Two Double Spikes

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 

The mixing relationship between the true ratio of the first double spike mixture (e.g., ) and the true ratio of the unknown (e.g., x, ) in the 

The second double spike includes an artificially enriched isotope that does not exist in natural samples or in the first double spike. For example, b in the Pb- Pb double spike does not exist in natural samples or in the first Pb- Pb double spike. Therefore, the second double spike has an additional isotope ratio w. 

The true ratio for the second double spike mixture is related to the measured ratio of the second mixture by 

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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. 

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). 

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. 

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). 

Another setback for manufacturers of fuel cells trying to break into the distributed generation market has been the tremendous volatility of natural gas prices. In just the five-year period from the beginning of 1999 to the end of 2003, we ve had two major spikes in the price of natural gas, during which time companies that have dual-fuel facilities have shifted from natural gas to oil. Since most stationary fuel cells run on hydrogen produced from natural gas, the volatility in the price of gas translates into volatility in the price of power from the fuel cell. Most companies are risk averse and very nervous about committing to a power source that is dependent on a fuel whose price can double in a short period of time. This is a particular problem with low-temperature fuel cells, which have less fuel flexibility and less efficiency. 

If the greatest accuracy is required for a given concentration, a double spike (a mixture of two enriched isotopes) may be used this subject is described in detail in Chapter 1. 

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 ... 

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. 

The third technique that is applied to correct stable isotope ratio measurements for instrumental mass bias involves the use of a double spike [114, 115]. In this case, a spike solution, which is highly enriched in two isotopes of the target... 

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. 

The accuracy of the method depends upon the precision with which the two volumes of solution and the corresponding diffusion currents are measured. The material added should be contained in a medium of the same composition as the supporting electrolyte, so that the latter is not altered by the addition. The assumption is made that the wave height is a linear function of the concentration in the range of concentration employed. The best results would appear to be obtained when the wave height is about doubled by the addition of the known amount of standard solution. This procedure is sometimes referred to as spiking. 

If the sample matrix is complex, it may be necessary to determine if there are any interference effects from the matrix, on the analyte response. This is usually done by spiking the sample with a known amount of analyte. Two equal portions of sample are taken and an appropriate quantity of analyte is added to one to effectively double the absorbance. A similar quantity of analyte is added to water to make a spike-alone solution. Readings are taken for sample, sample-plus-spike and spike-alone solutions and the amount of interference calculated as a percentage enhancement or... 

Clough and co-workers reported on the uncertainty contribution using single and double isotopi-cally enriched spikes in the isotope dilution approach employing a multiple ion collector ICP-MS combined with an HPLC and with cold vapour generation (CV) to form HPLC-CV-MC-ICP-MS for the determination of MeHg in fish tissue.8 Two fish tissue reference materials DORM-2 (NRC, Canada) and BCR 464 were employed in these studies. The amount of each certified reference... 

The major isomer isolated, and characterized by single-crystal X-ray diffraction, was found to be the 1,4 isomer rather than the 1,2 isomer (Eq. 11) [145]. In a 1,4 adduct of Ceo the double bond in a pentagon increases the energy of the Ceo cage by about 8 kcal mol compared with that of the 1,2 adduct [146, 147]. However, this disfavored energy increase is compensated by a decrease in steric hindrance when two bulky groups are placed in a 1,4-position. Thus, 1,4 adducts are usually the dominant products when bulky groups are added to Ceo [145, 148]. It has been shown that the 1,2 and 1,4 adducts of Ceo can be identified from their different absorption spectra [148]—the 1,2 adducts have a weak spike at ca 432 nm [149] and the 1,4 adducts have a broad absorption band at ca 445 nm [145, 148, 150]. 

The probability density function, written as pif), describes the fraction of time that the fluctuating variable/ takes on a value between/ and/ + A/. The concept is illustrated in Fig. 5.7. The fluctuating values off are shown on the right side while p(f) is shown on the left side. The shape of the PDF depends on the nature of the turbulent fluctuations of/. Several different mathematical functions have been proposed to express the PDF. In presumed PDF methods, these different mathematical functions, such as clipped normal distribution, spiked distribution, double delta function and beta distribution, are assumed to represent the fluctuations in reactive mixing. The latter two are among the more popular distributions and are shown in Fig. 5.8. The double delta function is most readily computed, while the beta function is considered to be a better representation of experimentally observed PDF. The shape of these functions depends solely on the mean mixture fraction and its variance. The beta function is given as... 

The homogenates were filtered through a double layer of Whatman 4 paper wetted with 2 ml of acetonitrile on a Buchner funnel. The filtrates were collected under slight vacuum in silanized glass 250 ml filter flasks. The Polytron vessel was rinsed with 25 ml of acetonitrile H20 1 4, followed by two rinses with 2 ml of acetonitrile. Each of these rinses in turn, and a final 3 rinses with 2 ml of acetonitrile were added to the filter cake, all of the filtrates were combined, and 50 ml of water was added to reduce the acetonitrile concentration to roughly 30% v/v. Cs columns were conditioned, the samples were applied, and abamectin was eluted and concentrated as described above for spiked water samples. 

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