Stable IsotopesPrinciples of stable isotope fractionationAnnual layers in a tropical ice capStable isotopes• Many elements of low atomic weight have two or morestable isotopes, e.g.:Hydrogen - H, D, T Carbon - 12C, 13CNitrogen - 14N, 15N Oxygen - 16O, 17O, 18OSulfur - 32S, 33S, 34S, 35S• The different masses cause isotopes to behave differentlyin physical and chemical processes. For example, 2H218O ismuch heavier than 1H216O and will be left behind duringevaporation.Stable Isotope geochemistry is concerned with variations of the isotopic compositionsof elements arising from physicochemical processes (vs. nuclear processes).Characteristics of a useful stable isotope system:1. large relative mass difference between stable isotopes (Δm/m)2. abundance of “rare” isotope is high (0.1-1%)3. element forms variety of compounds in natural systemExamples: 2H/1H, 7Li/6Li, 11B/10B, 13C/12C, 15N/14N, 18O/16O, 26Mg/24Mg, 30Si/28Si, 34S/32S, 37Cl/36Cl, 40Ar/36Ar, 44Ca/40Ca, 56Fe/54Fe - note convention of putting the heavy isotope above the light isotopeFractionation refers to the change in an isotope ratio that arises as a result of achemical or physical process.Occurs during:- isotopic exchange reactions in which the isotopes are redistributed among different molecules containing that element- unidirectional or incomplete reactions - physical processes like evaporation/condensation, melting/crystallization, adsorption/desorption, diffusionStable isotopesIsotope fractionation• The degree of fractionation depends on the relativeweights of the isotopes.– Commonly fractionated: H, C, N, O, S– Somewhat fractionated: Si, Fe, Cl– Fractionation impossible (monoisotopic): Be, F, Na, Al, P• Isotope fractionation during chemical processes iscaused by exchange reactions of the type:1/2C16O2 + H218O ↔ 1/2C18O2 + H216OAt equilibrium, we have for the preceding reaction:We use molar concentrations and not activities because theactivity coefficients cancel out.If CO2 and H2O did not discriminate between 16O and 18O, thenK would be equal to unity (K = 1.00).However, at 25°C, K = 1.0412, which implies that CO2 slightlyprefers 18O and H2O prefers 16O. This preference is small,but is large enough to cause isotopic fractionation.[ ] [ ][ ] [ ]OHOCOHOC1822161622182121=KWhy is K ≠ 1.0?Because 18O forms a stronger covalent bond with C than does 16O.The vibrational energy of a molecule is given by the equations:HOHνhElvibrationa21=mkπν21=Thus, the frequency of vibration depends on the mass of the atoms,so the energy of a molecule depends on its mass.h (Plank’s constant) = 6.63 x 10-34 Jsk (Boltzmann’s constant) = 1.38 x 10-23 J/Km = mass• The heavy isotope forms a lower energybond; it does not vibrate as violently.Therefore, it forms a stronger bond in thecompound.• The Rule of Bigeleisen (1965) - The heavyisotope goes preferentially into thecompound with the strongest bonds.Fractionation during physical processes• Mass differences also give rise to fractionation duringphysical processes (diffusion, evaporation, freezing, etc.).• Fractionation during physical process is a result ofdifferences in the velocities of isotopic molecules of thesame compound.• Consider molecules in a gas. All molecules have the sameaverage kinetic energy, which is a function of temperature.221mvEkinetic=Because the kinetic energy for heavy and lightisotopes is the same, we can write:In the case of 12C16O and 13C16O we have:Regardless of the temperature, the velocity of 12C16Ois 1.0177 times that of 13C16O, so the lightermolecule will diffuse faster and evaporate faster.LHHLmmvv=0177.1994915.2799827.28==HLvv• Regarding kinetics, lighter isotopes form weaker bonds incompounds, so they are more easily broken and hencereact faster. Thus, in reactions governed by kinetics, thelight isotopes are concentrated in the products.• At high temperatures, the equilibrium constant for isotopicexchange tends towards unity, i.e., at T → ∞, K → 1,because small differences in mass are less important whenall molecules have very high kinetic and vibrationalenergies.So at colder temperatures, isotopes will be more heavily fractionated.The isotope fractionation factorThe isotope fractionation factor is defined as:where RA, RB are the isotope ratios in two phases (e.g., carbonateand water, or water vapor and water)For example, consider: H2O(l) ↔ H2O(v) at 25°CbaabRR=α( )( )0092.1)(16181618===vlvllvOOOORROαThe differences in isotope ratios are relatively small and are expressed as parts per thousand (per mil) deviations from a standard.If δ > 0, this means that the sample is enriched in theheavy isotope relative to a standard.If δ < 0, this means that the sample is depleted in theheavy isotope relative to a standard.The relationship between α and δ is:The fractionation factor is a function of temperature:where A and B are constants.331010++=baabδδαBTAab+×=2610ln1000αExperimentally determinedequilibrium oxygen isotopefractionation factors as afunction of temperature.α varies inversely with TExperimentallydetermined equilibriumcarbon isotopefractionation factors as afunction of temperature.α varies inversely with TA useful approximationNatural logarithms of small numbers like 1.00X havethe property that1000 ln 1.00X ≈ Xas long as X ≤ 9.This approximation holds for αba for C, N, O and Sisotopes in many systems. This leads to thefollowing:so( )abbaababΔ=−≈≈−δδααln1011033BTAabab+×≈Δ≈26310ln10αWe define a measurement reporting convention (δ or “delta” units):Each isotopic measurement is reported relative to a standardNote that ‘deltas’ are named after the heavy isotope( ) ( )( )31618161816183181010 ×−=×−=standardstandardsamplestandardstandardsampleOOOOOORRROδ( ) ( )( )31213121312131310×−=standardstandardsampleCCCCCCCδ( ) ( )( )310×−=standardstandardsampleHDHDHDDδCanyon Diablo meteorite from Meteor Crater, Arizona (CDT).Isotope fractionation in the hydrosphereEvaporation of surface water in equatorial regionscauses formation of air masses with H2O vapordepleted in 18O and D compared to seawater.This moist air is forced into more northerly, coolerair in the northern hemisphere, where watercondenses, and this condensate is enriched in 18Oand D compared to the remaining vapor.The relationship between the isotopic composition ofliquid and vapor is:( )3318181010 −+=vlvlOOδαδAssuming that δ18Ov = -13.1‰ and αvl(O) = 1.0092 at