clumped isotope geochemistry: possibilities and complications
DESCRIPTION
Clumped Isotope GeochemistryTRANSCRIPT
Clumped Isotope Geochemistry: Possibilities and Complications
Kori VanDerGeestClimate Change Ind. Study Final Paper
Dec. 23rd, 2011
1
1. Introduction
The field of stable isotope geochemistry concerns itself with the variation of isotopic
composition in various sources due to different chemical, biological, and geological fractionation
processes. Many of the studies conducted within the realm of stable isotope geochemistry have
focused the concentration of isotopic species containing a single rare isotope. Single isotopes of
hydrogen, oxygen, carbon, sulfur, and nitrogen in molecules are studied most frequently because
they have low atomic masses, large relative mass differences between isotopes, and reasonably
large abundances (White 2005). Until recently, isotopes without these characteristics were
deemed inaccessible by analytical methods, as the sensitivity and precision of existing
instruments limited the detection of trace isotopic concentrations and fine differences in isotope
masses. For this reason, understanding of compounds containing one of these isotopes is
extensive and has provided the basis for a number of geochemical techniques used fields such as
paleoclimatology, paleontology, and carbon cycle science.
The fractionation of 18O and 13C isotopes is frequently used to examine a number of
global and local processes and their interdependencies, including the effects of climate on
hydrological cycles and the cycle of carbon from organic reservoirs to the atmosphere to solid
inorganic carbonate. For example, the oxygen isotope exchange equilibria between water and
carbonate minerals is often utilized as a paleothermometer, taking advantage of the spatially and
temporal widespread distribution of carbonates and their water-based formation. However, this
method depends upon the 18O isotope composition of ancient waters, which can be difficult to
ascertain with direct geochemical evidence. Additionally, carbon and oxygen isotopic
concentrations in atmospheric carbon dioxide are often analyzed to determine the sources and
sinks contributing to the observed CO2 budget. The sheer number and variability of these
2
sources and sinks, however, oftentimes overwhelms the few constraints provided by 18O and 13C
isotopes. Though myriad applications of these two isotopes have provided insight into many
geochemical systems, the study of 18O and 13C isotopes in compounds with a single isotopic
element may be coming to its limits of applicability. Additional methods of stable isotope
analysis are required in problems such as those outlined above.
In the past decade, studies of multiply-substituted isotopologues have shown increasing
promise as a widely-applicable analytical technique outside the limits of methods involving
singly-substituted molecules. An isotopologue is one of several compounds with the same
elemental composition, but different isotopic composition. For example, H2O, HDO, and D2O
are three isotopologues of water that differ in the number of hydrogen atoms and deuterium
atoms. An isotopologue is ‘singly-substituted’ when it contains only one isotope, and is called
‘multiply-substituted’ when two or more of its atoms are isotopes. Multiply-substitued
isotopologues are particularly rare isotopic species, and typically constitute tens of parts per
million within a population of molecules in most observed systems (Eiler 2007). As stated above,
previous limits of instrumental precision and sensitivity prevented the measurement and study of
these isotopologues. Only recently have advancements in analytical techniques been able to
quantify these rare species with sufficient precision, just as interest in the kinetic and
thermodynamic properties of multiply-substituted isotologues begins to grow.
Multiply-substituted isotopologues open new doors of geochemical exploration because
of the many unique properties that distinguish them from singly-substituted species. Each
multiply-substituted isotopologue is chemically unique,with distinctive bond vibration
frequencies, zero-point energies, and near-infrared absorption spectra, among other attributes.
These physical characteristics manifest themselves as unique isotopic fractionations that can
3
elucidate meaningful information about the natural processes in which they participate.
Additionally, the sheer number of different multiply-substituted isotopologues far outweighs the
number of singly-substituted isotopologues available for measurement and analytical application,
greatly expanding the field of stable isotope geochemistry.
2. Isotope Chemistry
a. Notation
A detailed discussion of isotope chemistry must be precluded by an explanation of
notation used. For notation specific to clumped isotope geochemistry, see the following section
on Analytical Approaches.
Because variation in isotopic concentrations is typically in the parts per thousand range,
values of isotopic concentration are reported as permil deviations from element-specific
standards. For example, the standard mean ocean water (SMOW) represents the standard for
oxygen isotope composition, while carbon isotope ratios are compared to the Pee Dee Belemite
carbonate (PDB) standard. Variation in isotopic concentration in this paper and in scientific
literature is referred to by its permil deviation. The formula for oxygen permil deviation is
defined as:
δ18O = 1000 × [ (18O/16O)sample - (18O/16O)SMOW ] / [ (18O/16O)SMOW
] , Eq. 1
Another useful value is an isotopologue’s fractionation factor, α, as it changes from one
phase, A, to a second, B:
αAB = RA/RB, Eq. 2
where R is the isotope ratio (18O/16O) for each of the two phases. This concept is also conveyed
as the difference between the permil deviations of the two phases, ΔAB = δA – δB.
4
b. Theory of isotopic fractionation
Isotopic fractionation in natural systems arises from the physical characteristics of
isotopic species on a quantum mechanical level. Although the electronic and nuclear attributes
of an element and its isotopes are identical, differences in mass nevertheless affect the
vibrational energy of the chemical bond formed between the isotope and a neighboring atom. In
the simple harmonic oscillator model of a chemical bond, the bond between two atoms is
modeled as a spring connected to a single mass, with the reduced mass of the two atoms, μ. One
can model the potential energy surface of a chemical bond as V, the potential energy of a spring:
V = ½ kx2 Eq. 3
where k is the force constant of the spring, and x is the displacement between the two atoms. A
fundamental concept in this simple but surprisingly accurate model is the zero point energy
(ZPE), or the energy of the bond at T = 0 K. The ZPE is defined as ½ h ν0, where h is Planck’s
constant, and ν0 is the frequency at which the bond oscillates. This fundamental frequency is
defined as
ν0 = 1
2 π ( kμ )
1/2
. Eq. 4
Through this relationship, one can see that the substitution of a light isotope for a heavier isotope
causes a lower fundamental frequency and ZPE for the bond. Bonds involving heavy isotopes
are lower in energy, and are thus stronger than bonds with lighter isotopes. Figure 1 depicts the
potential energy curve for the H2, D2, and HD molecules, where one can see that an increase in
the number of heavy isotopes decreases the energy of the molecule. Higher energy bonds
containing lighter isotopes require less energy to break, causing lighter isotopes to preferentially
enter into chemical reactions, while low energy bonds with heavy isotopes are harder to break,
5
making heavy isotopes less likely to participate in chemical reactions. This difference in ZPE is
responsible for thermodynamic equilibrium fractionation observed in isotopic compounds.
Figure 1. The potential energy curve for molecular hydrogen, highlighting the isotope-substitution effect on ZPEs. The bold curve represents the Morse potential curve (a more accurate model of chemical bonding based on the
anharmonic oscillator), while the lighter curve represents the simple harmonic oscillator model. Adapted from Criss (1999).
c. Temperature Dependence of Isotope Fractionation
Urey (1947) and Bigeleisen and Mayer (1947) first pioneered the study of stable isotope
geochemistry and made the pivotal observation that equilibrium constants of isotope exchange
reactions could be calculated from the partition function, q, of statistical mechanics, and by
extension the temperature of the reaction could be calculated from the fractionation factor. Urey
simplified the equations defining the partition functions for gaseous diatomic and polyatomic
molecules and their isotopomers, which are isotopologues will the same composition of isotopes,
but in symmetrically non-equivalent locations. He demonstrated that the simplified ratio of
6
partition functions for the pair of isotomers was dependent upon the inverse of the temperature,
in addition to the rotational state, the ZPE, and the vibrational energy spacings of the molecule.
The equilibrium constant can be defined both in terms of the partition functions of the
reactants and products involved in an isotopic exchange reaction (via statistical mechanics), and
the fractionation factor, as seen below:
K = q A
a qBb
qCc qD
d Eq. 5
where A and B are the products, and C and D are the reactants of an isotope exchange reaction.
a, b, c, and d are constants specific to the product or reactant (White 2005). Also,
αAB = (K/K∞)1/n Eq. 6
where K is the equilibrium constant, K∞ is the equilibrium constant at infinite temperature and n
is the number of isotopes exchanged (White 2005). With these relationships and the simplified
partition functions defined by Urey, the temperature dependence of isotope fractionation can be
ascertained. At low temperatures, ln K and ln α both vary linearly with 1/T, while at high
temperatures, these two functions vary linearly with 1/T2 (Criss 1999). As T approaches infinity,
α approaches 1, a state where the isotopic ratio of the reactants and products in the exchange
reaction are equal (Criss 199).
Though these theoretical dependencies provide insight into the chemical basis underlying
observed isotopic fractionation, they only apply to those fractionation processes at chemical
equilibrium. The deposition of calcareous shells by marine organisms often occurs in
equilibrium with the surrounding seawater, and atmospheric water varpor is oftentimes assumed
7
to be at isotopic equilibrium with the ocean water. However, processes associated to biological
systems, such as calcareous growth of algae, corals and benthic forams use chemical
disequilibrium to take advantage of kinetically controlled metabolic fractionations (Criss 1999).
d. Rule of Geometric Mean
The rule of geometric mean is another useful law governing isotope distribution, but it is
its failure to accurately describe multiply-substituted isotopes that has created the field of
clumped isotope geochemistry. According to Bigeleisen (1955), this rule states that in systems
where isotopic substitution can occur in multiple locations, the mixing of two isotopologues of
the same compound is not associated to a change in enthalpy: each substitution is
thermodynamically independent of the other. Following this rule, the change in bond energy
from an H–H bond to a doubly-substituted D–D bond will be twice the energy required to form a
singly-substituted H–D bond. This suggests that there is no energetic advantage to group heavy
isotopes together in one bond as opposed to placing them in bonds with lighter isotopes. In the
system of molecular hydrogen, the rule of geometric mean implies that the formation of H2 and
D2 is equivalent to the formation of two HC molecules.
Like many chemical theories, this rule is only an approximation for isotopically-
substituted molecules at the high temperature limit (Urey, 1947, Bigeleisen, 1955); at
temperatures relevant to Earth’s natural systems, a change in enthalpy is observed upon the
mixing of two isotopologues of the same compound. An examination of the symmetry of
isotopologues easily demonstrates the reason for this departure. For example, in the linear
molecule, N–N–O, the two nitrogen sites are clearly distinct, with the central N bound to both O
and N, while the terminal N is bound only to the second N. Structural differences due to
molecular asymmetry lead to the preferential partitioning of heavy isotopes into bonds formed
8
with other heavy isotopes, a phenomenon called the ‘clumping’ of heavy isotopes into multiply-
substituted isotopologues instead of singly-substituted isotopologues. The occurrence of
clumping of heavy isotopes varies kinetically and thermodynamically from one isotope to the
next, which manifests itself as isotopic fractionations during the conversion of one isotopic phase
to the next. Clumped isotope geochemistry uses these new and unexplored fractionation
processes to understand natural and theoretical geochemical processes.
3. Analytical Approaches
a. Instrument Requirements
Due to the low abundances of multiply-substituted isotopologues in naturally-occurring
systems, any type of analytical method used to quantify these rare species must meet a number of
basic demands. These requirements include: high sensitivity needed to detect trace abundances,
fine mass resolving power or high sample purity due to the large number of potential
interferences, high precision (10-5 are required as isotope signals are often less than 10-3), and
preservation of the origin bonds without re-distribution of the isotopes between different
compounds. Though this method makes a number of strict demands on its instrumentation,
gradual advances in mass spectroscopy have pushed this method from the realm of possibility to
reality.
Although not perfect, gas source isotope ratio mass spectrometry (IRMS) has proven to
be a functional and advantageous analytical approach to clumped isotope geochemistry. Gas
source IRMS is the principle instrument used to the ratio of light isotopes such as H/D, 13C/12C,
15N/14N, and 18O/16O, and is well known for its high precision – the precision is often limited by
the reproducibility of sample preparation rather than detector limitations. Three main
components constitute the gas source IRMS: 1) the source of positively-charged ions or
9
molecular ions, 2) a magnetic analyzer that alters the path of ions according to their mass-to-
charge ratio, and 3) a series of ion collectors that measure the abundance of each atom or
molecule with a particular mass-to-charge ratio. The sample and reference gases are injected
into a low pressure chamber where an electron beam from a heated filament or a strong
electrostatic field ionizes the gases, after which the ions are focused into a beam and passed
through a curved flight tube. Within the flight tube, a strong magnetic field separates the ions,
causing the lighter ions to turn with a tighter radius, as can be seen in Figure 2. The ions are
then collected in ion detectors designed to measure the current produced by ions with a particular
mass-to-charge ratio. The amount of current observed is directly proportional to the abundance
of isotopic species measured (Dunn 2009).
Figure 2. A schematic of a typical gas source isotope ratio mass spectrometer. Adapted from Dunn (2009).
10
Gas source IRMS is well-suited for isotopic analysis of multiply-substituted
isotopologues because 1) highly-sensitive ion detectors called multiple-Faraday collection arrays
can achieve a precision around 10-5 to 10-6 (Eiler 2007), sufficient to observe many rare
isotopologues, and 2) its required analyte is a molecular ion, which generally retains an
isotopologue’s isotopic identity throughout the course of sample preparation and analysis.
Several drawbacks of this analytical method include 1) instrumental noise levels attributed to the
detectors often prevent the measurement of very low-abundance species, 2) gas analytes are
required at room temperature, 3) the mass resolving power of IRMS is not strong enough to
resolve the distinct signals of isotopologues with the same mass, and 4) fragmentation and
recombination of analytes may lead to the re-distribution of isotopes in the system, destroying
the integrity of the original isotopic bonds (Eiler 2007).
Other analytical drawbacks include the large sample amounts and long counting times
required to retrieve meaningful data with analytes at such low concentrations, as well as the
significant contribution of volatile impurities such as organic compounds, organic halides and
sulfides to the mass spectroscopic data. These impurities can undergo fragmentation and
recombination to form observed isotopic ratios poorly representing the actual isotopic ratios
sought. Robust purification techniques often involving gas chromatography, crygogenic
separations, and exposure to reactive compounds designed to remove specific contaminants
(Eiler 2007).
Although few analytical methods provide the same number of desirous characteristics as
gas source IRMS, the robust growth of clumped isotope geochemistry requires the development
of alternative methods. Currently, only two instruments, a pair of modified Thermo-Finnegan
253 located at the California Institute of Technology, have produced published results using this
11
analytical method (Eiler and Schauble, 2004; Wang et al., 2004; Affek et al., 2006, 2007, 2009;
Guo and Eiler, 2005; Affek and Eiler, 2006; Ghosh et al., 2006, 2007; Came et al., 2007; Eagle
et al. 20010), necessitating the development of other instruments at other institutions. Thermal
ionization and secondary ion mass spectrometry hold high potential as alternative methods for
clumped isotope geochemistry, because they would enable the study of solid materials. However
both methods increase the likelihood of isotopic redistribution under high temperature situations.
Near-infrared absorption spectroscopy is also a promising alternative, as its high sensitivity
would not only be able to distinguish between isotopologues with the same cardinal masses (such
as 14N15N16O, and 15N14N16O), but it may also detect triply-substituted isotopologues. However,
the low precision of near-IR absorption methods currently limits its application to clumped
isotope geochemistry.
b. Definition of Δi
Data retrieved from gas source mass spectrometers currently used during clumped
isotope analyses are ultimately attained to calculate values of Δi, the excess or deficit of
isotopologue i relative to the amount expected if the isotopes were randomly distributed among
the different isotopologues. As of yet, the primary multiply-substituted isotopologues studied in
the literature have been the 47 amu isotopologues, including 13C18O16O, 12C18O17O, and 13C17O17O
(Eiler and Schauble, 2004; Wang et al., 2004; Affek et al., 2006, 2007, 2009; Guo and Eiler,
2005; Affek and Eiler, 2006; Ghosh et al., 2006, 2007; Came et al., 2007; Eagle et al. 20010).
The value of Δ47 for these species is calculated as follows:
Δ47 = [( R47
R¿47 −1)−( R46
R¿46−1)−( R45
R¿45 −1)]× 1000 Eq. 7
= δ47 – δ46 – δ45 Eq. 8
12
where R47is the observed isotopic ratio for the sample, R¿47is the isotopic ratio expected from a
stochastic distribution of isotopes among all isotopologues, and δi is the permil deviation for the
ith cardinal mass (Eiler and Schuable 2004). The term ‘stochastic distribution’ refers to a
reference sample of CO2 that has been raised to an approximate temperature of 1000oC (Affek
2007), where differences in thermodynamic stability between isotopologues no longer control the
ordering of stable C and O isotopes in chemical bonds. Instead, the C and O isotopes are
distributed randomly among the isotopologues, yielding an R¿i value that can be directly
calculated from the bulk isotopic abundances of the carbon and oxygen isotopes. For example,
R¿47is calculated as follows:
R¿47=
2 ∙ [18 ] ∙ [16 ] ∙ [13 ]+ [17 ]2 ∙ [13 ]+2 ∙ [18 ] ∙ [17 ] ∙ [12 ][16 ]2 ∙ [12 ]
Eq. 9
where [12] and [13] are the concentrations of 12C and 13C in a population of carbon atoms, while
[16], [17], and [18] are the concentrations of 16O, 17O, and 18O in a population of oxygen atoms.
These reaction conditions approximate the situation where the fractionation factor, α, approaches
1 as temperature approaches infinity.
Because the abundances of 12C18O17O and 13C17O17O are much lower than 13C18O16O, the
Δ47 value primarily yields information on the bonding of 13C and 18O isotopes (Eiler and
Schauble, 2004). Δ47 does not measure the abundance of the 13C or 18O isotopes in a sample, but
instead gives a measure of the fraction of isotopologues containing 13C and 18O that deviate from
the stochastic mean; it measures the number of bonds formed between 13C and 18O isotopes due
to a lowering of bond energy, an exception to the rule of geometric mean. Therefore, although
the value of Δi will vary according to the source examined and the fractionation processes acting
13
on that source, Δi is not dependent upon the bulk composition of the isotopes that constitue the
isotopologues examined.
4. Applications
a. Fractionation Systems
The processes that cause fractionation in bulk measurements of single isotopes such as
18O and 13C can also cause fractionation in multiply-substituted isotopologues, as multiply-
substituted compounds are found in the same systems that contain singly-substituted compounds,
just at lower abundances. One must keep in mind, however, that only those fractionation
processes that cause a deviation in isotopologue composition from the stochastic mean can be
used to observe clumped isotopic behavior. Many processes, including thermally-controlled
fractionation, vapor pressure isotope effects, diffusion, kinetic fractionations, mixing, and
gravitational gradients are predicted to produce observable deviations from the stochastic mean,
and thus represent potential subjects of study with the new perspective of clumped isotope
geochemistry.
Thermodynamically-controlled fractionation is directly dependent upon temperature, as
touched upon in the previous section, and its characteristics only hold true in homogenous
isotope exchange systems (where the reactants and products are both of the same physical phase)
that have reached equilibrium. When this condition has been met, one can assume several
characteristics of isotopic behavior: 1) heavy atoms adjacent to one another cause large Δi values,
as the isotopes are less randomly distributed, 2) increasing strength of bonds containing isotopes
also increases Δi values, and lastly 3) nearby bonds, such as the ionic bond between carbonate
ions to a cation in calcite and dolomite have little effect on Δi values (Eiler, 2007, Eagle, 2010).
The process of evaporation and condensation cause a distinct isotopic fractionation between the
14
vapor and condensed phases of compounds in Earth’s hydro-geological system. This is a
thermodynamically-controlled fractionation process that follows the typical constraints of
equilibrium fractionations summarized above and in previous sections.
Because diffusion across a space or over a membrane is mass-dependent, diffusion
processes involved in biochemistry and other natural and anthropogenic systems will lead to
isotope fractionations with an observable deviation from the stochastic mean. Kinetically-
controlled fractionations arise from the difference in energy required to break bonds between
heavy isotopes and those between lighter isotopes. Though the formation of isotopologues with
‘clumped’ heavy isotopes is thermodynamically favorable, in situations where thermodynamic
equilibrium has not been achieved, the formation of bonds between lighter isotopes is preferred,
as bonds with light isotopes have smaller bond dissociation energies and are thus more likely to
participate in chemical reactions. Many biological processes, such as photosynthesis, work
under non-equilibrium states, causing isotopic fractionation that has been studied extensively in
the context of bulk isotope composition, but has thus far been unexplored in terms of multiply-
substituted isotopologues. Also, though the zero point energies of isotopologues of several
relevant molecules have long been calculated (Urey, 1947, Bigeleisen and Mayer, 1947), no one
has yet taken those values to predict relative rates of reaction for different isotopologues (Eiler,
2007).
More frequently than not, when considering the bulk compositions of isotopes in large
bodies of air, one cannot determine whether the observed composition is the original
composition of the air sampled, or an amalgamation of air from different sources. Though the
abundances of isotopes such as 13C and 18O give a distinct signature to sources such as
combustion products of fossil fuels and ocean-based water vapor, these two analytical methods
15
cannot distinguish between the many sources and sinks that contribute to the composition of air.
With its increased sensitivity for detecting enriched or anthropogenic components, clumped
isotope geochemistry can provide additional constrains to analyses of air mixtures (Eiler and
Schauble, 2004, Affek 2006, Affek 2007).
Lastly, gravitational potential and thermal diffusion should also cause isotopic
fractionation of multiply-substituted isotope compositions. In a static gas column, gravitational
and thermal gradients can induce an isotopic gradient, with heavier isotopologues lower in the
column in the presence of a gravitational field or in the colder region of the column.
Measurements of fractionations of Δ15N2 across thermal gradients have been made, but without
sufficient precision to make meaningful predictions of Δ15N2 fractionations (Grachev and
Severinghaus, 2003). Theoretical calculations of fractionations in thermal gradients performed
in the same study suggest that Δ15N2 are small but measurable; they are also distinct from
gravitational fractionations, which suggests that clumped isotope measurements may be able to
distinguish the effects of both (Grachev and Severinghaus, 2003).
b. Carbonate Paleothermometry
Though the number of possible applications for clumped isotope geochemistry is
expansive, the number of researchers utilizing this method is small, and thus the extent of its
demonstrated use is quite limited. The field of carbonate paleothermometry has had more robust
research activity than any other potential field, due to the enormous contributions provided by
the clumped isotope analytical method.
Before the development of clumped isotope geochemistry and even now, the standard
method of carbonate paleothermometry involves the measurement of oxygen isotope exchange
16
equilibria between carbonate minerals and the water from which they form. The oxygen isotope
composition found in preserved carbonate minerals reflects the oxygen composition of the
meteoric water (water collected from precipitation) from which it formed, in a temperature-
controlled fractionation process. The δ18O of meteoric water is fundamentally controlled by the
isotopic composition of oxygen in evaporated ocean water. In an example of the vapor pressure
isotope effect, 18O preferentially precipitates out of water vapor in a temperature-dependent
fractionation process, which produces meteoric water that is heavier than the water vapor left
behind. If one can reasonably constrain the oxygen isotope composition of meteoric water, a
measurement of δ18O in a carbonate sample can yield the temperature of carbonate formation
using the following relationship described by Friedman and O’Neill (1977):
1000 ln αcalcite-water = ( 2.78×106
T2 ) – 2.89 Eq. 10
where T is the temperature in Kelvin and α is the fractionation factor for oxygen between
carbonate and water (see Section 2a for details). Paleotemperature curves constructed from this
relationship work within a specified range of temperatures, and are only applicable when the
δ18O value of the surrounding water is known and when one can assure that the carbonate
mineral examined has not been subject to post-depositional alteration. Such alterations may
cause oxygen isotopes to re-equilibrate at temperatures different from the one that determined
the original carbonate formation.
A number of approaches have been developed to circumvent these challenges, including
the modeling of δ18O in ancient oceans through indirect sources, such as oxygen isotope
compositions in benthic foraminifera (Shackleton, 1967), or reconstructions of sea-level changes
and glacial ice volumes (Dansgaard and Tauber, 1969). However, these methods only apply to
17
the Pleistocene marine records, and cannot be used for the large remaining portion of the
geogical record. Other methods are similarly limited to specific time periods, temperature ranges,
and geological systems (Ghosh, 2006). A new paleothermometer based upon the ‘clumping’ of
13C and 18O in carbonate bonds circumvents the difficulties encountered by typical methods
because the likelihood of 13C and 18O ‘clumpling’ is independent of the bulk composition of
oxygen isotopes in ancient waters and of carbon isotopes in dissolved inorganic carbonate.
Additionally clumped isotope thermometry may provide a method of rigorously constraining the
δ18O of ancient waters, using the well-constrained temperature values calculated from Δ47 values
and the relationship of δ18O and α to temperature described in Eq. 2 and 10. Though clumped
isotope geochemistry offers many advantages to the field of paleothermometry, like other
thermometric methods, it is only reliable when one can ensure that the isotopic composition of
the sample has not be altered during high-temperature post-depositional stress.
The focus of carbonate clumped isotope thermometry lies in the homogeneous
equilibrium defined by the isotope exchange reaction listed below:
M12C18O16O2 + M13C16O3 ⟷ M13C18O16O3 + M12C16O3 Reaction 1
where M is a metal such as Ca or Mg (Eiler, 2007). By measuring the deviation of δ47 in the
sample of carbonate from the δ47 value predicted from stochastic distribution, one can determine
the temperature at which the isotope exchange reaction occurred. However, as the only
instrumental method available for the measurement of multiply-substituted isotopologues is gas
source IRMS, the isotopic ratios of solid carbonates cannot be measured directly. Instead, the
carbonates must be converted to CO2 gas via phosphoric acid digestion. The exchange reaction
of CO2 isotopologues shown below must be then be examined in addition to Reaction 1:
12C18O16O + 16O 13C16O ⟷ 13C18O16O + 16O 12C16O. Reaction 2
18
By determining the Δ47 value for Reaction 2, one can back-calculate and determine the Δ47 value
for reaction 1, and finally approximate the temperature of carbonate formation.
A number of published studies have utilized the principles of clumped isotopes in
carbonate paleothermometry, thus establishing a standard process for sample preparation and
data analysis (Ghosh, et al., 2006). The phosphoric acid digest is a major procedural step that
converts carbonate minerals to bicarbonate to carbon dioxide for subsequent analysis via gas
source IRMS. Ghosh et al. observed consistent fractionation during the phosphoric acid
digestion that significantly altered the calculated values of carbonate Δ47, but could not provide a
well-supported explanation for the fractionation (2006). Though not well-understood,
preliminary studies have suggested that the phosphoric acid fractionation can be attributed to a
kinetic isotope effect during the degassing of H2CO3 to CO2 (Eiler, 2007). Though further
investigations are required to elucidate the processes responsible for phosphoric acid
fractionation, they are not necessary for the continued use of clumped isotope thermometry.
As a new technique, calibrations on a variety of geological carbonate sources are
currently being conducted, while material-specific effects and the optimum values of precision
are still being explored. Over the course of the past decade, a number of carbonate minerals have
been calibrated, finding each material’s relationship between Δ47 to temperature; these minerals
include synthetic and natural inorganic calcite (Ghosh et al., 2006, Ghosh, et al., 2007, Came, et
al., 2007, Eagle, et al., 2010, Eagle, et al., 2011, Eiler and Schauble, 2004), aragonitic corals and
otoliths (Ghosh et al., 2006, 2007), aragonitic mollusks and calcitic brachiopods (Came et al.,
2007), as well as fluorapatite and hydroxyapatite in animal teeth (Eagle, et al. 2010). Most
conventional stable isotope thermometric systems must address material-specific complexities,
19
such as vital effects, which are kinetically-controlled metabolic fractionations induced by
organisms that use disequilibrium effects to maximize growth.
Figure 3. The temperature dependence of Δ47 from CO2 produced by acid digestion of carbonate minerals. Data from various carbonate sources fit closely to the solid line produced for the calibration of inorganic calcite (Ghosh et
al., 2006). See text for further details. Adapted from Eiler (2007).
However, continued studies (Ghosh, et al., 2006, Ghosh, et al., 2007, Came et al., 2007, Eagle, et
al. 2010) report unexpected uniformity across calibration curves for different materials,
suggesting that vital effects and other material-specific complications have insignificant effects
on the accurate determination of carbonate formation temperatures. In their determination of
earth-surface temperatures during the Paleozoic era, Came et al. (2007) reported the best external
precisions achieved for the determination of Δ47 in carbon dioxide, which corresponded to an
uncertainty in temperature of ca. ± 1oC at earth-surface temperatures. They found that this
uncertainty increases with increasing temperature.
c. Determination of Ancient Body Temperatures
20
Recently, the application of clumped isotope paleothermometry to the determination of
body temperatures of extinct species has garnered much excitement within and outside of the
scientific community. Biologically precipitated apatite, a carbonate mineral, found in bone, teeth,
and scales has previously been used to better understand the diet, physiology, and behavior of
extinct organisms, or to reconstruct the climate of the past. δ18O values observed in apatite can
be used to determine the temperature at which the mineral was precipitated within the organism,
but, like other applications of δ18O thermometry, this method depends upon the oxygen isotope
concentration in the water within the organism. Only the most robust assumptions of diet,
animal physiology, humidity, and nearby meteoric water can provide significant constraints upon
the δ18O values needed to confidently estimate an organism’s body temperature (Eagle, et al.,
2010). Because clumped isotope thermometry is independent of the oxygen isotope
concentration in nearby water sources, Eagle et al. (2010) employed clumped isotope
thermometry in the determination of extinct organisms’ body temperature.
To determine the accuracy of clumped isotope thermometry with biologically-
precipitated apatite, Eagle et al first measured the Δ47 in the teeth of modern day rhinocerous and
elephant species. Assuming that typical mammalian body temperatures average around 37oC,
Eagle et al. predicted that the apatite samples would yield a Δ47 value of 0.596 ‰, as calculated
from the calibration curve for inorganic calcite constructed by Ghosh et al. (2006). With Δ47
values of .596 ± 0.008 ‰ and 0.597 ± 0.006‰ (1σ) for rhinocerous and elephant teeth,
respectively, Eagle et al. proposed that the calibration curves for carbonate minerals did not vary
significantly from one type of carbonate to the next, and determined that the clumped isotope
thermometer provided high-accuracy estimates of an organism’s body temperature.
21
Eagle et al. (2010) then moved to measure the body temperatures of several extinct
species, including a woolly mammoth from the late Pleistocene, as well as a Miocene
rhinocerotid and alligator species. Though the dentin, or outer portion, of the teeth examined
were found to be altered by diagenesis, the enamel of the teeth samples produced temperatures
for all three species that closely resembled (within one standard deviation) the estimated
temperature of their modern-day counterparts. Following the publication of their paper in 2010,
Eagle et al. (2011) published a second paper, describing an application of this technique to large
Jurassic sauropods, whose physiology and thermal regulation is currently under debate. They
determined the body temperature of these large dinosaurs to be 4 to 7oC lower than predicted,
indicating that sauropods have specialized thermal regulation systems to prevent overheating, a
common challenge in large-bodied animals (Eagle, et al. 2011).
5. Future Work: Possibilities and Challenges
The possibilities of clumped isotope geochemistry are predicted to be significant and
spread across numerous fields within geochemistry, but as of yet, these possibilities are
unexplored and a number of challenges still exist. Clumped isotope geochemistry has provided
many advantages to carbonate thermometry, expanding the portion of the geological record that
can be analyzed using paleothermometry. Because it is independence of bulk isotope
composition of the water from which the carbonate sample grew, clumped isotope
paleothermometry is suitable for application to and interpolation of past times and diverse
settings. Additionally, clumped isotope techniques can provide rigorous constraints on the
original values of δ18O and δ13C in a carbonate sample should they be undetermined due to post-
depositional isotopic alteration or other geological complications.
22
Outside of paleothermometry, the principles of clumped isotope geochemistry hold
particular promise as applications to the budgeting of CO2 and other atmospheric gases, as well
as eludiction of mechanisms of isotopic fractionation in natural systems. 18O and 13C isotopes are
typically used to identify and characterize the different sources and sinks that contribute to the
CO2 composition in urban air masses, but the sheer number of potential CO2 sources and sinks
renders these methods insufficient; clumped isotope analyses can provide additional constraints
to these systems, distinguishing each source and sink with signature Δi values for CO2 and other
multiply-substituted isotopes. Currently, a variety of methods within biochemistry and physical
chemistry have provided a thorough understanding isotopic substitution in artificially enriched
materials, but the knowledge of the physical, biological, and chemical behavior of isotopically
enriched processes has yet to be applied to isotopic fractionation in natural systems. Clumped
isotope geochemistry may serve as a useful tool in proposed methods of mechanism elucidation,
such as the study of vital effects to obtain information on the fractionation between seawater and
animal body water (Adkins et al., 2003).
Clumped isotope geochemistry, being a relatively new technique, faces a number of
challenges that must be met before it can fulfill the number of exciting promises it has made. An
obvious preclusion to the development and diversification of this method is the growth of the
number of practitioners of clumped isotope geochemistry. Currently, only two mass
spectrometers located at the California Institute of Technology have the technical capabilities to
measure rare multiply-substituted isotopes, severely limiting the number and breadth of studies
utilizing this technique. At this stage in the development of clumped isotope geochemistry,
technical innovation of sample preparation and analytical instrumentation would make this
method simpler, more reliable, and less time consuming. For example, automation of sample
23
preparation would expedite the analytical process, and the development of clumped isotope
instruments with higher resolution and better sensitivity would improve contaminant detection
and augment the pool of rare isotopologues able to be studied. In particular, a high-precision
near-infrared absorption spectrometer could be designed to detect multiply-substituted
isotopologues and distinguish between species of the same cardinal mass, a development that
would greatly expand the scope of clumped isotope geochemistry. Instruments and extraction
techniques should also be developed to enable the analysis of solid carbonate as well as gases
such as SO2 and other compounds out gassed in geological minerals. Finally, the knowledge
base of equilibrium fractionations, the fractionation of simple physical processes, such as
diffusion, and kinetic isotope effects on unidirectional biochemical reactions need to be
expanded even if one were limited the scope of research to analytes that have been reliably
measured in the past (Eiler, 2007). Inspite of these challenges, the future holds immense
possibility for clumped isotope geochemistry and the fields soon to take advantage of its
potential.
6. References
Adkins, J.F., Boyle, E.A., Curry, W.B., Lutringer, A., 2003. Stable isotopes in deep-sea corals and a new mechanism for “vital effects”. Geochim. Cosmochim. Acta 67 (6), 1129–1143.
Affek H. P., and Eiler J. M., 2006. Abundance of mass 47 CO2 in urban air, car exhaust, and human breath. Geochimica et Cosmochimica Acta 70, 1–12.
Affek H. P., Xu X. and Eiler J. M., 2007. Seasonal and diurnal variations of 13C18O16O in air: Initial observations from Pasadena, CA. Geochim. Cosmochim. Acta 71 (21), 5033–5043.
Bigeleisen, J., 1955. Statistical mechanics of isotopic systems with small quantum corrections .1. General considerations and the rule of the geometric mean. J. Chem. Phys. 23 (12), 2264–2267.
Bigeleisen, J., Mayer, M.G., 1947. Calculation of equilibrium constants for isotopic exchange reactions. J. Phys. Chem. 13, 261–267.
24
Came RE, et al., 2007. Coupling of surface temperatures and atmospheric CO2 concentrations during the Palaeozoic era. Nature 449(7159):198–201.
Criss, R. E., 1999. Principles of Stable Isotope Distribution. Oxford University Press, New York, 59-76.
Dansgaard, W., Tauber, H., 1969. Glacier oxygen-18 content and Pleistocene ocean temperatures. Science 166, 499.
Dunn, S., 2009. “Gas Source Mass Spectrometry: Stable Isotope Geochemistry.” Geochemical Instrumentation and Analysis. http://serc.carleton.edu/research_education/geochemsheets/techniques/gassourcemassspec.html (accessed Dec 20, 2011).
Eagle, R. A., Schauble E. A., Tripati A. K., Tutken T., Hulbert R. C. and Eiler J. M., 2010. Body temperatures of modern and extinct vertebrates from 13C–18O bond abundances in bioapatite. Proc. Natl. Acad. Sci. USA 107, 10377–10382.
Eagle, R. A., Tütken, T., Martin, T. S., Tripati, A. K., Fricke, H. C., Connely, M., Cifelli, R. L., Eiler, J. M., 2011. Dinosaur Body Temperatures Determined from Isotopic (13C-18O) Ordering in Fossil Biominerals. Science 333, 443.
Eiler, J. M., 2007. ‘Clumped-isotope’ geochemistry—The study of naturally-occurring, multiply-substituted isotopologues. Earth Planet. Sci. Lett. 262, 309-327.
Eiler J. M., and Schauble E., 2004. 18O13C16O in Earth’s atmosphere. Geochim. Cosmochim. Acta. 68 (23), 4767–4777.
Friedman I. and O’Neil J. R., 1977. Compilation of Stable Isotope Fractionation Factors of Geochemical Interest. U. S. Geological Survey Professional Paper. 440-KK.
Ghosh, P., Adkins, J., Affek, H., Balta, B., Guo, W.F., Schauble, E.A., Schrag, D., Eiler, J.M., 2006. 13C–18O bonds in carbonate minerals: a new kind of paleothermometer. Geochim. Cosmochim. Acta 70 (6), 1439–1456.
Ghosh, P., Eiler, J., Campana, S.E., Feeney, R.F., 2007. Calibration of the carbonate ‘clumped isotope’ paleothermometer for otoliths. Geochim. Cosmochim. Acta 71, 2736–2744.
Grachev, A.M., and Severinghaus, J.P., 2003. Laboratory determination of thermal diffusion constants for 29N2/28N2 in air at temperatures from −60 to 0 °C for reconstruction of magnitudes of abrupt climate changes using the ice core fossil-air paleothermometer. Geochim. Cosmochim. Acta 67 (3), 345–360.
Shackleton, N.J., 1967. Oxygen isotope analyses and Pleistocene temperatures re-assessed. Nature 215, 5096.
Urey, H.C., 1947. The thermodynamic properties of isotopic substances. J. Chem. Soc. 562–581.
25
White, W. M., 2005. “Stable Isotope Theory: Equilibrium Fractionations.” EAS 656 Lecture Notes. http://www.geo.cornell.edu/geology/classes/Geo656/656notes05/656_05Lecture27.pdf (accessed Dec 20, 2011).
26