Epsilon notation

Epsilon notation is defined similarly, although the deviations are in parts per 10,000. Comparison between these numbers is straightforward as shown in Figure 2, which plots the co-variations in Fe/ Fe and Te/ Fe of layers from BIFs in both 5 and e notation. The mass-dependent fractionation line, based on a simple harmonic oscillator approximation (Criss 1999), lies close to a line of 1.5 1 for 5 Fe-5 Te variations. For example, point A in Figure 2 has an 5 Te value of+15.0, which would be approximately equal to a 5 Fe value of+1.00, as defined here, assuming normalization to an identical reference reservoir. 

The results can be reported in the conventional delta notation of stable isotopes, which is the relative deviation in parts per one thousand of a given isotopic ratio in a sample with respect to the same ratio in a standard sample. Reporting results in the epsilon notation (in parts per 10,000 as in Zhu et al. 2000, 2002) may seem legitimate, but so far stable isotope data have overwhelmingly been reported in per mil and competing notations are a source of confusion. 

This epsilon notation gives the difference between the measured ratio in the sample and the CHUR value for the present time in parts per 10 000. The difference in the 147Sm/144Nd ratio relative to the CHUR (the elemental fractionation) is given by ... 

There is a variety of possible models for the depleted mantle. These are shown for Nd in terms of the epsilon notation (deviadon from CHUR) in Figure 6.17. 

Figure 6.3 The evolution of Nd/ Nd with rime in an individual sample (Tabic 6.4, No. 234J compared with two models of the mantle — CHUR (the chondritic uniform reservoir) and depleted mantle, A model Nd age Is the time at which the sample had the same Nd/ " d ratio as its mantle source. In this case there are two possible solutions, depending upon which mande model Is preferred. The CHUR model age is approximately 1.67 Ga and the DM model age is approximately 1.98 Ga. A similar diagram can be constructed using the epsilon notation (see Section 6,3.4) in place of...

Nd isotopes this inay be quantified in tenns of the epsilon notation (see Section 6.3.4). The general isotopic characteristics of crustal reservoirs are given in Table 6.5 and typical isotopic compositions of crustal rocks are presented in Table 6.6. 

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