MIT OpenCourseWare http://ocw.mit.edu 12.740 PaleoceanographySpring 2008For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.1 Spring 2006 The 14C story. I. Production and simple age calculation A. Produced by cosmic ray -> neutron -> 14N -> 14C + proton; production rate proportional to 14N, cosmic ray flux and energy dispersion. ~600 moles 14C/year are formed. This builds up a steady-state inventory of ~5000 x 103 moles of 14C on the earth: dN = -λN dt 530 moles/year = -.693 x N moles 5730 yrs B. 14C: t1/2 = 5730 ± 40 years (Godwin, 1962). 1. By convention, 14C dates are reported relative to previously accepted 5568 year half-life (Libby) . This convention was decided upon so as not to avoid dividing the literature between dates that are not consistent with the currently-accepted half life, and those that are. In other words, we are consistent by being consistently wrong! C. If (14C/12C) in the atmosphere is constant, if the object to be dated obtained its carbon directly from the atmosphere, and if the object to be dated is closed, then dN = -λN dt N/No= e-λt II. A minor complication: Carbon isotopes are fractionated by organisms relative to air: 13C/12Cplants ~ -20 permil relative to atmosphere (which is -7 permil relative to ocean surface waters), and 14C/12C is fractionated by about twice that amount. So you must measure δ13C and correct for isotope fractionation of 14C: 13C/12C⎡ ( ⎤ 13C =A. Definition: δ⎢ 13C/12C )sample − 1⎥ *1000 ⎣( )s tan dard ⎦ 14C =⎡ Activitysample ⎤ B. Definition: δ− 1 *1000 ⎣⎢ Activitys tan dard ⎦⎥ where Activitystd is taken to be 95% of the NBS oxalic acid standard (to approximate pre-industrial pre-nuclear bomb (PIPN) atmospheric carbon).2 C. ∆14C 1. δ14C cannot be used to directly calculate the age of a sample; it must be corrected for two effects. The first effect is the isotope mass fractionation, so 14C is corrected by subtracting twice the mass fractionation for 13C. The second effect arises because we want a scale where a sample of pre-industrial, pre-nuclear (PIPN) wood has a "zero" value on the scale; i.e., we want to define the corrected value X such that X/Xo = e-λt gives t=0 for PIPN (together, these require a correction of δ14C so that it is equivalent to a constant δ13C=-25‰). 2. Then: ∆14C = δ14C - (2δ13C + 50)(1 + δ14C/1000) The "50" term here arises as an adjustment to make a piece of wood have the correct age; since the δ13C of this wood is -25‰, twice that is 50‰ (for 14C). This multiplication of δ13C by 2 is the "twice-the-isotope fractionation per amu mass difference" correction. Relationship between measured ∆14C and radiocarbon age: C14age⎛− ⎞ 80331000 ⎜ e − 1⎟ = ∆14Cmeasured ⎝ ⎠ Relationship between measured ∆14C, true age, and initial ∆14C: − C14age⎛ ⎞ 8033 1000⎜ e − CalAge − 1⎟ =∆14Cinitial⎜ ⎟ 8266 ⎠⎝ e D. For some purposes, we need to know the absolute concentration of 14C (moles per kg, for example). For seawater, the conversion is: [14C] = 1.176 x 10-12 (1 + ∆14C/1000) ΣCO2 where ΣCO2 is expressed in terms of µmoles/kg. E. For ocean waters and other relatively "young" (<2500 yr) things: ∆14C decreases by 10°/°° every 80 years. III. 14C measurement: A. Counting measurement (β gas counting or liquid scintillation), need tens of grams,3 low background (anticoincidence counters), and time. 1. Convert CaCO3 --> CO2 --> C2H2 (acetylene) a. Gas (proportional) counting β decay leads to gas discharge (count) b. liquid scintillation C2H2 --> C6H6 (benzene) add 'cocktail' of scintillators which gives off light for each β decay B. Accelerator measurement: counts atoms rather than waiting for them to decay: advantage lies in much smaller sample sizes that can be handled. -->Van de Graf accelerator (accelerates ions to high velocities) -->Mass spectrometer (separates m/e) -->Stripper (thin sheet) which strips electrons from ions (Some ions are unstable; this is important because it helps get rid of N) -->Solid State Detector (measures ∆E/E, which is different for each isotope; this is important because it allows for further separation of N and the C isotopes). Image removed due to copyright considerations. Source for above illustrations: Bennett (1979) American Scientist 67:450-457, figure 4. Image removed due to copyright considerations. Source for above illustrations: Bennett (1979) American Scientist 67:450-457. C. Where sample contamination and size is not limiting, samples may be enriched by thermal diffusion separation.4 IV. What regulates 14C /12C in the atmosphere? A. Most recently, the burning of (very old) fossil fuels with no radiocarbon has been diluting the 14C concentration of the atmosphere (Suess Effect): Image removed due to copyright considerations. Source: Stuiver and Quay (1981) EPSL 53:349-362. B. 14C is produced (indirectly) by thermal neutrons created by the interaction of cosmic rays with the upper atmosphere. 1. Cosmic rays: 92% protons; 6% helium nuclei; 1% electrons; 1% gamma rays, heavier nuclei, and other elementary particles. Origin is outside solar system; flux is assumed constant, but this is a question for astrophysicists, not paleoceanographers! What is the origin of cosmic rays? It appears that there are many potential sources; perhaps none of them is dominant. (An object thought to be a black hole (Cygnus X-3) is emitting cosmic rays; it would take only about 30 of these in the galaxy to account for the cosmic ray flux; a recent study (Physics Today, Jan. 2005, p. 19-21) attributes most of the cosmic rays to the shock fronts of supernova remnants. Note that only about 0.1% of the cosmic ray flux towards the earth reaches the earth's surface at sea level. 2. Cosmic rays are focused by earth's magnetic field [which is variable; e.g westward drift of secular field; slow changes in intensity (as estimated from the magnetization of dated ceramics and rocks); magnetic reversals] which in turn are influenced by solar wind. During solar flares (which run in 11 year cycles), the cosmic ray flux changes measurably [and so it is possible to calculate the change in the production rate of carbon 14 from (a) measured neutron flux, which is higher at high latitudes, and (b) known cross-section for reaction. It has been suggested that long-term variations in 14C/12C [as measured in tree rings of known age, as by H.