Isotopes as tracers of magmatic sources

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.

What was its ⁸⁷Sr/⁸⁶Sr 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 “pseudo-age” is often referred to as a “T_CHUR”.

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 e_Nd 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.

Plot a (quantitative) Sm-Nd 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

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 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 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??)