Stable Isotopes: Natural variations in the ratios of isotopes can be used to trace
the flow of mass or the extent to which a process has occurred.
Issues of Notation: Example is from C isotopes, but the same conventions apply to O.
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Stable Carbon Isotopes:
C: 98.89%
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C: 1.11%
Isotopic fractionation: Sorting of isotopes between substances as a consequence of
differences in molecular bond energies or rates of transport for different isotopes of an element
Isotopic Notation: Because one isotope is common and the other is rare, and because
isotope fractionations are often small, naturally-occurring isotopic differences between
substances are often very small, in the range of parts per thousand. They are easier to
remember if we report isotopic compositions of materials using: δ  values
(
(13C/12C)sample - (13C/12C)standard
!13C =
(13C/12C)standard
)
x 1000 =
(
(13C/12C)sample
-1
(13C/12C)standard
)
x 1000
δ values indicate relative enrichment or depletion in 13C to 12C.
Higher δ values, relatively more 13C, less 12C: Heavier
Lower δ values, relatively less 13C, more 12C: Lighter
The units are parts per thousand or per mil (‰)
Fractionations are measured using fractionation factors or isotopic offsets
The Fractionation Factor (α ) between two substances, a and b, is defined as:
(13C/12C)a
1000 + "13Ca
!a/b = (13C/12C) = 1000 + "13C
b
b
The Isotopic Offset between a and b, is defined as:
Δ 13C a/b = δ 13Ca - δ 13Cb ≈ 1000lnα a/b
Why are C isotopes useful in constraining the burial history of carbon?
Photosynthesis strongly favors 12C over 13C-bearing CO2
During CaCO3 precipitation, 13C-bearing HCO3 forms stronger bonds than 12C-bearing HCO3
Plants (C-H materials) are light. Calcite (C-O material) is heavy.
"13CCO 2/plant = 16‰
marine algae
modern !13C = -23‰
"13CCO 2/calcite = -9‰
dissolved CO 2
modern !13C = -7‰
protist calcite
modern !13C = +2‰
BIOLOGICAL CARBON PUMP
Bury greater amounts of C-H material, suck 12C out of surface environment.
Bury greater amounts of C-O material, suck 13C out of surface environment.
Volcanic outgassing pumps CO2 into the system with a known, relatively constant value.
Changes in C isotope ratios of surface waters are recorded in rocks and fossils.
Isotopes monitor the balance between volcanic input, organic C burial, and carbonate C burial.
How can we calculate the rate of organic carbon burial?
1. At steady state, amount of carbon entering and exiting the ocean must be the same.
Fluxin (Gt/yr) = Fluxout (Gt/yr)
Where Fluxout = Fluxorganic + Fluxcarbonate. Fluxin comes from volcanoes and weathering.
Rather than deal with true fluxes, which may be hard to quantify, we'll convert to proportional
fluxes. Divide both sides of the flux equation above by Fluxin.
1 = fcarb + forg
Where fcarb and forg are the proportions of C buried as organic matter and carbonate.
2. δ values can serve as labels of mass flow of different types of carbon.
δ values can be manipulated algebraically.
For example, if you want to balance isotope as well as the mass fluxes, all you need to do is
multiply the fluxes above by their isotope values.
(1) δ 13Cinput = (fcarb)δ 13Ccarb + (forg)δ 13Corg
We can make two useful equations relating forg (which is related to O2 input to the
atmosphere) δ13Ccarb to out of this relationship if we rearrange and substitute.
Remember/define:
δ 13Cinput = -5‰ (volcanism, weathering)
Δ 13Ccarb-org = δ 13Ccarb - δ 13Corg = +25‰ (fractionation of C b/w inorganic and organic pools)
forg = 1 - fcarb
Time for some algebra
δ 13Cinput = (1-forg)δ 13Ccarb + (forg)(δ 13Ccarb - Δ 13Ccarb-org)
δ 13Cinput = δ 13Ccarb - forgδ 13Ccarb + forgδ 13Ccarb - forgΔ 13Ccarb-org
δ 13Cinput = δ 13Ccarb - forgδ 13Ccarb + forgδ 13Ccarb - forgΔ 13Ccarb-org
δ 13Cinput = δ 13Ccarb - forgΔ 13Ccarb-org
Equation 1: forg = (δ 13Ccarb - δ 13Cinput)/Δ 13Ccarb-org
Substitute using modern values: forg = (δ 13Ccarb +5)/25
Equation 2: δ 13Ccarb = δ 13Cinput + forgΔ 13Ccarb-org
Substitute using modern values: δ 13Ccarb = -5 + 25forg
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Higher δ Ccarb values indicate higher proportional burial of 12C-enriched organic matter.
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Lower δ Ccarb values indicate proportionally greater burial of 13C-enriched carbonate.
The second equation and the equation for δ 13Corg are plotted on the next page. They
illustrate, quantitatively, how δ 13Ccarb and δ 13Corg change with changes in the burial flux
of organic C.