Isotopic compositions are expressed as the ratio of
12C to 13C of the sample compared with that of a standard.
This standard will have a known value relative to the international working
standard of CO2
produced from fossil Belemite CaCO3 from a strata of marine sediment called
"The Peedee Formation" with 100% Phosphoric acid (vPDB standard Chicago,
Belemntella americana, Peedee Formation, Cretaceous, South Carolina).
Because the differences between most samples and the standard are very small,
the results are expressed as part per thousand (per mil or ‰). (Craig 1953):
∂13C = (13C/12C)sample - ( 13C/12C)standard X 1000
∂ is delta, ie. the change in ratio from the standard value.
Isotope ratios values are expressed as parts per thousand (‰)
E.g. If a sample has an isotopic composition of 0‰ it
has the same isotopic composition as the standard. A sample with stable isotope
composition 2.07‰ contains 2.07 parts per thousand more of the heavy isotope
(13C) than that of the standard. A sample with a stable carbon
isotope ratio of -14.56‰ contains 14.56 parts per thousand less 13
C than the standard.
1. Kinetic isotopic fractionation results when rates of reactions or physical processes differ.
2. Equilibrium isotopic fractionation occurs because the thermodynamicproperties of isotopically substituted species differ.
| Photosynthesis | Tends to remove the light 12C isotope, with C4 plants showing a relatively smaller carbon fractionation than C3 plants. |
| Respiration/decomposition | Tends to release light carbon and oxygen |
| Evaporation | Water molecules composed of light isotopes will evaporate before those composed of heavy isotopes. Evaporation will lead to preferential degassing of light CO2 from surface waters. |
| Locality | The same species may have different ∂13 C values in different localities (ca. 1 to 4 ‰) at different latitudes, altitudes or micro-environments. |
| Diagenises | Could result in residual plant proto-kerogen in sediment moving toward lighter isotopic values. This is because the more labile compounds of a plant are depleted in heavy isotopes in relation to the whole plant. Conversely, bacteria preferentially use 12 C-enriched functional groups and hence enrich the residual kerotene in 13C. |
Fractionation is a function of the vibrational energies
of molecules and the shifts in these resulting from the phenomenon causing
the fractionation.
The vibrational frequency of a molecular bond is inversely
proportional to the masses of the atoms in the molecule. (The substitution
of a heavy isotope into a molecule lowers this energy). This results
in molecules formed from light isotopes being slightly more reactive than
the heavier isotope.
At thermodynamic equilibrium, the heavier isotope preferentially
substitutes into compounds having higher vibrational frequencies. For example
oxygen bonds to ions with high ionic potential (charge/radius) and low atomic
mass, leading to high vibrational frequencies. Hence heavy oxygen-18 will
tend to be incorporated preferentially in minerals containing oxygen.
Temperature effects equilibrium fractionation, but has
proved hard to predict. The temperature at which equilibrium calcium
carbonate precipitation occurs is recorded in the 16O/18
O ratio of the carbonate, Hays & Grossman (1991) express the relationship
with temperature for calcite formed from meteoric waters as:
toC = 15.7-4.36(∂c-∂w)-0.12(∂
c-∂w)2
where ∂c is the ∂18O isotope
ratio of the calcite sample and ∂w is the ∂18O ratio of the oxygen
in the H2O at the time of calcification.