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formed a horizontal array of points
a
0
-
f
0
in the figure,
varying in
87
Rb/
86
Sr ratio but not
87
Sr/
86
Sr.
As time passes, each
87
Rb nucleus that decays forms an
87
Sr nucleus, and therefore each sample will evolve along
a trend of falling
87
Rb/
86
Sr and rising
87
Sr/
86
Sr, repr-
esented by the arrows in Figure 10.4. If each axis were
plotted at the same scale, the arrows would have grad-
ients of −45° since
87
Sr increases at the rate at which
87
Rb
falls. Usually, however, the
87
Sr/
86
Sr axis is expanded in
such plots (see the scaling ratio shown) so the arrows in
Figure 10.4 will appear steeper than −45°.
87
Sr/
86
Sr will
increase more quickly in samples with a high
87
Rb/
86
Sr
ratio, so the arrow lengths increase from sample
a
to
sample
f
: as time passes each composition will migrate
upward and to the left by a distance proportional to
87
Rb/
86
Sr. After a given time (e.g. at
t = t
1
), the compos-
itions will still define a linear trend, but one whose grad-
ient depends on the time elapsed since
t
= 0 (an
isochron
).
The intercept of the isochron with the
y
-axis represents
the composition of a hypothetical sample having
87
Rb/
86
Sr = 0. Because there is no
87
Rb in this notional 'sam-
ple', there can be no increase in
87
Sr in it, which is why the
isochron appears to pivot about this point. The intercept
preserves the initial value of the Sr isotope ratio shared by
all of the cogenetic samples at the outset (
a
0
,
b
0
, etc.).
Scaling ratio
between
y
and
x
axes
f
2
d
2
e
2
c
2
(
b
2
87
Sr
f
1
e
1
86
Sr
0
d
1
c
1
a
2
b
1
a
1
t
= 0
a
0
c
0
d
0
e
0
b
0
f
0
87
Rb/
86
Sr
Figure 10.4
How
87
Sr/
86
Sr and
87
Rb/
86
Sr ratios evolve with
time, shown on a graph of
87
Sr/
86
Sr versus
87
Rb/
86
Sr.
Points
a, b, c, d, e
and
f
represent the whole-rock isotopic
compositions of six
cogenetic
igneous rocks (same age, same
magma source) from the same intrusive complex. Their
compositions differ in composition owing to geochemical
differentiation during magma crystallization (over an
interval of time short by comparison with the age of the
complex).
t
1
and
t
2
represent different elapsed times after
crystallization. The vertical rectangle indicates the relative
expansion on the
x
and
y
axes.
The isochron plot
If we collect and analyse rocks
a-f
today (e.g. at
t = t
2
),
we will find that these cogenetic samples define a sloping
linear trend (
a
2
-
f
2
). Because the trend is determined by
the common age of the samples, the best-fit line
through
a
2
-
f
2
is called an
isochron
(Greek: 'same age').
The isochron may be represented algebraically (see
Box 10.4) by an
isochron equation
:
the
radiogenic daughter
isotope
87
Sr in a sample, ratioed to
the amount of a reference, non-radiogenic isotope
86
Sr
(the reasons for doing so are explained in Box 10.4). The
horizontal axis represents the amount of the
radioactive
parent
nuclide
87
Rb in the sample, also divided by
86
Sr.
Imagine we wish to establish the age of an ancient
intrusive complex, comprising a variety of igneous
rock types related to each other by magma different-
iation. Suppose the field evidence is consistent with the
rocks being cogenetic, that is, formed at essentially the
same time
2
as fractionation products of the same par-
ent magma. Let the shaded dots in Figure 10.4 represent
samples
a-f
of these diverse rock types. Since magma
melting and crystallization fractionate element ratios
but not isotope ratios
, we can assume that all of the crys-
tallized igneous rocks
a-f inherited the
87
Sr/
86
Sr ratio of
the magma source region
and so initially (at
t
= 0) they
87
=
87
+
87
Sr
Sr
Sr
Sr
Rb
Sr
(
)
e
λ
t
−
1
(10.2)
Rb
86
86
86
t
0
t
87
Sr
Sr
Here
represents a sample's current Sr isotope
86
t
abundance ratio (how much
87
Sr there is in relation to
86
Sr, in atomic proportions) measured by mass spec-
87
Rb
Sr
trometry.
is calculated from the ratio of the
86
t
sample's Rb and Sr element concentrations (determined
by routine analytical methods and again given in atomic
proportions,), and
λ
Rb
is the
87
Rb decay constant
We assume the time taken for the parent magma to cool and
fractionate is short compared to the age of the complex.
2
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