Carbon and nitrogen isotope analyses. For analyses of 13C and 15N ratios, ~0.1-mg solid samples were weighed and placed into tin cups that were crimped tightly closed. The analytical system
used was an elemental analyzer–isotope-ratio mass spectrometer (EA-IRMS), and consisted of an elemental analyzer (EA, Carlo
Erba 1108, Carlo Erba, Italy), a continuous-flow interface (Conflo II, Thermo Fisher Scientific, Bremen, Germany) and an isotope-ratio
mass spectrometer (Finnigan MAT Delta Plus XL, Thermo Electron, Waltham, MA). The oxidation furnace of the EA was operated
at 1020 °C, the reduction furnace temperature was at 650 °C, and the chromatographic column was heated at 60 °C. Isotope ratios
are reported in terms of δ13C values relative to the international Vienna Pee Dee Belemnite (VPDB) standard and δ15N values relative to the international Air, both of which are IAEA standards. The δ notation is explained later in this article.
Sulfur isotope analyses. Individual solid samples of 0.08–0.10 mg were mixed with 0.5 mg V2O5, weighed into tin cups, and sealed. The analysis was accomplished using a second EA–IRMS, that was composed of an elemental
analyzer (Eurovector, model 3000r), an interface (Dilutor, Micromass Ltd.), and an isotope-ratio mass spectrometer (Isoprime,
Micromass Ltd.). The oxidation furnace of the EA was operated at 1030 °C. The gas flows were 10 mL O2/min and 150 mL He/min. Isotope ratios are reported in terms of δ34S values relative to the international Canyon Diablo troilite (CDT) standard.
Hydrogen and oxygen isotope analyses. Before analysis, solid samples were equilibrated for several days at ambient temperature with water vapor by exposure to the
laboratory atmosphere to fully exchange labile H/D sites and any water present in a hydrated form (6–9). Following equilibration,
~0.2 mg-samples were weighed into silver boats which were then crimped tightly. For solid samples, researchers used a thermal
conversion–elemental analyzer (TCEA, Finnigan, Thermo) interfaced to an isotope-ratio mass spectrometer (TCEA–IRMS, Finnigan
Delta Plus XL, Thermo). The same system was used for liquid samples, but a direct liquid-injection port was fitted in place
of the autosampler. The TCEA pyrolyzes the samples at 1350 °C to quantitatively generate H2 and CO, which are separated chromatographically at 85 °C. Isotope ratios are reported in terms of δD values and δ18O values relative to the international Vienna Standard Mean Ocean Water (VSMOW) standard.
Terminology for isotopic relationships between precursors and products.
Isotopic calculations are based on only two systems of equations. The first system uses mass balances and the second involves
integrated forms of rate equations that pertain only to kinetically controlled isotopic fractionations. Equations describing
mass balances are exact when cast in terms of fractional abundances [e.g.,
13C/(12C + 13C)]. In contrast, the assessments of differential rates are based on isotope ratios (e.g.,
13C/12C). When these systems must be blended, either approximations or equations with multiple terms are used. Additional information
is available in reference 10.
The relevant isotopic parameters are stoichiometry (n), isotopic abundance (δ), the magnitude of the isotopic effect (ε), and a variable related to the conversion of reactants
to products (f). The following is an explanation of these terms.