Radiogenic Isotope Geochemistry II Lecture 30 Basics of

Radiogenic Isotope Geochemistry II Lecture 30

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.

Basics of Radiogenic Isotope Geochemistry • We start with: • Rearrange and integrate: • and get: o Half-life: or N t • Our radionuclide will decay to a radiogenic daughter so that D = N 0 - N and • and usually there will have been some daughter around to begin with, D 0, so our equation is:

The Isochron Equation o (Aside: an approximation: for t<<1/λ, eλt = 1 + λt hence o 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/D is the parent/daughter ratio. Hence for the Rb-Sr system, we have: • For reasons that will become apparent, we call this the Isochron Equation.

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: o o • In geochronology, we want to know t, time. o • The decay constant, which we can determine experimentally (though not without uncertainty). The parent daughter ratio (e. g. , 87 Rb/86 Sr) The initial ratio, R 0, the radiogenic isotope ratio at t = 0 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. o 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. , 84 Sr and 88 Sr, compare the measured ratio to the ‘known’ value and apply a correction to the ratio of interest. , e. g. , 87 Sr/86 Sr. Since fractionation depends on mass, the fractionation of the 87 Sr/86 Sr ratio will be half that of the 86 Sr/88 Sr ratio.

Isochrons • • • This equation has the form y = a + bx. Plotting the radiogenic isotope ratio against the parent daughter ratio, the intercept with be R 0 and 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.

Isochrons • Assumptions inherent in geochronology: o o • 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 o o o 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.

Isotope Geochemistry o The best summary statement of isotope geochemistry was given by Paul Gast in a 1960 paper: • In a given chemical system the isotopic abundance of 87 Sr is determined by four parameters: the isotopic abundance at a given initial time, the Rb/Sr ratio of the system, the decay constant of 87 Rb, 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 timeintegrated 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 87 Sr. 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. o This statement applies to other decay systems, many of which were ‘developed’ well after 1960.

Decay Systems of Geologic Interest Parent Decay mode λ , yr-1 Half-life, yr Daughter Ratio Parent 40 K β+, e. c. , β- 5. 549 × 10 -10  1. 25 × 109  40 Ar, 40 Ca 40 Ar/36 Ar 40 K 87 Rb β- 1. 42 × 10 -11 4. 88 × 1010  87 Sr/86 Sr 87 Rb 138 La β- 2. 67 × 10 -12 2. 60 × 1011  138 Ce/142 Ce, 138 La 138 Ce/136 Ce 147 Sm α 6. 54 × 10 -12 1. 06 × 1011  143 Nd/144 Nd 147 Sm 176 Lu β- 1. 867 × 10 -11 3. 71 × 1010  176 Hf/177 Hf 176 Lu 187 Re β- 1. 64 × 10 -11 4. 23 × 1010  187 Os/188 Os 187 Re 232 Th α 4. 948 × 10 -11 1. 40 × 1010  208 Pb, 4 He 208 Pb/204 Pb, 232 Th 3 He/4 He 235 U 238 U α α, s. f. 9. 849 × 10 -10 7. 04 × 108  207 Pb, 4 He 207 Pb/204 Pb, 235 U 3 He/4 He 1. 5513 × 10 -10 4. 47 × 109  206 Pb, 4 He 206 Pb/204 Pb, 3 He/4 He 238 U

Decay Systems

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. 87 Sr/86 Sr evolves to high values in the crust, low ones in the mantle.

Sr Isotope Chronostratigraphy • • We can’t generally radiometricly date sedimentary rocks, but there is an exception of sorts. 87 Sr/86 Sr has evolved very non-linearly in seawater. This is because the residence time of Sr in seawater is short compared to 87 Rb half-life, so 87 Sr/86 Sr is controlled by the relative fluxes of Sr to the oceans: o o • • • Rivers and dust from the continents The mantle, via oceanic crust and hydrothermal systems. Changes in these fluxes result in changes in 87 Sr/86 Sr over time. Sr is concentrated in carbonates precipitated from seawater. By comparing the 87 Sr/86 Sr 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.