Analytical Methods Committee, AMCTB No. 84

Received
7th February 2018
, Accepted 7th February 2018

First published on 27th February 2018

When using a beam to make a measurement in situ, irrespective of scale, the process implicitly includes the taking of a sample. Therefore, the uncertainty of the measurement result needs to include the uncertainty generated by the sampling process, which is usually dominated by the heterogeneity of the analyte at that scale. Reliable estimates of the uncertainty of beam measurements are essential to judge their fitness-for-purpose (FFP) and hence to enable their rigorous interpretation. This approach can be applied to a wide range of techniques for the analytical assessments of materials, from handheld portable X-ray Fluorescence (pXRF) at the millimeter scale, to Secondary Ion Mass Spectrometry (SIMS) at the micron scale.

The scale of the measurements, and the mass of the primary sample taken, varies between analytical procedures. For example, pXRF interrogates a test portion mass in the milligram range, with a ‘beam’ diameter of around 5 mm (Fig. 1b). By contrast SIMS often has a test portion in the picogram range, with a beam diameter of around 5 μm (Fig. 1c). In such situations, this test portion for a single beam sample is the same as the primary sample. When pXRF or SIMS are applied in situ, they are in effect taking a sample of the test material, as well as making a chemical analysis. For some procedures (e.g. pXRF and EPMA) the sample is ‘interrogated’ in place, non-destructively, but for others (e.g. SIMS and LA-ICPMS) the sample is removed and destroyed. In all these cases, this process can be usefully described as ‘beam sampling’.

Beam sampling usually produces much quicker results than macro-sampling, and automation is often possible, but it is susceptible to small-scale heterogeneity within the sampling target. Macro-sampling can effectively eliminate the effects of small-scale heterogeneity, given sufficient physical preparation. For example, it is usually possible to increase the mass of the primary sample, within limits of logistics and cost. In contrast, the mass interrogated by beam sampling is defined by the analytical procedure used, and is fixed within relatively small limits, as described above for pXRF and SIMS. It is therefore typical that beam measurements have more uncertainty than measurements made on bulk materials. This is because heterogeneity adds to the uncertainty associated with a measurement and arises from very small samples showing variation due to small-scale heterogeneity that is effectively averaged by macro-sampling.

Application of the duplicate method to beam sampling can be problematic if the beam measurement is locally destructive, which precludes placing duplicate samples within a given distance (e.g. 50 μm for SIMS). When this is the case, the duplicate sample has to be taken at the minimum distance to avoid interaction between the two measurements. Heterogeneity then has to be assumed to be negligible at that scale, although ideally that assumption should be subsequently verified.

The resultant measurements are interpreted using analysis of variance (ANOVA). Variance within the duplicate pairs gives an estimate of the analytical measurement repeatability. Variance between the pairs gives an estimate of the heterogeneity. The sum-squares of these two components gives an estimate of the measurement repeatability at the larger scale, e.g., of a whole crystal fragment if that is the sampling target. The full measurement uncertainty can then be estimated by including other factors such as bias against matched certified reference materials (CRMs), and between-lab variance.

The concept of beam sampling can therefore be applied to a wide variety of different analytical procedures and objectives. One possible objective is to estimate the overall mean composition of a sampling target (e.g. a specified volume of a crystal fragment), in which case composite beam measurements can be applied. A particular example of this is the characterisation of a candidate reference material (RM) for beam analysis. One objective in this situation is to certify the mean concentration and its uncertainty for the required analytes in the material. This uncertainty on the mean has to include the contribution from the analyte heterogeneity at the relevant spatial scale. There are two published examples of quantifying heterogeneity for this purpose: one using SIMS on quartz fragments,^{2} and the other using pXRF on RM powders,^{5} both employing the ‘duplicate method’.

Alternatively, a second possible objective is to spatially resolve the variation of the analyte concentration across the crystal fragment, when an estimate of the uncertainty of the beam measurement at each location is needed. For example, if the aim is to establish whether the analyte concentration at the core of the crystal is different to that at its rim, then that difference must be shown to be significantly greater than can be explained by the measurement uncertainty. This situation is equivalent to the aim of traditional geochemical mapping at any scale (e.g. usually 10 m to 1000 km). For this purpose, an estimate of the measurement uncertainty is required, and reliable geochemical mapping requires that the measurement uncertainty should account for less than 20% of the total variance.^{3} This is one approach to judging the fitness of measurements (beam or bulk) for this particular purpose. A more general approach to judging FFP at the macro-scale balances the overall measurement uncertainty against the costs that might result from decisions based upon measurements with uncertainty that is too high, or too low.^{3} This particular method also differentiates the relative contributions made by sampling and analysis to the total uncertainty, thus enabling the most cost-effective approach to reducing the overall uncertainty. At the micro-scale, this approach appears to be equally applicable. Reducing the uncertainty from sampling at the macro-scale would normally be achieved by increasing either the mass of samples, or the number of increments in a composite sample. This could be similarly applied to the use of composite measurements at the micro-scale to reduce the effects of small-scale heterogeneity.

2 M. H. Ramsey and M. Wiedenbeck, Quantifying isotopic heterogeneity of candidate reference materials at the picogram sampling scale, Geostand. Geoanal. Res., 2018, 42(1), 5–24, DOI: 10.1111/ggr.12198.

3 Measurement uncertainty arising from sampling: a guide to methods and approaches, ed. M. H. Ramsey and S. L. R. Ellison, Eurachem, 2007, https://eurachem.org/images/stories/Guides/pdf/UfS_2007.pdf.

4 Joint Committee for Guides in Metrology, International Vocabulary of Metrology – Basic and General Concepts and Associated Terms, VIM, 3rd edn, 2008, p. 136.

5 P. D. Rostron and M. H. Ramsey, Quantifying heterogeneity of small test portion masses of geological reference materials by PXRF: implications for uncertainty of reference values, Geostand. Geoanal. Res., 2017, 41(3), 459–473, DOI: 10.1111/ggr.12162.

This Technical Brief was prepared by the Subcommittee for Sampling Uncertainty and Sampling Quality (Chair Prof M. H. Ramsey) and approved by the Analytical Methods Committee on 02/02/2018.

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