Fig. 7 : The slope of all multipoint normalizations by isotope range of the standards. Dashed horizontal lines indicate the slopes for each facility derived from an 8-point normalization composed of all certified reference standards.

Normalizations are significantly impacted by matrix and extrapolation effects

Even when results are constrained to three-point normalizations, the matrix of the standard relative to the quality controls has a significant effect on the accuracy of the normalization (Fig. 3). Bounded normalizations where the matrixes of the standards were mixed relative to the quality controls exhibited median errors 63%-195% greater than those where the matrixes were matched. The mechanism behind this matrix effect is unclear, particularly because the isotope composition of the plant-based standards were quantified using high organic certified reference materials20. In accordance with typical EAIRMS usage, the plant-based standards were weighed to a higher mass and analyzed with a higher oxygen dosing and a greater sample dilution for C, and thus it is possible that these instrumentation factors are contributing to the matrix effect observed in this study. Although past work has suggested that matrix matching between organic and inorganic samples would reduce normalization errors28, this study posits that matrix effects should be considered even within organic samples. In studies where matrix-matched certified reference materials do not exist (e.g., sediment; glass fiber filters), the effects of matrix-mixing should be considered as a source of imprecision that will not be reflected in the variance of the standards alone.
Similarly, this study shows that extrapolating beyond the isotope range of the standards– not an uncommon occurrence when analyzing a wide variety of biological samples – increases median normalization errors by 81%-135%, even when the analysis is constrained to matrix-matched normalizations (Fig. 4). Normalizations with a smaller isotope range are more likely to require extrapolation, but the lack of significant relationship between isotope range and normalization error for bounded, matrix-matched, three-point normalizations (Fig. 5) indicates that extrapolation is the primary factor driving inaccuracy. Overall, our results provide experimental evidence to support the emerging consensus37 that calibration standards for EAIRMS should have isotope values that span the full natural range of the measured elements, regardless of the isotope values of the samples being analyzed.

Instrument linearity cannot be predicted by reference gas diagnostics alone.

Although reference gas linearity diagnostics are anecdotally used as a means of assessing instrument performance, we quantified instrument linearity using replicate analyses of working standards across a range of sample weights. At both facilities, a large linearity effect was observed in the reported isotope composition of the working standards that was not reflected by reference gas linearity diagnostics, which inject pulses of reference gas into the IRMS to assess the linearity effect. The linearity effect does not correspond to incomplete combustion in the elemental analyzer (Fig. S1), suggesting that other factors, such as a N blank introduced during sample preparation, are driving our observations. These results show that, while reference gas linearity diagnostics may be useful for confirming normal instrument operation, they are not representative of the linearity effect that will be observed when analyzing solid samples. We suggest running replicate measurements of a solid standard at varying sample weights to determine the peak amplitudes at which linearity has an effect and applying a linearity correction curve when necessary. In our study, N linearity was observed at peak amplitudes corresponding to ~0.06 mg of N, meaning that instrument linearity is of particular importance for samples with a low N content such as sediment and plant tissue. The high magnitude of the linearity effect observed in both facilities across a range of sample matrixes reinforces the importance of this instrument effect for any facility measuring stable isotopes in biological samples.

Conclusion – best practices for biological applications of EAIRMS

Through an experimental assessment of isotope normalizations across a variety of sample matrixes and isotope ranges, we assessed how the number, matrix, and isotope range of the calibration standards effected normalization error on two EAIRMS systems. In the first known assessment of normalization methods for both N and C, we found that three-point and four-point normalizations have the lowest normalization errors and are most resilient to the effects of sample matrix effects and extrapolation.
Past work has identified two-point normalizations as a common and acceptable means of normalizing isotope results2,17. In contrast, some of the observed two-point normalizations had deviations more than 1‰ and were significantly less accurate than three-point and four-point normalizations. We posit that two-point normalizations are vulnerable to the effects of matrix-mixing and extrapolation and should not be considered sufficient for EAIRMS normalization in biological applications. Although normalizations using at least three standards were more resilient to these factors, we found that mixing the matrix between the samples and the standards and extrapolating outside of the curve reduced accuracy regardless of how many standards were analyzed. No significant impact was observed with the isotope range of three-point normalization but maximizing the isotope range will reduce the likelihood of extrapolation. Thus, we recommend users of EAIRMS systems normalize their results using at least three calibration standards that span a large isotope range and are matrix matched with the samples being analyzed, and to include at least one additional independent quality control standard.
In our interlaboratory comparison of instrument linearity, we found that linearity error was substantial, especially for N, regardless of instrument or sample matrix. Diagnostic reference gas linearity testing was unable to reproduce the observed linearity effect, suggesting that the reference gas is not a useful predictor of real-world instrument linearity. Although reference gas diagnostic testing may be a beneficial tool for assessing nominal instrument operation, the linearity response of the instrument should be assessed experimentally by analyzing solid standards across a range of masses.
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