Δ13C#Reference standard

{{Short description|Measure of relative carbon-13 concentration in a sample}}

Image:Benthic foraminifera.jpg samples]]

In geochemistry, paleoclimatology, and paleoceanography δ¹³C (pronounced "delta thirteen c") is an isotopic signature, a measure of the ratio of the two stable isotopes of carbon—¹³C and ¹²C—reported in parts per thousand (per mil, ‰).{{cite book|last=Libes|first=Susan M.|title=Introduction to Marine Biogeochemistry, 1st edition.|year=1992|publisher=Wiley|location=New York}} The measure is also widely used in archaeology for the reconstruction of past diets, particularly to see if marine foods or certain types of plants were consumed.{{cite journal |last1=Schwarcz |first1=Henry P. |last2=Schoeninger |first2=Margaret J. |title=Stable isotope analyses in human nutritional ecology |journal=American Journal of Physical Anthropology |date=1991 |volume=34 |issue=S13 |pages=283–321 |doi=10.1002/ajpa.1330340613|doi-access=free }}

The definition is, in per mille:

: $\delta \ce{^{13}C} = \left( \frac{(\ce{^{13}C}/\ce{^{12}C})_\mathrm{sample}}{(\ce{^{13}C}/\ce{^{12}C})_\mathrm{standard}} - 1 \right) \times 1000$

where the standard is an established reference material.

δ¹³C varies in time as a function of productivity, the signature of the inorganic source, organic carbon burial, and vegetation type. Biological processes preferentially take up the lower mass isotope through kinetic fractionation. However some abiotic processes do the same. For example, methane from hydrothermal vents can be depleted by up to 50‰.McDermott, J.M., Seewald, J.S., German, C.R. and Sylva, S.P., 2015. [http://www.pnas.org/content/pnas/112/25/7668.full.pdf Pathways for abiotic organic synthesis at submarine hydrothermal fields]. Proceedings of the National Academy of Sciences, 112(25), pp.7668–7672.

Reference standard

The standard established for carbon-13 work was the Pee Dee Belemnite (PDB) and was based on a Cretaceous marine fossil, Belemnitella americana, which was from the Peedee Formation in South Carolina. This material had an anomalously high ¹³C:¹²C ratio (0.0112372{{Cite journal|last=Craig|first=Harmon|date=1957-01-01|title=Isotopic standards for carbon and oxygen and correction factors for mass-spectrometric analysis of carbon dioxide|url=https://dx.doi.org/10.1016/0016-7037%2857%2990024-8|journal=Geochimica et Cosmochimica Acta|language=en|volume=12|issue=1|pages=133–149|doi=10.1016/0016-7037(57)90024-8|bibcode=1957GeCoA..12..133C|issn=0016-7037|url-access=subscription}}), and was established as δ¹³C value of zero.

Since the original PDB specimen is no longer available, its ¹³C:¹²C ratio can be back-calculated from a widely measured carbonate standard NBS-19, which has a δ¹³C value of +1.95‰.{{Cite journal|last1=Brand|first1=Willi A.|last2=Coplen|first2=Tyler B.|last3=Vogl|first3=Jochen|last4=Rosner|first4=Martin|last5=Prohaska|first5=Thomas|date=2014-03-20|title=Assessment of international reference materials for isotope-ratio analysis (IUPAC Technical Report)|journal=Pure and Applied Chemistry|language=en|volume=86|issue=3|pages=425–467|doi=10.1515/pac-2013-1023|issn=1365-3075|hdl=11858/00-001M-0000-0023-C6D8-8|s2cid=98812517|hdl-access=free}} The ¹³C:¹²C ratio of NBS-19 was reported as $0.011078/0.988922=0.011202$ .{{Cite journal|last1=Meija|first1=Juris|last2=Coplen|first2=Tyler B.|last3=Berglund|first3=Michael|last4=Brand|first4=Willi A.|last5=De Bièvre|first5=Paul|last6=Gröning|first6=Manfred|last7=Holden|first7=Norman E.|last8=Irrgeher|first8=Johanna|last9=Loss|first9=Robert D.|date=2016-01-01|title=Isotopic compositions of the elements 2013 (IUPAC Technical Report)|journal=Pure and Applied Chemistry|language=en|volume=88|issue=3|pages=293–306|doi=10.1515/pac-2015-0503|issn=1365-3075|doi-access=free|hdl=11858/00-001M-0000-0029-C408-7|hdl-access=free}} Therefore, one could calculate the ¹³C:¹²C ratio of PDB derived from NBS-19 as $0.011202 / (1.95/1000 +1)= 0.011202/1.00195=0.01118$ .

Note that this value differs from the widely used PDB ¹³C:¹²C ratio of 0.0112372 used in isotope forensics{{Cite book|last=Meier-Augenstein|first=Wolfram|url=https://www.worldcat.org/oclc/975998493|title=Stable isotope forensics : methods and forensic applications of stable isotope analysis|date=28 September 2017|isbn=978-1-119-08022-0|edition=Second|location=Hoboken, NJ|oclc=975998493}} and environmental scientists;{{Cite book|title=Stable Isotopes in Ecology and Environmental Science|date=2007-07-14|publisher=Blackwell Publishing Ltd|isbn=978-0-470-69185-4|editor-last=Michener|editor-first=Robert|location=Oxford, UK|language=en|doi=10.1002/9780470691854|editor-last2=Lajtha|editor-first2=Kate|editor-link2=Kate Lajtha}} this discrepancy was previously attributed by a Wikipedia author to a sign error in the interconversion between standards, but no citation was provided. Use of the PDB standard gives most natural material a negative δ¹³C.[http://www.uga.edu/sisbl/stable.html#calib Overview of Stable Isotope Research]. The Stable Isotope/Soil Biology Laboratory of the University of Georgia Institute of Ecology. A material with a ratio of 0.010743 for example would have a δ¹³C value of −44‰ from $(0.010743\div 0.01124 - 1) \times 1000$ .

The standards are used for verifying the accuracy of mass spectroscopy; as isotope studies became more common, the demand for the standard exhausted the supply. Other standards calibrated to the same ratio, including one known as VPDB (for "Vienna PDB"), have replaced the original.Miller & Wheeler, Biological Oceanography, p. 186.

The ¹³C:¹²C ratio for VPDB, which the International Atomic Energy Agency (IAEA) defines as a δ¹³C value of zero is 0.01123720.{{cite web |url=https://www-pub.iaea.org/MTCD/publications/PDF/te_825_prn.pdf |title=Reference and intercomparison materials for stable isotopes of light elements |publisher=International Atomic Energy Agency |date=1995}}

Causes of ''δ''<sup>13</sup>C variations

Methane has a very light δ¹³C signature: biogenic methane of −60‰, thermogenic methane −40‰. The release of large amounts of methane clathrate can affect global δ¹³C values, as at the Paleocene–Eocene Thermal Maximum.

{{cite journal

|title=Sedimentary response to Paleocene-Eocene Thermal Maximum carbon release: A model-data comparison

|journal=Geology

|volume=36 |issue=4 |pages=315–318

|year=2008

|doi=10.1130/G24474A.1

|bibcode=2008Geo....36..315P}}

More commonly, the ratio is affected by variations in primary productivity and organic burial. Organisms preferentially take up light ¹²C, and have a δ¹³C signature of about −25‰, depending on their metabolic pathway. Therefore, an increase in δ¹³C in marine fossils is indicative of an increase in the abundance of vegetation.{{Citation needed|date=April 2019}}

An increase in primary productivity causes a corresponding rise in δ¹³C values as more ¹²C is locked up in plants. This signal is also a function of the amount of carbon burial; when organic carbon is buried, more ¹²C is locked out of the system in sediments than the background ratio.

Geologic significance

C₃ and C₄ plants have different signatures, allowing the abundance of C₄ grasses to be detected through time in the δ¹³C record.{{cite journal | author = Retallack, G.J. | year = 2001 | title = Cenozoic Expansion of Grasslands and Climatic Cooling | journal = The Journal of Geology | volume = 109 | issue = 4 | pages = 407–426 | doi = 10.1086/320791 | bibcode=2001JG....109..407R| s2cid = 15560105 }} Whereas {{c4}} plants have a δ¹³C of −16 to −10‰, {{c3}} plants have a δ¹³C of −33 to −24‰.{{Cite journal| last1 = O'Leary | first1 = M. H.| title = Carbon Isotopes in Photosynthesis| jstor = 1310735| journal = BioScience| volume = 38| issue = 5| pages = 328–336| year = 1988| doi = 10.2307/1310735}}

=Positive and negative excursions=

Positive δ¹³C excursions are interpreted as an increase in burial of organic carbon in sedimentary rocks following either a spike in primary productivity, a drop in decomposition under anoxic ocean conditions or both.{{cite journal | title=Oxygen dynamics in the aftermath of the Great Oxidation of Earth's atmosphere | first1=Donald E. | last1=Canfield| first2=Lauriss | last2=Ngombi-Pemba | first3=Emma U. | last3=Hammarlund | journal=Proceedings of the National Academy of Sciences of the United States of America | date=15 October 2013 | volume=110 | issue=42 | pages=16736–16741 | doi=10.1073/pnas.1315570110| pmid=24082125 | pmc=3801071 | bibcode=2013PNAS..11016736C | doi-access=free }} For example, the evolution of large land plants in the late Devonian led to increased organic carbon burial and consequently a rise in δ¹³C.{{cite web |url=https://www.lpi.usra.edu/meetings/impact2000/pdf/3072.pdf |title=THE LATE DEVONIAN MASS EXTINCTION – IMPACT OR EARTH-BOUND EVENT? |first1=M.M. |last1=Joachimsk |first2=W. |last2=Buggisch |website=Lunar and Planetary Institute}}