Stable Isotopes Physical Fundamentals 92107

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Stable Isotopes Physical Fundamentals
9/21/07

• Lecture outline
• principles of stable isotope fractionation
• equilibrium fractionation
• kinetic fractionation
• mass-independent fractionation

spectrometer light intake
Annual layers in a tropical ice cap
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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/crystalliza
tion, adsorption/desorption, diffusion

• Characteristics of a useful stable isotope
  system
• large relative mass difference between stable
  isotopes (Dm/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
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Notation
We can define a fractionation factor (a)
Where RA, RB are the isotope ratios in two
phases (ex. carbonate and water, or water vapor
and water, etc) NOTE a is close to 1 because
ratios differ by parts per thousand
a 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
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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 Whites (Cornell) upcoming
Geochemistry textbook
at 25?C, so 18O/16O is larger in CO2 than in H2O
at equilibrium
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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

Effect of vibrational E in harmonic oscilllator
model
Which bond is broken most easily?
zero point energy
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Temperature-dependence of equilibrium
fractionation

• From these plots we can see that
• a varies inversely with T
• the harmonic oscillator model
• approximation holds up well

data
harmonic oscilllator model
for Tlt200C
for Tgt200C
harmonic oscilllator model
data
So at colder temperatures, isotopes will be more
heavily fractionated.
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Composition-dependence of equilibrium
fractionation
General rule of thumb the heavy isotope will be
concentrated in the phase in which it is most
strongly bound (or lowest energy state).
Solidgtliquidgtwater, covalentgtionic, etc. Ex
18O in carbonates - heavily enriched in
carbonate because O tightly bonded to small,
highly charged C4, vs. weaker H - so
D18Ocal-water d18Ocarb-d18Owater 30 Ex
quartz (SiO2) most enriched mineral Lattice
configuration (aragonite vs. calcite) plays a
secondary role (D18Oarag-cal0.5) Chemical
substitutions in the lattice (ie. Ba instead of
Ca) also have a small effect D18OBa-cal-water
25 (vs. 30 for Ca-cal)
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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
12 216 44) and 13C16O2 (mass 13 216
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
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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 d13C) and bacterial
  reduction (low d34S))

NOTE The tell-tale sign of kinetic
fractionation is fractionation that is directly
proportional to the mass difference (Dm). 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)
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Mass-independent fractionation
Observed in meteorites and in atmospheric
photo-chemical reactions, mechanism unknown.
mass-independent
Thiemens and Heidenreich, 1983 Theimens, 1999
(review)