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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
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
e λ
represents a sample's current Sr isotope
abundance ratio (how much 87 Sr there is in relation to
86 Sr, in atomic proportions) measured by mass spec-
is calculated from the ratio of the
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.
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