Isotope uncertainty evaluation

An accurate uncertainty statement of the measurement result is arguably as important as the accuracy of the measurement result itself. However, since the process of isotope amount ratio measurement is far from trivial, so is also the evaluation of the uncertainty. Consider the following example as an illustration of current problems in conceptual understanding of the uncertainty evaluation of the measurement results. 

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. 

Virtually all published uncertainty evaluations of mass spectrometric methods assume independent ion currents or isotope amount ratios for all simultaneously measured isotopes [62, 63]. It is unclear why this paradigm has received such widespread acceptance. Isotopic signals in mass spectrometry are always correlated, provided that they are well above the background noise. The method of internal standardization is made possible precisely because mass spectrometric signals are correlated. 

Yang, L., Mester, Z., and Sturgeon, R. E. (2002) Species-specific isotope dilution-based calibration for trace element speciation and its combined uncertainty evaluation determination of tributyltin in sediment by HPLC-ICP-MS. Anal. Chem., 74,2968-76. 

A further advancement comes from inter-laboratory comparison of two standards having different isotopic composition that can be used for a normalization procedure correcting for all proportional errors due to mass spechomehy and to sample preparation. Ideally, the two standard samples should have isotope raUos as different as possible, but still within the range of natural variations. There are, however, some problems connected with data normalization, which are still under debate. For example, the CO2 equilibration of waters and the acid extraction of CO2 from carbonates are indirect analytical procedures, involving temperature-dependent fractionation factors (whose values are not beyond experimental uncertainties) with respect to the original samples and which might be re-evaluated on the normalized scale. 

Proponents of the SI for chemistry must consider that proportionality is deeply embedded in chemical thinking.3 Many of the potentially most reliable analytical techniques - for instance isotope-dilution mass spectrometry - yield ratios in the first place. In complex series of ratio measurements the uncertainty propagation is more straightforward than when sums and differences from standards - such as for mass determinations - are involved. Consistent with the use of SI, the value of a ratio is called a measurement when numerator and denominator are multiplied by a unit and the related uncertainties have been evaluated. 

Alternatively, interlaboratory consensus values based on a range of different methods are used to try to address systematic effects. Such approaches leave open the question concerning traceability, or how closely the certified value agrees with the true value. The establishment of traceability to SI requires the use of primary methods, such as isotope dilution mass spectrometry, or the use of other well understood and validated methods, where any systematic effects have been fully evaluated and corrected for. The uncertainty budget must include appropriate allowance for any suspected residual... 

The main uncertainty in the evaluation of xenon isotopes is the composition of terrestrial nonradiogenic xenon (see Section 4.11.2.5). However, the arguments presented above appear... 

Eisenbud, M. 1987. Environmental Radioactivity. 3rd ed. New York, NY Academic Press. Encinar, J. R., Alonso, J. I. G., Sanz-Medel, A., Main, S., and Turner, P. J. 2001. A comparison between quadrupole, double focusing and multicollector ICP-MS instruments Part I. Evaluation of total combined uncertainty for lead isotope ratio measurements. J. Anal... 

The combined (in quadrature) relative systematic uncertainty bounds for E and V have been determined to be 0.070. This relative systematic uncertainty is within the boundary condition established within the NUREG. It should be stressed that the areas evaluated represent only a portion of the analytical evaluation performed by the current "state-of-the-art software systems. Peak search and complex spectral fitting algorithms have not been addressed directly to date in this evaluation. An attempt will be made to address some of these items in a later section through evaluation of samples containing added isotopes of known quantity. 

Precision and accuracy. As in all other techniques, precision is a measure of reproducibility while accuracy deals with the closeness of the result with the true value. The precision of an AMS measurement is evaluated from the reproducibility or spread of repeat measurements of the isotopic ratio of a sample. In AMS, stable and radioactive isotopes are measured simultaneously. The precision in AMS is limited by the uncertainty of the counts of the ions arriving in the detector. Precision or uncertainty is also dependent on the sample size. To have a more accurate result all the instruments required in various steps of AMS measurement should be calibrated properly (Hotchkis et al. 2000). 

By choice we do not provitte an automatic feedback for the scaling and alteraUon of neutron cross-sections. Our basic axiom is that any computerized anMysis of evaluated nuclear constants most not offend tte physics of nuclear processes, must foke place within the constraints of experimentally measured or inferred uncertainties, be addressable selectively to any reaction and energy domain of an isotope, mid be.,subservlent to human judgment. 

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