ESS 480/580 Advanced Methods in Isotope Geochemistry
Clumped Isotope Geochemistry – ASSIGNMENT 1
The goal of this exercise is for you to work through some basic geochemical concepts,
definitions and calculations to prepare you for the readings, discussions and assignments
in the rest of the class. You are welcome to work together, but each student must
understand and submit her or his own work.
The most well developed application of clumped isotope geochemistry to date is the
carbonate clumped isotope thermometer. In contrast to conventional stable isotope
thermometry based on the temperature-dependent oxygen isotope fractionation between
carbonate and water (where the measured 18O of carbonate value is a function of both
temperature and the 18O of the water from which the carbonate precipitated), the
abundance of 13C-18O bonds in carbonate is sensitive to temperature alone. To highlight
this great advantage of carbonate clumped isotope thermometry, the examples below
mostly deal with oxygen isotopes.
Basic Definitions
The isotopic composition of O and of all other elements whose isotopes are fractionated
is expressed as the ratio R of the isotopic abundance of the heavy isotope divided by the
abundance of the light isotope:
R = _abundance of rare isotope
= H
abundance of abundant isotope
L
(Equation 1)
where H and L are simply the number of each atom in the system, the heavy (rare) and
light (common) isotopes respectively, and N is the sum of all atoms, or H + L. The
notation xR is often used, where x is the mass of the rare isotope.
Isotopes of Oxygen
16
8
17
8
18
8
O
O
O
Abundance %
99.762
0.038
0.200
Mass, amu
15.994915
16.999131
17.999160
Table 1
(1) Using Equation 1 and the abundances listed in Table 1, calculate the value for 18R in
the case of O. In other words, show your steps and calculate a numerical value. (1 point)
1
The isotope ratio of O is measured by mass spectrometry and expressed relative to
standard mean ocean water (SMOW). This value is often given in “per mil” (‰), or
tenths of a percent (5 per mil = 0.5% = 0.005). Mass spectrometers are not accurate
enough to give absolute isotope ratios, thus sample values are measured vs. standards.
The use of a standard reduces systematic errors in measurements made on different mass
spectrometers and permits R values to be expressed in terms of a parameter called delta
(), which for O is defined as:
æ RSA - RST ö
÷ ´1000‰
è RST ø
d18O = ç
(Equation 2)
where RSA = 18O/16O ratio of the sample and RST = 18O/16O ratio of the standard
(SMOW), and 18O is the difference between the R values of the sample and standard
expressed in per mil relative to the R value of the standard.
(2) Explain concisely in words what a positive 18O value signifies. A negative value?(1
point)
(3) Explain concisely in words the benefit of multiplying by 1000‰ in Equation 2. (1
point)
When a compound such as liquid water undergoes a change in state by evaporating to
form water vapor under equilibrium conditions at a constant temperature, the 18O/16O
ratio of the vapor differ from that of the remaining liquid water. This phenomenon is
evidence that isotopic fractionation takes places during evaporation of liquid water to
form water vapor.
Fractionation is defined as tiny differences in chemical and physical behavior of isotopic
molecules or compounds due to slight differences in mass: heavier molecules have lower
mobility at the same temperature as lighter molecules, therefore they also have lower
diffusion velocity and smaller collision frequency (slower reaction time). Heavier
molecules also have higher binding energies, or the energy it takes to separate molecules,
so they have lower vapor pressures (in other words, they evaporate less easily than lighter
2
molecules)—this also slows reaction times. These processes can be described by the
isotope fractionation factor:
For example,
L-V = RL
(Equation 3)
RV
Where RL is the isotope ratio of the liquid and RV is the isotope ratio of the vapor in
equilibrium with the liquid at a constant temperature. The convention is to express
fractionation factors in terms of liquid-vapor or solid-liquid ratios, which in most cases
results in  > 1, depending on temperature.
The effects of isotopic mass on isotope behavior are usually very small, so 
very close to one. Therefore, fractionation, or deviation of 
B-A = B-A -1 = RB -1
RA
(Equation 4)
The fractionation of O isotopes between water and calcium carbonate is temperature
dependent – and this forms the basis of the oldest and most widely used type of
geochemical paleothermometer, the carbonate-water thermometer (Urey, 1947; McCrea,
1950; Epstein, 1953). The temperature dependence of the fractionation factor 
describing the equilibrium oxygen isotope fractionation between marine, surface, or
ground waters and carbonate minerals that precipitate from those waters have been
determined empirically, e.g., for the mineral calcite (CaCO3):
10 lna
3
calcite
water
18.03 ´10 3
=
- 32.42
T
(Equation 5a)
which can be approximated between 273.15 and 373.15K by:
18Ocalcite = 18Owater + 32.42 + 18.030.T-1
(Equation 5b)
(Kim and O'Neil, 1997). Unlike temperature proxies based on leaf physiognomy,
alkenones, or other non-equilibrium phenomena, the carbonate-water thermometer has
the great advantage of being thermodynamically based and therefore applicable to ancient
samples deposited millions of years ago. Unfortunately, whereas carbonate minerals are
widespread and frequently well preserved in the geologic record (e.g., soil calcite,
limestone or shells deposited in oceans and lakes), ancient waters generally are not.
Unless an independent constraint can be brought to bear, this approach amounts to
solving one equation with two unknowns (T and 18Owater).
Recall that T (Kelvin) = T (°C) +273.15
Fractionation values and values of isotopic composition are typically reported relative to
the values for international standards, such as SMOW for water or CO2, or PDB (Pee Dee
Belemnite) for carbonate.
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Most investigators calibrate mass spectrometric measurements to analyses of commercial
CO2 gas, which is calibrated by analysis of carbonate standards prepared and anayzed by
the National Bureau of Standards, e.g., NBS-19 marble (18O = -2.20‰ PDB).
The 18O values of carbonate samples measured relative to PDB can be converted to the
SMOW scale by the equation:
d18OSMOW =1.03091×d18OPDB + 30.91
(Equation 6a)
d18OPDB = 0.97002 ×d18OSMOW - 29.98
(Equation 6b)
Gas-source isotope-ratio mass spectrometers measure…you guessed it, gases. So if you
want to use such an instrument to analyze the isotopic composition of a carbonate
sample, you must first digest the carbonate in phosphoric acid to produce CO2 gas,
fractionating O isotopes in the process. The raw isotopic values from the mass
spectrometer therefore represent the 18O value of CO2 (vs. SMOW), and we must
account for fractionation in order to compute the isotopic value of the original carbonate
sample.
(4) Given the 18O value of a CO2 sample measured on a mass spectrometer (vs. SMOW,
listed below), calculate the 18O value of the carbonate sample (vs. PDB). Show each
step in the calculation using R values to perform the transformations. (7 points)
Measured 18OSMOW value of CO2 = 37.8‰
The following empirical constants may be useful:
R18OSMOW = 0.0020052 (from Gonfianti et al 1993)
= 1.01015 (25°C, for 24 hour acid digestion, from Sharma et al., 2002)
a CO2
calcite
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(5) If you only had the 18O value of carbonate and Equation 5, you could not uniquely
determine both the temperature and 18O value of the water from which the carbonate
precipitated.
(a) Assume that clumped isotope thermometry gives you an independent estimate of 23°C
for the carbonate growth temperature, and use this information to calculate the 18O
value of water (vs. SMOW) in equilibrium with the calcite sample at the time of
precipitation. Try the calculation with equation 5a. Clearly show each step and report
the numerical value in ‰. (3 points)
(b) Try the calculation with the approximation in 5b. Clearly show each step and report
the numerical value in ‰. How different are the results for (a) and (b)? Note: depending
on how you do this, you can get different, wrong answers using (b)! (2 points)
(6) Graduate students only: After checking your work on paper, create a MATLAB script
or function or Excel spreadsheet that takes as input (1) the 18O value (SMOW) of CO2
derived from acid digestion of a calcite sample at 25°C and (2) the temperature of calcite
precipitation and outputs the 18O value (PDB) of calcite and the 18O value (SMOW) of
water in equilibrium with the calcite at the time the calcite mineral precipitated. EMAIL
your script or spreadsheet to [email protected]. (4 points)]
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