## 2.31.2. Isotope Symbols, Units, and Reference Standards[¶](#isotope-symbols-units-and-reference-standards "Permalink to this headline")
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Carbon has two primary stable isotopes, 12C and 13C. 12C is the most abundant, comprising about 99% of all carbon. The isotope ratio of a compound, \\({R}\_{A}\\), is the mass ratio of the rare isotope to the abundant isotope

(2.31.2)[¶](#equation-30-2 "Permalink to this equation")\\\[R\_{A} =\\frac{{}^{13} C\_{A} }{{}^{12} C\_{A} } .\\\]

Carbon isotope ratios are often expressed using delta notation, \\(\\delta\\). The \\(\\delta^{13}\\)C value of a compound A, \\(\\delta^{13}\\)CA, is the difference between the isotope ratio of the compound, \\({R}\_{A}\\), and that of the Pee Dee Belemnite standard, \\({R}\_{PDB}\\), in parts per thousand

(2.31.3)[¶](#equation-30-3 "Permalink to this equation")\\\[\\delta ^{13} C\_{A} =\\left(\\frac{R\_{A} }{R\_{PDB} } -1\\right)\\times 1000\\\]

where \\({R}\_{PDB}\\) = 0.0112372, and units of \\(\\delta\\) are per mil (‰).

Isotopic fractionation can be expressed in several ways. One expression of the fractionation factor is with alpha (\\(\\alpha\\)) notation. For example, the equilibrium fractionation between two reservoirs A and B can be written as:

(2.31.4)[¶](#equation-30-4 "Permalink to this equation")\\\[\\alpha \_{A-B} =\\frac{R\_{A} }{R\_{B} } =\\frac{\\delta \_{A} +1000}{\\delta \_{B} +1000} .\\\]

This can also be expressed using epsilon notation (\\(\\epsilon\\)), where

(2.31.5)[¶](#equation-30-5 "Permalink to this equation")\\\[\\alpha \_{A-B} =\\frac{\\varepsilon \_{A-B} }{1000} +1\\\]

In other words, if \\({\\epsilon }\_{A-B} = 4.4\\) ‰ , then \\({\\alpha}\_{A-B} =1.0044\\).

In addition to the stable isotopes 12C and 13C, the unstable isotope 14C is included in CLM. 14C can also be described using the delta notation:

(2.31.6)[¶](#equation-30-6 "Permalink to this equation")\\\[\\delta ^{14} C=\\left(\\frac{A\_{s} }{A\_{abs} } -1\\right)\\times 1000\\\]

However, observations of 14C are typically fractionation-corrected using the following notation:

(2.31.7)[¶](#equation-30-7 "Permalink to this equation")\\\[\\Delta {}^{14} C=1000\\times \\left(\\left(1+\\frac{\\delta {}^{14} C}{1000} \\right)\\frac{0.975^{2} }{\\left(1+\\frac{\\delta {}^{13} C}{1000} \\right)^{2} } -1\\right)\\\]

where \\(\\delta^{14}\\)C is the measured isotopic fraction and \\(\\mathrm{\\Delta}^{14}\\)C corrects for mass-dependent isotopic fractionation processes (assumed to be 0.975 for fractionation of 13C by photosynthesis). CLM assumes a background preindustrial atmospheric 14C /C ratio of 10\-12, which is used for A:sub::abs. For the reference standard A\\({}\_{abs}\\), which is a plant tissue and has a \\(\\delta^{13}\\)C value is \\(\\mathrm{-}\\)25 ‰ due to photosynthetic discrimination, \\(\\delta\\)14C = \\(\\mathrm{\\Delta}\\)14C. For CLM, in order to use the 14C model independently of the 13C model, for the 14C calculations, this fractionation is set to zero, such that the 0.975 term becomes 1, the \\(\\delta^{13}\\)C term (for the calculation of \\(\\delta^{14}\\)C only) becomes 0, and thus \\(\\delta^{14}\\)C = \\(\\mathrm{\\Delta}\\)14C.

