Geoscience Reference
In-Depth Information
Elemental
fractionation
Isotopic
homogenization
Figure 4.1
Left: Cats and dogs interact vigorously affecting site occupation (tree or yard). Just like two
elements with different chemical properties, they arrange themselves so as to achieve the most
stable configuration. Right: White cats and black cats have very similar properties and like
isotopes of the same element are arranged randomly among the available sites. The most likely
arrangement is an identical proportion of isotopes in each site.
the tree and dogs on the ground in the yard, under the tree. Cats and dogs are two different
elements in competition for the same sites: they arrange themselves spontaneously so as to
move to the most stable configuration! Any alternative configuration is either intrinsically
unstable (dogs in the tree, cats on the ground) or out of equilibrium (cats and dogs on the
ground). Now, we clear these animals out and then release into the yard a few dozen cats
that only differ by the color of their fur, either black or white. The probability that a cat
will take to the tree or the ground is independent of the color of its coat, the energy of
interaction is low, and the most likely arrangement is one of maximum entropy where the
proportion of white and black cats is the same at each site. Our black and white cats are
isotopes with very similar properties that share the sites evenly regardless of their energy
level.
If elements and their isotopes are allowed to move easily between sites in crystals, liq-
uids, and gases, either because the liquid and gaseous states enable effective mixing or
because thermal diffusion allows atoms to move rapidly, the elements with variable prop-
erties will arrange themselves in accessible sites so as to minimize the total energy of
the system. On the other hand, isotopic exchanges of a single element between phases
contribute little to the energy balance of the system and such isotopes will be evenly dis-
tributed so as to maximize the entropy of the system. For the needs of geochronology, both
natural mass fractionation and instrumental mass bias are purely and simply eliminated
by internal normalization against some arbitrary reference ratio (see box). As carbonates
precipitate out from seawater, the
87
Sr
86
Sr ratio is exactly the same in calcite and in the
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