Isotope mass-independent

The distance between the two interacting atoms will be denoted by r, and /g will denote the average distance (or the equilibrium distance in a hypothetical vibrationless state) of the unperturbed system. (The distance will be independent of the isotopic mass.) A displacement... 

The important fact that must be remembered is that in the Born-Oppenheimer approximation, Equation 2.8, the potential energy for vibrational motion is Eeiec(S) which is independent of isotopic mass of the atoms. In the adiabatic approximation, the potential energy function is Eeiec(S)+C and this potential will depend on nuclear mass if C depends on nuclear mass. 

Stable isotope analysis of Earth, Moon, and meteorite samples provides important information concerning the origin of the solar system. 8lsO values of terrestrial and lunar materials support the old idea that earth and moon are closely related. On the other hand three isotope plots for oxygen fractionation in certain meteoric inclusions are anomalous. They show unexpected isotope fractionations which are approximately mass independent. This observation, difficult to understand and initially thought to have important cosmological implications, has been resolved in a series of careful experimental and theoretical studies of isotope fractionation in unimolecular kinetic processes. This important geochemical problem is treated in some detail in Chapter 14. 

Isotope Effects in Unimolecular Processes Mass Independent Isotope Fractionation and the Ozone Problem... 

Abstract The theoretical framework needed for interpretation of kinetic isotope effects on unimolecular reactions is reviewed. Application to the satisfactory rationalization of the theoretically puzzling mass independent isotope effect observed for oxygen isotope fractionation in extraterrestrial samples is described. 

The last parts of this chapter will deal with the so-called mass independent isotope effects which have been rationalized in recent years to be a consequence of unimolecular processes and which have become one of the most fascinating of present day isotope effect studies. 

Mass Independent Isotope Fractionation in the Laboratory, the Stratosphere, and the Troposphere... 

Fig. 14.4 Oxygen isotopic composition of atmospheric species measured to date (After Thiemens, M., Ann. Rev. Earth Planet. Sci. 34, 217 (2006)). For these data, m, Equation 14.31 is approximately (0.7 < m < 0.9) indicating for these materials the fractionation is better described as anomalous rather than mass independent ...

Theory of Mass Independent Isotope Fractionation of Ozone... 

The work of Thiemens, Mauersberger, and their collaborators has now definitively established a pervasive mass independent isotope fractionation for oxygen containing molecules found in the atmosphere, upper atmosphere, and in space. These results, initially surprising because they are inconsistent with ordinary equilibrium... 

Marcus, R. A. Mass independent isotope effect in the earliest processed solids in the solar system. A possible chemical mechanism../. Chem. Phys. 121, 8201 (2004). 

Thiemens, M. H. History and applications of mass-independent isotope effects. Ann. Rev. Earth Planet. Sci. 34, 217 (2006). 

Thiemens, M. H. and Heidenreich, J. E. The mass independent fractionation of ozone. A novel isotope effect and its possible cosmochemical implications. Science 219, 1073 (1983). 

Equations (8) and (10) are applicable to stable isotope systems where isotopic fractionation occurs through mass-dependent processes which comprise the majority of cases described in this volume. These relations may also be used to identify mass-independent fractionation processes, as discussed in Chapter 2 (Birck 2004). Mass-dependent fractionation laws other than those given above distinguish equilibrium from kinetic fractionation effects, and these are discussed in detail in Chapters 3 and 6 (Schauble 2004 Yormg and Galy 2004). Note that distinction between different mass-dependent fractionation laws will generally require very... 

Elements beyond zinc. Despite extensive investigations carried out in parallel with the FUN inclusions, clear-cut mass-independent isotopic heterogeneities (e.g., more than 5 cr of a single measurement) have not been identified yet in normal inclusions for the rest of the elements besides extinct radioactivities. Nevertheless, there are consistent hints for excesses of about 2 e in Zr (Harper et al. 1991 Schonbachler et al. 2003) which is an r-process isotope for which some coupling may exist with neutron-rich statistical equilibrium (Meyer 1994). 

Thiemens MH (1988) Heterogeneity in the nebula evidence from stable isotopes. In Meteorites and die Early Solar System. Kerridge JF and Matthews MS (eds) University of Arizona Press, Tucson, p 899-923 Thiemens MH (1999) Mass independent isotope effects in planetary atmospheres and die early solar system. Science 283 341-345... 

Thiemens MH, Heidenreich JE (1983) The mass independent fractionation of oxygen a novel isotope effect and its possible cosmochemical implications. Science 219 1073-1075 Thiemens MH, Jackson TL, Brenninkmeijer CAM (1995) Observation of a mass-independent oxygen isotopic composition in terrestrial stratospheric COj, the link to ozone chemisdy, and the possible occurrence in the Martian atmosphere. Geophys Res Lett 22 255-257 Timmes FX, Woosley SE, Weaver TA(1995) Galactic chemical evolution hydrogen through zinc. Astrophys J Suppl 98 617-658... 

Thiemens M, Savarino J, Farquhar J, Bao HM (2001) Mass-independent isotopic compositions in terrestrial and extraterrestrial solid and their applications. Accounts Chem Res 34 645-652... 

Weston RE (1999) Anomalous or mass-independent isotope effects. Chemical Reviews 99 2115-2136... 

Efforts to measure Mo isotope variations, using thermal ionization mass spectrometry (TIMS), can be traced back to the early 1960s. Early studies were provocative Murthy (1962 1963) reported that the Mo isotope composition in some iron meteorites deviated from that of others, and from terrestrial Mo, by 10 %o/amu, while Crouch and Tuplin (1964) reported mass dependent variations and mass independent isotopic anomalies among terrestrial molybdenites. As discussed below, Wetherill (1964) subsequently demonstrated isotopic uniformity among iron meteorites to better than 1 %o/amu. It is likely that earlier reports were affected by analytical artifacts due to inadequate correction of Mo isotope fractionation during analysis. 

The major analytical complication in Mo isotope analysis is precise correction for isotope fractionation during Mo purification and mass spectrometric analysis. This subject is reviewed in general by Albarede and Beard (2004), and is discussed here in particular reference to Mo. It is important to recognize that this challenge is fundamentally dififerent in mass dependent stable isotope studies as compared to investigations of mass-independent Mo isotope variations produced by nucleosynthesis. The latter have received attention in recent years for high-precision determination of Mo isotope composition (e.g., Dauphas et al. 2002a,b Yin et al. 2002), but are not relevant here. 

Note Csl and Au both bear the advantage of being monoisotopic. This insures the peak top to exactly represent the theoretical isotopic mass of the respective cluster ion, independent of its m/z ratio or actual resolution (Chap. 3.3.5, 3.4). Csl, KI, and other alkali salts providing more narrow-spaced cluster ion series can alternatively be employed as saturated solutions in glycerol. [45-47]... 

One of the first chemical reactions for which SIKIE was identified was the association reaction of Oj and O to produce ozone. The initial key observation was that stratospheric ozone was enriched in 0 at levels up to 40% above natural abundance. Following laboratory experiments, which showed that the enhancement occurred independently of isotopic mass (i.e., " O3 and were equivalently... 

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