Isochron equation

Ca = 0.000031, and Ca = 0.001824. The high relative abundance of °Ca (a result of its mass number A, which is a multiple of 4 and thus exceptionally stable cf section 11.3) is one of the two main problems encountered in this sort of dating (in Ca-rich samples, the relative enrichment in °Ca resulting from °K decay is low with respect to bulk abundance). The other problem is isotopic fractionation of calcium during petrogenesis (and also during analysis see for this purpose Russell et al., 1978). These two problems prevent extensive application of the K-Ca method, which requires extreme analytical precision. The isochron equation involves normalization to the Ca abundance... 

The low decay energy prevents accurate determinations of half-life by direct counting. Reported half-lives range from 3 to 6.6 X 10 ° a. The most recent direct determination (Lindner et al., 1989) assigns a half-life of (4.23 0.13)Xl0 °a to the decay process of equation 11.117, which is fairly consistent with the indirect estimates of Hirt et al. (1963) [(4.3 0.5) X 10 ° a]. The isochron equation is normalized to the °Os abundance ... 

To use Equation l-47c for dating, one has to overcome the difficulty that there are two unknowns, the initial amount of Nd and the age. With this in mind, the most powerful method in dating, the isochron method, is derived. To obtain the isochron equation, one divides Equation l-47c by the stable isotope of the product (such as " Nd) ... 

Therefore, to kineticists and informed geochronologists, the age obtain from an isochron equation or from Example 1-5 is an apparent age, and is called the closure age (Dodson, 1973) because it means the age since the closure of the mineral, not necessarily since the formation of the mineral. The closure age may differ from the true age or formation age because of diffusive loss (or exchange) of the daughter nuclide. For the closure age to be the same as the formation age, the mineral must have cooled down rapidly (for volcanic rocks) or formed at not-so-high a temperature (for metamorphic rocks) so that diffusive loss from the mineral is negligible. 

After transformation into the isochron equation, both the age and the initial isotopic ratio ( Nd/ Nd)o can be obtained. That is, in a given mineral, the initial concentration of the daughter nuclide Nd as well as the initial concentration of the parent nuclide in each mineral can be found. Hence, with the isochron method, we determine not only the age, but also the initial amount of the daughter and parent nuclides. 

Using Pb as the normalizing isotope of Pb, the isochron equation may be written as... 

Converting the above equation into a linear equation similar to the isochron equation requires a couple of steps. First, we normalize the above equation to a stable and nonradiogenic Mg isotope ( " Mg), yielding... 

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