Stable Isotopes – Physical Fundamentals 9/27/12

1. Stable Isotopes – Physical Fundamentals 9/27/12 • Lecture outline: • principles of stable isotope fractionation • equilibrium fractionation • kinetic fractionation • mass-independent fractionation spectrometer light intake Annual layers in a tropical ice cap

2. Introduction to Stable Isotope Geochemistry Stable Isotope geochemistry is concerned with variations of the isotopic compositions of elements arising from physicochemical processes (vs. nuclear processes). fractionation refers to the change in an isotope ratio that arises as a result of a chemical or physical process. Occurs during: - isotopic exchange reactions in which the isotope are redistributed among different molecules containing that element - unidirectional or incomplete reactions - physical processes like evaporation/condensation, melting/crystallization, adsorption/desorption, diffusion • Characteristics of a useful stable isotope system: • large relative mass difference between stable isotopes (Δm/m) • abundance of “rare” isotope is high (0.1-1%) • element forms variety of compounds in natural system Examples: 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 isotope

3. Notation We can define a fractionation factor (α): Where RA, RB are the isotope ratios in two phases (ex. carbonate and water, or water vapor and water, etc) NOTE: α is close to 1 because ratios differ by parts per thousand α approaches 1 as temperature increases We define a measurement reporting convention (d or “delta” units): Note that ‘deltas’ are named after the heavy isotope So each isotopic measurement is reported relative to a standard

4. Fractionation types • There are three types of isotope fractionation: • equilibrium fractionation • kinetic fractionation • mass-independent fractionation (far less important) • Equilibrium fractionation • - arises from the translational, rotational, and vibrational motions of • 1. molecules in gases and liquids • 2. atoms in crystal lattices • energy of these motions is mass-dependent • systems will move to the lowest energy configuration • usually largest in covalent bonds, minimal in ionic bonds • Ex: most imp. From William White’s (Cornell) upcoming Geochemistry textbook at 25°C, so 18O/16O is larger in CO2 than in H2O at equilibrium

5. Equilibrium fractionation (cont) • So why does equilibrium fractionation occur? • a molecule with a heavy isotope sits • at a lower zero point energy level • than the same molecule with all light • isotopes • bonds with high potential energies • are broken more readily • bond strengths vary for light and heavy • isotopes of an element • What about temperature? • the difference in zero point energies • for light vs. heavy molecules decreases • with increasing T • - bond strengths converge at high T, • fractionation factor goes to 1 at high T Effect of vibrational E in harmonic oscilllator model Which bond is broken most easily? zero point energy

6. Temperature-dependence of equilibrium fractionation • From these plots we can see that: • α varies inversely with T • the harmonic oscillator model • approximation holds up well: data harmonic oscilllator model for T<200C for T>200C harmonic oscilllator model data So at colder temperatures, isotopes will be more heavily fractionated.

7. Composition-dependence of equilibrium fractionation IMPORTANT rule of thumb: the heavy isotope will be concentrated in the phase in which it is most strongly bound (or lowest energy state). Solid>liquid>water, covalent>ionic, etc. Ex: 18O in carbonates - heavily enriched in carbonate because O tightly bonded to small, highly charged C4+, vs. weaker H+ - so Δ18Ocal-water = δ18Ocarb-δ18Owater = 30‰ Ex: quartz (SiO2) most enriched mineral Lattice configuration (aragonite vs. calcite) plays a secondary role (Δ18Oarag-cal=0.5‰) Chemical substitutions in the lattice (ie. Ba instead of Ca) also have a small effect: Δ18OBa-cal-water = 25‰ (vs. 30‰ for Ca-cal)

8. Kinetic fractionation - arises from fast, unidirectional, incomplete reactions (many biologically-mediated rxns) • Velocities of gas molecules are different • - kinetic energies of molecules of ideal gas are equal • - so differences in mass (heavy vs. light isotopes) must be compensated for by velocity Consider two molecules of CO2: 12C16O2 (mass = 12 + 2*16 = 44) and 13C16O2(mass = 13 + 2*16 = 45) if their energies are the same, then: and the ratio of their velocities is: assuming ideal gas SO… 12C16O2 can diffuse 1.1% further than 13C16O2 in a given amount of time This can be observed as gas moves through a fine capillary tube (12C16O2 arrives first). In reality, gas are not ideal, velocity difference is reduced by collisions, reduced fractionation

9. Kinetic fractionation (cont) • 2. Lighter isotope will be preferentially reacted (back to vibrational E plot) • easier to break C-H bonds than C-D bonds • when reactions do not go to equilibrium, lighter isotope will be enriched in products • usually very large kinetic fractionations in biologically-mediated rxns • (ex: photosynthesis (low δ13C) and bacterial reduction (low δ34S)) NOTE: The tell-tale sign of kinetic fractionation is fractionation that is directly proportional to the mass difference (Δm). You can identify a kinetic process by comparing d values for different isotope systems ie. 18O/16O vs. 13C/12C (2/1) 18O/16O vs. 17O/16O (2/1)

10. Mass-independent fractionation Observed in meteorites and in atmospheric photo-chemical reactions, mechanism unknown. mass-independent Thiemens and Heidenreich, 1983; Theimens, 1999 (review)