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
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.