In the third installment of this tutorial, the authors explain the determination of the isotopic composition of a sample from a mass spectrometric measurement, and the methods of calculation as well as the units used. This tutorial outlines the practices in common usage so that researchers new to this field can obtain a good understanding of the fundamentals involved.

The reporting of isotopic compositions from mass spectrometric (MS) measurements is not a straightforward matter because in most cases, some degree of correction is necessary to extract the true isotopic composition from the measured ion currents. Also, there is no consensus on the units in which to make the report (1). As the measurement technology and its role in the application progressed, both the methods of correction and the units have developed independently for each isotopic species under investigation. Originally, isotope practice was developed to determine small changes in natural abundance, and the notations and conventions adopted are considered by some to be unsuitable for modern high-throughput, high-enrichment work, as is practiced in tracer techniques (2).

The rationalization of stable isotopic composition reporting by the adoption of the International System of Units (SI) has been considered recently (3). In fact, the "natural" way of reporting isotopic composition is to use fractional abundance, F, defined as the quantity of a particular isotope divided by the total quantity of that element in the sample. Fractional abundance is therefore a dimensionless quantity, closely analogous to mole fraction. Unfortunately, in cases of polyisotopic species, it is often not possible to measure all of the isotopes present, and recourse is made to normalizing the quantity of the particular isotope to that of the major (most abundant) isotope present. On this basis, the isotopic abundances, R, defined in terms of the ratio to the major isotope, are related to fractional abundance via

where the subscript i specifies the particular isotopic species, and the summation runs over all the isotopes present.

Many researchers prefer to express abundance as the deviation from that observed in some standard material, and this gives rise to the concept of excess abundance ΔRⁱ_samp = Rⁱ_samp – Rⁱ_std. This scheme is favored by scientists working with nitrogen isotopes, who often quote abundance in terms of atom percent excess.

Scientists working with other light isotopes such as hydrogen, carbon, and oxygen, in the geochemical field, took this one step further and adopted a scale known as the delta value, defined in the next section; this is currently the most adopted way of reporting isotope determinations using commercial instrumentation.