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will be more similar than that of two distinct elements, and, indeed, the chemistry of two
isotopes of a heavy element, e.g. lead, is virtually unchanged. The applications of isotopic
fractionation to the mapping of low- and medium-temperature phenomena are fundamen-
tal. The principles are rather similar to those set out in the previous chapter for chemical
fractionation.
3.1 Principles of stable isotope fractionation
99.8% of natural oxygen) and
18
O are distributed
between liquid water and vapor. The reaction can be written:
16
O(
Let us imagine how isotopes
≈
H
1
2
O
liq
+
H
1
2
O
vap
⇔
H
1
2
O
liq
+
H
1
2
O
vap
(3.1)
The four compounds appearing in this equation are chemically identical two by two, but
differ by their isotopic abundances: they are known as isotopomers of H
2
O. The mass
action law governing this equilibrium is written:
H
1
2
O
H
1
2
O
H
1
2
O
H
1
2
O
18
O
16
O
18
O
16
O
liq
=
α
O
vap
liq
=
liq
(
T
,
P
)
(3.2)
/
vap
vap
O
vap
The notation
for the fractionation coefficient now replaces that of parti-
tion coefficients
K
to signal that the exchange concerns just a single nucleus. Fractionation
coefficients are defined likewise for many stable isotope pairs, such as deuterium/hydrogen
2
H/
1
H (D/H),
13
C/
12
C,
15
N/
14
N,
34
S/
32
S, etc., between such varied phases as gases, nat-
ural solutions, magmatic liquids, and minerals. The isotopes exchanged have the same
outer electron configuration. Their chemical properties are therefore very similar and their
molar volumes almost identical, making
α
liq
(
T
,
P
)
/
α
very close to unity and virtually independent of
pressure.
The Second Principle of Thermodynamics states that, because the stability of a system
is only achieved when its energy is at its minimum, somewhere behind any fractionation
factor looms a term that accounts for the exchange of energy between the different partici-
pants of a reaction. Before we set out to discuss the physics of stable isotope fractionation,
let us therefore first summarize a few simple ideas about the different forms of internal
energy in a system. Energy can be stored in different ways:
1. Translational energy. Even when a gas as a whole is at re
st,
its atoms and molecules
move freely and therefore have a mean kinetic energy
2
m
2
, where the bar indicates
that the squared-velocity is averaged and
m
is the mass of the atom. Translational energy
is the unique form of energy of monatomic species such as rare gases (He, Ne, etc.).
2. Rotational energy. Molecules have a momentum of inertia
I
which measures the mean
squared-deviation of the mass from the main rotation axis and, for a given angular veloc-
ity
v
1
2
. Rotating charges, such as electrons, can be seen
as little current loops, which act as little magnets, and the energy of the magnetic field
is proportional to the magnetic moment.
ω
, the rotational energy is
2
I
ω
