1. Isotope Geochemistry

2. Measuring Isotopes
While different, isotopes of the same element exist in certain fractions corresponding to their natural abundance (adjusted by fractionation)
We measure isotopes as a ratio of the isotope vs. a standard material (per mille ‰)
Where Ra is the ratio of heavy/light isotope and a is the fractionation factor ‰

3. Fractionation
A reaction or process which selects for one of the stable isotopes of a particular element
If the process selects for the heavier isotope, the reaction product is ‘heavy’, the reactant remaining is ‘light’
Isotope fractionation occurs for isotopic exchange reactions and mass-dependent differences in the rates of chemical reactions and physical processes

4. Temperature effects on fractionation
The fractionation factors, a, are affected by T (recall that this affects EA) and defined empirically:
Then,
As T increases, D decreases – at high T D goes to zero
Where A and B are constants determined for particular reactions and T is temp. in Kelvins

5. Equilibrium vs. Kinetic fractionation
Fractionation is a reaction, but one in which the free energy differences are on the order of 1000x smaller than other types of chemical reactions
Just like other chemical reactions, we can describe the proportion of reactants and products as an equilibrium or as a kinetic function

6. FRACTIONATION DURING PHYSICAL PROCESSES
Mass differences also give rise to fractionation during physical processes (diffusion, evaporation, freezing, etc.).
Fractionation during physical process is a result of differences in the velocities of isotopic molecules of the same compound.
Consider molecules in a gas. All molecules have the same average kinetic energy, which is a function of temperature.

7. Because the kinetic energy for heavy and light isotopes is the same, we can write:
In the case of 12C16O and 13C16O we have:
Regardless of the temperature, the velocity of 12C16O is times that of 13C16O, so the lighter molecule will diffuse faster and evaporate faster.

8. Equilibrium Fractionation
For an exchange reaction:
½ C16O2 + H218O ↔ ½ C18O2 + H216O
Write the equilibrium:
Where activity coefficients effectively cancel out
For isotope reactions, K is always small, usually 1.0xx (this K is for example)

9. WHY IS K DIFFERENT FROM 1.0?
Because 18O forms a stronger covalent bond with C than does 16O.
The vibrational energy of a molecule is given by the equations:
Thus, the frequency of vibration depends on the mass of the atoms, so the energy of a molecule depends on its mass.

10. The heavy isotope forms a lower energy bond; it does not vibrate as violently. Therefore, it forms a stronger bond in the compound.
The Rule of Bigeleisen (1965) - The heavy isotope goes preferentially into the compound with the strongest bonds.

11. Equilibrium Fractionation II
For a mass-dependent reaction:
Ca2+ + C18O32-  CaC18O3
Ca2+ + C16O32-  CaC16O3
Measure d18O in calcite (d18Occ) and water (d18Osw)
Assumes 18O/16O between H2O and CO32- at some equilibrium
T ºC = (d18Occ - d18Osw) (d18Occ-d18Osw)2

12. Empirical Relationship between Temp
Empirical Relationship between Temp. & Oxygen Isotope Ratios in Carbonates
At lower temperatures, calcite
crystallization tends to incorporate a
relatively larger proportion of 18O
because the energy level (vibration)
of ions containing this heavier isotope
decreases by a greater amount than ions
containing 16O.
As temperatures drop, the energy level
of 18O declines progressively by an
amount that this disproportionately
greater than that of the lighter 16O.
Consider from here what the value of alpha is (essentially the y-axis)

13. Distillation
2 varieties, Batch and Rayleigh distillation dependent on if the products stay in contact and re-equilibrate with the reactants
Batch Distillation:
df = di – (1 – F) 103lnaCO2-Rock
where the isotope of the rock (di) depends on it’s initial value (df) and the fractionation factor
Rayleigh Distillation
df - di =103(F(a – 1) – 1)

14. RAYLEIGH DISTILLATION
Isotopic fractionation that occurs during condensation in a moist air mass can be described by Rayleigh Distillation. The equation governing this process is:
where Rv = isotope ratio of remaining vapor, Rv° = isotope ratio in initial vapor, ƒ = the fraction of vapor remaining and a = the isotopic fractionation factor

15. Effect of Rayleigh distillation on the 18O value of water vapor remaining in the air mass and of meteoric precipitation falling from it at a constant temperature of 25°C.
Complications:
1) Re-evaporation
2) Temperature dependency of 

16. Using isotopes to get information on physical and chemical processes
Fractionation is due to some reaction, different isotopes can have different fractionation for the same reaction, and different reactions have different fractionations, as well as being different at different temperatures and pressures
Use this to understand physical-chemical processes, mass transfer, temperature changes, and other things…

19. Volatilization calcite + quartz = wollastonite + carbon dioxide
CaCO3 + SiO2 = CaSiO CO2
As the CO2 is produced, it is likely to be expelled
Batch vs. Rayleigh Fractionation – In batch fractionation the CO2 stays in the system and continues to re-equilibrate while in Rayleigh factionation the CO2 is separated and does not re-eqiulibrate

20. Other volatilization reaction examples…

22. Alta Ski Area – Tertiary pluton intruding paleozoic sedimentary rocks, including quartz-bearing dolomites – this material metamorphosed, look at role of isotopes in deciphering that the rocks were metamorphosed by not only a large amount of heat and associated volatilization reactions, but also by a significant flux of hydrothermal waters. The interpretation is that because the petrology indicates fluid-rich conditions nearestthe contact that the water was primarily magmatic – I am not sure about that though, the volume of fluid needed seems pretty high for that…

24. Data shows that the mineral assemblages found in the area grade into higher T closer to the contact – the periclase formed at the contact reqires H2O (The x-axis is H2O vs. CO2 fluid compositional space!)

25. Indicates the isotopic fractionation is not just from the devolatilization reactions – if they were the isotope values should fall into the field from the Raleigh equation…

26. Suggestion that there may be some sort of mass loss from the interaction of meteoric water

27. Model results indicating there needed to be significant water flow (200-800 m3/m2)

28. ISOTOPE FRACTIONATION IN THE HYDROSPHERE
Evaporation of surface water in equatorial regions causes formation of air masses with H2O vapor depleted in 18O and D compared to seawater.
This moist air is forced into more northerly, cooler air in the northern hemisphere, where water condenses, and this condensate is enriched in 18O and D compared to the remaining vapor.
The relationship between the isotopic composition of liquid and vapor is:

29. Assuming that 18Ov = -13.1‰ and vl(O) = 1.0092 at 25°C, then
and assuming Dv = -94.8‰ and vl(H) = at 25°C, then
These equations give the isotopic composition of the first bit of precipitation. As 18O and D are removed from the vapor, the remaining vapor becomes more and more depleted.
Thus, 18O and D values become increasingly negative with increasing geographic latititude (and altitude.

30. Map of North America showing contours of the approximate average D values of meteoric surface waters.

31. Because both H and O occur together in water, 18O and D are highly correlated, yielding the meteoric water line (MWL): D  818O + 10

32. Deviation from MWL
Any additional fractionation process which affects O and D differently, or one to the exclusion of the other will skew a water away from the MWL plot
These effects include:
Elevation effects - (dD -8‰/1000m, -4‰/ºC)
Temperature (a different!)
Evapotranspiration and steam loss
Water/rock interaction (little H in most rocks)

33. Kinetic Fractionation
lighter isotopes form weaker bonds in compounds, so they are more easily broken and hence react faster. Thus, in reactions governed by kinetics, the light isotopes are concentrated in the products.
Again, isotope reactions can be exchange reactions or mass-dependent chemical or physical reactions – kinetic factors may affect any of these!

34. Kinetic fractionation I – SO42- reduction
SO42- + CH4 + 2 H+  H2S + CO2 + 2 H2O
This reaction is chemically slow at low T, bacteria utilize this for E in anoxic settings
Isotope fractionation of S in sulfide generated by microbes from this process generates some of the biggest fractionations in the environment (-120‰ for S)
THEN we need to think about exchange reactions with H2S or FeS(aq) as it may continue to interact with other S species

35. S isotopes and microbes
The fractionation of H2S formed from bacterial sulfate reduction (BSR) is affected by several processes:
Recycling and physical differentiation yields excessively depleted H2S
Open systems – H2S loss removes 34S
Limited sulfate – governed by Rayleigh process, enriching 34S
Different organisms and different organic substrates yield very different experimental d34S
Ends up as a poor indicator of BSR vs. TSR

36. Iron Isotopes
Earth’s Oceans 3 Ga had no oxygen and lots of Fe2+, cyanobacteria evolved, produced O2 which oxidized the iron to form BIFs – in time the Fe2+ was more depleted and the oceans were stratified, then later become oxic as they are today
This interpretation is largely based on iron isotopes in iron oxides and sulfide minerals deposited at those times (Rouxel et al., 2005)
No one has yet bothered to measure how iron isotopes change when iron sulfide minerals precipitate – that’s where we come in…

37. Mass-independent fractionation
Mass effects for 3 stable isotopes (such as 18O, 17O, and 16O) should have a mass-dependent relationship between each for any process
Deviation from this is mass-independent and thought to be indicative of a nuclear process (radiogenic, nucleosynthetic, spallation) as opposed to a physico-chemical process
Found mainly associated with atmospheric chemistry, effect can be preserved as many geochemical reactions in water and rock are mass-dependent

38. S-isotopic evidence of Archaen atmosphere
Farquar et al., 2001; Mojzsis et al., 2003 found MIF signal in S isotopes (32S, 33S, 34S) preserved in archaen pyrites precipitated before 2.45 Ga
Interpreted to be signal from the photolysis of SO2 in that atmosphere – the reaction occurs at nm light, indicating low O2 and O3 (which very effficiently absorb that wavelength)