radioactive isotope geochemistry. figure 01: simple bohr-type model of a lithium atom
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Radioactive Isotope Geochemistry
FIGURE 01: Simple Bohr-type model of a lithium atom
Radioactive Isotopes
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
Isotopic variations between rocks, etc. due to:1. Mass fractionation (as for stable isotopes)
Only effective for light isotopes: H He C O S
Isotopic variations between rocks, etc. due to:1. Mass fractionation (as for stable isotopes)2. 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 basalt40K more 40Ar over time in rhyolite than in basalt40Ar/39Ar ratio will be different in each
Isotopic variations between rocks, etc. due to:1. Mass fractionation (as for stable isotopes)2. Daughters produced in varying proportions
resulting from previous event of chemical fractionation
3. TimeThe longer 40K 40Ar decay takes place, the greaterthe difference between the basalt and rhyolite will be
Radioactive Decay
The Law of Radioactive Decay
- µ -dNdt
N or dNdt
= Nl
# p a
ren t
ato
ms
time
1
½
¼
D = Nelt - N = N(elt -1)
age of a sample (t) if we know: D the amount of the daughter nuclide produced N the amount of the original parent nuclide remaining
l the decay constant for the system in question
FIGURE 03: Low atomic weight part of the chart of the nuclides
The K-Ar System40K either 40Ca or 40Ar
40Ca is common. Cannot distinguish radiogenic 40Ca from non-radiogenic 40Ca
40Ar is an inert gas which can be trapped in many solid phases as it forms in
them
The appropriate decay equation is:40Ar = 40Aro + 40K(e-lt -1)
Where le = 0.581 x 10-10 a-1 (proton capture)
and l = 5.543 x 10-10 a-1 (whole process)
lleæ
èçöø÷
Sr-Rb System
· 87Rb 87Sr + a beta particle (l = 1.42 x 10-11 a-1)
· Rb behaves like K micas and alkali feldspar
· Sr behaves like Ca plagioclase and apatite (but not clinopyroxene)
· 88Sr : 87Sr : 86Sr : 84Sr ave. sample = 10 : 0.7 : 1 : 0.07
· 86Sr is a stable isotope, and not created by breakdown of any other parent
For values of lt less than 0.1: elt-1 lt
Thus for t < 70 Ga (!!) reduces to:
87Sr/86Sr = (87Sr/86Sr)o + (87Rb/86Sr)lt
y = b + x m
= equation for a line in 87Sr/86Sr vs. 87Rb/86Sr plot
Recast age equation by dividing through by stable 86Sr
87Sr/86Sr = (87Sr/86Sr)o + (87Rb/86Sr)(elt -1)
l = 1.4 x 10-11 a-1
a b c to86Sr
87Sr
o( )
86Sr
87Sr
86Sr
87Rb
Begin with 3 rocks plotting at a b c at time to
After some time increment (t0 t1) each sample loses some 87Rb and gains an equivalent amount of 87Sr
a b c
a1
b1
c1t1
to
86Sr
87Sr
86Sr
87Rb
86Sr
87Sr
o( )
At time t2 each rock system has evolved new line
Again still linear and steeper line
a b c
a1
b1
c1a2
b2
c2
t1
to
t2
86Sr
87Sr
86Sr
87Sr
o( )
86Sr
87Rb
Isochron technique produces 2 valuable things:1. The age of the rocks (from the slope = lt)2. (87Sr/86Sr)o = the initial value of 87Sr/86Sr
. Rb-Sr isochron for the Eagle Peak Pluton, central Sierra Nevada Batholith, California, USA. Filled circles are whole-rock analyses, open circles are hornblende separates. The regression equation for the data is also given. After Hill et al. (1988). Amer. J. Sci., 288-A, 213-241.
Figure 9-13. Estimated Rb and Sr isotopic evolution of the Earth’s upper mantle, assuming a large-scale melting event producing granitic-type continental rocks at 3.0 Ga b.p After Wilson (1989). Igneous Petrogenesis. Unwin Hyman/Kluwer.
The Sm-Nd System
Both Sm and Nd are LREE Incompatible elements fractionate melts Nd has lower Z larger liquids > does Sm
147Sm 143Nd by alpha decayl = 6.54 x 10-13 a-1 (half life 106 Ga)
Decay equation derived by reference to the non-radiogenic 144Nd 143Nd/144Nd = (143Nd/144Nd)o
+ (147Sm/144Nd)lt
FIGURE 06: Sm-Nd isochron plot f
Data from DePaolo, D. J. and Wasserburg, G. J. (1979)
Evolution curve is opposite to Rb - Sr
Estimated Nd isotopic evolution of the Earth’s upper mantle, assuming a large-scale melting or enrichment event at 3.0 Ga b.p. After Wilson (1989). Igneous Petrogenesis. Unwin Hyman/Kluwer.
The U-Pb-Th SystemVery complex system.
3 radioactive isotopes of U: 234U, 235U, 238U 3 radiogenic isotopes of Pb: 206Pb, 207Pb, and 208Pb
Only 204Pb is strictly non-radiogenic U, Th, and Pb are incompatible elements, &
concentrate in early melts Isotopic composition of Pb in rocks = function of
238U 234U 206Pb (l = 1.5512 x 10-10 a-1) 235U 207Pb (l = 9.8485 x 10-10 a-1) 232Th 208Pb (l = 4.9475 x 10-11 a-1)
The U-Pb-Th SystemConcordia = Simultaneous co-
evolution of 206Pb and 207Pb via:
238U 234U 206Pb235U 207Pb
Concordia diagram illustrating the Pb isotopic development of a 3.5 Ga old rock with a single episode of Pb loss. After Faure (1986). Principles of Isotope Geology. 2nd, ed. John Wiley & Sons. New York.
FIGURE 11: Holmes-Houterman diagram
FIGURE 12: A two-stage Holmes-Houterman diagram
Modified from Long, L. E. (1999)
The U-Pb-Th SystemDiscordia = loss of both
206Pb and 207Pb
Concordia diagram illustrating the Pb isotopic development of a 3.5 Ga old rock with a single episode of Pb loss. After Faure (1986). Principles of Isotope Geology. 2nd, ed. John Wiley & Sons. New York.
The U-Pb-Th SystemConcordia diagram after 3.5 Ga total evolution
F Concordia diagram illustrating the Pb isotopic development of a 3.5 Ga old rock with a single episode of Pb loss. After Faure (1986). Principles of Isotope Geology. 2nd, ed. John Wiley & Sons. New York.