavy isotopes at low temperature) will be counter-balanced by the effects of entropy: this implies that as temperature increases, clumping must decrease and eventually reach a purely stochastic distribution at high temperature (i.e. > 1000˚C).
Gosh et al. (2006) were first to demonstrate that this theoretical assumption holds through for actual carbonates by calibrating Δ47 for a range of different carbonates ranging from controlled precipitation experiments to various biological material (see figure 2, left, from Eiler et al., 2007). Initial results suggested that a single calibration line could be derived for all carbonate phases: in other words, clumped isotopes were thought free of any “vital effects” or mineral-specific fractionation effects that plague standard δ18O measurements.
Guo et al. (2009) subsequently provided a theoretical calibration for a number of different mineralogies, taking into account acid fractionation factors for any given temperatures.The initial assumption of a relatively “simple” calibration line still holds true for most of the existing carbonate species, making clumped isotopes one of the most promising paleothermometer for paleoclimate and diagenesis (see e.g., Eagle et al., 2011, Tripati et al., 2011). More recent calibrations that our lab was involved with include the Anderson et al 2020 calibration, which is a reference inter-lab calibration. However, otherwork has shown that disequilibrium exists for some specific carbonate species. For instance, speleothemes (cave deposits) display disequilibrium, i.e. their Δ47 is not reflecting cave temperatures (Affek et al., 2008, Däron et al., 2011). Furthermore, some species of deep-sea corals and mollusks have shown disequilibrium interpreted as vital effects (Thiagarajan et al., 2011, Zaarur et al., 2011). Clearly, clumped isotope research has entered an exciting new era where our understanding of the fundamental processes leading to clumping of heavy isotopes in carbonates will increase through new and improved calibration and fundamental work.
Multi-lab calibrations. Over the years, many clumped isotope calibrations were devised. Our lab contributed notably to the high-temperature calibration. We also contributed to the recent Anderson et al 2020 interlab calibration (left)
Reconstructing fluid δ18O: the flip side of the ‘clumped isotope’ coin
Traditional stable isotopes (δ18O) in carbonates have been used for decades as a paleothermometer, and/or to fingerprint geological processes. This is because δ18O in carbonates is a function of both temperature of precipitation and fluid composition (see figure on the right, where isobaric lines of equal δ18O in carbonate exist for a range of precipitation temperature and fluid composition). This dual dependency of temperature and fluid composition has plagued δ18O for decades, as to estimate one of the two parameters one needs to know the other (which is almost never the case for geological records, or very rarely the case). Clumped isotope is a gas source stable isotope application, meaning that δ18O and δ13C are measured simultaneously to Δ47 in the same sample. Because Δ47 is independent of fluid δ18O compositon and thus only reflects temperature, both the δ18O composition of the fluid can be reconstructed using clumped isotope. This is a major breakthrough as it allows the estimate of fluid oxygen isotope composition even in the absence of fluid inclusions or other independent temperature estimates. This in turns allows for unambiguous fingerprinting of processes such as diagenetic transformation and paleoenvironmental changes. Some examples of published applications making use of the ability to reconstruct fluid δ18O include reconstructing changes in strength of the Asian monsoon (Suarez, 2011), reconstructing the history of cementation (Dennis and Schrag, 2010, Huntington, 2011), and reconstruction of paleo-elevation (Ghosh et al., 2006b).
How are clumped isotopes measured?
In principle, clumped isotopes are based on measuring the difference in the abundance of the doubly substituted isotopologue of mass 47 (i.e.δ47) between a given sample and the expected stochastic distribution of the sample. The difference between the stochastic distribution and the actual distribution in a sample is what is measured for the clumped isotope paleothermometer (or Δ47, more about the principle of clumped isotopes here). However, subtle non-linearity effects in mass spectrometers arise, and a correction needs to be applied. In practice, the initial correction comes from measuring a ‘heated gas line’, i.e. a series of gases of different bulk isotopic composition (and thus different δ47) whose Δ47 values are pushed to stochastic distribution by heating the gas for 2 hours at 1000°C in a muffle furnace. The figure in the right represents the heated gas line obtained for a 2 months window at Imperial College.
The heated gas line can be considered as a primary reference frame, using the terminology of Dennis et al., 2011. When an unknown sample is measured, the difference between it’s Δ47 and that of the heated gas line is termed the Δ47[SA vs HG]. Because the heated gas is considered as stochastic, Δ47[SA vs HG] is de facto a measure of how far from stochastic the abundance of the doubly substituted isotopologue is (see Huntington et al., 2009, for in depth discussion of the heated gas line and the primary reference frame). This parameter needs to be corrected for stretching and acid fractionation (see Huntington et al., 2009, Guo et al., 2009, and Dennis et al., 2011), and can then be converted to temperature using for instance the calibration of Ghosh et al. (2006a).
Carbonate reference frame. Many labs, including ours, have moved away from a gas reference frame to a carbonate reference frame, using the standards ETH1-4.
In recent years, a second (or absolute) reference frame was proposed based on measuring a heated gas line and in addition a range of CO2 gases equilibrated with water at known temperatures (Dennis et al., 2011). This absolute reference frame, based on at least three lines (typically heated gas, i.e. stochastic, 50˚C equilibration and 25˚C equilibration) improves interlaboratory calibrations. The theoretical clumped isotope value for a simple CO2 gas equilibrated at a known temperature can be calculated using the laws of thermodynamic, and the difference between the actual result and the theoretical result forms the basis of this new absolute reference frame. Furthermore, recent advances have moved away from a purely CO2 based calibration to calibrations and reference frames based on solid standards of carbonates (Bernasconi et al, 2021).