where m is the expansion coefficient, b is the intercept, and n is the number of measurements of standards. Past work investigating C isotopes has shown that normalizations using two or more standards substantially reduce normalization errors compared to one-point anchoring11,17 because the expansion coefficient is rarely equal to one when multipoint normalizations are used21, but Eq. 3 assumes an expansion coefficient of one. The addition of supplementary standards to produce a three- or four-point normalization allows a coefficient of determination (r2) to be calculated and theoretically reduces the extrapolation of errors stemming from isotope heterogeneity of the standards, although experimental assessments17 and Monte Carlo simulations21 of this hypothesis have so far been limited to C. Furthermore, past assessments of how many standards should be used in a normalization have not concurrently considered the effects of scenarios such as matrix mixing and extrapolation, which may require additional standards to ensure acceptable results.
Finally, we note that single or multipoint anchoring can also be accomplished by analyzing one or multiple isotope standards to calculate an intercept (Eq. 5) and applying an expansion coefficient (m ) calculated from a previous analysis of multiple standards to conduct a pseudo-linear normalization (Eq. 6) assuming that the expansion coefficient is stable over time17. This normalization method is susceptible to changes in instrument performance over days or weeks and with different instrument tunings and is thus not investigated in this work. Here, we perform one-point anchoring and two-point, three-point, and four-point linear normalizations for N and C on two EAIRMS systems in two laboratories to experimentally assess their accuracy and interlaboratory comparability.

1.2 Standard matrix, normalization isotope range, and instrument linearity

The impact of sample matrix and isotope range of the standards on normalization accuracy have not been as thoroughly investigated as the number of standards. Past work has identified matrix effects between organic and inorganic standards for N28, but laboratories that process biological samples frequently analyze a variety of organic sample matrixes (e.g., muscle tissue29, plants30, soils22) that have different preparation techniques and combustion properties. Although proper application of the “identical treatment” protocol would suggest matching the matrix of the sample and of the standard31, some sample matrixes, such as sediment and particulate organic matter collected on glass fiber filters, do not have corresponding certified reference materials available for purchase, which thwarts matrix matching. The effect of matrix on the isotope results of organic samples complicates the interpretation of biological stable isotopes32,33and requires additional experimental assessment.
The isotope range of the normalization curve, and how it may affect the accuracy of results, presents another area of uncertainty. Laboratories may use standards that have very different isotope compositions, thus generating a normalization curve with a large isotope range (i.e., >40‰). Conversely, analysts may tightly bracket their samples by using normalization curves with a comparatively small isotope range. Furthermore, when a sample has an isotope composition that exceeds the range of normalization standards, extrapolation beyond the normalization curve may be required. Past work on C isotopes has suggested that tightly bracketing unknown samples may marginally improve accuracy if the normalization is not extrapolated21, but this investigation was constrained to two-point C normalizations. In this study, we explore how the matrix and isotope range of standards impacts the accuracy of one-point, two-point, three-point, and four-point normalizations for N and C.
The impact of instrument linearity and subsequent linearity corrections is a final aspect of stable isotope analyses that may hinder the reproducibility of biological studies. Linearity, the mass-dependent change in reported isotope composition from an IRMS, is anecdotally well known and yet has not been subjected to an experimental interlaboratory comparison34. This characteristic of IRMS systems is of particular importance for biological applications because there can be large variations in the organic matter content of the samples, particularly for sediments and particulate organic matter. Because the amount of N2 and CO2 that enters the IRMS is proportional to the amount of organic matter in biological samples, instrument linearity can become the most important determinant of analysis precision for samples with high variations in organic matter content. Operators of EAIRMS systems frequently develop their own linearity corrections, if they correct for the phenomenon at all, but the magnitude and variability of instrument linearity between facilities is unknown. Whether linearity is dependent on the matrix being analyzed or can be predicted from reference gas diagnostics are additional areas of uncertainty. We seek to better understand how linearity affects EAIRMS isotope results for biological applications by performing reference gas diagnostics and replicate analyses of working standards of different organic matter compositions and sample weight at two laboratories.

Methods

  1. Stable isotope analysis

Eight certified reference materials and five in-house working standards were analyzed at the University of New Mexico Center for Stable Isotopes (UNM-CSI) and the United States Environmental Protection Agency, Atlantic Coastal Environmental Sciences Division (U.S. EPA). These standards encompassed a δ 15N range of -4.52‰ to +37.83‰ and a δ 13C range of -35.05‰ to -1.17‰ (Fig. 1), and the sample matrix and reference information is included in Table 1. For the normalization analysis, the eight certified reference materials were weighed to between 0.15 and 3.3 mg depending on the N content of the sample matrix to provide ~0.05 mg of N. Dilutions were then computed for each matrix to provide ~0.04 mg C to the IRMS. Each standard was run 4 times at each facility and were run in an alternating order to mitigate the effects of instrument drift. To quantify instrument linearity, the five working standards were weighed to between 0.09 and 40 mg and analyzed using a constant matrix-specific C dilution to produce a range of 0.013-0.16 mg of N and 0.009-0.10 mg of C across all working standards. At both facilities, the elemental analyzer was configured to inject a longer O2 dosing for standards with plant matrixes (USGS90, USGS91, CSI Blue Grama, and CSI Green Chile) and soil matrixes (CSI Soil). Analyses at UNM-CSI were performed on a Costech 4010 combustion EA paired with a ThermoFinnigan Delta-V continuous-flow IRMS (by a Conflo IV), while analyses at the U.S. EPA were performed on an Elementar Vario Isotope Select EA paired with an Elementar VisION continuous-flow IRMS. The pooled standard deviation (±1σ) of the certified reference materials were ± 0.115 forδ 15N and ±0.044 forδ 13C at the U.S. EPA, and ± 0.084 forδ 15N and ±0.069 forδ 13C at UNM-CSI. Pooled standard deviations of each certified reference standard are shown in Table 1.
Table 1 : Certified isotope composition and associated uncertainty (±1σ) of certified standard reference materials used in this study.