Geoscience Reference
In-Depth Information
T (
°
C)
500
100
50
0
40
35
Albite-
H
2
O (liq)
30
Calcite-
H
2
O (liq)
25
20
Quartz-
H
2
O (liq)
H
2
O (liq)-
H
2
O (vap)
15
Quartz-
albite
10
5
0
0
2
4
6
8
10
12
14
16
10
6
/
T
2
(K)
Figure 3.6
Fractionation of oxygen isotopes between a mineral phase and water, or between different
mineral phases. Notice that preferential incorporation of
18
O is normally favored by the mineral
structure and that isotopic fractionation decreases rapidly with increasing temperature.
Temperature may be understood through the Boltzmann distribution (see box), which
determines the fraction of a population of atoms that populates a certain energy level. At
moderately low temperatures, typically below ambient temperature, there is not enough
energy to open up many vibrational levels and all the atoms are in their ground state. The
exchange energy is constant and fractionation temperature dependent. In this case, which
only finds useful applications when hydroxyl groups are involved, the law of mass action
requires the temperature dependence of ln
α
/
T
. Temperature in this case only attests to
the total available vibrational energy and therefore indirectly constrains the relative occu-
pation of the available levels. Higher temperatures have an additional effect: they open
up new grounds for occupation. The more energy available, the more vibrational quanta
can wander up the energy levels. In this case, which is a straight outcome of the quantum
theory, we observe (
Fig. 3.6
) fractionation laws of the type:
in 1
A
T
2
+
ln
α
=
C
(3.20)
where
A
and
C
are constants. These laws, to whom the names of Bigeleisen, Mayer,
and Urey are attached for their
1947
papers, are widely used for thermometry of mag-
matic, metamorphic, or hydrothermal systems. The symmetry constant
C
is usually zero
for isotopic exchange between anhydrous isotopomers so that fractionation at magmatic
temperatures is normally small or negligible.
Since bond energy varies with the inverse square-root of the mean mass of the atoms
that form the molecule
(Eq. 3.11)
,
the thermodynamic fractionation factor between iso-
topes generally falls very quickly with increasing mean atomic mass as it varies with the
difference between smaller and smaller quantities. At 500-800
◦
C, fractionations of 20-80
per mil (
) are commonly observed for the D/H ratio, of 2-8
for oxygen isotopes, and
fall to less than 1
for zinc and copper isotopes.
A last effect deserves attention when we deal with molecules with very different degrees
of symmetry. For example, the molecule CO has only one single possible configuration,
