Geoscience Reference
In-Depth Information
Geological age
T
0
T
1
0
Fractionation
event
147
Sm
144
Nd
λ
147
Sm
143
Nd
144
Nd
0
t
=
0
(initial)
t
f
Today
Time
Figure 4.12
Evolution of the
143
Nd
144
Nd isotopic ratio by radiogenic decay of
147
Sm. This ratio changes
almost linearly with time
t
and the slope of the evolution curve indicates the
147
Sm
/
144
Nd, and
therefore the Sm/Nd ratio, of the system. Magmatic, sedimentary, or metamorphic events, here
represented as occurring at
T
1
, may fractionate the Sm/Nd ratio of various sub-systems.
/
D
)
0
obtained as intercepts of isochrons were once a
by-product of geochronology. These ratios, which describe the values of
87
Sr/
86
Sr,
143
Nd/
144
Nd,
176
Hf/
177
Hf, etc., at the time the rocks formed, have become, together with
the isotopic ratios measured in modern samples, a prime source of geochemical informa-
tion about parent/daughter ratios in various geological systems. If
(4.28)
is considered not
as an isochron equation but as expressing a change in the
143
Nd
The initial isotopic ratios (
D
/
144
Nd ratio versus time
(
Fig. 4.12
), we have a means of evaluating the mean Sm/Nd ratio of the system. Let us
recast this equation as:
/
143
Nd
144
Nd
143
Nd
144
Nd
0
+
147
Sm
144
Nd
1
e
−
λ
147
Sm
t
t
=
−
(4.33)
0
The slope of the evolution curve (the so-called growth curve) in
Fig. 4.12
is simply obtained
by taking the derivative of 1
e
−λ
147
Sm
t
with respect to
t
. Because of the very slow decay
of
147
Sm, the approximation e
−
λ
147
Sm
t
−
≈
1
−
λ
147
Sm
t
holds. This slope is very nearly equal
144
Nd)
0
. Upon division by the appropriate isotopic abundance factors
(here 0.15/0.24) and multiplication by the ratio of atomic masses of the two elements
(150.4/144.2), the
147
Sm/
144
Nd ratio can be converted into a Sm/Nd weight ratio.
Let us first use the chronometric equation to infer the mean “time-integrated” par-
ent/daughter ratio that apparently prevailed during the entire history of a particular sample,
from the Earth formed to the sample as part of the modern world. The initial
143
Nd
λ
147
Sm
(
147
Sm
to
/
144
Nd
/
