The fractionation factor

The fractionation The parameter / is a fractionadon factor (often written as and is the 

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For example, if a carbonaceous sample (S) is examined mass spectrometrically, the ratio of abundances for the carbon isotopes C, in the sample is Rg. This ratio by itself is of little significance and needs to be related to a reference standard of some sort. The same isotope ratio measured for a reference sample is then R. The reference ratio also serves to check the performance of the mass spectrometer. If two ratios are measured, it is natural to assess them against each other as, for example, the sample versus the reference material. This assessment is defined by another ratio, a (the fractionation factor Figure 48.2). 

Instead of the fractionation factor (apQ) for two substances (P,Q), a slightly different fractional abundance (/pq) may be defined ... 

That is, terms of the form (1 — jr -I- jr< )/) appear in the denominator for all reactant sites having exchangeable protons and similarly in the numerator for all transition state sites. If there is no change in the fractionation factor for a site, its contribution cancels. If the solvent is a reactant, its term disappears because the solvent fractionation factor is unity by definition. 

The fractionation factor toward D versus H for the species 1 is defined relative to that for the solvent s. Represented as , it is defined as... 

Results have been expressed in a number of ways. In the Raleigh model that has been extensively used, the fractionation factor a is given by R/Rq = when the fraction of remaining substrate is/and where R is the isotopic composition of the substrate during degradation and Rq is the initial value. The enrichment factor e where e = 1000 (a - 1) has also been used. There are certain conditions that must be fulfilled for the Raleigh model to be applicable ... 

Isotope ratios for and Cl were measured for the aerobic degradation of dichlorometh-ane by a methanotroph MC8b (Heraty et al. 1999). Values of the fractionation factor (a) were 0.9586 for carbon and 0.9962 for chlorine, and kinetic isotope effects were 1.0424 for carbon and 1.0038 for chlorine. 

Figure 8. Partition coefficients (Kd) for Th and Pa and the fractionation factor (F) between Th and Pa plotted as a function of the opal and calcium carbonate percentage in settling particulate material. Note the tendency for the Kd for Th to increase with increasing carbonate fraction and decrease with increasing opal fraction. Pa shows the opposite behavior so that F increases with low opal fraction or high carbonate fraction. This plot is modified from Chase et al. (in press-b) but excludes the continental margin data also shown in that study and instead focuses exclusively on open-ocean sites.

Besides the outer sphere electron transfers, we have identified (Albery, 1975d) another class of reactions that exhibit Case III behaviour, and this example is proton transfer to cyanocarbon bases. These reactions were studied by Long and co-workers. First, by using tritium, they measured the fractionation factor for the tritium as it was pulled off the carbon as in [1], The results... 

When species or phases are in isotopic equilibrium, their isotopic ratios differ from one another by predictable amounts. The segregation of heavier isotopes into one species and light isotopes into the other is called isotope fractionation. The fractionation among species is represented by a fractionation factor a, which is determined empirically. The fractionation factor between species A and B is the ratio... 

As a rule, isotopes fractionate more strongly at low temperatures than they do at high temperature. Variation of the fractionation factor with absolute temperature 7k can be fit to a polynomial, such as,... 

In react, dataset isotope.dat contains polynomial coefficients that define temperature functions for the fractionation factors of species, minerals, and gases. The factors describe fractionation relative to a reference species chosen for each element. The reference species for oxygen and hydrogen is solvent water, H2O. CO2 and H2S, in either aqueous or gaseous form, serve as reference species for carbon and sulfur. 

Equation 19.13 is useful because it allows us to use the system s total isotopic composition, 818 Ox, to determine the compositions of the solvent and each species and mineral. The calculation proceeds in two steps. First, given <5180t and the fractionation factors aj-w and otp -w f°r the various species and minerals, we compute the composition of the solvent, applying Equation 19.13. Second, we use this result to calculate the composition of each species and mineral directly, according to Equations 19.10 and 19.11. 

The rate of change of Sm/Nd fractionation in the mantle (assumed to be at steady-state, which is not inconsistent with observations, see Albarede and Brouxel, 1987), will provide additional relationships for the fractionation factors D. Inserting expression (7.4.6) for k values into equations (7.4.5) produces... 

Since the reaction is not reversible, the EIE could not be measured. However, the secondary deuterium EIE could be estimated using the fractionation factors published by Hartshorn and Shiner (1972). This approach predicted that the secondary EIE, (KH/KD)sec, would be equal to 1.115 at 45°C. This corresponds to a (Kh/Kt)kc = 1.170 in the absence of tunnelling. Because the secondary tritium KIE is much larger than the EIE, it seems likely that tunnelling is important in this reaction. 

Now consider the phase equilibrium of a mixture of isotopes (see Fig. 7.18c for example) with isotopic analyses for each phase carried out under equilibrium conditions. Labeling the isotopomers in the two component case as primed and unprimed, as before, the fractionation factor, a and a" = 1/a, are defined... 

In 1947 Harold Urey, the 1934 Nobel Laureate, recognized that the temperature dependence of the isotope exchange equilibrium between water and calcite (the principal mineral in marine limestones) could be employed as a paleo-thermometer. At 298.15 K the fractionation factor for calcite-water is 1.0286,... 

The isotopic abundance of deuterium in the L30+ ion will differ from that in the water with which it is equilibrated. This is expressed in terms of the fractionation factor / which is the ratio of D/H ratios in the lyonium ion and the mixed solvent (water)... 

In pure D20(x = 1) this becomes KH/KD = ( >ALi703< >AL(j-i)j 1)- Consequently the observed value of KH/KD can only be used to eliminate one, not both, of the fractionation factors. The other must be considered as an adjustable parameter. That accepted, the available experimental results are consistent with Equation 11.69. 

The fractionation laws relating two or more isotope ratios are described by a relationship between the fractionation factors for the isotope ratios. Using Mg as an example, the three isotopes Mg, Mg, and Mg define two fractionation factors... 

The notation we use here is identical to that used Canfield (2001) and by most of the sulfur isotope community. The fractionation factor, a. B, is defined ... 

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