Isotopes as tracers of magmatic sources
I. RbSr isotopes and evolution in course of time
A. Basic equation of the RbSr system
The RbSr (and SmNd) system is somehow more complicated
than the UPb (on zircon) system, because real rocks and minerals always
contain some of the daughter nuclide (D, ^{87}Sr in this case). This
problem is overcome by the use of the “isochron” technique that involves the
nonradiogenic isotope of Sr, ^{86}Sr (see G214).
^{87}Rb → ^{87}Sr (l= 1.42 10^{11}
yr^{1})
^{86}Sr is stable.
Establish the basic
isochron equation, which is a relation between ^{87}Sr/^{86}Sr,
(^{87}Sr/^{86}Sr)_{0} and ^{87}Rb/^{86}Sr
– in yesterday’s notation, it’s a relation involving N, D and D_{0}.
This equation can be used in several ways:

By building an isochron diagram
(as you did last year in G214), i.e. ^{87}Sr/^{86}Sr = f (^{87}Rb/^{86}Sr).
In this diagram, a suite of cogenetic samples plot along a line, whose slope is
a function of the time.

By building “isotopic evolution
diagrams”, ^{87}Sr/^{86}Sr = f(t). In this diagram, a sample
evolves along a line of slope = ^{87}Rb/^{86}Sr.
B. Using isotopic evolution diagrams
1. Forward evolution
The primitive mantle has the following isotopic
characteristics: its ^{87}Rb/^{86}Sr ratio is 0.027, and its
original (at T=4.5 Ga) ^{87}Sr/^{86}Sr value was 0.699.
Draw the line of
evolution of this mantle (“CHondritic Uniform Mantle”, or CHUR) from past to
present.
At time T = 3.65 Ga (that’s yesterday’s sample…), the mantle
melted and produced a magma which eventually cooled into a rock of ^{87}Rb/^{86}Sr
= 0.15.
Draw its line of
evolution. What is the presentday ^{87}Sr/^{86}Sr of this
sample?
Now consider a sediment formed at 3.2 Ga from this rock,
with a ^{87}Rb/^{86}Sr of 0.25.
Draw its line of
evolution.
2. From present to past
Now plot on your
previous diagram a granitic sample with presentday values as follows, and draw
its evolution line back into the past.
^{87}Rb/^{86}Sr

^{87}Sr/^{86}Sr

0.35

0.7145

This rock formed at 2.0 Ga.
 What was its ^{87}Sr/^{86}Sr
at this time? (i.e., original Sr value).
 Among the 3 rocks plotted above, what
is its most likely source (i.e., the rock that melted to form the granitic
magma)
 If that rock was a pure product from
the mantle, what would be its age?
This “pseudoage” is often referred to as a “T_{CHUR}”.
Note that, as rock “evolves” by successive melting or
erosion event, they “move” to higher ^{87}Rb/^{86}Sr ratios –
i.e. to rock that are richer in Rb. This is because Rb is, in general, a more
incompatible elements than Sr and therefore it is more readily concentrated in
the melts.
II. Various isotopic tracers
A. SmNd system
The isochron method (and, consequently, the use of initial
ratios) can be used for many other systems, e.g.
^{144}Nd is stable; the ratio ^{143}Nd/^{144}Nd
can be used to interpret rock sources.
This ratio has a very restricted range of variation;
therefore, the “e” notation is commonly
used. It works just like the d for O
isotopes (G214), by calculating the deviation from a standard, except that an e unit is 10^{4}, whereas a d unit is 10^{3} difference with the
standard. The standard for Nd isotopes is commonly the “CHUR”, or CHondritic
Uniform Reservoir:
Typical variations for e_{Nd}
are between 10 and +10.
Note that, for SmNd system, more “evolved” rocks have lower
^{147}Sm/^{144}Nd values than more “primitive” rocks: in other
terms, they evolve “under” the CHUR line instead of above as previously.
 Plot a (quantitative) SmNd evolution
diagram for the mantle, and for a more evolved sample (as we did above).
 Indicate on the graph what e_{Nd} represents.
B. Pb isotopic systems
^{238}U → (…) → ^{206}Pb (l = 1.5512 10^{10} yr^{1})
^{235}U → (…) → ^{207}Pb (l = 9.8485 10^{10} yr^{1})
(yes, the same systems we looked at yesterday –but they’re
not used in the same way here ! And yes, it is possible to get isochron ages
from any of the two systems, without needing the Concordia method).
^{204}Pb is stable in both case; ^{206}Pb/^{204}Pb
and ^{207}Pb/^{204}Pb are therefore used as tracers.
^{232}Th → (…) → ^{208}Pb (l = 4.4975 10^{11} yr^{1})
^{204}Pb is stable again; ^{208}Pb/^{204}Pb
is yet another tracer.
C.
Other systems
^{176}Lu →^{176}Hf (l = 1.94 10^{11}
yr^{1})
(^{178}Hf stable, ^{176}Hf/^{178}Hf
or e_{Hf})
D. Isotopic characteristic of Earth’s reservoirs
Empirically determined. Different part of the Earth appear
to have different characteristics. Two example:

Mantle/crust difference. Clearly
seen using SrNd diagrams.

Differences within the mantle
itself, reflected in the chemistry of erupted lava. Mostly seen with the
various Pb isotopes. It appears that there is a geographic logic behind this
(why??)