text: In order to study trace metal stable isotope biogeochemistry, it is necessary to compare the relative abundances of isotopes of trace metals in a given biological, geological, or chemical pool to a standard (discussed individually for each isotope system below) and monitor how those relative abundances change as a result of various biogeochemical processes. Conventional notations used to mathematically describe isotope abundances, as exemplified here for Fe, include the isotope ratio (R), fractional abundance (F) and delta notation (δFe). Furthermore, as different biogeochemical processes vary the relative abundances of the isotopes of a given trace metal, different reaction pools or substances will become enriched or depleted in specific isotopes. This partial separation of isotopes between different pools is termed isotope fractionation, and is mathematically described by fractionation factors α or ε (which express the difference in isotope ratio between two pools), or by "cap delta" (Δ; the difference between two δ values). For a more complete description of these notations, see the isotope notation section in Hydrogen isotope biogeochemistry.