Decay chains secular equilibrium

A useful analogy for understanding secular equilibrium is visualizing a decay chain as a series of pools of water (Fig. 2). These pools eventually lead to a continuously filling pool representing a stable isotope of lead (either ° Pb, ° Pb or ° Pb). Over the timescale... 

The previous section showed that if the decay chain remains undisturbed for a period of approximately 6 times the longest half-lived intermediate nuclide then the chain will be in a state of secular equilibrium (i.e., equal activities for all the nuclides). The key to the utility of the U-series is that several natural processes are capable of disrupting this state of equilibrium. 

Secular equilibrium materials. For materials that have remained a closed system for sufficient time that secular equilibrium has been achieved, the half-lives of nuclides within the decay chain can be calculated from the relationship A,pP = A,dD. If the atom ratio P/D is measured, and one of the decay constants is well known, then the other can be readily calculated. Limitations on this approach are the ability to measure the atom ratios to sufficient precision, and finding samples that have remained closed systems for a sufficient length of time. This approach has been used to derive the present recommended half lives for °Th and (Cheng et al. 2000 Ludwig et al. 1992). 

The solution to the general decay equations is often given in textbooks (e.g., Faure 1986). However, this solution is given for initial abundances of the daughter nuclides that are equal to zero. In the most general cases, the initial abundances of the daughter nuclides are not equal to zero. For example, in many geological examples, we make the assumptions that the decay chain is in secular equilibrium. The solutions of these equations can also be used to solve simple box models of U-series nuclides where first order kinetics are assumed. 

This section describes the continuous flux melting model used in Bourdon et al. (2003) and has many similarities with the model of Thomas et al. (2002). A significant difference is that the model described here keeps track of the composition of the slab as it dehydrates. This model is based on mass balance equations for both the mantle wedge and the slab. We assume secular equilibrium in the U-series decay chain initially ... 

Since Ra and " Ra are both produced by recoil from the host mineral, it might be assumed that the production rates are equal. However, the relative recoil rates can be adjusted by considering that the parent nuclides near the mineral surface may not be in secular equilibrium due to ejection losses i.e., the activity of Th may be lower than that of Th due to recoil into groundwater of the intermediate nuclide Ra. Krisnaswami et al. (1982) calculated that the recoil rate of " Ra is 70% that of Ra if radionuclides are depleted along the decay chain in this way. 

The near vertical lines (solid) are isochrons. Ages reported in Ma. The secular equilibrium case, where the activity ratios of all parent-daughter pairs in the U-series decay chains are unity is shown by a dashed line. Ages (in Ma) are represented by squares. 

The application of the decay chain to the dating of deep sea sediments was by Piggott and Urry in 1942 using the Ionium method of dating. Actually they measured a (itself through Rn) assuming secular equilibrium had been established between... 

Secular Equilibrium A condition that occurs when a chain of radionuclides has reached a steady state condition, in which the rate of decay of daughter nuclides is balanced by their rate of formation by decay of each parent. In this condition, the radioactivity (measured in disintigrations per minute) of each radionuclide in a chain is the same. 

The above condition of equal activity of all radioactive nuclides in a decay chain (except for branch decays) is known as secular equilibrium. More detailed solutions for the concentration evolution of intermediate species can be found in Box 2-6. 

The half-lives of 238U, 235U, and 232Th are all very much longer than those of the radioactive daughter isotopes in their decay chains. Therefore, a condition known as secular equilibrium is quickly established in which the decay rates of the daughter isotopes in the decay chain equal that of the parent isotope. In a closed system, once secular equilibrium is... 

The naturally occurring heavy element decay chains (see below) where 238U - 206Pb, 235U - 207Pb, and 232Th - 208Pb and the extinct heavy element decay series Np —> Bi are examples of secular equilibrium because of the... 

The temporal resolution of the multiple parent-daughter pairs within the uranium decay chain, 238U- Th (approaching secular equilibrium with a 75 ka half-life), °Th- Ra (1,500 a) and (—32 ka) is a powerful tool. It has been used to estimate the elapsed time between subduction modification of the mantle and lava emption to the surface, and to identify multiple... 

The equations and solutions for closed-system radioactive decay chains have been known since Bateman (1910). To understand the behavior of these systems, however, it is useful to express them as a linear system of ordinary differential equations and use some basic results from linear algebra to discuss the general solutions. This treatment helps to elucidate the ideas of secular equilibrium and relaxation to equihbrium. 

Any disturbance from secular equilibrium decays back toward secular equilibrium through the decay of the shorter-lived supported chains. If the chains have significantly different decay rates, they are reasonably well decoupled and can be used to date processes comparable to the lifetimes of each chain (e.g., Condomines et al., 1988 Rubin et al., 1994 Thompson et al., 2003). As a useful rule of thumb, the time taken for a parent-daughter pair to return to approximate secular equilibrium, is about five half-lives of the shorter lived nuclide. In five half-lives, —97% of initial disequilibrium has decayed. Whether any detectable disequilibrium actually remains depends on the precision of measurements and degree of initial disequilibrium. 

In a decay chain shown in Table 1 at secular equilibrium the activities of the coupled radionuclides are equal. In a closed system, this occurs after roughly hve half-lives of the shorter-lived daughter have elapsed ( parent and daughter refer to the first and subsequent nuclides in the decay series being considered). For example, Rn (half-life = 3.8 d) is in secular equilibrium with its parent, Ra (half-life = 1,620 yr), in 20d. 

The half-life of U is four orders of magnitude greater than any of the intermediate daughters. Therefore, any closed system, regardless of the initial state, will approach a state of secular equilibrium such that the activities of all the intermediate daughters are the same and are equal to the activity (Bateman, 1910). External processes that fractionate nuclides within the decay chain disrupt the state of secular equilibrium. The subsequent growth or decay of the intermediate nuclides back towards equilibrium with can be used to date the fractionation event (see Ivanovich et al., 1992). Uranium-thorium dating of speleothems is possible because of the extreme... 

In the 13 radiodecay chain there are, between Ra and "Pb, three alpha decays and two beta decays taking place within a reasonably short time span compared to the half-lives of " Ra and Vb (Table 11-11). When a radioactive daughter has a short half-life compared to the parent, so-called secular equilibrium is achieved when parent and daughter remain together. Mathematically this relationship is expressed ... 

The temporal resolution of the multiple parent-daughter pairs within the uranium decay chain, 23 u 230rj (approaching secular equilibrium with a 75 ka half-life), (1,500 a) and... 

Th and U decay chains. They are found in association with Th and U minerals at the same radioactivity level (secular equilibrium) but - due to their much shorter half-lives - in very small mass concentrations. 

Unlike uranium, intermediate daughter isotopes from Th decay all have short half-lives such that secular equilibrium is achieved across the chain within 30 years. 

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