U & Th Decay Series Isotope Geochemistry. Lecture 33. U and Th Decay Series. Decay Series and Radioactive Equilibrium. - PowerPoint PPT Presentation
Thermodynamics, Systems, Equilibrium & Energy
U & Th Decay Series Isotope GeochemistryLecture 33U and Th Decay Series
Decay Series and Radioactive Equilibrium238U, 235U, and 232Th decay to Pb through a series of decays (8, 7, and 6, respectively). Since the daughters tend to be neutron-rich, some also - 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:
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.
ActivitiesTraditionally, 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). Well 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.
234U-238U Dating234U is the great-granddaughter of 238U, and the first long-lived daughter in the chain. Well 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) hasnt been exactly constant through time.
230Th-234U Dating234U -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.
In 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.
Decay Series Summary
Shorter-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).(Youll have to take EAS6560 to learn about these!)Noble Isotope GeochemistryIsotopes 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 -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.Helium
He 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 -decay (a wee-tad of 3He is produced by interactions on Li such as 6Li(n,)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. He in seawater
High 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.Ne IsotopesNe 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(,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.
K-Ar40Ca is the principal product of 40K decay, but is so abundant the 40Ca/44Ca ratio doesnt 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 10s 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