Radioactive Isotope Geochemistry

FIGURE 01: Simple Bohr-type model of a lithium atom

Radioactive Isotopes l Unstable isotopes decay to other nuclides l The rate of decay is constant, and not affected by P, T, X… l Parent nuclide = radioactive nuclide that decays l 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 40 K  40 Ar by radioactive decay Basalt  rhyolite by FX (a chemical fractionation process) Rhyolite has more K than basalt 40 K  more 40 Ar over time in rhyolite than in basalt 40 Ar/ 39 Ar 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. Time The longer 40 K  40 Ar decay takes place, the greater the difference between the basalt and rhyolite will be

Radioactive Decay The Law of Radioactive Decay  dN dt N or dN dt =N # parent atoms time  1½¼

D = Ne t - N = N(e t -1)  age of a sample (t) if we know: D the amount of the daughter nuclide produced D the amount of the daughter nuclide produced N the amount of the original parent nuclide remaining N the amount of the original parent nuclide remaining the decay constant for the system in question the decay constant for the system in question

FIGURE 03: Low atomic weight part of the chart of the nuclides

The K-Ar System 40 K  either 40 Ca or 40 Ar F 40 Ca is common. Cannot distinguish radiogenic 40 Ca from non-radiogenic 40 Ca F 40 Ar is an inert gas which can be trapped in many solid phases as it forms in them

The appropriate decay equation is: 40 Ar = 40 Ar o + 40 K(e - t -1) Where e = x a -1 (proton capture) and = x a -1 (whole process) and = x a -1 (whole process) e      

Sr-Rb System  87 Rb  87 Sr + a beta particle ( = 1.42 x a -1 )  Rb behaves like K  micas and alkali feldspar  Sr behaves like Ca  plagioclase and apatite (but not clinopyroxene)  88 Sr : 87 Sr : 86 Sr : 84 Sr ave. sample = 10 : 0.7 : 1 : 0.07  86 Sr is a stable isotope, and not created by breakdown of any other parent

For values of t less than 0.1: e t -1  t Thus for t < 70 Ga (!!) reduces to: 87 Sr/ 86 Sr = ( 87 Sr/ 86 Sr) o + ( 87 Rb/ 86 Sr) t y = b + x m = equation for a line in 87 Sr/ 86 Sr vs. 87 Rb/ 86 Sr plot Recast age equation by dividing through by stable 86 Sr 87 Sr/ 86 Sr = ( 87 Sr/ 86 Sr) o + ( 87 Rb/ 86 Sr)(e t -1) = 1.4 x a -1 = 1.4 x a -1

a bc toto 86 Sr 87 Sr o () 86 Sr 87 Sr 86 Sr 87 Rb Begin with 3 rocks plotting at a b c at time t o

After some time increment (t 0  t 1 ) each sample loses some 87 Rb and gains an equivalent amount of 87 Sr a bc a1a1 b1b1 c1c1 t1t1 toto 86 Sr 87 Sr 86 Sr 87 Rb 86 Sr 87 Sr o ()

At time t 2 each rock system has evolved  new line Again still linear and steeper line a bc a1a1 b1b1 c1c1 a2a2 b2b2 c2c2 t1t1 toto t2t2 86 Sr 87 Sr 86 Sr 87 Sr o () 86 Sr 87 Rb

Isochron technique produces 2 valuable things: 1. The age of the rocks (from the slope = t) 2. ( 87 Sr/ 86 Sr) o = the initial value of 87 Sr/ 86 Sr. 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,

Figure 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 l Both Sm and Nd are LREE F Incompatible elements fractionate  melts F Nd has lower Z  larger  liquids > does Sm

147 Sm  143 Nd by alpha decay = 6.54 x a -1 (half life 106 Ga) = 6.54 x a -1 (half life 106 Ga) l Decay equation derived by reference to the non-radiogenic 144 Nd F 143 Nd/ 144 Nd = ( 143 Nd/ 144 Nd) o + ( 147 Sm/ 144 Nd) t + ( 147 Sm/ 144 Nd) t

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. 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 System Very complex system. F 3 radioactive isotopes of U: 234 U, 235 U, 238 U F 3 radiogenic isotopes of Pb: 206 Pb, 207 Pb, and 208 Pb s Only 204 Pb is strictly non-radiogenic l U, Th, and Pb are incompatible elements, & concentrate in early melts l Isotopic composition of Pb in rocks = function of  238 U  234 U  206 Pb( = x a -1 )  235 U  207 Pb( = x a -1 )  232 Th  208 Pb( = x a -1 )

The U-Pb-Th System Concordia = Simultaneous co- evolution of 206 Pb and 207 Pb via: 238 U  234 U  206 Pb 235 U  207 Pb 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. 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 System Discordia = loss of both 206 Pb and 207 Pb 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. 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 System Concordia 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.