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MIT 12 740 - Oxygen Isotope Paleoclimatology

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Readings:Urey (1947) Thermodynamic properties of isotopes; statistical dynamical equations and infra-red spectroscopy Calcite geothermometerIsotope Statistical Mechanics:Isotope Statistical Mechanics:Temperature dependence of equilibrium constant:Isotope Measurement: the mass spectrometer1950: Nier double focussing mass spectrometerMass spectrometric isotope measurement of CO2Mass spectrometric isotope measurement of CO2Mass spectrometric isotope measurement of CO2Mass spectrometric isotope measurement of CO2Oxygen isotope paleothermometryOxygen isotope paleothermometry equationsOxygen isotope paleothermometry equationsOxygen isotope paleothermometry equationsOxygen isotope paleothermometry equationsOxygen isotope paleothermometry: the early applicationsMIT OpenCourseWare 12.740 Paleoceanography Spring 2008 For information about citing these materials or our Terms of Use, visit: Isotope Paleoclimatology12.740 Lecture 2 Spring 2008Readings:Part 1:DISCUSSION READING:These notes!SUPPLEMENTARY REFERENCESBemis, B. E., H. J. Spero, et al. (1998). "Reevaluation of the oxygen isotopic composition of planktonic foraminifera: experimental results and revised paleotemperature equations." Paleoceanogr. 13: 150-160.Broecker, W.S. and V. Oversby, Distribution of trace isotopes between coexisting phases, Ch. 7 in Chemical Equilibria in the Earth.Epstein, S., R. Buchsbaum, H.A. Lowenstam, and H.C. Urey (1953) Revised carbonate-water isotopic temperature scale, Bull. Geol. Soc. Am. 62: 417-426Grossman, E. L. and T.-L. Ku (1986). "Oxygen and carbon isotope fractionation in biogenic aragonite: temperature effects." Chem. Geol. (Isotope Geosci.) 59: 59-74.Hoefs, J. (1980) Stable Isotope Geochemistry, Springer-Verlag, Berlin, 208 p.Kim, S.-T. a. J. R. O’Niel (1997) "Equilibrium and non-equilibrium oxygen isotope effects in synthetic carbonates." Geochim. Cosmochim. Acta 61: 3461-3475.Lynch-Stieglitz, J., W. Curry, et al. (1999). "A geostrophic transport estimate for the Florida Current from the oxygen isotope composition of benthic foraminifera." Paleoceanogr. 14: 360-373.Matsumoto, K. and J. Lynch-Stieglitz (1999). "Similar glacial and Holocene deep water circulation inferred from southeast Pacific benthic foraminiferal carbon isotope composition." Paleoceanogr. 14: 149-163.Rye, D.M. and M. Sommer II (1980) Reconstructing Paleotemperature and Paleosalinity Regimes with Oxygen Isotopes, in Skeletal Growth of Aquatic Organisms, eds. D.C. Rhodes and R.A. Lutz, Plenum, New York, pp. 169-202.Urey, H.C. (1947) The thermodynamic properties of isotopic substances, J. Chem. Soc. 1947: 562-581.Urey (1947) Thermodynamic properties of isotopes; statistical dynamical equations and infra-red spectroscopyBecause of the differences in the energy levels of the isotopes, isotope fractionation between equilibrium species is a function of temperature.The vibration frequency of two objects connected by a spring depends on their masses (and the “spring constant”). Similarly, the rotation characteristics and translational movements depend on mass. These factors are the fundamental causes of isotopic fraction.Stable isotope ratios:(18O/16O)sample(18O/16O)standardδ18O = [ -1]x 1000Ground-state energies:Figure by MIT OpenCourseWare.Adapted from source: Broecker and Overs by Chemical Equilibria in the Earth, p. 151.Calcite geothermometer• Ground-state differences lead to kinetic differences between isotopes (lower activation energies for lighter isotopes); differences in the energy-levels between the isotopes lead to changes in equilibrium distributions (rough rule of thumb: the heavier isotope "prefers" the more immobile state; i.e. at equilibrium water vapor is ~0.9% lighter than water).• Rotation - Vibration - Translation• Calcite geothermometer:•CaC16O3+ H218O <-> CaC16O218O + H216O•[CaC16O218O] [H216O]• (1) K(T) = ______________________________ = exp[-ΔG0/RT]•[CaC16O3] [H218O]• In theory, the equilibrium constant can be derived from the statistical mechanics of quantum energy states (in practice, not so easy; gases are not too bad, solids are possible, liquids are hard…):Isotope Statistical Mechanics:Assumes that all states which conserve total (quantized) energy are equally probable. For example, suppose there are 5 particles with a total energy of five units (with a range of zero to five quantized at 1). One possible state is for all five particles to have 1 unit of energy; another is for one particle (but which one?) to have all of the energy; these alternatives are considered equally probable.Energy 5 _______ _a______ __b____ _______ _______ Level 4 _______ ________ _______ _______ _______ 3 _______ ________ _______ ___c___ _______ 2 _______ ________ _______ __b____ ____d__ 1 _abcde_ ________ _______ _______ _abc___ 0 _______ __bcde__ _a_cde_ _a__de_ _____e_ etc.exp [ Ei/kT ](2) fi= _______________Σ exp [ Ei/kT ]Isotope Statistical Mechanics:= exp [ Ei/kT ](2) fi_______________Σ exp [ Ei/kT ](3) q = Σ exp [Ei/kt] for each mode (rot,vib,trans)(4) qtot= [(qtransqrotqvib)N/N! ]1/Nbut for large N, (N!)1/N= e/N, so(5) qtot= qtransqrotqvibe / NqH2O(16)qCaCO(16)O2(18)(6) ΔGo= -RT ln ________________________qH2O(18)qCaCO3(16)and(7) S = E/T + R ln qTemperature dependence of equilibrium constant:(8) As a generalization, we expect less isotopic fractionation at high temperatures, because differences between the occupancy of isotope energy levels becomes smaller (but note that this decrease depends on the specific molecules/phases involved; significant isotope fractionation exists for silicate phases at very high temperatures).Fractionation factor:(9)typically, fractionation factors are close to unityand become closer as temperature increases:∂lnK(T)∂T=−ΔH0RT2α=18O/16O()calcite18O/16O()waterIsotope Measurement: the mass spectrometerHence:M/e = 4.824 x 10-5r2B2/ VwhereM = atomic mass unitse = electronic charge (1,2,3,...)r = radius (centimeters)V = acceleration potential (volts)B = magnetic field strength (gauss)1950: Nier double focussing mass spectrometerNier (1950): designed the modern double-focusing mass spectrometer, to compensate for differences in initial ion velocities Although the electrostatic acceleration by V is the same for all ions coming off of the filament, they

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