Radiogenic growth

The concentration of the radioactive nuclide (reactant, such as Sm) decreases exponentially, which is referred to as radioactive decay. The concentration of the daughter nuclides (products, including Nd and He) grows, which is referred to as radiogenic growth. Note the difference between Equations l-47b and l-47c. In the former equation, the concentration of Nd at time t is expressed as a function of the initial Sm concentration. Hence, from the initial state, one can calculate how the Nd concentration would evolve. In the latter equation, the concentration of Nd at time t is expressed as a function of the Sm concentration also at time t. Let s now define time t as the present time. Then [ Nd] is related to the present amount of Sm, the age (time since Sm and Nd were fractionated), and the initial amount of Nd. Therefore, Equation l-47b represents forward calculation, and Equation l-47c represents an inverse problem to obtain either the age, or the initial concentration, or both. Equation l-47d assumes that there are no other ot-decay nuclides. However, U and Th are usually present in a rock or mineral, and their contribution to " He usually dominates and must be added to Equation l-47d. 

The other side of radioactive decay is radiogenic growth. As the parent decays away, the number of atoms of the daughter increases. Let D denote the number of daughter atoms (note that D is not diffusivity here), then D grows as... 

The most commonly used radioactive-radiogenic system in thermochronology is the " °K-" °Ar system, often refined as the °Ar- Ar method. Recently, the U-Th-He method has been developed with applications to understand erosion. Below, the closure temperature relation is first derived using a simple method. Then, diffusive loss and radiogenic growth of °Ar are examined in more detail. 

The next section discusses diffusive loss and radiogenic growth in more detail. Because the full problem of diffusive loss and radiogenic growth is complicated, to build our understanding of the problem, we start from simple cases and move to more realistic cases. Readers who do not wish to go through the detailed mathematical analyses may jump to Section 5.2.3. 

S.2.2 Mathematical analyses of diffusive loss and radiogenic growth... 

Without considering radiogenic growth, effectively we are considering a non-radiogenic isotope such as Ar. Two effective shapes, plane sheet and solid sphere, are considered here. The effective shape is not necessarily the physical shape diffusive anisotropy must also be considered in determining the effective shape (Section 3.2.11 and Figure 3-13). 

The above solutions are for diffusive loss only, without considering radiogenic growth. For the case of continuous radiogenic growth of " Ar, the fraction of Ar loss is significantly smaller because recently produced Ar would not have had much time to diffuse away. 

S.2.2.2 Isothermal diffusive ioss and constant radiogenic growth rate... 

In this section, we treat the full problem of time-dependent D and time-depen-dent radiogenic growth. To avoid confusion, we use symbol f to denote time and t to denote age. The relation between them is shown in Figure 5-17, where tf is time since formation (also the formation age), tc is the time of closure, and f is the closure age. 

It has been recognized that the Lu-Hf isotopic system in zircon is a powerful tool for deciphering the evolution of the earth s crust and mantle. " Zircon normally contains 0.5-2 wt % Hf, which results in an extremely low Lu/Hf ratio (" Lu/" Hf < 0.002) and consequently a negligible radiogenic growth of Hf due to the decay of Lu. Therefore, the Hf/" Hf ratio of zircon can be regarded as the initial value at the time when it crystaUized. LA-ICP-MS with a multiple ion collector system has also been employed to study the hafnium isotopic composition of zircon and baddeleyite standards in U-Pb geochronology. °°... 

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