# I.  Rb-Sr isotopes and evolution in course of time

## A.   Basic equation of the Rb-Sr system

The Rb-Sr (and Sm-Nd) system is somehow more complicated than the U-Pb (on zircon) system, because real rocks and minerals always contain some of the daughter nuclide (D, 87Sr in this case). This problem is overcome by the use of the “isochron” technique that involves the non-radiogenic isotope of Sr, 86Sr (see G214).

87Rb → 87Sr (l= 1.42 10-11 yr-1)
86Sr is stable.

Establish the basic isochron equation, which is a relation between 87Sr/86Sr, (87Sr/86Sr)0 and 87Rb/86Sr – in yesterday’s notation, it’s a relation involving N, D and D0.

This equation can be used in several ways:
-          By building an isochron diagram (as you did last year in G214), i.e. 87Sr/86Sr = f (87Rb/86Sr). 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”, 87Sr/86Sr = f(t). In this diagram, a sample evolves along a line of slope = 87Rb/86Sr.

## B.   Using isotopic evolution diagrams

### 1.      Forward evolution

The primitive mantle has the following isotopic characteristics: its 87Rb/86Sr ratio is 0.027, and its original (at T=4.5 Ga) 87Sr/86Sr 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 87Rb/86Sr = 0.15.

Draw its line of evolution. What is the present-day 87Sr/86Sr of this sample?

Now consider a sediment formed at 3.2 Ga from this rock, with a 87Rb/86Sr of 0.25.

Draw its line of evolution.

### 2.      From present to past

Now plot on your previous diagram a granitic sample with present-day values as follows, and draw its evolution line back into the past.

 87Rb/86Sr 87Sr/86Sr 0.35 0.7145

This rock formed at 2.0 Ga.

1. What was its 87Sr/86Sr at this time? (i.e., original Sr value).
2. Among the 3 rocks plotted above, what is its most likely source (i.e., the rock that melted to form the granitic magma)
3. If that rock was a pure product from the mantle, what would be its age?

This “pseudo-age” is often referred to as a “TCHUR”.

Note that, as rock “evolves” by successive melting or erosion event, they “move” to higher 87Rb/86Sr 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.   Sm-Nd system

The isochron method (and, consequently, the use of initial ratios) can be used for many other systems, e.g.
147Sm → 143Nd (l= 6.54 10-12 yr-1)
144Nd is stable; the ratio 143Nd/144Nd 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 eNd are between -10 and +10.

Note that, for Sm-Nd system, more “evolved” rocks have lower 147Sm/144Nd values than more “primitive” rocks: in other terms, they evolve “under” the CHUR line instead of above as previously.

1. Plot a (quantitative) Sm-Nd evolution diagram for the mantle, and for a more evolved sample (as we did above).
2. Indicate on the graph what eNd represents.

## B.   Pb isotopic systems

238U → (…) → 206Pb (l = 1.5512 10-10 yr-1)
235U → (…) → 207Pb (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).

204Pb is stable in both case; 206Pb/204Pb and 207Pb/204Pb are therefore used as tracers.

232Th → (…) → 208Pb (l = 4.4975 10-11 yr-1)
204Pb is stable again; 208Pb/204Pb is yet another tracer.

## C.   Other systems

176Lu 176Hf (l = 1.94 10-11 yr-1)
(178Hf stable, 176Hf/178Hf or eHf)

## 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 Sr-Nd 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??)