Double Spike Method

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). 

Dodson (1963) was the first to systematically investigate the theory of Pb isotope double spiking. The calculations related to Pb isotope double spiking may be made iteratively (Compston and Oversby, 1969) or analytically (Gale, 1970). Further development and application of the double spiking theory include the studies by Hamelin et al. (1985), Galer (1999), Johnson and Beard (1999), and Thirlwall (2000). 

The fractionation curve for the unspiked sample (unknown) from the linear mass fractionation law is described by 

Now we need the equation from the single spike as a mixing. For single spike, we only need to measure one isotope ratio. But for double spike, we need three isotopic ratios. According to Eq. (11.11), we have 

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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. 

The double spike method needs a run of un-spiked sample and the second run of the mixture. In contrast, two double spike method (Kuritani and Nakamura, 2003) requires two runs of mixtures spiked with different double spikes. Here we explain the theory of the Pb- ° Pb and ° Pb- ° Pb two double spikes (Kuritani and Nakamura, 2003). The true ratio of the first double spike mixture (e.g., is related to the measured ratio of the first mixture (e.g., ) by... 

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. 

Like the traditional mass bias correction approaches, the double-spike method also relies on the choice of the mass bias model. The original formalism of the double spikes employed the linear mass bias law and, although double-spike calibration equations adapted for the exponential mass bias discrimination are available, linear models are still often used owing to their simplicity (see, for example, [50-52]). The caveat here is that erroneous results can be obtained when a linear correction is applied to data that do not follow such behavior. This is illustrated below. 

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 ... 

In addition to the double-spike technique, an extension to triple spikes has been proposed by Galer [50]. However, as noted by Rudge et al. [27], no advantage has been found yet to justify the triple-spike calibration because the double-spike method always delivers smaller uncertainties than triple-spike calibration. 

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. 

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