ESS 109C Isotope Geochemistry Notes

May 7, 2007

 

Chemical and physical separation of isotopes

 

  1. Class notes & homeworks are available online –
                            http://www2.ess.ucla.edu/~schauble/Isotope_geochemistry/
  2. Stay tuned for HW#4 and Midterm.

  3. Stable isotope chemistry
    1. So far we have largely assumed that all isotopes of an element behave the same in chemical reactions

                                               i.     Concordia – lead loss assumed to affect all lead isotopes the same

                                             ii.     40Ar*/39Ar* -- 40K/39K assumed constant in crystals

    1. In reality, isotopes are separable, albeit weakly

                                               i.     d14C – 14C/12C  is ~2-4% lower in plants than atmosphere, even for zero-age plants.

                                             ii.     Industrial-scale methods of 235U enrichment for nuclear fuel are also chemical.

    1. Terminology of isotope separation

                                               i.     Delta-notation – relative deviation in an isotope ratio from a standard material, in per mil (ä)

dhX = [(hX/lX)sample/(hX/lX)standard – 1] x 1000

1.     Example: d13C = [(13C/12C)sample/(13C/12C)PDB – 1] x 1000
PDB = Pee Dee Belemnite, a marine carbonate (CaCO3) shell fossil from South Carolina (Cretaceous)
(photo filched from virtual.clemson.edu)
Chosen for historical reasons, the original standard material is no longer available, but still used for reporting.

                                             ii.     Fractionation factor – change in isotope ratio induced by a particular process or reaction

For an incipient reaction involving element X, Reactant ˆ Product

a(Rxn) = (hX/lX)product/(hX/lX)reactant

A non-fractionating reaction has a(Rxn) = 1.
a(Rxn) > 1 implies product is enriched in heavy isotope.
a(Rxn) < 1 implies product is enriched in light isotope.

1.     Example: Photosynthesis, CO2 + H2O + light ˆ [CH2O]x + O2
a(CO2 – CH2O) Å 0.98-0.99

                                            iii.     Relationship between d hX and a(Rxn) --
 a(Rxn) = (1000 + d hX (product))/ (1000 + d hX (reactant))

    1. Chemistry of isotope separation

                                               i.     Diffusion – light isotopes tend to diffuse faster than heavy isotopes

1.     FickÕs law diffusion (pinhole diffusion)
Precise for ideal gas (no collisions between gas molecules), applied approximately or with modification to many other types of reaction kinetics.

Collision rate with a wall (pinhole or co-reactant) proportional to velocity

D = const. x v

<KE/molecule> = 3/2kT = ½ mv2

v = (3kT/m)1/2

a(Diffusion) = D(hX)/D(lX) = v(hX)/v(lX) = (3kT/m[hX])1/2/(3kT/m[lX])1/2 = (m[lX]/ m[hX])1/2

                                             ii.     Gravitational settling

                                            iii.     Equilibrium