Element Isotope Abundance (%)

Stable isotopes Element Isotope Abundance (%)

Hydrogen [1] 1H 99.985 2H 0.015

Carbon [6] 12C 98.89 13C 1.11

Nitrogen [7] 14N 99.63 15N 0.37

Oxygen [8] 16O 99.759 17O 0.037 18O 0.204

Sulfur [16] 32S 95.00 33S 0.76 34S 4.22 36S 0.014 “delta” notation % – per cent (parts per hundred) ‰ – per mil (parts per thousand) R = ratio of two isotopes of the same element (e.g., 13C/12C, 34S/32S)

δ = 1000 × (Rsample − Rstandard) / Rstandard ‰ The heavy isotope is the numerator, so positive δ values mean the sample is heavier than the standard, and negative values mean it is lighter e.g., ⎛ 13 C ⎞ ⎛ 13 C ⎞ ⎜ ⎟ − ⎜ ⎟ ⎜ 12 C ⎟ ⎜ 12 C ⎟ 13 ⎝ ⎠sample ⎝ ⎠standard δ 1000C ×= ‰ ⎛ 13 C ⎞ ⎜ ⎟ ⎜ 12 ⎟ ⎝ C ⎠standard Stable isotope standards

Element d value Ratio (R) Standard R of Standard

Standard Light Antarctic Precipitation (SLAP) 0.000089089 Hydrogen δ D 2H/1H Vienna Standard Mean Ocean Water (VSMOW) 0.00015575

Carbon δ 13C 13C/12C Vienna Pee Dee Belemnite (VPDB) 0.0112372

Nitrogen δ 15N 15N/14N Air 0.003676

Standard Light Antarctic Precipitation (SLAP) 0.0018939

Oxygen δ 18O 18O/16O Vienna Standard Mean Ocean Water (VSMOW) 0.0020052

Vienna Pee Dee Belemnite (VPDB) 0.0020672

Sulfur δ 34S 34S/32S Canyon Diablo Troilite (CDT) 0.045005 Stable isotope standards

H, O Standard Mean Ocean Water (SMOW) (actually VSMOW is a mixture of distilled water samples from the world’s oceans) C, O Pee Dee Belemnite (PDB) (VPDB is finely-ground and homogenized belemnite fossils from the Cretaceous Pee Dee Formation of South Carolina) N atmosphere S Canyon Diablo meteorite (CD) (troilite, an iron sulfide, from the Canyon Diablo iron meteorite that formed Meteor Crater in northern Arizona) Stable isotope standards

• Isotopes of a given element vary in their nuclear properties, but since these are stable isotopes, their nuclear properties don’t affect their behaviour in ordinary life • Their mass is the remaining difference, and it can result in fractionation of isotopes • At a given temperature, all isotopes of an element will have (on average) the same energy E • Since E = ½ m v2, heavier isotopes will have smaller v, and will move more slowly than light isotopes • Mass-dependent fractionation can therefore result from several processes Diffusion With equal energy, light atoms are faster than heavy ones. They travel further in the same time. Collisions with other atoms don’t alter their average equality of energy. Light 235 238 [ UF6 diffuses through a membrane more rapidly than UF6] Heavy Evaporation When a liquid is evaporating, the faster light atoms (or molecules) Light have more “tries” at breaking loose from the liquid bonds, and so the Heavy vapour is enriched in light atoms relative to heavy. 2 1 16 1 18 1 16 [ H H O will evaporate faster than H2 O, but slower than H2 O] 19 20 18

The fractionation effects are normally much smaller than shown here—a few percent at most. Condensation The slower heavy atoms are more easily “captured” by the Light bonding that holds the liquid together, and so the liquid is Heavy enhanced in the heavy atoms relative to the light. [water in rain is “heavier” than the water in the cloud it formed from] Molecular bonds

Light When bound, together in a solid, or with a smaller group of atoms in a molecule, atoms are constrained by the chemical Heavy bonding to vibrate in place. Light atoms vibrate faster than heavy ones. This difference can either strengthen or weaken the bond, depending on the details of the bonding.

In this example, the light atom broke away, but there is no simple way of predicting how mass differences will affect the chemical bond. The more chemical processes an atom passes through, the greater the potential mass fractionation. Living systems are webs of ceaseless chemical reactions, so they have considerable potential to fractionate isotopes.

Water cycle

Carbon cycle http://homepage.mac.com/uriarte/carbon13.html Isotopes and diet

The most important application in archaeology is inferring diet (and related factors) from stable isotopes in bones and teeth Related factors include • Hunting, gathering and agricultural practices • Economic and social structures • Climate patterns • Patterns of migration and commerce Sometimes changes of diet over an individual’s lifetime can be determined (especially from teeth) Isotopes and diet

• Most food plants follow a chemical pathway for capturing CO2 called C3, because it forms a molecule with three carbon atoms This mechanism is followed by most plants, and leads to δ13C values around −27 ±7 ‰ These plants include rice, wheat, rye, barley, cassava, potatoes, algae and spinach • Many plants in semitropical regions, with high temperatures and abundant sunlight, follow a pathway called C4, forming four-carbon molecules

This mechanism is more efficient in using water and CO2, and leads to δ13C values around −13 ±4 ‰ These plants include maize, sorghum, sugarcane and millet • There is also a third mechanism, called CAM, but it operates in only a limited number of desert plants Isotopes and diet

• Most plants derive their nitrogen from the soil. Soil δ15N values are variable, depending on local conditions. δ15N values are plus a few per mil (~3-5‰) • Some plants (legumes) have symbiotic bacteria that can allow the plant to use atmospheric nitrogen. δ15N values are near zero per mil (~1-2‰) • At each step up the food chain, about +5‰ is added, so δ15N values are an index of level in the food chain, and can distinguish plant and meat diets, for instance. • Note however that agricultural practices, such as the use of animal manure as fertilizer, may also affect nitrogen isotopes. Isotopes and diet • For archaeologists, the most useful material for analyzing dietary isotope ratios is bone or teeth. • Bone contains a protein called collagen, which can be separated by dissolving the hard bone away. Bone collagen has a δ13C about 5‰ greater than the δ13C of the food source. • The mineral part of bone and teeth is largely the mineral apatite, which also contains carbon. The δ13C of apatite is about 10‰ greater than the δ13C of the food source. • Collagen is a protein, so it can be analyzed for both C and N isotopes. Apatite can only be analyzed for C. In both cases, careful sample preparation is required to ensure that only the proper component is being sampled. • Can also directly analyze food residue found in storage and cooking utensils.

Carbon vs. nitrogen isotope ratios in common New World food groups. Human collagen from Patagonia Dietary change in Belize Coastal Ecuador and Peru Coastal Ecuador and Peru Hydrogen and oxygen isotopes

• H and O isotopes in organisms are mostly derived from H2O. • Isotope ratios vary geographically due to regional variations in the water cycle (precipitation, runoff, ground water) and therefore local water supply. • There is no guarantee that these differences persist over periods of significant climate change! • Further research and calibration of isotope variations with time is needed to make geographic inferences reliable.