1. Radiogenic Isotope Geology G214, 2005 Lecture 1: Introduction

2. Modelled evolution of Rb/Sr in mantle and crust

3. Modelled evolution of Sm/Nd in mantle and crust

4. Fundamentals Unstable isotopes decay to other nuclides
The rate of decay is constant, and not affected by P, T, X…
Parent nuclide = radioactive nuclide that decays
Daughter nuclide(s) are the radiogenic atomic products

5. Table of the elements

6. Radiogenic Isotope Systems
The radiogenic isotope systems that are of interest in geology include the following
K-Ar
Rb-Sr
Sm-Nd
Re-Os
U-Th-Pb
Lu-Hf
These system develop through radioactive decay of parent isotopes to daughter isotopes.

7. DECAY TYPES Beta Decay 19K40 -> 20Ca40 + b- +  + Q Alpha Emission
Where b- is the beta particle, n is the antineutrino and Q stands for the maximum decay energy.
Alpha Emission
92U238 -> 90Th He4 + Q
Where 2He4 is the alpha particle and Q is the total alpha decay energy
Branched Decay
71Lu176 -> 72Hf176 via negative beta decay
72Hf176 -> 70Yb176 positron decay or electron capture.

8. Why is this useful?
Isotopic variations between rocks and minerals due to
Mass fractionation (as for stable isotopes): only effective for light isotopes: H, He, C, O, S
Daughters produced in varying proportions resulting from previous event of chemical fractionation
40K  40Ar by radioactive decay
Basalt  rhyolite by FX (a chemical fractionation process)
Rhyolite has more K than basalt
more40K  more 40Ar over time in rhyolite than in basalt
40Ar/39Ar ratio will be different in each
Time: the longer 40K  40Ar decay takes place, the greater the difference between the basalt and rhyolite will be

9. The Decay Constant
Over time the amount of the daughter (radiogenic) isotope in a system increases and the amount of the parent (radioactive) isotope decreases as it decays away. If the rate of radioactive decay is known we can use the increase in the amount of radiogenic isotopes to measure time.
The rate of decay of a radioactive (parent) isotope is directly proportional to number of atoms of that isotope that are present in a system.
Mathematically, this is expressed as;
-dN/dt = lN,
where N = the number of parent atoms and l is the decay constant
The negative sign means that the rate decreases over time

10. The Radiogenic Decay Equation
The previous relationship is used to derive the radioactive decay equation which has the following form
D = Do + N (elt – 1)
This equation is used extensively in radiogenic dating studies
In principle, D and N are measurable quantities, while Do is a constant whose value can be either assumed or calculated from data for cogenetic samples of the same age.
If these three variables are known then the above equation can be solved for t to give an “age” for the rock or mineral in question.

11. The Rb-Sr system
Strontium has four naturally occurring isotopes all of which are stable
38Sr88, 38Sr87, 38Sr86, 38Sr84
Their isotopic abundances are approximately
82.53%, 7.04%, 9.87%, and 0.56%
However the isotopic abundances of strontium isotopes varies because of the formation of radiogenic Sr87 from the decay of naturally occurring Rb87
Therefore the precise isotopic composition of strontium in a rock or mineral depends on the age and Rb/Sr ratio of that rock or mineral.

12. The Rb-Sr System Sr87 = Sr87i + Rb87(elt –1)
If we are trying to date a rock using the Rb/Sr system then the basic decay equation we derived earlier has the form
Sr87 = Sr87i + Rb87(elt –1)
In practice, it is a lot easier to measure the ratio of isotopes in a sample of rock or a mineral, rather than their absolute abundances. Therefore we can divide the above equation through by the number of Sr86 atoms which is constant because this isotope is stable and not produced by decay of a naturally occurring isotope of another element.

13. The Rb-Sr System This gives us the equation
87Sr/86Sr = (87Sr/86Sr)i + 87Rb/86Sr(elt – 1)
To solve this equation, the concentrations of Rb and Sr and the 87Sr/86Sr ratio must be measured.
The Sr isotope ratio is measured on a mass spectrometer whilst the concentrations of Rb and Sr are normally determined by XRF or ICPMS.

14. First a little bit about Rb and Sr
Rb behaves like K  micas and alkali feldspar
Sr behaves like Ca  plagioclase and apatite (but not clinopyroxene)
Rock Type Rb ppm K ppm Sr ppm Ca ppm
Ultrabasic ,000
Basaltic , ,000
High Ca granite , ,300
Low Ca granite , ,100
Syenite , ,000
Shale , ,100
Sandstone , ,100
Carbonate 3 2, ,300
Deep sea carbonate 10 2, ,400
Deep sea clay , ,000

15. The Isochron Technique
Requires 3 or more cogenetic samples with a range of Rb/Sr
3 cogenetic rocks derived from a single source by partial melting, FX, etc.
3 coexisting minerals with different K/Ca ratios in a single rock

16. Why have same value of 87Sr/86Sr?
(87Sr/86Sr)o = value at time to

20. What can we learn from this?
After each period of time, the 87Rb in each rock decays to 87Sr producing a new line
This line is still linear but is steeper than the previous line.
We can use this to tell us two important things
The age of the rock
The initial 87Sr/86Sr isotope ratio

21. Determining the Age of a Rock

22. Determining the Age of a Rock

23. Let’s look now at the initial ratio

24. The initial ratio How do we know if a series of rocks are co-genetic?
For rocks to be co-genetic, implies that they are derived from the same parent material.
This parent material would have had a single 87Sr/86Sr isotope value, ie the initial isotope ratio
Therefore, all samples derived from the same parent magma should all have the same 87Sr/86Sr isotope ratio
If they don’t, it implies that they are derived from a different parent source.

30. Other Systems
U-Th-Pb are used to date both metamorphic and igneous systems
During partial melting and fractional crystallisation of magma, U and Th are concentrated in the liquid phase and become incorporated into the more silica-rich products.
Therefore igneous rocks of granitic composition are more enriched in U and Th than basaltic or ultramafic rocks
Consequently, the continental crust has more U and Th than the upper mantle.

31. Using U-Pb data for determining ages

32. U-Th-Pb in Rocks Which minerals in rocks contain U, Th and Pb? Zircon
Monazite
Titanite
Allanite

33. Growth zoning in zircon grain

34. What is the problem here?
How do we tie the growth and breakdown of accessory phases to metamorphic reactions?
Careful study of thin-sections to clarify what metamorphic reactions are taking place and how the growth and breakdown of zircon and other accessory phases are linked to these reactions

35. Let’s come back to what we’ve been looking at in this course
Barrovian Metamorphism of Pelites
Chlorite to Biotite Zone
phengite + chlorite -> biotite + phengite-poor muscovite + quart z + H2O
Garnet Zone
chlorite + muscovite -> garnet + biotite + quartz + H2O
Sillimanite Zone
staurolite + muscovite + quartz -> garnet + biotite + sillimanite + H2O
No accessory phases mentioned!

36. A Recent Study….
A SHRIMP U–Pb and LA-ICP-MS trace element study of the petrogenesis of garnet–cordierite–orthoamphibole gneisses from the Central Zone of the Limpopo Belt, South Africa
Ian S. Buick, Jörg Hermann, Ian S. Williams, Roger L. Gibson and Daniela Rubatto

37. Objectives of the study
Constraining the timing of high-grade metamorphism is commonly difficult because age determinations that involve U–Pb geochronology of accessory phases (monazite, zircon, titanite, xenotime) need to be linked to pressure–temperature–time (P–T–t) paths through the growth/resorption of major P–T sensitive rock-forming minerals such as garnet. Making this link is non-trivial in high-grade rocks because accessory phases may: 1) pre-date and be unrelated to metamorphism (e.g., detrital zircon); 2) form during prograde metamorphic reactions involving other accessory phases and/or silicate minerals; 3) form at the metamorphic peak; 4) precipitate after the metamorphic peak, during the crystallisation of partial melt or exsolution of fluid at the solidus; 5) form along the retrograde P–T–t path due to breakdown of major rock-forming minerals; or 6) form due to solid state recrystallisation of pre-existing grains at any time during metamorphism.

40. What did they conclude?
Garnet shows little major element zoning but significant trace element zonation characterised by core to rim increases in Y and the HREE and decreases in Sc and the LREE, followed by minor increases within 100 μm of the rim due to incipient garnet resorption. Zoning patterns for Y and the HREE were controlled by the breakdown of accessory phases (allanite and xenotime ± apatite).
Allanite + Xenotime + Sillimanite = Monazite + Garnet + Quartz + H2O
Used this information to accurately constrain the timing of high-grade metamorphism in this part of the Limpopo Belt.