Isotope fractionation refers to a non-atomic process whereby the relative proportions of different isotopes are changed. It is conventional to ignore this topic altogether in basic chemistry classes, as isotopes are largely interchangeable in chemical equations. However, changes in isotope ratios provide a valuable tool in attempting to determine the chemical and physical history of a substance of interest. Stable isotope geochemistry has been particularly invaluable in determining the Earth's climate history of the past few million years.
Measurement and reporting conventions:
Isotopes are always measured in ratios, and fractionation as a ratio of ratios, as follows:
R = (abundance of heavy isotope)/(abundance of light isotope)
Conventionally, a Greek alpha is used here, but E2 makes that impossible. a is the fractionation factor.
a = Rproducts/Rreactants
Fractionation is seldom actually measured in terms of the actual fractionation factor, which usually requires offensively many significant figures to be interesting. Since the factor is generally very close to 1 (most isotope effects are small), we take:
dproduct - dreactant = (a - 1) * 1000
As with the last, this variable is usually written with a Greek delta rather than a d. The units of d are called "per mil", one tenth of the more conventional "percent". It should be noted that this is a relative measure, and d is usually measured with respect to some reference ratio. Scientists have agreed upon reference ratios for the most common stable isotope systems. Near the reference ratio, it is a reasonable approximation to add and subtract d; there is roughly a 2 per mil fractionation between a +5 per mil reactant and a +7 per mil product. However, this estimate breaks down with greater differences from the reference.
Gravitational fractionation:
Probably the simplest form of fractionation, this will only become significant in poorly mixed fluids, such as distinct layers of the stratosphere. Basically, heavier isotopes are pulled more strongly by gravity, being denser, and will slowly settle to the bottom of a fluid column, resulting in increasing enrichment with time.
Kinetic isotope fractionation:
This type of fractionation typically arises when a material moves to occupy new space or undergoes a new reaction and is separated before there is time for thorough mixing to occur. Given a uniform energy distribution, for instance, heavier isotopes will move more slowly. Lighter isotopes, with their greater velocities, may react more quickly.
Equilibrium isotope fractionation:
This is probably the most commonly studied variety of isotope fractionation, and that which occurs most commonly. Generally, either the reactants or products of a chemical reaction or phase change will be slightly enriched in heavier isotopes.
The equilibrium constant (Keq) for an isotope exchange process of the type:
AX + BX' <=> AX' + BX
will be related to the partition functions Q for the various species as:
Keq = (QAX'/QAX)/(QBX'/QBX)
where A and B are the unchanged parts of the molecule and X and X' represent the normal and substituted isotope, respectively. This equilibrium constant is often equivalent to a, our fractionation factor from earlier.
Points of interest:
- Isotope fractionation factors are greater at lower temperatures, where thermal energy E = nkT does not overwhelm isotope effects (This is particularly important)
- Light isotopes are generally enriched in biogenic compounds
- Light isotopes are generally enriched in vapor phases
- Light isotopes are generally enriched in reduced species and heavy isotopes are enriched in oxidized species, e.g., there is more heavy 13C in CO2 than in CH4
- It follows from this that reactions which involve a change in oxidation state result in a greater degree of stable isotope fractionation than those that do not
- Where two minerals of the same oxidation state are in equilibrium with one another, the mineral with the heaviest cation will have the lightest stable isotope composition, e.g., there is more heavy 34S in ZnS (sphalerite) than in PbS (galena)
- The extent of stable isotope fractionation is inversely proportional to the square of the relative mass difference between two isotopes. This means that the extent of stable isotope fractionation between 100Ru and 101Ru is less than 1% of that between 10B and 11B. In practice, this means that stable isotope fractionation is effectively below detection limits for elements with masses greater than 40, i.e., for elements with masses greater than that of Ca
Sources:
Most of this comes from a class I took at Caltech with Dr. Hugh Taylor. Kudos to him.
I refreshed my memory and stole pieces from two websites:
http://gfd.gly.bris.ac.uk/enviro-geochem/Level2Iso/Module8/mod8.html
http://paos.colorado.edu/~whitneye/fractionation.html