δ13C
In geochemistry, paleoclimatology, archaeology, and paleoceanography δ13C (pronounced "delta carbon thirteen") is a normalized ratio of the two stable isotopes of carbon—13C and 12C—reported in parts per thousand (per mille, ‰).
The definition is, in per mille:
![{\displaystyle \delta {{\vphantom {A}}_{\hphantom {}}^{\hphantom {13}}{\mkern {-1.5mu}}{\vphantom {A}}_{{\vphantom {2}}{\llap {\smash[{t}]{}}}}^{{\smash[{t}]{\vphantom {2}}}{\llap {13}}}\mathrm {C} }=\left({\frac {({{\vphantom {A}}_{\hphantom {}}^{\hphantom {13}}{\mkern {-1.5mu}}{\vphantom {A}}_{{\vphantom {2}}{\llap {\smash[{t}]{}}}}^{{\smash[{t}]{\vphantom {2}}}{\llap {13}}}\mathrm {C} }/{{\vphantom {A}}_{\hphantom {}}^{\hphantom {12}}{\mkern {-1.5mu}}{\vphantom {A}}_{{\vphantom {2}}{\llap {\smash[{t}]{}}}}^{{\smash[{t}]{\vphantom {2}}}{\llap {12}}}\mathrm {C} })_{\mathrm {sample} }}{({{\vphantom {A}}_{\hphantom {}}^{\hphantom {13}}{\mkern {-1.5mu}}{\vphantom {A}}_{{\vphantom {2}}{\llap {\smash[{t}]{}}}}^{{\smash[{t}]{\vphantom {2}}}{\llap {13}}}\mathrm {C} }/{{\vphantom {A}}_{\hphantom {}}^{\hphantom {12}}{\mkern {-1.5mu}}{\vphantom {A}}_{{\vphantom {2}}{\llap {\smash[{t}]{}}}}^{{\smash[{t}]{\vphantom {2}}}{\llap {12}}}\mathrm {C} })_{\mathrm {standard} }}}-1\right)\times 1000}](./_assets_/eb734a37dd21ce173a46342d1cc64c92/ad4a2fc51a8f08aebed2a6cac104da521542659d.svg)
where the standard is an established reference material.
The δ13C of a given compound can vary based on the sources of the precursor material and the biogeochemical processes it has undergone. For example, carbon dioxide derived from ecosystem respiration can be differentiated from carbon dioxide formed from the combustion of fossil fuels using δ13C, as the precursor materials (modern organic matter and petroleum, respectively) have different isotopic values—the basis of the "Suess Effect". In the case of photosynthesis, two plants grown adjacently with the same source of carbon dioxide may be isotopically distinguishable due to differing biochemical mechanisms and physiologies preferentially selecting for a given isotope—a process known as "isotopic fractionation".