Sample Bracketing

FIGURE 9-18. Sample bracketing technique with linear and nonlinear calibration curves. [From W. G. Schrenk, in Flame Emission and Atomic Absorption Spectroscopy, Vol. 2, Edited by J. A. Dean and T. C. Rains, Marcel Dekker, New York (1971), Chapter 12. Used by permission of Marcel Dekker Inc.] 

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Measured by Omellas (Ref 9) for confined samples bracketted terms are computed by Mader (Ref 7) and interpolated to the density shown... 

The wheat sample residue level is determined from the relative mass spectral responses of the analytes to the corresponding isotopically labeled internal standards. The sample relative response is compared with the average relative response of a standard solution of analyte and internal standard analyzed before and after the sample (bracketing standards). Both samples and standards receive the same amount, 100 ng, of each internal standard to facilitate the comparison. The calculations to determine the residue level in wheat tissues are outlined in Section 7.3.1. 

Solutions. Correction for cXjj is most often made using a standard-sample bracketing technique (e g., Galy et al. 2001). In this protocol, standard and sample isotope ratios obtained by multiple measurement cycles are compared and the sample result expressed as a deviation from the standard. Cross contamination between the sample and the standard is avoided by washing the analytical instrumentation with dilute (usually about O.IN) HNO3 for several minutes between analyses. Introduction of Mg in dilute HNO3 (e.g., 0. IN) into the MC-ICPMS... 

The centrifuge was fabricated using an eight position sample bracket mounted within a forced-convection oven. Individual sample... 

Perfusate and sample total CO2 concentrations are measured by microcalorimetry (Levine et al. 1996). A standard curve is run before sample analysis, and standard samples bracket the determination of sample and perfusate C02 determination. 

Figure 4.4. (a) FIA manifold for simultaneous determinations of pH and pCa. 5, point of injection (30 (xL) pH, flowthrough capillary glass electrode FC, flowthrough cell containing a PVC-membrane-based calcium-selective electrode and the common reference electrode, details of which are shown below (b). The carrier solution (A and B) is TRIS buffer of pH 7.4, the connecting tubes (a and b) being made as short as possible. The carrier solution supplied via line B to the tip of the reference electrode is included in order to stabilize the reference electrode junction potential for sera measurements. In (c) is shown the potenti-ometric determination of the ionized calcium content in six serum samples, bracketed by two calibration runs of aqueous calcium standards (0.5-5 mA/), all assays made in triplicate. 

Sample bracketing is a technique especially useful if only a few samples are to be determined. After an initial run is made on the unknown, two standards, one of a concentration higher and one of a concentration lower than the unknown, are chosen and their signal intensities determined. These data are plotted as shown in Figure 9-18, where A and B are the standards and X is the unknown. If the calibration curve is linear, the concentration of X can be determined directly from the reading obtained from the concentration axis or from the equation... 

Special methods for handling analytical problems frequently are useful. Most of these are described in Chapter 9 and are mentioned here as a reminder. Some of the more common special techniques that can be used, in addition to scale expansion described above, include sampling bracketing, standard addition, and dilution methods. 

An alternative correction method is based on, essentially, standard-sample bracketing, where analyses of unknowns are interspersed with analyses of standards. The basic assumption in this case is that the amount of elemental and... 

If the intercept ratio is used without standard-sample bracketing, there should be a check on the percentage of oxides formed, as this is likely to be different for U than for Pb, and may affect the U/Pb ratios. This can easily be done on singlecollector instruments by monitoring oxides for co-aspirated solutions [60]. In the case of standard-sample bracketing, it is assumed that the level of oxide formation is similar for sample and standard. 

The main thing that the spreadsheets need to do is to allow the user to decide which part of their time-resolved signal is used, and then reference that to the same part of the signal for bracketing standards, or use it for deterrnining the zerotime intercept. If standard-sample bracketing is used, errors on the unknown and the standards need to be combined in quadrature [56], and an assessment needs to be made on the way to incorporate errors related to drift. Error correlations are a further concern, especially for the use of traditional concordia diagrams [13]. 

The technique of internal normalization is commonly apphed in both MC-ICP-MS and TIMS for the precise correction of the instrumental mass bias (see also Chapter 5) that is encountered during the analysis of radiogenic isotopic compositions [33, 34]. The ICP ion source of MC-ICP-MS, however, also features two characteristics that play an important role for isotopic analysis, where internal normalization cannot be applied. First, an ICP source operates at steady state and therefore mass fractionation is not primarily a time-dependent process, as in TIMS where the measured isotopic compositions change with time due to the progressive evaporation of a sample from the filament. The steady-state operation of an ICP ion source is beneficial for the correction of instrumental mass bias by external standardization, where the isotope ratio data obtained for a sample are referenced to the values obtained for bracketing analyses of an isotopic standard [27, 35]. Hence, this procedure is commonly termed standard-sample bracketing. 

The steady-state operation of the ICP source is beneficial for the correction of instrumental mass bias by standard-sample bracketing, where the raw (measured and uncorrected) isotope ratio data of a sample are referenced to the results obtained for an isotopic standard, which is preferentially analyzed before and after each sample [27, 35]. This technique is similar to the standardization method commonly used in gas source isotope ratio mass spectrometry. To account best for drifts in instrumental mass bias, which can be particularly severe for light elements such as Li and B, data collection often utilizes multiple but short analytical measurements for samples that are each bracketed by standard analyses. Switching between samples and standards can be very rapid, if long washout protocols are not required, and mass spectrometric measurements of about 5 min or less have been used to optimize the precision of Li and Mg isotope ratio measurements by MC-ICP-MS [111, 112]. 

The principal advantage of the standard-sample bracketing approach is that its application is very straightforward and only two interference-free isotopes are needed, in principle, for an analysis. The method, however, is also particularly susceptible to the generation of analytical artifacts from variations in instrumental mass bias that are induced by residual matrix elements, which are present in the sample solutions but absent in the pure reference standards (Figure 10.10). Hence this approach is typically used only for elements (i) that are present at high concentrations in samples (e.g., the major elements Mg, Si, and Fe of silicate meteorites or Fe from iron meteorites) or (ii) for which the technique of external normalization is not readily applicable (e.g., Ii, B see below). 

Figure 10.10 Comparison of Cd isotope ratio data obtained using different normalization procedures for repeated measurements of two terrestrial rocks samples and the Allende CVS chondrite (from [38]). (a) Comparison of results obtained by standard-sample bracketing and by external normalization (based on added Ag) using the empirical method of Marechal et al. [37], The bracketing approach yields inaccurate results for some samples, due to matrix-induced changes in instrumental mass bias, (b) Comparison of results obtained by external normalization using Ag using either the exponential law in combination with standard-sample bracketing or the empirical technique of Marechal et al. [37]. Both methods yield similar results for all samples. The isotopic data are shown as eCd/amu values, which denote the variation in Cd isotopic composition relative to a terrestrial standard and normalized to a mass difference of lu [38, 113].

For ultimate precision and accuracy, either MC-TIMS or MC-ICP-MS is required. Achievable precisions for MC-ICP-MS are of the order of 0.002-0.01% [299-302]. These techniques have been developed and applied exclusively to study natural isotope fractionation phenomena in geological samples. While double-spiking techniques are required for TIMS to differentiate between natural and instrumental fractionation [297], measurement bias has been corrected for in MC-ICP-MS measurements by normalization to the isotope ratios of a doped zirconium or ruthenium standard [301], a palladium standard ]302] or by standard sample bracketing using a molybdenum standard ]303]. 

Standard-sample bracketing consists of measuring samples of interest between appropriate certified isotopic standards, and applying a correction to the sart5)les according to the ratio measurements of these standards. Accurate and precise analysis relies on a stable instrument and complete matching between sample and standard matrices to avoid any variations of mass bias or introduced interferences (see later). This external normalisation approach is also more time consuming due to the increased number of standards analysed. 

With no stable isotope pair within the U system or a suitable AME, a standard-sample bracketing protocol is usually employed to correct for mass bias. Human urine generally contains very low concentrations of U (generally 1-5 ng/L), so an isotope dilution strategy is required, together with ion-counting detection (ideally a Daly photomultiplier or discrete dynode secondary electron multiplier) and a multi-static (rather than multi-dynamic) peak-jumping routine, for precise measurement of the total U concentration and the minor isotopes of and even... 

Analyze the quality control reference materials before every batch of samples. Bracket the samples with the reference material. If the reference material does not meet the specification in 10.1, the samples analyzed immediately preceding the reference material are considered suspect and should be rerun. Retming of the mass spectrometer and drift with time may require recalibration of the GC/MS system (see Section 9). 

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