Double spike

For precise measurement of isotopic composition by mass spectrometry, it is also common to use either a natural, known isotopic ratio to correct for instrumental mass fractionation (e g., internal normalization) or to add a tracer for this purpose. For example for natural uranium samples, one can use the natural U/ U of 137.88 to correct for fractionation. Alternatively, one can use an added double spike of ratio -unity... 

Variable mass-discrimination (generally a problem only for TIMS analyses of Th or of U when not double-spiked and not normalized via... 

J. L. Mann and W. R. Kelly. Measurement of Sulfur Isotope Composition (834S) by Multiple-Collector Thermal Ionization Mass Spectrometry Using a 33S-36S Double Spike. Rapid Commun. Mass Spectrom., 19(2005) 3429-3441. 

Encinar JR, Rodriguez-Gonzalez P, Fernandez JR, Alonso JIG, Diez S, Bayona JM, Sanz-Medel A. Evaluation of accelerated solvent extraction for butyltin speciation in PACS-2 CRM using double-spike isotope dilution-GC/ICPMS. Anal. Chem. 2002 74 5237-5242. 

A related example of linearized error propagation during the isotope dilution measurement of lead in rock samples using the double-spike technique is given by Hamelin et al. (1985). o... 

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. 

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. 

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. 

Rigorous correction for instrumental mass bias is required if the precision of an isotope ratio measurement needs to be greater than l%o per mass unit. This concept is well illustrated by the definitive Ca isotope work of Russell et al. (1978), which used a double-spike approach. Prior to the Ca isotope investigation of Russell et al. (1978), natural mass-dependent Ca... 

Figure 9. Sketch of the double spike Zn- Zn method. The surface is constructed by drawing an infinite number of straight-lines through the point representing the spike composition (supposed to be known with no error) and each point of the mass fractionation line going through the point representing the measured mixture. One of these straightlines, which is to be determined from the calculations, is the sample-spike mixing line (stippled line). Each determination of the Zn isotope composition of a sample involves only one run for the mixture of the sample with the spike. Since all natural samples plot on the same mass fractionation line, any reference composition will adequately determine isotope composition of the sample, note that, since the instrumental bias is not linear with mass, the mass discrimination lines are curved.

In principle, double-spike techniques represent the most suitable approach to determine the isotope composition of elements with four isotopes or more (Fe, Zn). In most cases, these techniques involve the addition of an isotope which is usually minor in natural samples, such as Zn or Fe, implying that the risk introduced by memory effects on these spike isotopes must be carefully weighed against the added gain in precision from using the double spike. Such a risk is clearly more present with MC-ICP-MS than with TIMS. 

Carlson RW, Hauri EH (2001) Extending the ° Pd- ° Ag chronometer to low Pd/Ag meteorites with multicollector plasma-ionization mass spectrometry. Geochim Cosmochim Acta 65 1839-1848 Clayton, RN, Onuma N, Mayeda TK (1976) Distribution of the presolar component in Allende and other carbonaceous chondrites. Earth Planet Sci Lett 30 10-18 Compston W, Oversby VM (1969) Lead isotopic analysis using a double spike. J Geophys Res 74 4338-4348 Criss RE (1999) Principles of Stable Isotope Distribution. University Press, Oxford... 

Gale NH (1970) A solution in closed form for lead isotopic analysis using a double spike. Chem Geol 6 305-310... 

Hamelin B, Manhes G, Albarede F, Allegre CJ (1985) Precise lead isotope measurements by the double spike technique a reconsideration. Geochim Cosmochim Acta 49 173-182 Hart SR, Zindler A (1989) Isotope fractionation laws A test using calcium. Int J Mass Spectr Ion Proc 89 287-301... 

Taylor PDF, Maeck R, De Bievre P (1992) Determination of the absolute isotopic composition and Atomic Weight of a reference sample of natural iron. Int J Mass Spectrom Ion Processes 121 111-125 Taylor PDF, Maeck R, Hendrickx F, De Bievre P (1993) The gravimetric preparation of synthetic mixtures of iron isotopes. Int J Mass Spectrom Ion Processes 128 91-97 Thirlwall MF (2002) Multicollector ICP-MS analysis of Pb isotopes using a Pb- Pb double spike demonstrates up to 4000 ppm/amu systematic errors in Tl-normalization. Chem Geol 184 255-279... 

EXAMPLE OF DOUBLE-SPIKE CALCULATION USING ANEWTON-RAPHSON ITERATION... 

The limitations discussed above also apply approximately to measurements of mass dependent Ca isotope effects. The additional problem is to separate mass dependent fractionation in nature from mass dependent fractionation in the mass spectrometer. The maximum observed natural fractionation is about +0.1% per mass unit, whereas instrumental fractionation is about +0.5% per mass unit (for TIMS and much larger for ICPMS). The separation is accomplished with the use of a double spike (Russell et al. 1978b). The approach is illustrated here using the methods of Skulan et al. (1997), but other researchers have used slightly different algorithms and double spike isotopes (Zhu and MacDougall 1998 Heuser et al. 2002 Schmitt et al. 2003a). 

Table 1. Compositions of natural Se and Cr and currently used double spikes (atom %).

A double spike technique is essential for TIMS analyses of Se and Cr, and may also be useful in MC-ICP-MS analysis. Briefly, two spike isotopes with a known ratio are added to each sample, and the measured ratio of the spike isotopes is used to determine and correct for instrumental bias. Examples of Se and Cr double spikes currently in use are given in Table 1. The fact that small amounts of the spike isotopes are present in the samples and small amormts of nominally unspiked isotopes are found in the spikes is not a problem, as the measurements allow highly precise mathematical separation of spike from samples. Algorithms for such calculations are described by Albarede and Beard (2004) and, specifically for Se, by Johnson etal. (1999). 

The double-spike technique of Rosman (1972) has been revived by Tanimizu et al. (2002), who used a Zn- Zn spike and obtained precisions in the range of a fraction of a per mil. Jackson and Gunther (2003) describe a laser-ablation technique of isotopic measurement, which provides a precision comparable to the standard solution nebulization methods. 

Isotopic double spike. The most rigorous approach is to use an isotopic double spike , in which samples are doped with a known quantity of spike Mo which consists of two isotopes in a known ratio (Wetherill 1964 Siebert et al. 2001). These spike isotopes serve as an internal standard to monitor mass fractionation of the sample subsequent to spiking. The fundamental advantage over the element spike is that the spike isotopes follow exactly the same fractionation behavior as the isotopes of interest. A disadvantage is the need to carefully prepare and calibrate the double spike. 

Mo is particularly suitable for double spike analysis because it has a large number of stable isotopes. It is not surprising, therefore, that Wetherill (1964) used this approach to demonstrate isotopic homogeneity between terrestrial and meteorite Mo samples, employing a Mo- Mo spike and TIMS. This study was one of the earliest applications of the double spike method. 

In a more recent TIMS Mo isotope double spike study using a multiple collector system, Wieser and de Laeter (Wieser and DeLaeter 2003) reported precision of better than 0.1 %o/ amu mass difference ( 2ct) using a Mo- Mo spike. 

The utility of the double spike is not limited to TIMS. The method has also been applied very successfully in MC-ICP-MS (Siebert et al. 2001). Using a Mo- Mo spike, precision of 0. l%o ( 2ct) was reported in measurement of 5 Mo, and has been applied to a range of natural materials (McManus et al. 2002 Siebert et al. 2003). 

Error in Equation 65 found on page 152 (in Appendix B Example of double-spike calculation using aNewton-Raphson iteration.)... 

A substantial improvement in K-Ca dating was achieved by Marshall and De Paolo (1982), who combined the double-spike technique of Russell et al. (1978) with high-precision measurements on chromatographically separated sample aliquots. 

Figure 11.23 shows the isochron obtained by Marshall and De Paolo (1982) for the granite batholith of Pikes Peak (Colorado). The effectiveness of the double-spike technique is evident, especially when we see that aliquot-spiked samples do not fall on the best-fit interpolant (York s algorithm York, 1969). The obtained age (1041 32 Ma) is consistent with that previously obtained with Rb-Sr whole rock analyses (1008 13 Ma see Marshall and De Paolo, 1982, for references). The initial ratio ( Ca/ Ca)o of 151.0 is identical, within the range of uncertainty, to upper mantle values, indicating negligible contamination by old crust components the relative K/Ca abundance in the earth s mantle is about 0.01, a value too low to alter the primordial (" Ca/" Ca)o composition. 

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