1. Stable Isotopes – Physical Fundamentals 9/27/12
Lecture outline:
principles of stable isotope fractionation
equilibrium fractionation
kinetic fractionation
mass-independent fractionation
spectrometer light
intake
Annual layers in a tropical ice cap

2. Introduction to Stable Isotope Geochemistry
Stable Isotope geochemistry is concerned with variations of the isotopic compositions
of elements arising from physicochemical processes (vs. nuclear processes).
fractionation refers to the change in an isotope ratio that arises as a result of a
chemical or physical process.
Occurs during:
- isotopic exchange reactions in which the isotope are
redistributed among different molecules containing that element
- unidirectional or incomplete reactions
- physical processes like evaporation/condensation,
melting/crystallization, adsorption/desorption, diffusion
Characteristics of a useful stable isotope system:
large relative mass difference between stable isotopes (Δm/m)
abundance of “rare” isotope is high (0.1-1%)
element forms variety of compounds in natural system
Examples: 2H/1H, 7Li/6Li, 11B/10B, 13C/12C, 15N/14N, 18O/16O, 26Mg/24Mg,
30Si/28Si, 34S/32S, 37Cl/36Cl, 40Ar/36Ar, 44Ca/40Ca, 56Fe/54Fe
- note convention of putting the heavy isotope above the light isotope

3. Notation We can define a fractionation factor (α):
Where RA, RB are the isotope ratios in two phases
(ex. carbonate and water, or water vapor and water, etc)
NOTE: α is close to 1 because ratios differ by parts per thousand
α approaches 1 as temperature increases
We define a measurement reporting convention (d or “delta” units):
Note that ‘deltas’ are
named after the heavy isotope
So each isotopic measurement is
reported relative to a standard

4. Equilibrium fractionation
Fractionation types
There are three types of isotope fractionation:
equilibrium fractionation
kinetic fractionation
mass-independent fractionation (far less important)
Equilibrium fractionation
- arises from the translational, rotational, and vibrational motions of
1. molecules in gases and liquids
2. atoms in crystal lattices
energy of these motions is mass-dependent
systems will move to the lowest energy configuration
usually largest in covalent bonds, minimal in ionic bonds
Ex:
most imp.
From William White’s (Cornell)
upcoming Geochemistry
textbook
at 25°C, so 18O/16O is larger in CO2
than in H2O at equilibrium

5. Equilibrium fractionation (cont)
So why does equilibrium fractionation occur?
a molecule with a heavy isotope sits
at a lower zero point energy level
than the same molecule with all light
isotopes
bonds with high potential energies
are broken more readily
bond strengths vary for light and heavy
isotopes of an element
What about temperature?
the difference in zero point energies
for light vs. heavy molecules decreases
with increasing T
- bond strengths converge at high T,
fractionation factor goes to 1 at high T
Effect of vibrational E in harmonic oscilllator model
Which bond is broken
most easily?
zero point energy

6. Temperature-dependence of equilibrium fractionation
From these plots we can see that:
α varies inversely with T
the harmonic oscillator model
approximation holds up well:
data
harmonic oscilllator model
for T<200C
for T>200C
harmonic oscilllator model
data
So at colder temperatures,
isotopes will be more heavily
fractionated.

7. Composition-dependence of equilibrium fractionation
IMPORTANT rule of thumb: the heavy isotope will be concentrated in the phase in which
it is most strongly bound (or lowest energy state). Solid>liquid>water, covalent>ionic, etc.
Ex: 18O in carbonates
- heavily enriched in carbonate because O tightly bonded to small,
highly charged C4+, vs. weaker H+
- so Δ18Ocal-water = δ18Ocarb-δ18Owater = 30‰
Ex: quartz (SiO2) most enriched mineral
Lattice configuration (aragonite vs. calcite) plays a secondary role (Δ18Oarag-cal=0.5‰)
Chemical substitutions in the lattice (ie. Ba instead of Ca) also have a small effect:
Δ18OBa-cal-water = 25‰ (vs. 30‰ for Ca-cal)

8. Kinetic fractionation
- arises from fast, unidirectional, incomplete reactions (many biologically-mediated rxns)
Velocities of gas molecules are different
- kinetic energies of molecules of ideal gas are equal
- so differences in mass (heavy vs. light isotopes) must be compensated for by velocity
Consider two molecules of CO2: 12C16O2 (mass = *16 = 44)
and 13C16O2 (mass = *16 = 45)
if their energies are the same, then:
and the ratio of their velocities is:
assuming
ideal gas
SO… 12C16O2 can diffuse 1.1% further than 13C16O2 in a given amount of time
This can be observed as gas moves through a fine capillary tube (12C16O2 arrives first).
In reality, gas are not ideal, velocity difference is reduced by collisions, reduced fractionation

9. Kinetic fractionation (cont)
2. Lighter isotope will be preferentially reacted (back to vibrational E plot)
easier to break C-H bonds than C-D bonds
when reactions do not go to equilibrium, lighter isotope will be enriched in products
usually very large kinetic fractionations in biologically-mediated rxns
(ex: photosynthesis (low δ13C) and bacterial reduction (low δ34S))
NOTE:
The tell-tale sign of kinetic fractionation is fractionation that is directly proportional to the mass difference (Δm).
You can identify a kinetic process by comparing d values for different isotope systems
ie. 18O/16O vs. 13C/12C (2/1)
18O/16O vs. 17O/16O (2/1)

10. Mass-independent fractionation
Observed in meteorites and in atmospheric photo-chemical reactions,
mechanism unknown.
mass-independent
Thiemens and Heidenreich, 1983; Theimens, 1999 (review)