Mass dependent fractionation

It is clear from figure 6 that the terrestrial data do not cluster about a single point but instead lie along a line of slope 0.5 on the three-isotope diagram, indicating isotopic variation due to mass-dependent fractionation. Since mass fractionation effects in Mg have not been observed in terrestrial materials [30,31], this distribution of observed isotope ratios must be due to fractionation in the ion probe. The physical process which produces the... 

Figure 14.6 compares measured and calculated isotope fractionations for all 16 possible ozone isotopomers prepared from an enriched oxygen precursor. In this figure (160160160, 160160170, 160170160, 160160180, etc. are represented as 666, 667, 676, 677, 767, 668, 686, 678, 777, 688, 868, 778, 787, 788, 878, and 888). The calculations are those of Gao and Marcus described in sections below. They are in quantitative agreement with experiment. It is interesting that isotope fractionations observed in product ozone for the totally symmetric isotopomers, 8170 = 1000 ln(777/666) and 8lsO = 1000 ln(888/666), are negative they show the heavy isotope to be depleted. Moreover, these totally symmetric effects lie on the mass dependent fractionation line [ln(777/666)]/[ln(888/666)] 0.5. That... 

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... 

Figure 4. Illustration of mass-dependent fractionation of Mg isotopes, cast in terms of 5 values. 5 Mg and 5 Mg values based on Mg/ Mg and Mg/ Mg ratios, respectively. A common equilibrium fractionation model, as defined by exponential relations between a values (fractionation factors) for different isotope ratios, is shown in the gray line. A simple linear relation, where the slope is proportional to the mass difference of the isotope pair, is shown in the black line. Additional mass-dependent fractionation laws may be defined, and all are closely convergent over small ranges (a few per mil) in isotope compositions at 5 values that are close to zero.

In principle, the three isotope method may be widely applied to new isotope systems such as Mg, Ca, Cr, Fe, Zn, Se, and Mo. Unlike isotopic analysis of purified oxygen, however, isotopic analysis of metals that have been separated from complex matrices commonly involves measurement of several isotopic ratios to monitor potential isobars, evaluate the internal consistency of the data through comparison with mass-dependent fractionation relations (e.g., Eqn. 8 above), or use in double-spike corrections for instrumental mass bias (Chapter 4 Albarede and Beard 2004). For experimental data that reflect partial isotopic exchange, their isotopic compositions will not lie along a mass-dependent fractionation line, but will instead lie along a line at high angle to a mass-dependent relation (Fig. 10), which will limit the use of multiple isotopic ratios for isobar corrections, data quality checks, and double-spike corrections. 

Johnson TM, Bullen TD (2004) Mass-dependent fractionation of selenium and chromim isotopes in low-temperature environments. Rev Mineral Geochem 55 289-317 Kim S-T, O Neil JR (1997) Equilibrium and nonequilibrium oxygen isotope effects in synthetic carbonates. Geochim Cosmochim Acta 61 3461-3475... 

For the following text, isotopic anomalies always stands for non-linear or non-mass dependent variations linear or mass dependent have the same meaning although mass dependent fractionation may not be strictly linear (Rayleigh). Usually, in the first approach the difference is not essential for description... 

The excess was first suggested to have a nuclear origin in stars. Almost pure O is produced in He-buming shells in massive stars, and in supemovae. On the other hand it has been shown that non-mass dependent fractionation can be produced in the laboratory by non-nuclear processes (Thiemens and Heidenreich 1983 Thiemens 1988). Similar non-linear effects have been found for O isotopes in atmospheric gases (Schueler et al. 1990 Thiemens et al. 1995). Although stellar nucleosynthesis is indeed at the origin of the O observed in the universe, the link between O isotopic anomalies in inclusions and nucleosynthesis is still under debate (Thiemens 1999 Clayton 2002). 

Unlike O, mass dependent fractionation is widespread for Ca in inclusions it ranges from -3.8 to 6.7 %o (Niederer and Papanastassiou 1984) which is about four times the terrestrial range (Schmitt et al. 2003). However, 80% of samples fall within an interval of 2%o. The mass fractionation is the result of complex sequences of condensation and vaporization. The connection to Mg isotopic fractionation is not obvious for these samples as the resolution of Mg measurements is much smaller. 

The nucleosynthetic sources for Ti isotopes are very similar to those of the isotopes of Ca, and Ti requires a neutron-rich zone to be produced in significant amoimts. In addition to the nonlinear effects, absolute isotopic compositions have been measured in a number of samples using double spike techniques (Niederer et al. 1985). Mass dependent fractionation effects are rarely resolved and are small, below 1 %o/amu except in one sample, where it reaches 1.3 %o/amu. In general the fractionation is in favor of the heavy isotopes partial condensation or evaporation may explain of this observation. 

Silicon. Normal inclusions are spread on a mass dependent fractionation line over a few %o/amu around the solar system average. FUN inclusions display a heavy isotope enrichment from 5 to 15 %o/amu in a similar way to Mg. Non-linear effects are small and indicate an excess of Si smaller than 0.5 %o (Clayton et al. 1984). 

Titanium-calcium. The first evidence for isotopic anomalies in the iron-group was found in Ti showing up to 10% excesses of Ti in hibonites from the Murray CM2 meteorite (Hutcheon et al. 1983 Fahey et al. 1985 Ireland et al. 1985 Hinton et al. 1987). Further studies in Murchison showed that Ti extended from -7% to +27% associated with Ca variation from -6% to +10% (Ireland 1988 Ireland 1990). Except for the magnitude of the variations, this is similar to the results from Allende inclusions. Only a few samples display mass-dependent fractionation for which it ranges up to 1.3 %/amu. In the majority of the samples, it is absent or very low (less than 1 %o/amu) for Ca-Ti. There is no correlation between the presence of linear fractionation and the magnitude of Ti effects. Ti variations are also present, but about an order of magnitude smaller than Ti. Variations affecting these two isotopes are related but not strictly correlated (Ireland 1988). 

Figure 5. Relative abundances of the Kr, Xe isotopes (Huss and Lewis 1994) in presolar diamonds have been measured in bulk samples (= many grains) and are plotted relative to solar wind abundances. The terrestrial atmosphere is shown for comparison and displays a pattern close to mass dependent fractionation relative to the solar wind. The primary nucleosynthetic processes at the origin of the different nuclei are also listed. Both Kr and Xe are elevated in the r-process isotopes, whereas only Xe is also enriched in the p-isotopes. These patterns are a strong argument in favor of a supernova origin for the diamonds. Ne isotopes in presolar diamond is within the field of bulk meteorite data.

Recent discoveries of oxygen and sulfur fractionations (e.g., Farquhar et al. 2000 Thiemens et al. 2001) that appear to have unusual mass dependence has renewed interest in variations in the mass dependence of different fractionation mechanisms (Gao and Marcus 2002 Young et al. 2002). Usually, mass-dependent fractionations scale in proportion to differences in isotopic mass ... 

Typically, the relative instrumental mass-dependent fractionation is on the order of 1 to 5%o per mass unit, but this fractionation is variable during the course of the analysis, as well as variable from hlament to hlament. The degree of instrumental mass bias can be minimized by use of a double or triple hlament ionization source, as compared to a single hlament source. In the double and triple hlament source the temperature of the evaporation hlament... 

Corrections for instrumentally-produced mass fractionation that preserve natural mass dependent fractionation can be approached in one of two ways a double-spike method, which allows for rigorous calculation of instrumental mass fractionation (e.g., Dodson 1963 Compston and Oversby 1969 Eugster et al. 1969 Gale 1970 Hamelin et al. 1985 Galer 1999 see section Double-spike analysis ), or an empirical adjustment, based on comparison with isotopic analysis of standards (Dixon et al. 1993 Taylor et al. 1992 1993). The empirical approach assumes that standards and samples fractionate to the same degree during isotopic analysis, requiring carefully controlled analysis conditions. Such approaches are commonly used for Pb isotope work. However, it is important to stress that the precision and accuracy of isotope ratios determined on unknown samples may be very difficult to evaluate because each filament load in a TIMS analysis is different. 

For thermal ionization mass spectrometry the exponential law appears to be the best model that describes the mass-dependent fractionation taking place in the TIMS source for a wide variety of elements (e.g., Russel et al. 1978 Wasserburg et al. 1981 Hart and Zindler 1989 Beard and Johnson 1999). 

Figure 10. On this unusually fractionated block of 40 cycles, the effect of the noise-induced correlation observed on Zn isotopes can be separated from the mass fractionation effects. The solid line corresponds to mass-dependent fractionation, while the dashed line is defined by counting statistics. When the larger Zn/ "Zn and Zn/ "Zn ratios are plotted against each other (top), counting statistics tend to pull the results away from the mass fractionation line. When the smaller "Zn/"Zn is considered (bottom), counting statistics has essentially no effect. Data acquired using the VG Plasma 54 of Lyon.

Figure 11. When the ratios on each axis have no common isotope and in the absence of mass-dependent fractionation, they are statistically independent. These data represent a run of 40 cycles in which Zn/ Zn and Zn/ Zn were measured. The horizontal array (uncorrelated variables) indicates that, in the present case, the variability of the isotopic ratios can be ascribed to counting statistics and not to mass-dependent fractionation. Data acquired using the VG Plasma 54 of Lyon.

For elemental interferences, mass difference between overlapping species is normally too small to be resolvable. An efficient separation chemistry is most commonly the solution, but the utmost care must be exercised to maintain quantitative yields because ion exchange chromatography can produce mass-dependent fractionations as shown for the elution of Ca (Russell and Papanastassiou 1978), Cu and Zn (Marechal et al. 1999 Marechal and Albarede 2002), and Fe (Anbar et al. 2000 Roe et al. 2003). 

With the advent of multiple-collector inductively coupled plasma-source mass spectrometry (MC-ICPMS) it is now possible to measure Mg/ Mg and Mg/ Mg of Mg in solution with a reproducibility of 30 to 60 ppm or better (Galy et al. 2001). What is more, ultraviolet (UV) laser ablation combined with MC-ICPMS permits in situ analysis of Mg-bearing mineral samples with reproducibility of 100 to 200 ppm (Yoimg et al. 2002a). These new analytical capabilities allow mass-dependent fractionations of the isotopes of Mg to be used as tracers in natural systems. 

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