3Decay Series and Radioactive Equilibrium 238U, 235U, and 232Th decay to Pb through a series of α decays (8, 7, and 6, respectively). Since the daughters tend to be neutron-rich, some also β- decay. Most of these are too short-lived to be useful, but the longer-lived ones have uses in geology, geochronology, and oceanography.Consider a daughter (e.g., 234U) that is both radiogenic and radioactive. The rate of change of its abundance is its rate of production less its rate of decay:The steady-state condition is:andSo that:This is the condition that a system to which a system will eventually return if perturbed; i.e., the (radioactive) equilibrium condition.The rate at which a system returns to equilibrium occurs at a predictable rate. Therefore, the extent of disequilibrium is a function of time and can be used for geochronology.
4‘Activities’Traditionally, decay series nuclides were measured by measuring their decay (using alpha or gamma detectors). As a consequence, the abundances were traditionally reported as their (radio)activity: the number of decays per unit time (usually dpm, although the SI unit is the bacquerel, dps).Activity is related to atomic abundance through the basic equation:the quantity on the left is the activity.The activity is written as the isotope in parentheses, e.g., (234U). We’ll now mainly use activity and this notation.The longer-lived nuclides are now measured by mass spectrometry, but use of activity has stuck, partly because it is useful.Radioactive equilibrium is the condition where activities of parent and daughter are equal.
5234U-238U Dating234U is the great-granddaughter of 238U, and the first long-lived daughter in the chain. We’ll ignoring the two short-lived intermediates (assuming they quickly come to equilibrium).The half-live of 234U is 246,000 yrs, that of 238U is 4.47 billion years. On times scales of interest in this system, the abundance (and activity) of 238U does not change.The activity of 234U then can be expressed as:After long times, the activity ratio will be 1. Before that, it will be a function of time. If we know the initial ratio, we can use it as a geologic clock.Coral carbonates incorporate U from seawater, which has (234U/238U) ≈ 1.15 (why?). After many half-lives, the ratio will decline to 1. Hence we can use this to date corals. Unfortunately, (234U/238U) hasn’t been exactly constant through time.
6230Th-234U Dating234U α-decays to 230Th (half-life: 75,000 yrs). Disequilibrium between U and Th is greater than among U isotopes, and in this sense this is a better geochronological tool.We can consider two possibilities:234U and 238U were also in disequilibrium (e.g., corals), in which case we much take account of the (234U/238U) ratio.234U and 238U were also in equilibrium (volcanic rocks), in which case we can ignore 234U and treat 230Th as if it were the direct daughter of 238U.For the former case:This technique has been extensively used for dating corals (which exclude Th, so the ratio on the left starts at close to 0). Because corals also incorporate C, it has been used to calibrate 14C dates beyond the point where they can be calibrated by dendrochronology.Because reef-building corals live at sealevel, dating of fossil corals has provided a record of sealevel change as the last glacial period ended. This tells us how ice volume changed.It is also used to date carbonates in caves, and by dating ‘spelothem’ coatings on cave painting, constrain the age of the cave paintings.
7230Th-238U DatingIn volcanic rocks, we can assume 234U and 238U are in equilibrium. Here we divide by the activity of the long-lived Th isotope, 232Th (half-life 14 billion years). It does not decay appreciably on the time scales of interest.The relevant equation is:If we plot a series of cogenetic samples on a (230Th/232Th) vs (238U/232Th) plot, the slope will be a function of time. Unlike the conventional isochron equation, the intercept is also a function of time.The line pivots around the ‘equipoint’ and after many half-lives will have a slope of 1: the equiline.
8Decay Series SummaryShorter-lived radionuclides have also been used for dating, including 226Ra (t1/2 = 1600 yr), 231Pa (t1/2 33,000 yrs), and 210Pb (t1/2 = 22 yrs).Short-lived radionuclides are also used to place constraints on rates and extent of melting in the mantle, on mantle Th/U ratios, and on sedimentation rates and processes within the ocean related to adsorption phenomena (of Th in particular).(You’ll have to take EAS6560 to learn about these!)
9Noble Isotope Geochemistry Isotopes of all 6 noble gases are produced to some degree by nuclear processes:4He by alpha decay40Ar by 40K decayheavy Xe isotopes (and Kr) by U fissionRn by U decayExtinct radionuclides: 129Xe/130Xe varies in the Earth (and solar system) due to decay of the ‘fossil’ radionuclide 129I (t1/2 = 16 Ma). Other Xe isotopes also show effects of 244Pu fission (t1/2 = 82 Ma), but hard to separate from 238U fission.Ne by nuclear reactions initiated by interactions with neutrons and α-particles (these can also produce 3He).All to some degree by cosmic-ray interactions (in the atmosphere or at the surface of planetary bodies).The last two processes affect other elements, but are more significant on the noble gases because they are so rare.
10HeliumHe is the only element for which the Earth is not a closed system - it is light enough to ‘bleed’ to space from the atmosphere. He continually leaks from the Earth to replace it; residence time in the atmosphere is a couple of million years.The usual (but not universal) convention in the case of 3He is to put the radiogenic isotope in the denominator, i.e., 3He/4He. Ratios are commonly reported relative to the atmospheric value (1.4 x 10-6) as R/RA.These ratios are very low in the crust because it is outgassed and 4He is produced by α-decay (a wee-tad of 3He is produced by interactions on Li such as 6Li(n,α)3He - limiting the ratio to ~0.01 R/RA.Higher ratios are found in mantle-derived volcanic rocks - telling us that the mantle has not been completely outgassed. OIB have higher 3He/4He (in most, but not all, cases), indicating they come from a less degassed reservoir. This supports the notion that OIB are produced by mantle plumes that rise from the deepest part of the mantle.
11He in seawaterHigh 3He/4He values were first discovered in deep ocean water over mid-ocean ridges - pumped into the ocean by hydrothermal systems (this led to the discovery of ‘black smokers’).3He/4He is still used to ‘prospect’ for hydrothermal vents and as a tracer of ocean circulation.
12Ne Isotopes Ne isotopes vary in the solar system due to mass dependent fractionationcosmogenic production (not relevant to planetary interiors)‘nucleogenic’ production, particularly of 21Ne through reactions such as 18O(α,n) 21Ne.Atmospheric Ne is depleted in light Ne isotopes in proportion to mass - indicating mass dependent fractionation, due to preferential escape of lighter Ne isotopes.The degree to which this happened in the early Earth or in the precursor materials that formed the Earth is not entirely clear.Ne in mantle-derived rocks is less light isotope-depleted and some ratios approach those in the Sun.‘Mantle’ and crustal Ne (including Ne dissolved in old groundwater and petroleum) is also enriched in 21Ne - a consequence of nucleogenic production.MORB tend to have higher 21Ne/22Ne than OIB. Nucleogenic production rate depends on U/Ne ratio - so these data also suggest the OIB reservoir is less degassed than the MORB ones.Most or all volcanic rocks suffer some atmospheric contamination, so the data lie on line point to atmospheric Ne.
13K-Ar40Ca is the principal product of 40K decay, but is so abundant the 40Ca/44Ca ratio doesn’t change much.Since Ar is a rare gas, radiogenic 40Ar is readily detected.Because volcanic rocks almost completely degas upon eruption, Ar/K ratios are near 0, and any initial Ar can, to a first approximation, be neglected (or assumed to have the atmospheric ratio). Because of the short half-life of 40K, 40Ar builds up rapidly, so this is an excellent system for dating relatively young materials (as young as 10’s of thousands of years).Since Ar is a rare gas, it is quite mobile and the K-Ar system is readily reset (but it can be an advantage if you are dating low-T events or processes, like catagenesis (genesis of oil and gas).In a commonly used version of this technique, the sample is irradiated with neutrons in a reactor, producing 39Ar from 39K (the principal K isotope). The K/Ar ratio can be determined from the 39Ar/36Ar ratio simultaneously with the 40Ar/36Ar ratio - this is known as ‘40-39’ dating.The 40Ar/36Ar ratio of the atmosphere is constant at 396. The initial ratio of the solar system was <<1: Thus virtually all the Ar in the atmosphere is radiogenic - derived from degassing of the Earth’s interior. This helps us understand this process.To account for the Ar in the atmosphere requires a K concentration in the silicate Earth of ~120 ppm. Estimates of K in the Earth range from about 160 to 240 ppm. This implies that 50% to 75% of the Earth’s Ar is now in the atmosphere. Conversely, as much as 50% may still be in the mantle (crust has very little).40Ar/36Ar ratios in MORB are higher (up to 40,000) than they are in OIB (up to ~10,000). Since this depends on the K/Ar ratio, it also indicates that the MORB source reservoir is more degassed than the OIB source reservoir.
14Cosmogenic NuclidesCosmic rays are high energy nuclei (mainly of H and He) from space. When they collide with nuclei in the atmosphere or the surface of the Earth, they induce nuclear reactions. The resulting particles also have high energies and can induce further reactions. The one of greatest interest is 14N(n,p)14C where the neutron is a secondary particle.A number of other nuclides are produced in this way that are useful in geochemistry and geochronology: 3He, 10Be, 21Ne, 26Al, and 36Cl. Production restricted to the atmosphere or uppermost meter of the solid Earth.Some of these are used to ‘date’ exposure of surfaces (lava flows, glacial moraines). 10Be (t1/2 15 Ma) is used to trace subduction of sediments into the mantle and also in dating sediments.36Cl (t1/2 300 ka) is used to date water in hydrology.Cosmogenic nuclides are also used to date meteorites - exposure ages are much less than ‘formation’ ages, telling us meteorites come from larger bodies in which they were shielded from cosmic rays.
15Carbon-14 Dating14C in a sample of carbon withdrawn from the atmosphere (by, for example, photosynthesis) will decay according toAssuming constant production of 14C in the atmosphere, and therefore a constant specific activity (dpm/g C), we can determine t simply by measuring the activity of 14C in the sample (traditionally by β-counting, but increasingly by accelerator mass spectrometry).The catch is that specific activity has not been constant due to:Variable production rates partly linked to solar activity (enhanced solar wind tends to deflect cosmic rays from the inner solar system).Dilution by non-radiogenic carbon (anthropogenicly by fossil fuel burning, naturally as CO2 exsolved from the ocean at the end of the last ice age.Addition of ‘bomb’ carbon from atmospheric nuclear tests.This variability requires calibration of 14C ages by U-Th dating and ‘dendrochronology’.
16‘Fossil’ Radionuclides The young Solar System was ‘hot’ in many senses, including radioactive, as we’ll see in Chapter 10. We know this from the presence of their decay products.The short-lived nuclides decay away and are now gone, but some (146Sm, 129I, 244Pu) were still around when the Earth formed and even when some of the oldest rocks formed.Mantle Xe has higher 129Xe/130Xe than the atmosphere. This indicates much of the atmosphere has formed before 129I had decayed away (16Ma × 5 = 80 Ma), producing high 129Xe/130Xe in a relatively Xe-poor mantle.Degassing of the Earth’s interior must have been a two step process: extensive early degassing, to account for atmosphere’s 129Xe deficit and much slower subsequent degassing to account for 40Ar.There is also evidence of the presence of 244Pu - but it complicated.
17142Nd/144Nd and extinct 146SmModern terrestrial rocks have higher 142Nd/144Nd than chondrites (chondrites themselves vary).This indicates the Earth, or the ‘observable’ part of it - the crust and the mantle giving rise to magmas, have 146Sm/144Nd higher than chondritic. This suggests the Earth has higher than chondritic Sm/Nd.Two common explanations: an earlier-formed low Sm/Nd crust either sunk to the bottom of the mantle or was lost through ‘collisional erosion’.Also possible 146Sm or 142Nd were not uniformly distributed in solar nebula.Early Archean (~3.8 Ma) rocks from Isua, Greenland and Nuvvuagittug, Labrador (and now a few other places) have 142Nd/144Nd different than the modern terrestrial value.146Sm would have been effectively extinct by then.The precursors/sources of these rocks must have formed very early with higher and lower Sm/Nd ratios than the bulk Earth.Among other things, it tells us that the Earth began to differentiate into incompatible element-enriched and depleted reservoirs (such as crust and residual mantle) very early.