Radiogenic Isotope Geochemistry II

1. Radiogenic Isotope Geochemistry II Lecture 30

2. Basics of Radiogenic Isotope Geochemistry • What makes radioactive decay useful to geochemists is that it occurs at a rate that is constant and completely independent of external influences*. • The probability that a nucleus will decay is expressed by the decay constant, λ, which has units of inverse time and is unique to each radioactive nuclide. • The rate of decay is given by the basic equation of radioactive decay: • where N is the number of radioactive nuclides. This is a first order rate equation, like the ones we saw in kinetics. But unlike the rate constant, k, of kinetics, λ is a true constant and independent of everything. • This is the only equation we need in radiogenic isotope geochemistry! . Because we can derived a whole bunch of other equations from it. 

3. Basics of Radiogenic Isotope Geochemistry • We start with: • Rearrange and integrate: • and get: or • Half-life: • Our radionuclide will decay to a radiogenic daughter so that D = N0 - N and • and usually there will have been some daughter around to begin with, D0, so our equation is: N t

4. The Isochron Equation • (Aside: an approximation: for t<<1/λ, eλt = 1 + λt hence • Essentially this says that for long-lived radionuclides, the growth of the daughter is a linear function of t.) • It is more convenient to measure and work with ratios than with absolute abundances. Consequently, we divide the abundance of the radiogenic daughter by the abundance of a non-radiogenic daughter of that element, to form the ratio RD. Our equation becomes: • where RP/Dis the parent/daughter ratio. Hence for the Rb-Sr system, we have: • For reasons that will become apparent, we call this the IsochronEquation.

5. Geochronology • It is the constant rate of decay of the parent that gives rise to the time dependence, but since it easier to measure what is there rather than what is not, we tell time by measuring the accumulation of the daughter. • The above equation tell us that a radiogenic isotope ratio is a function of: • The decay constant, which we can determine experimentally (though not without uncertainty). • The parent daughter ratio (e.g., 87Rb/86Sr) • The initial ratio, R0, the radiogenic isotope ratio at t = 0 • Time. • In geochronology, we want to know t, time. • We can measure the radiogenic isotope ratio, the parent/daughter ratio and the decay constant, but we still have two unknowns. How do we proceed? • We measure these parameters in two or more samples for which t and the initial ratio are the same. With two equations, we can solve for both. • Measurement is by mass spectrometry. In the mass spectrometer, different isotopes of the same element behave somewhat differently. This produces isotopic fractionation that degrade our measurements. Fortunately, in most cases we can correct for this by measuring the ratio of a pair of non-radiogenic isotopes, e.g., 84Sr and 88Sr, compare the measured ratio to the ‘known’ value and apply a correction to the ratio of interest., e.g., 87Sr/86Sr. Since fractionation depends on mass, the fractionation of the 87Sr/86Sr ratio will be half that of the 86Sr/88Sr ratio.

6. Isochrons • This equation has the form y = a + bx. • Plotting the radiogenic isotope ratio against the parent daughter ratio, the intercept with be R0and the slope will be eλt -1. • Since the slope is a function of time, it is called an isochron. • We determine the slope statistically using linear regression (a more sophisticated form than usually used). From the slope, we easily solve for t: • Most geochronology is based on this approach. Rb-Sr isochron for a achondritic meteorite. Individual points are individual minerals. t = 4.57±0.02 Ga.

7. Isochrons • Assumptions inherent in geochronology: • All analyzed samples forming part of the isochron had the same radiogenic isotope ratio at t = 0. (System was in isotopic equilibrium). This is most likely to occur as a result of a thermal event (allowing for high diffusion rates) - so dating is restricted it igneous and metamorphic events. • The system (and analyzed ‘subsystems’ such as minerals) remained closed to loss or gain of both parent and daughter since time 0. • Accuracy and precision of the age depends on • Fit of the isochron (analytical, geological disturbance). • Range of isotope (and parent-daughter) ratios - the greater the spread, the more accurate the age. • Uncertainty in decay constant. Rb-Sr isochron for a achondritic meteorite. Individual points are individual minerals. t = 4.57±0.02 Ga.

8. Isotope Geochemistry • The best summary statement of isotope geochemistry was given by Paul Gastin a 1960 paper: • In a given chemical system the isotopic abundance of 87Sr is determined by four parameters: the isotopic abundance at a given initial time, the Rb/Sr ratio of the system, the decay constant of 87Rb, and the time elapsed since the initial time. The isotopic composition of a particular sample of strontium, whose history may or may not be known, may be the result of time spent in a number of such systems or environments. In any case the isotopic composition is the time-integrated result of the Rb/Sr ratios in all the past environments. Local differences in the Rb/Sr will, in time, result in local differences in the abundance of 87Sr. Mixing of material during processes will tend to homogenize these local variations. Once homogenization occurs, the isotopic composition is not further affected by these processes. • This statement applies to other decay systems, many of which were ‘developed’ well after 1960.

9. Decay Systems of Geologic Interest

10. Decay Systems

11. The Rb-Sr System • Both elements incompatible (Rb more so than Sr). • Both soluble and therefore mobile (Rb more so than Sr). • Range of Rb/Sr is large, particularly in crustal rocks (good for geochronology). • Subject to disturbance by metamorphism and weathering. • Both elements concentrated in crust relative to mantle - Rb more so than Sr. • 87Sr/86Sr evolves to high values in the crust, low ones in the mantle.

12. Sr Isotope Chronostratigraphy • We can’t generally radiometricly date sedimentary rocks, but there is an exception of sorts. • 87Sr/86Sr has evolved very non-linearly in seawater. This is because the residence time of Sr in seawater is short compared to 87Rb half-life, so 87Sr/86Sr is controlled by the relative fluxes of Sr to the oceans: • Rivers and dust from the continents • The mantle, via oceanic crust and hydrothermal systems. • Changes in these fluxes result in changes in 87Sr/86Sr over time. • Sr is concentrated in carbonates precipitated from seawater. By comparing the 87Sr/86Sr of carbonates with the evolution curve, an age can be assigned. • This quite accurate in the Tertiary (and widely used by oil companies), less so in earlier times.