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Clumped Isotope Geochemistry
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Clumped Isotope Geochemistry: Possibilities and Complications Kori VanDerGeest Climate Change Ind. Study Final Paper Dec. 23 rd , 2011 1
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Page 1: Clumped Isotope Geochemistry: Possibilities and Complications

Clumped Isotope Geochemistry: Possibilities and Complications

Kori VanDerGeestClimate Change Ind. Study Final Paper

Dec. 23rd, 2011

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Page 2: Clumped Isotope Geochemistry: Possibilities and Complications

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

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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

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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.

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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,

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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

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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

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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

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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

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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).

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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

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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

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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

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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

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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

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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

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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

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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

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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,

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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

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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.

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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.

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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

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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.

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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.

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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).

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