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.