Initial isotope ratio

If analyses for 3 or more cogenetic samples are available and believed to share the same initial or detrital and both the age and initial isotopic ratios are... 

Equations 7.17 and 7.18 show that KIEs can be obtained by comparing isotopic ratios of reactant or product with the initial isotope ratio of reactant as the reaction progresses. 

A specific example of applications in the second category is the dating of rocks. Age determination is an inverse problem of radioactive decay, which is a first-order reaction (described later). Because radioactive decay follows a specific law relating concentration and time, and the decay rate is independent of temperature and pressure, the extent of decay is a measure of time passed since the radioactive element is entrapped in a crystal, hence its age. In addition to the age, the initial conditions (such as initial isotopic ratios) may also be inferred, which is another example of inverse problems. 

Because the above equation is identical to the diffusion equation of a stable component, it can be solved the same way. After solving for w, then C can be found as we . For diffusion of two isotopes, one stable and one radioactive, because they have the same diffusivity, the concentration profile for the radioactive nuclide is simply the concentration profile of the stable isotope multiplied by either (i) Toe , where Fq is the initial isotopic ratio, or (ii) F, where F is the isotopic ratio at the time of measurement of the profiles. 

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. 

Figure 5-9 Al- Mg isochron for a calcium-aluminum-rich inclusion (CAI) E60. The initial isotopic ratio of (26ai/27ai)o 4,52 X 10 . Adapted from Amelin et al. (2002).

Equation (8.47), with t = 0 and the composition of lead from meteoritic troilite used for the initial isotopic ratio of lead, was used by Clair Patterson (1955,1956) to determine the age of the Earth. In the 1950s, the largest uncertainty in determining the age of the Earth was the composition of primordial lead. In 1953, Patterson solved this problem by using state-of-the-art analytical techniques to measure the composition of lead from troilite (FeS) in iron meteorites. Troilite has an extremely low U/Pb ratio because uranium was separated from the lead in troilite at near the time of solar-system formation. Patterson (1955) then measured the composition of lead from stony meteorites. In 1956, he demonstrated that the data from stony meteorites, iron meteorites, and terrestrial oceanic sediments all fell on the same isochron (Fig. 8.20). He interpreted the isochron age (4.55+0.07 Ga) as the age of the Earth and of the meteorites. The value for the age of the Earth has remained essentially unchanged since Patterson s determination, although the age of the solar system has been pushed back by —20 Myr. 

Three types of isochron diagrams are used in discussions of short-lived radionuclides. An internal isochron is one based entirely on measurements from the object being dated. By measuring several minerals with different parent/daughter elemental ratios, one can obtain an array of data that gives both the initial ratio (NR/Ns)a and the initial isotopic ratio of the daughter element Figure 8.25 shows an example of an internal isochron for an... 

Often, however, the sample does not lend itself to measurements of multiple phases. In these cases, one can create a model isochron in which the initial isotopic ratio of the daughter element (D(/Dref) is assumed and is used to anchor the -intercept. With this assumption, a single measurement can provide the initial ratio [(NR/Ns)o of an object. A third type of isochron diagram makes the assumption that a group of bodies all formed from the same homogeneous isotopic reservoir at the same time. This whole-rock isochron is constructed from bulk measurements of each sample, and the resulting slope and initial ratio describe the reservoir from which all of the samples formed. 

Using the total abundance of elemental H = 2.79 x lo10 per million silicon atoms in solar-system matter and an initial isotope ratio in the Sun of D/H = 1.5 x 10-5, as determined in today s interstellar medium (ISM), the D isotope has... 

A practical application of eqs. (16.6), (16.7) and (16.8) is the calculation of the age of the solar system. MS analysis of meteorites containing negligible amounts of U gives the following values for the isotope ratios of the Pb isotopes 2 Pb Pb = 9.4 and 207pb 204pb 2Q 3 jf these values are assumed to be the initial isotope ratios at the time of formation of the solar system, the age is obtained from the present isotope ratios of the Pb isotopes in the solar system and the ratios of the present abundances of U and Pb, for example by application of eq. (16.6) ... 

Usually, the isotopic separation within one equilibrium stage is very small, and therefore, this effect is very difficult to measure. To solve this problem one can either transfer the whole effect into one phase, or one can apply a multiplication process (see Chap. 2.5). By means of a mass balance it was shown that the isotopic shift in one phase (e.g. phase A) increases, the smaller the mass ratio becomes for phases A/B. In the other phase (phase B) the isotope ratio approximates the initial ratio which is equal to the ratio of the starting material This procedure has the advantage that, except for the initial isotope ratio, only that of the phase with the smaller sample amount has to be analyzed for the determination of a. One disadvantage is the relatively small amount of enriched isotopes in the phase to be analyzed. 

Ca/ °Ca)f4 o isotope ratio of stage No. N and initial isotope ratio... 

In these experiments the calcium distribution ratio between the Dowex 50 resin and the solution was established to be about ten by using the corresponding amounts of exchanger and CaCL salt. With such a distribution ratio, the isotopic fractionation effect is almost completely shifted into the solution, whereas the initial isotope ratio is present in the resin phase (see Chap. 2,4). Under this condition and under... 

The initial 143Nd/144Nd ratio of the bulk silicate Earth is obtained from the measurement of initial isotope ratios in primitive chondritic meteorites. Over time, therefore, the Earth should evolve along an evolution line, defined by the Sm/Nd ratio of chondrites. However, during mantle melting both Nd and the parent element Sm are incompatible (i.e. they are readily incorporated into the melt phase during... 

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