Isotope double-spike method

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. 

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. 

Another way to do the correction of Pb isotope mass fractionation is to use double spike method, which will be discussed in Chapter 11. 

The spike in most cases is single spike, but it can be double spike. Single spike method provides the information of the concentration of the sample, whereas the double-spike method can yield the concentration of the sample and the mass fractionation factor that can be used to calculate the true isotopic ratios in the sample. Take Pb isotope as an example. Natural Pb samples have 1.4% ° Pb, 24.4% ° Pb, 22.1% ° Pb and 52.4% ° Pb. A single spike is made by artificially concentrating one of the minor Pb isotopes, for example Pb. A double spike is made by artificially concentrating two minor isotopes. For example, we can concentrate Pb and b isotopes to make ° Pb- Pb double spike or concentrate Pb and Pb to make Pb- ° Pb double spike. 

A single spike is enriched in one minor isotope whereas a double spike is enriched in two minor isotopes (Fig. 11.3). Double spike method needs two runs. The first run is to measure the un-spiked sample and the second run is to measure the spiked mixture. Double spike method not only provides the concentrations of the sample but also corrects the mass fractionation in mass spectrometers (and thus giving the true isotopic ratios). 

Snow, J.E. and Friedrich, J.M. (2005) Multiple in counting ICPMS double spike method for precise U isotopic analysis at ultra-trace levels. Int. J. Mass Spectrom., 242, 211-215. 

Calibration using the double-spike method is an ingenious application of isotope dilution in mass spectrometry. Admixing the measurand and the spike (calibrant) results in a mixture, the isotopic composition of which is governed by the conservation of matter. Two sets of equations can be established one that describes the conservation of matter during the mixing, and the other that expresses the relationship between the measured and true isotope amount ratios, that is, the discrimination law ... 

Uncertainty evaluation is often perceived as a passive (a posteriori) part of the analysis process. The double-spike method of isotope ratio calibration, however, has demonstrated that uncertainty evaluation is an active research tool and the results obtained this way are significant in steering the entire field of mass bias correction. 

Chapter 8). The same is true for the results from the double-spike method. Finding the optimal isotopic composition of the spike, however, has proved to be a challenge. 

Gumming, G.L. (1973) Propagation of experimental errors in lead isotope ratio measurements using the double spike method. Chem. Geol., 11, 157-165. 

The primary disadvantages of the double-spike technique are that (i) the preparation and calibration of a new double spike require significant effort and (ii) four interference-free isotope signals are needed for accurate data reduction, and this also rules out double-spike analysis of elements that feature only two or three isotopes. In many cases, however, these factors will be outweighed by the advantages of the method (i) it offers an instrumental mass bias correction that is similar in application and reliability to internal normalization and hence is even more robust towards matrix effects than external normalization (ii) the approach can correct for laboratory-induced mass fractionation effects, if the spike is added to the samples prior to the chemical processing and (iii) precise elemental concentration data are obtained as a byproduct of the double-spike method. Hence the double-spike method has recently found increasing popularity in MC-ICP-MS stable isotope analysis of non-traditional elements. 

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. 

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.

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). 

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. 

A major advantage of the double-spike technique is that the mass bias correction factor can be directly determined for each sample, thus eliminating the bias due to variations in the sample matrix. In this regard, double-spike calibration is an isotopic extension of the classical method of standard additions. This advantage has resulted in the rapid adoption of this technique for many elements other... 

Thermal ion mass spectrometry has traditionally been the method of choice to obtain precise Pb isotope determinations, with a typical RSD of 0.01% (2o) for the Pb/ ° Pb ratio. Moreover, TIMS allows precise measurement of all four Pb isotopes, especially with the double or triple spike techniques [54], allowing the radiogenic ones ( b, ° Pb, ° Pb) to be normalized to Pb which is non-radiogenic. Also, to distinguish among anthropogenic Pb sources, it can be... 

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