Double-spike calibration

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. 

Although the mathematics of double-spike calibration is not new, it is not trivial. Owing to the complexity of nonlinear solutions, most opt for an approximate (linear) solution, which, in turn, may come at the expense of biased results. 

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... 

Table S.2 A gedanken experiment for double-spike calibration of natural lead using NIST equal-atom lead reference material SRM 982. (a) True isotope amount ratios in the sample ( natural lead), calibrator (NIST SRM 982), and their equimolar mixture, (b) Measured" isotope amount ratios subjected to Russell s law of less than 1% bias for the ratio N( ° Pb)/ N( ° Pb). (c) Estimated isotope amount ratios of natural lead using the traditional doublespike equations (assumed linear discrimination), showing a 0.5% bias in N( ° Pb)/N( ° Pb).

Note that even if we are to adopt a more fitting discrimination law for the double-spike calculus, we still have to accept the equality of the discrimination functions between the isotopes of the same element - an assumption that is now shown experimentally to be incorrect [17]. To date, this remains the breaking point in the chain of metrological traceability for double-spike calibration results. 

A major obstacle in implementing double-spike calibration is the difficulty in obtaining an appropriate isotopically enriched calibrant (in addition to the fact that... 

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. 

Calibration of the measured isotope amount ratio, 787/86, is achieved by admixing known amounts of strontium that is enriched in Sr and Sr [24-27]. The isotopic composition of the double-spike strontium has to be known. Matrix matching does not have to be achieved per se. If the amount ratio of the non-radiogenic strontium isotopes, say N( Sr)/N( Sr), is well known and does not vary significantly in Nature, it can be used to calibrate the measured ratio 787/86 without any admixing of the double spike [28]. In both of its variations, this procedure involves the selection of an appropriate mass bias correction model, such as the exponential law (see below). 

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... 

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. 

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. 

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. 

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. 

Mass spectrometer bias removed through use of double spiking technique calibrated by gravimetric standards. ... 

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. 

Compounds that contain halogens and are aromatic display response on both (e.g., chlorobenzene) detectors. Compounds that have a double bond, such as vinyl chloride, are ionized on the PID (11.7 keV), but show a much weaker response than on the Hall detector. Common quality control samples such as a method blank, a matrix spike and a matrix spike duplicate, and a laboratory control sample are required when analyzing samples by this method. A continuing calibration or check standard is injected every 12 h to verify the calibration. 

---