Isotope measurement uncertainty

All values of the IRMM Isotopic Reference Materials are traceable to the SI (the international system of base quantities and base units). Isotopic measurement results corrected by means of these Isotope Ratio Reference Materials have reduced (ISO/BIPM) uncertainties. Isotopic measruements carried out against these Spike Reference Materials are traceable to the SI, if carried out properly. Further details are available from IRMM website see Chapter 8. 

Thorium. Multiple-collector measurement protocols by TIMS for thorium isotopic analysis typically involve the simultaneous measurement of Th and °Th (for silicate rocks), or Th and °Th, then Th and Th (for low- Th samples), using an axial ion counter and off-axis Faraday collector (Table 1). Various methods are used to correct for the relative gain between the low-level and Faraday detectors and 2a-uncertainties of l-5%o are typically obtained (Palacz et al. 1992 Cohen et al. 1992 McDermott et al. 1993 Rubin 2001). Charge-collection TIMS protocols enable Th, °Th and Th to be monitored simultaneously on a multiple-Faraday array and can achieve measurement uncertainties at the sub-permil level (Esat et al. 1995 Stirling et al. 1995). 

In the past three years, MC-ICPMS has emerged as an alternative to TIMS for precise measurement of the U-series isotopes with comparable or better precision. U-Th isotopes can now be routinely measured at the sub-permil level. Previously, this had only been demonstrated using charge-collection TIMS applied to thorium isotope measurement. Data collection efficiency, sample size requirements, and detection limits can also be greatly improved over TIMS. For the U- U- Th system applied to carbonate samples, this has extended the dating range beyond 600,000 years, and °Th-age uncertainties of 2000 years are now attainable on 300,000 year-old samples (e g., Stirling et al. 2001). 

A practical difficulty of SIMS Li isotope measurement is the paucity of appropriate mineral and rock standards with well characterized isotopic compositions. Although the estimated uncertainties are larger than for the more widespread TIMS and MC-ICP-MS techniques, the capacity to measure at very restricted spatial scales makes this a promising area of exploration, particularly for samples of restricted size and those with complex small-scale structure. The complimentary nature of in situ and bulk data in Li isotope studies shows promise for better understanding complex processes, e.g., fluid-rock interaction (Decitre et al. 2002). 

The best precision is obtained for isotope ratios near unity (unless the element to be determined is near the detection limit, when the ratio of spike isotope to natural isotope should be between 3 and 10) so that noise contributes only to the uncertainty of natural isotope measurement. Errors also become large when the isotope ratio in the spiked sample approaches the ratio of the isotopes in the spike (overspiking), or the ratio of the isotopes in the sample (underspiking), the two situations being illustrated in Fig. 5.11. The accuracy and precision of the isotope dilution analysis ultimately depend on the accuracy and precision of the isotope ratio measurement, so all the precautions that apply to isotope ratio analysis also apply in this case. 

Individual uncertainties of the proton and deuteron charge radii introduce by far the largest contributions in the uncertainty of the theoretical value of the isotope shift. Uncertainty of the charge radii are much larger than the experimental error of the isotope shift measurement or the uncertainties of other theoretical contributions. It is sufficient to recall that uncertainty of the 15 Lamb shift due to the experimental error of the proton charge radius is as large as 50 kHz (see (12.11)), even if we ignore all problems connected with the proton radius contribution (see discussion in Subsects. 12.1.5, 12.1.6). 

Table 5.3. Measurement uncertainty budget for the measurement of cholesterol in serum by isotope dilution/GCMS...

IDMS is based on measurements of masses and isotope ratios only. Some important advantages, compared with other calibration strategies, such as external calibration and standard additions, are that instrumental instabilities such as signal drift and matrix effects will have no influence in the final concentration in the sample, high accuracy and small measurement uncertainties are enabled, possible loss of substance of the isotope-diluted sample will have no influence on the final result and there is no need to resort to an external instrumental calibration or standard additions to the sample. 

Worldwide acceptance of analytical results requires reliable, traceable, and comparable measurements. A key property of a reliable result is its traceability to a stated reference. Traceability basically means that a laboratory knows what is being measured and how accurately it is measured. It is also an important parameter where comparability of results is concerned and is usually achieved by linking the individual result of chemical measurements to a commonly accepted reference or standard. The result can therefore be compared through its relation to that reference or standard. Every link in the traceability chain must be based on the comparison of an unknown value with a known value. The stated reference might be an International System of unit (SI) or a conventional reference scale such as the pH scale, the delta scale for isotopic measurements, or the octane number scale for petroleum fuel. In order to be able to state the uncertainty of the measurement result, the uncertainty of the value assigned to that standard must be known. Therefore a traceability chain should be designed and then demonstrated using the value of the respective standard with its uncertainty.11... 

Reconstruction of faunal records in deep-sea sediments and oxygen isotope measurements have been yielding useful information of the ocean s paleotemperature. However, the lack of these tools in the case of continents has hampered the estimation of paleotemperature in continents. The latter estimate has mainly been made on somehow indirect approach such as pollen data, periglacial feature, and soil carbonate, all of which suffer from considerable uncertainty stemming from the assumption that must be made to convert the observation to temperature. The advantage of the noble gas thermometer, as compared to the other paleotemperature methods, is that it is based on the relatively simple physical principle that directly relates noble gas concentration to the ambient temperature (see Stute Schlosser, 1993, for a recent review of the noble gas paleotemperature method). However, in actual practice, we need some cautions. 

Calcium-41 decays by electron capture to with a half-life of only 103 kyr. It has the distinction of being the shortest-lived isotope for which firm evidence exists in early solar system materials, and this fact makes it key for constraining the timescale of last nucleosynthetic addition to solar system matter (in the external seeding scenario). It also makes " Ca exceedingly difficult to detect experimentally, because it can only be found to have existed in the oldest materials and then in only very small concentrations. Fortunately, its daughter potassium is rather volatile and calcium is concentrated in refractory minerals (the C in CAI) leading to large fractionations. Hutcheon et al. (1984) found hints for " Ca in Allende refractory inclusions, but could not clearly resolve excesses above measurement uncertainties. 

We will now see that this is equally valid for IDMS of bi-isotopic elements (Eq. 4 and Fig. 2) and in the poly-isotopic case (Eq. 5 and Fig. 3). We note that R can be chosen 2 ways the major isotope abundance being in the denominator or in the nominator of Rx or Ry. We arbitrarily choose the latter, hence Ry 1 and quite different from Rb ( 1). We note that Ry is then little affected by Rb- Also because Ry appears in both nominator and denominator of Eq. 4, any uncertainty on Ry, will have very little effect on the uncertainty of Wx/A/y. On the other hand Rx will be small (the major isotope abundance will now be in the denominator of Rx) with respect to Rb or to 1, so any uncertainty on Rx will not contribute to the uncertainty of A/x/Wy. Consequently only the uncertainty of Rb in the denominator will largely determine the uncertainty of N /Ny and hence of the IDMS result. The precision with which an isotope dilution ratio can be measured, determines the precision of an IDMS determination as far as the isotopic measurement is concerned. Further limitations are, or may be ... 

Uncertainties in physical constants may or may not be significant, depending on the measurement. Half-lives in particular tend to be well known and usually contribute only negligible uncertainty to the result of a radioanalytical measurement. Errors in radiation emission probabilities may contribute additional uncertainty to some measurements. Uncertainties for both categories are available from tables of isotopes and the public Web site of the National Nuclear Data Center at Brookhaven National Laboratory. 

Natural abundance values are also followed by uncertainties in the last digit(s) of the stated values. This uncertainty includes both the estimated measurement uncertainty and the reported range of variation in different terrestrial sources of the element (see Reference 3 and 4 for more details). The absence of an entty in the Abundance column indicates a radioactive nuclide not present in nature or an element whose isotopic composition varies so widely that a meaningful natural abundance cannot be defined. 

The detection limit of a linear calibration is defined as three times the standard uncertainty of the concentration of the blank. This definition is, however, not an ideal representation of the detection limit in ID-MS. A formulation for the detection limit for ID-MS is available [45], where the ID-MS detection limit is described as a function of the enrichment of the isotopic spike and of the uncertainties in the measurement of the spiked isotope. It states that when the spike is not enriched isotopically, the detection limit is infinite and unusable. When the spike is enriched in either isotope, the ID-MS measurement uncertainties approach the linear calibration detection limit. 

The advantage of using eqn [12] rather than eqn [3] is that the isotope amount fractions in the sample and the spike are not correlated, which simplifies the calculation of the measurement uncertainty of the analytical result. 

Usually, when studying much older volcanic rocks, the time resolution achieved does not allow such close events to be distinguished. The U-Pb zircon method applied after precise in situ isotope measurements now makes such studies possible because the absolute uncertainties on ages from quaternary zircons is much better than the events to identify. 

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