Geoscience Reference
In-Depth Information
Normalizing Eq. (6.27)by[
86
Sr]
now
gives
[
87
Sr]
now
[
86
Sr]
now
=
[
87
Sr]
0
[
86
Sr]
now
+
[
87
Rb]
now
[
86
Sr]
now
(e
λ
t
−
1)
87
Sr
86
Sr
87
Sr
86
Sr
87
Rb
86
Sr
(6.29)
(e
λ
t
now
=
0
+
−
1)
now
This is the equation of a straight line with intercept [
87
Sr
86
Sr]
0
and slope
/
86
Sr]
now
are measured for
various minerals in a rock and plotted against each other, the slope of the resulting
line
8
1. When the ratios [
87
Sr
86
Sr]
now
and [
87
Rb
e
λ
t
−
/
/
86
Sr]
0
is
called the
initial ratio
. The straight line is called an
isochron
. Alternatively, from
any locality a set of rock samples selected to have varying ratios of rubidium to
strontium can be used. An example of such a whole-rock isochron is shown in
Fig. 6.2(a).
This method presumes that the initial strontium isotope ratio was the same for
all the minerals in the rock or for all the rocks from the chosen locality and means
that the age
t
can be determined without having to make any assumptions about
[
87
Sr]
0
, the original amount of strontium-87. The rubidium-strontium method
became popular in the 1960s because the measurements were accessible to early
mass-spectrometer techniques. The main disadvantages are that rubidium and
strontium are often mobile - that is, they can be transported in or out of the rock
by geochemical processes - and that rubidium does not occur in abundance (in
particular, not in limestones and ultramafic rocks); thus, not all rocks are suitable
for dating by this method. In addition, because the half-life of
87
Rb is very long,
it may sometimes be difficult to date very young rocks accurately.
The initial ratio [
87
Sr
1, from which
t
can be determined. The intercept [
87
Sr
is e
λ
t
−
/
86
Sr]
0
is an indicator of whether the samples have been
derived from the remelting of crustal rocks, or otherwise reset, or are of deeper
origin. Since
/
10
−
11
yr
−
1
),
t
is very much less than unity for
all geological ages. Therefore, a good approximation to Eq. (6.29)is
87
Sr
86
Sr
λ
is small (1.42
×
λ
87
Sr
86
Sr
87
Rb
86
Sr
now
λ
now
=
0
+
t
(6.30)
When [
87
Sr
86
Sr]
now
is plotted against
t
(Fig. 6.2(b)), Eq. (6.30)isthe equation
of a straight line with a slope
/
86
Sr]
0
, and
describes the increase in the strontium ratio with time. Rocks derived from the
Archaean mantle have an initial ratio of roughly 0.700, and it is believed that,
when the Earth formed, the ratio was 0.699 (the value for some meteorites). The
ratio for modern oceanic basalts (which are mantle-derived) is 0.704, and this
increase of the initial ratio for strontium is attributed to the accumulation of
[
87
Rb
86
Sr]
now
and an intercept [
87
Sr
λ
/
/
8
The slope and intercept and their errors can be obtained by least-squares fitting of straight lines to
data points as described in Appendix 4.
