Notation delta

Isotope ratios are reported using the delta (8) notation in parts per thousand or per mil (%o) 8 X = (Rsample — Rstandard) x 1000/R... 

The most abundant isotope of carbon has a mass of 12 atomic mass units, 12C. A less abundant stable isotope is 13C. And much less abundant is the radioactive isotope t4C, also called radiocarbon. It is convenient to express the abundances of these rare isotopes in terms of ratios of the number of atoms of the rare isotope in a sample to the number of atoms of the abundant isotope. We call this ratio r, generally a very small number. To arrive at numbers of convenient magnitude, it is conventional to express the ratio in terms of the departure of r from the ratio in a standard, which I call. v, and to express this departure in parts per thousand of s. Thus the standard delta notation is... 

The vast majority of isotopic data are reported in delta notation , where the isotopic composition is cast as the deviation of an isotopic ratio relative to the same ratio in a standard (e.g., O Neil 1986a) ... 

Figure 6. Plot of the Zn/ Zn and Zn/ Zn ratios in delta notation for ferromanganese nodules from different localities in the ocean (Marechal et al. 2000). The dashed line represents the linear mass fractionation line going through the origin and has a slope of two.

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. 

Isotope ratio mass spectrometry (IR-MS) makes use of these facts to determine the origin or the age of a sample. For convenience, the minor changes in isotopic ratios are expressed using the delta notation stating the deviation of the isotopic ratio from a defined standard in parts per thousand (%c). [8,10] The delta value of carbon, for example, is calculated from... 

Copper isotope ratios are reported in the familiar delta notation ... 

Because isotopic changes caused by chemical processes are so small, the isotopic data are typically reported as deviations in parts per thousand from a standard composition. For example, the shift in the 13C/12C ratio relative to a standard is given in delta notation by ... 

Oxygen isotopic compositions of minerals in CAIs on an oxygen three-isotope diagram. Axes are given in delta notation 81S0 =[((180/160)sampie/(180/160)s,andard)-1] x 1000, and similarly for S170. After Clayton et al. (1977). 

The deuterium content in Nature is usually expressed in D/H ratios in terms of 5 valnes (the delta notation) defined as... 

Because the variations in the actual isotopic ratio of carbon are very smalls results are reported u delta notation or parts per thousand variation in the ratio from that of the PDB... 

In introducing the delta notation, we also adopt the term e, (where e = a — 1), and the close... 

Cerling s primary objective was the identification of the processes controlling the carbon-isotope composition of soil CO2, and a quantitative means of describing the process. In terms of notation, carbon isotopes in compounds are evaluated as the ratio (R) of the rare to common stable isotope of carbon ( C/ C) and are reported in delta notation 8 C(%o) = (RJRstd 1)1,000, where R and R td refer to the carbon-isotope ratios of the sample and the international standard, respectively (Friedman and O Neil, 1977). 

Box 7.2 The delta notation for expressing stable isotope ratio values... 

Stable isotope (see Box 1.1) abundances cannot at present be determined with sufficient accuracy to be of use in studies of their natural variations. Mass spectrometers can, however, measure the relative abundances of some isotopes very accurately, resulting in stable isotope ratio measurements, for example oxygen —180/160, carbon — 13C12C and sulphur—3%/32S. Stable isotope ratios are reported in delta notation (8) as parts per thousand (%o per mil) relative to an international standard, i.e. ... 

Oxygen-isotopic ratios were determined by the CO2 equilibrium method of Epstein and Mayeda (1953). The hydrogen-isotopic ratios of water were determined by the method of Friedman and Woodcock (1957). The data are reported in the usual delta notation with SMOW as the standard (Craig, 1961). Our analyses of I.A.E.A. SLAP was —424.6%o 5D and —55.95%o... 

CSIA yields data of the isotopic composition of a single compound relative to an international standard that is usually expressed as delta notation (S) values in parts per thousand (%o) according to Eq. 1. The most common ones, the carbon and hydrogen isotopic compositions (R), are reported as and relative to Vienna Pee Dee Belemnite standard (V-PDB) and Vienna Standard Mean Ocean Water (V-SMOW), respectively [20] ... 

Delta notation of stable carbon isotopes, which is used for stable isotopic data, and is equal to [(/ sampie - f standard)// standard)llOOO, where R is the ratio of - C to C. 

Delta notation A relative measure of the difference, typically in the ratios of molar concentrations of stable isotope of hydrogen, carbon, nitrogen, oxygen, or sulfnr, between a substance and an agreed-npon standard material. 

By convention, light stable isotope values are reported using the delta notation, in parts per thousand. For example, the isotope ratio of the stable... 

Relative measurements are most commonly used to express small variations in the natural abundance of light stable isotopes and find applications in areas such as the geosciences and ecological research. No consensus exists on the appropriate units in which isotope ratios are reported, especially in the biomedical field. Most isotope ratio mass spectrometers (IRMS) report isotopic abundance in terms of delta notation ( parts per thousand or per mil ), which is a convention determined by geochemistry, because most of the original IRMS instruments were developed in isotope geochemistry laboratories. Delta units are not SI units. The SI base unit for quantity is the mole, from which atom fraction and mole fraction are derived. The units of stable isotope abundance, at.% and mol.%, are the atom and mole... 

Differences in C-enrichment level are universally expressed using the delta notation shown below ... 

We make another small point about delta notation after introducing the affinity in Chapter 18 (page 567). 

Another point that is sometimes made about delta notation is that it is commonly used in two different ways (MacDonald, 1990 Spencer, 1973). One way is the scalar difference just mentioned, as in describing the difference in V, G, etc., between two equilibrium states for example, before and after the expansion of a gas. The other is in using the progress variable, as in... 

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