Calibration with Double Spikes

Isotope amount ratio calibration with double spikes involves measuring the relative amounts of at least four isotopes of an element (there are over 30 elements fulfilling the condition of availability of 4 isotopes). For two of these isotopes, the relative isotopic abundance is significantly enhanced by the addition of an enriched isotopic spike to the sample. Such an approach circumvents the bias incurred 

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  

Note that the isotopic composition for the mixture (m) of measurand (analyte, a) and spike (s) can be expressed as a linear combination of the two. However, the mixing coefficient, q, is not the amount ratio of the analyte and spike (x) rather, these two variables are linked by the following expression [27]  

If the discrimination law is known or assumed, then we have three unknowns q and one variable for each of the two discrimination functions. Assume, for 

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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. 

Nonprimed symbols refer to the anal54ical sample prior to extraction, clean-up, etc. Symbols marked with a single prime ( ) refer to the sample extract solution (possibly spiked with internal standard). Symbols marked with a double prime (") refer to a solution of pure analytical standard used for calibration, possibly spiked with an internal standard. Symbols marked with three primes (" ) denote a calibrator prepared by spiking a matrix blank with a known amount of calibration standard, possibly spiked with an internal standard, and taken through the entire analytical procedure. 

Practical disadvantages associated with use of the double-spike technique include the required availability of the high-purity enriched double spikes, the effort required to calibrate the isotopic composition of the spike, the need to avoid possible cross-contamination between the analysis of unspiked and spiked samples, the requirement for at least four interference-free isotopes of the analyte, and the need for two analyses of the sample - unspiked and spiked. 

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