InterCarb: A Community Effort to Improve Interlaboratory Standardization of the Carbonate Clumped Isotope Thermometer Using Carbonate Standards

Abstract

Increased use and improved methodology of carbonate clumped isotope thermometry has

greatly enhanced our ability to interrogate a suite of Earth-system processes. However, interlaboratory

discrepancies in quantifying carbonate clumped isotope (Δ

) measurements persist, and their specific

sources remain unclear. To address interlaboratory differences, we first provide consensus values from

the clumped isotope community for four carbonate standards relative to heated and equilibrated gases

with 1,819 individual analyses from 10 laboratories. Then we analyzed the four carbonate standards along

with three additional standards, spanning a broad range of δ

and Δ

values, for a total of 5,329 analyses

on 25 individual mass spectrometers from 22 different laboratories. Treating three of the materials as

known standards and the other four as unknowns, we find that the use of carbonate reference materials

BERNASCONI ET AL.

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InterCarb: A Community Effort to Improve

Interlaboratory Standardization of the Carbonate

Clumped Isotope Thermometer Using Carbonate

Standards

S. M. Bernasconi

, M. Daëron

, K. D. Bergmann

, M. Bonifacie

A. N. Meckler

, H. P. Affek

, N. Anderson

, D. Bajnai

, E. Barkan

, E. Beverly

8,9

D. Blamart

, L. Burgener

, D. Calmels

4,11

, C. Chaduteau

, M. Clog

B. Davidheiser-Kroll

, A. Davies

14,21

, F. Dux

15,34

, J. Eiler

, B. Elliott

, A. C. Fetrow

J. Fiebig

, S. Goldberg

, M. Hermoso

4,18

, K. W. Huntington

, E. Hyland

M. Ingalls

16,20

, M. Jaggi

, C. M. John

, A. B. Jost

, S. Katz

, J. Kelson

, T. Kluge

21,22

I. J. Kocken

, A. Laskar

, T. J. Leutert

5,25

, D. Liang

, J. Lucarelli

T. J. Mackey

3,26

, X. Mangenot

4,16

, N. Meinicke

, S. E. Modestou

, I. A. Müller

S. Murray

, A. Neary

, N. Packard

, B. H. Passey

, E. Pelletier

, S. Petersen

, A. Piasecki

5,28

A. Schauer

, K. E. Snell

, P. K. Swart

, A. Tripati

, D. Upadhyay

, T. Vennemann

I. Winkelstern

9,31

, D. Yarian

, N. Yoshida

32,33

, N. Zhang

, and M. Ziegler

Geological Institute, ETH Zürich, Zürich, Switzerland,

Laboratoire des Sciences du Climat et de l’Environnement,

LSCE/IPSL, CEA-CNRS-UVSQ, Université Paris-Saclay, Gif-sur-Yvette, France,

Department of Earth, Atmospheric

and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA,

Universit

é

de Paris, Institut

de Physique du Globe de Paris, CNRS, Paris, France,

Bjerknes Centre for Climate Research and Department of

Earth Science, University of Bergen, Bergen, Norway,

Institute of Earth Sciences, Hebrew University of Jerusalem,

Jerusalem, Israel,

Institute of Geosciences, Goethe University Frankfurt, Frankfurt am Main, Germany,

Now at

Department of Earth and Atmospheric Sciences, University of Houston, Houston, TX, USA,

Department of Earth

and Environmental Sciences, University of Michigan, Ann Arbor, MI, USA,

Department of Marine, Earth and

Atmospheric Sciences, North Carolina State University, Raleigh, NC, USA,

Now at Geosciences Paris Sud (GEOPS),

Universit

é

Paris-Saclay, CNRS, Orsay, France,

Scottish Universities Environmental Research Centre (SUERC),

Scotland, UK,

University of Colorado Boulder, Boulder, CO, USA,

Now at Stockholm University, Stockholm,

Sweden,

Now at School of Earth and Life Sciences, University of Wollongong, Wollongong, Australia,

Geological

and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA,

Department of Earth, Planetary, and

Space Sciences, University of California Los Angeles, Los Angeles, CA, USA,

Univ. Littoral Côte d’Opale, Univ. Lille,

CNRS, Laboratoire d’Oc

é

anologie et de G

é

osciences (UMR 8187 LOG), Wimereux, France,

University of Washington,

Seattle, WA, USA,

Now at Department of Geosciences, The Pennsylvania State University, University Park, PA, USA,

Imperial College, London, UK,

Now at Karlsruher Institut für Technologie KIT, Karlsruhe, Germany,

Department

of Earth Sciences, University of Utrecht, Utrecht, The Netherlands,

Institute of Earth Sciences, Academia Sinica,

Taipei, Taiwan,

Now at Max Planck Institute for Chemistry, Mainz, Germany,

Now at Department of Earth and

Planetary Sciences, University of New Mexico, Albuquerque, NM, USA,

Macquarie University, Sydney, Australia,

Now at Department of Earth Sciences, Dartmouth College, Hanover, NH, USA,

Department of Marine Geosciences,

Rostiel School of Marine and Atmospheric Sciences, University of Miami, Miami, FL, USA,

Institute of Earth

Surface Dynamics, University of Lausanne, Lausanne, Switzerland,

Now at Geology Department, Grand Valley State

University, Allendale, MI, USA,

Earth-Life Science Institute, Tokyo Institute of Technology, Tokyo, Japan,

National

Institute of Information and Communications Technology, Tokyo, Japan,

School of Geography, University of

Melbourne, Melbourne, Australia

Key Points:

•

The exclusive use of carbonate

reference materials is a robust

method for the standardization of

clumped isotope measurements

•

Measurements using different acid

temperatures, designs of preparation

lines, and mass spectrometers are

statistically indistinguishable

•

We propose new consensus

values for a set of seven carbonate

reference materials and updated

guidelines to report clumped isotope

measurements

Supporting Information:

Supporting Information may be found

in the online version of this article.

Correspondence to:

S. M. Bernasconi and M. Daëron,

stefano.bernasconi@erdw.ethz.ch

;

daeron@lsce.ipsl.fr

Citation:

Bernasconi, S. M., Daëron, M.,

Bergmann, K. D., Bonifacie, M.,

Meckler, A. N., Affek, H. P., et al.

(2021). InterCarb: A community

effort to improve interlaboratory

standardization of the carbonate

clumped isotope thermometer

using carbonate standards.

Geochemistry, Geophysics, Geosystems

, e2020GC009588.

https://doi.

org/10.1029/2020GC009588

10.1029/2020GC009588

Special Section:

Clumped Isotope Geo

chemistry: From Theory to

Applications

This article is a companion to Daëron

(2021),

https://doi.org/10.1029/

2020GC009592

RESEARCH ARTICLE

1 of 25

Geochemistry, Geophysics, Geosystems

Introduction

Carbonate clumped isotope (Δ

) thermometry is the most developed branch of the rapidly evolving field

of clumped isotope geochemistry. Given the broad range of applications in Earth Sciences (e.g., Affek &

Eiler,

2006

; Dale et al.,

2014

; Eagle et al.,

2010

; Ferry et al.,

2011

; Ghosh, Adkins, et al.,

2006

; Ghosh, Gar

zione, & Eiler,

2006

; Grauel et al.,

2013

; Guo & Eiler,

2007

; Huntington et al.,

2011

; Mangenot et al.,

2018

;

Passey & Henkes,

2012

; Veillard et al.,

2019

) and the improvement of analytical methods including auto

mation (Adlan et al.,

2020

; Bernasconi et al.,

2018

2013

; Defliese & Lohmann,

2015

; Dennis et al.,

2011

;

Fiebig et al.,

2019

; Ghosh, Adkins, et al.,

2006

; He et al.,

2012

; Hu et al.,

2014

; Huntington et al.,

2009

;

Meckler et al.,

2014

; Müller, Fernandez, et al.,

2017

; Passey et al.,

2010

; Petersen et al.,

2016

2019

; Schmid

& Bernasconi,

2010

), the last 5–10 years have seen an increasing number of laboratories implementing this

technique. The great potential of this thermometer can only be fully exploited if precision and accuracy are

sufficient to resolve differences of a few degrees in formation temperatures. In addition, widely available ref

erence materials that match the sample matrices are necessary so that data can be robustly compared across

laboratories (Meier-Augenstein & Schimmelmann,

2019

). Currently the situation in the field of carbonate

clumped isotope geochemistry is far from satisfactory. Published values for the ETH reference materials, the

only carbonates that have been recently measured in many different laboratories worldwide, differ by up to

0.053‰ (see Bernasconi et al.,

2018

; Thaler et al.,

2020

for recent comparisons). For paleoclimate applica

tions, however, a repeatability across laboratories of 0.01‰ or better is a necessary goal for meaningful data

comparison. This clearly calls for better standardization procedures to improve laboratory comparability.

The data normalization scheme currently used in clumped isotope geochemistry of carbonates in many

laboratories is based on the comparison of the composition of the CO

liberated from carbonates by reaction

with phosphoric acid with that of a set of CO

gases with different bulk and clumped isotope compositions

(Dennis et al.,

2011

). These gases are prepared either by heating CO

at 1000 °C (heated gases; HG) or by

equilibration with water at low temperatures (equilibrated gases at e.g., 25 °C, 50 °C; EG). By compar

ing the measured compositions with the theoretical predictions of the equilibrium thermodynamic abun

dance of multiply substituted isotopologues in heated and equilibrated gases (Wang et al.,

2004

; and updates

in Petersen et al.,

2019

), the measurements are standardized to the scale that was named the “absolute

reference frame” (ARF) by Dennis et al. (

2011

). In more recent publications, the ARF is often referred to as

the “Carbon Dioxide Equilibration Scale” (CDES), a terminology introduced by Passey and Henkes (

2012

This approach was designed to allow different laboratories to link their measurements to an internation

ally recognized scale firmly anchored to theory using relatively easy and established laboratory protocols

to produce CO

standard gases of known isotopic composition. Early comparisons of Δ

47 CDES

values for

carbonates analyzed in different laboratories and corrected with HG/EG normalization were promising

(Dennis et al.,

2011

). While Bonifacie et al. (

2017

) reported similar Δ

47 CDES

values for nine dolomite samples

covering a range of almost 0.4‰ measured both at Caltech and IPGP laboratories with HG/EG normali

zation, Spooner et al. (

2016

) found that carbonate standardization improved agreement between data they

obtained on samples analyzed both at Caltech and WHOI laboratories, compared to when they were using

HG/EG normalization. Such recurrent cases of poor interlaboratory reproducibility (see also Bernasconi

et al.,

2018

; Thaler et al.,

2020

) suggest that there are still unexplained differences in the results among

laboratories (see Petersen et al.,

2019

for a recent review).

Apart from preservation problems, two known issues still limiting the reliability of this method to yield

accurate temperature reconstructions are: (1) the lack of internationally recognized carbonate reference

materials for a precise interlaboratory calibration, and (2) that published Δ

-temperature calibrations pro

duced in different laboratories have differed in both temperature dependence (slope) and absolute value

BERNASCONI ET AL.

10.1029/2020GC009588

2 of 25

is a robust method for standardization that yields interlaboratory discrepancies entirely consistent with

intralaboratory analytical uncertainties. Carbonate reference materials, along with measurement and

data processing practices described herein, provide the carbonate clumped isotope community with a

robust approach to achieve interlaboratory agreement as we continue to use and improve this powerful

geochemical tool. We propose that carbonate clumped isotope data normalized to the carbonate reference

materials described in this publication should be reported as Δ

(I-CDES) values for Intercarb-Carbon

Dioxide Equilibrium Scale.

Received 11 DEC 2020

Accepted 19 MAR 2021

Author Contributions:

Conceptualization:

S. M. Bernasconi,

M. Daëron, K. D. Bergmann, M.

Bonifacie, A. N. Meckler

Data curation:

M. Daëron

Formal analysis:

S. M. Bernasconi, M.

Daëron, K. D. Bergmann, M. Bonifacie,

A. N. Meckler

Investigation:

S. M. Bernasconi,

M. Daëron, K. D. Bergmann, M.

Bonifacie, A. N. Meckler, H. P. Affek,

N. Anderson, D. Bajnai, E. Barkan,

E. Beverly, D. Blamart, L. Burgener,

D. Calmels, C. Chaduteau, M. Clog,

B. Davidheiser-Kroll, A. Davies, F.

Dux, J. Eiler, B. Elliott, A. C. Fetrow, J.

Fiebig, S. Goldberg, M. Hermoso, K. W.

Huntington, E. Hyland, M. Ingalls, M.

Jaggi, C. M. John, A. B. Jost, S. Katz, J.

Kelson, T. Kluge, I. J. Kocken, A. Laskar,

T. J. Leutert, D. Liang, J. Lucarelli, T. J.

Mackey, X. Mangenot, N. Meinicke, S.

E. Modestou, I. A. Müller, S. Murray,

A. Neary, N. Packard, B. H. Passey, E.

Pelletier, S. Petersen, S. Petersen, A.

Piasecki, A. Schauer, K. E. Snell, P.

K. Swart, A. Tripati, D. Upadhyay, T.

Vennemann, I. Winkelstern, D. Yarian,

N. Yoshida

Methodology:

S. M. Bernasconi, M.

Daëron, K. D. Bergmann, M. Bonifacie,

A. N. Meckler

Software:

M. Daëron

Writing – original draft:

S. M.

Bernasconi, M. Daëron, K. D.

Bergmann, M. Bonifacie, A. N. Meckler

Writing – review & editing:

M. Bernasconi, M. Daëron, K. D.

Bergmann, M. Bonifacie, A. N. Meckler,

H. P. Affek, N. Anderson, D. Bajnai,

E. Barkan, E. Beverly, D. Blamart, L.

Burgener, D. Calmels, C. Chaduteau, M.

Clog, B. Davidheiser-Kroll, A. Davies, F.

Dux, J. Eiler, B. Elliott, A. C. Fetrow, J.

Fiebig, S. Goldberg, M. Hermoso, K. W.

Huntington, E. Hyland, M. Ingalls, M.

Jaggi, C. M. John, A. B. Jost, S. Katz, J.

Kelson, T. Kluge, I. J. Kocken, A. Laskar,

T. J. Leutert, D. Liang, J. Lucarelli, T. J.

Mackey, X. Mangenot, N. Meinicke, S.

E. Modestou, I. A. Müller, S. Murray,

A. Neary, N. Packard, B. H. Passey, E.

Pelletier, S. Petersen, S. Petersen, A.

Piasecki, A. Schauer, K. E. Snell, P.

K. Swart, A. Tripati, D. Upadhyay, T.

Vennemann, I. Winkelstern, D. Yarian,

N. Yoshida

Geochemistry, Geophysics, Geosystems

(intercept). Possible reasons for the differences in slopes and intercepts of the Δ

temperature dependence

have been widely discussed in the literature (e.g., Bonifacie et al.,

2017

; Daëron et al.,

2016

; Fernandez

et al.,

2017

; Katz et al.,

2017

; Kelson et al.,

2017

; Kluge et al.,

2015

; Petersen et al.,

2019

; Schauer et al.,

2016

Discrepancies have been attributed to analytical artifacts such as CO

-acid re-equilibration at different acid

digestion temperatures (see Swart et al.,

2019

; Wacker et al.,

2013

, for a recent discussion) and to slight

pressure imbalances between sample and reference gas (Fiebig et al.,

2016

). Other factors proposed to in

fluence the calculated slopes of the calibrations are the limitations of the data sets used in the individual

studies, in particular in terms of the number of samples and replicates and of the temperature range cov

ered by the available samples (Bonifacie et al.,

2017

; Fernandez et al.,

2017

). However, the discrepancies in

the intercepts of the calibrations, for example, between Kelson et al. (

2017

) and Peral et al. (

2018

), and a

generally poor laboratory comparability remain problems that could be mitigated by using a more robust

standardization method.

Petersen et al. (

2019

), in a recent effort to resolve differences in calibrations, compiled raw data of a num

ber of published temperature calibrations and recalculated them all in a consistent way using the revised

IUPAC correction parameters to correct for the

O abundance (Daëron et al.,

2016

; Schauer et al.,

2016

The goal was to test whether data processing differences and/or the use of consistent but incorrect

O-cor

rection parameters in the calculations were the root causes of inconsistencies. The result of this study was

that differences among calibrations were reduced but not eliminated by the recalculation, implying that

other factors must be responsible for the remaining discrepancies. These differences have pushed many

laboratories to use laboratory-specific calibrations performed with the same analytical approach, as they at

least partially take into consideration possible procedural differences (Petersen et al.,

2019

). However, if a

laboratory changes analytical procedures or has not generated a robust in-house calibration, this approach

is problematic. Achieving an interlaboratory reproducibility at the level of accuracy necessary for meaning

ful interpretations of the observed variations is a requirement for Δ

thermometry to reach its potential as

a mature analytical method with broad acceptance and quantitative usefulness.

While the definition of the CDES was a major milestone (Dennis et al.,

2011

), a known problem with this

approach is that while the CO

standard gases equilibrated at known temperature (HG or EG) can be confi

dently used for correction of mass spectrometric fractionations/nonlinearities and for effects of the purifi

cation procedures, they cannot account for the effects of the phosphoric acid reaction on the composition of

the produced CO

. Among the factors responsible for discrepant calibrations and laboratory comparability,

two important ones cannot be tested with a gas-based standardization: (1) the absolute value and tempera

ture dependence of the phosphoric acid fractionation factor (see Petersen et al.,

2019

for a recent compila

tion) and (2) possible CO

equilibration effects during acid digestion of the sample. Swart et al. (

2019

) pre

sented evidence that equilibration of CO

with water or hot metal surfaces during phosphoric acid reaction

and transfer of the CO

to the mass spectrometer could be a factor leading to the alteration of the apparent

temperature dependence of clumped isotopes in carbonates and on the absolute value of calculated Δ

. As

many laboratories use custom built extraction lines with different designs and volumes of tubing and of acid

vessels, these factors are impossible to precisely quantify for each laboratory and may further contribute to

interlaboratory discrepancies.

We propose that these issues can be circumvented if carbonates, which undergo the same acid digestion as

the samples, are used for normalization instead of or in addition to gases, consistent with the principle of

identical treatment of sample and standards (Carter & Fry,

2013

; Werner & Brand,

2001

). In addition, nor

malizing results to accepted carbonate reference material values, as is commonly done with conventional

carbon and oxygen isotope analysis in carbonates, removes the requirement to precisely quantify acid frac

tionation factors at different temperatures (Bernasconi et al.,

2018

A carbonate standardization approach was introduced by Schmid and Bernasconi (

2010

) and improved by

Meckler et al. (

2014

), with the following benefits: (1) the use of carbonates can more easily be fully auto

mated, eliminating time-consuming and possibly error-prone manual preparation of CO

standard gases

(equilibrated at known temperature) by individual users on separate extraction lines; (2) in some automat

ed systems designed for the measurement of small carbonate samples (e.g., the Kiel Device), the heated

and equilibrated gases had to be measured through a different capillary than the gases produced by acid

digestion of carbonates with potential biases that would go unrecognized; and (3) in these same systems

BERNASCONI ET AL.

10.1029/2020GC009588

3 of 25

Geochemistry, Geophysics, Geosystems

the equilibrated and heated gases are measured at constant ion beam intensity in bellow mode, whereas the

samples are measured with decreasing ion beams in microvolume mode. These features argue in favor of

carbonate standardization

a priori

, but it remains critical to assess

a posteriori

whether the results of this

approach are as robust and accurate as expected and whether they significantly improve the interlaboratory

reproducibility of Δ

measurements. Discussions at the Sixth International Clumped Isotope Workshop

in Paris in 2017 led to the present interlaboratory comparison exercise (InterCarb) to evaluate the benefits

and drawbacks of a carbonate-based standardization approach as an alternative to the use of gas standards.

The primary goal of this study was to test whether the exclusive use of carbonate reference materials as a

substitute for heated and equilibrated gases can minimize interlaboratory discrepancies and provide an al

ternative to the measurement of heated and equilibrated gases for the entire community. This is particularly

important because of the increasing number of laboratories using commercial small-sample automated de

vices which cannot easily be standardized using the HG-EG approach. The InterCarb exercise also provides

an opportunity to define the best community-derived consensus Δ

values for the ETH standards of Meck

ler et al. (

2014

). Although these standards are already used in many laboratories, their current nominal

values are based on measurements from the ETH laboratory only. The InterCarb exercise can similarly

establish community accepted values for other common carbonate reference materials, some of which have

been in use for several years, in order to provide the community with a self-consistent set of carbonate ref

erence materials with a broad range of bulk and clumped isotope compositions.

1.1.

Nomenclature and Data Processing

Clumped isotope compositions are reported as an excess abundance of the CO

isotopologue of cardinal

mass 47 (dominantly the isotopologues

O) compared to a stochastic distribution according to the

formula:





47*

Δ /1

RR

where

is the ratio of the abundances of the set of minor isotopologues with mass 47 (mostly

and trace amounts of

O and

) divided by the abundance of the most abundant isotopologue

with mass 44 (

). The stochastic ratio

47*

is calculated using the measured abundance of

C and

and measured or calculated abundance of 17O in the sample (Affek & Eiler,

2006

). According to the IUPAC

guidelines the formula does not include the factor 1,000 (Coplen,

2011

; though Δ

is commonly reported

in units of per mil, which implies multiplication by a factor of 1,000). Also, we omit here the classically

included terms involving

* and

*, which are assumed to be zero by definition when computing δ

and δ

O, and in practice never exceed ±0.00002‰ in our calculations (Daëron et al.,

2016

). The measured

abundance of isotopologues with m/z 47 in the sample with respect to the working gas (WG) in the mass

spectrometer is reported in the traditional delta notation as:





δ /1

RR

The δ

scale is a measure of the difference between the sample of interest and the WG of the specific in

strument, therefore, it cannot be compared across laboratories. The same notation is used for masses 45,

46, 48, and 49.

The CO

gas-based standardization scheme for clumped isotope thermometry in carbonates relies on a set

of CO

standard gases with different bulk compositions (δ

C and δ

O, leading to different δ

), preferably

chosen by the user to encompass the δ

values of unknown samples that have been (1) heated at 1000 °C to

reach a near-stochastic distribution of all isotopologues, or (2) equilibrated with water at low temperature

to reach equilibrium enrichments in the mass-47 isotopologues (Dennis et al.,

2011

). The heated gases,

having a near-stochastic distribution of the heavy isotopes among all isotopologues, define the zero point

of the CDES scale, through the assumption that at 1000 °C these gases achieve a Δ

= 0.0266‰, and the

water-equilibrated gases define a second, generally higher point on this scale (e.g., at 25 °C Δ

= 0.9196‰).

The theoretical values linking measurements to theory were calculated by Wang et al. (

2004

) and revised

BERNASCONI ET AL.

10.1029/2020GC009588

4 of 25

Geochemistry, Geophysics, Geosystems

by Petersen et al. (

2019

). A wide range in δ

values of gases used for

normalization is generally chosen to allow for accurate correction for an

apparent dependence of Δ

on δ

, which is caused by inaccurate pres

sure-dependent background corrections on the m/z 47 collector observed

on many instruments (Bernasconi et al.,

2013

; He et al.,

2012

). The large

range in Δ

(i.e., 25 °C, 1000 °C), on the other hand, is necessary to cor

rect for scale compression caused by processes of scrambling and mole

cule recombination in the source of the mass spectrometer or elsewhere

in the sample preparation, transfer lines and/or the capillaries (Dennis

et al.,

2011

; Swart et al.,

2019

). With properly chosen CO

standard gases

with widely varying δ

values it is possible to cover the entire range of

natural carbonate compositions, avoiding extrapolations in the δ

versus

compositional space (Figure

). Note that with measurement errors

(typically no better than 0.010‰) being relatively large compared to the

natural compositional range (less than 0.5‰; Figure

), the large (0.9‰)

difference in Δ

of the CO

standard gases minimizes errors introduced

by uncertainties resulting from the measurement of HG and EG.

Meckler et al. (

2014

) attempted to achieve a similar framework as the

gas-based standardization but with carbonate standards. They de

scribed four carbonates that were developed at ETH Zürich to serve as

replacements for HG’s and EG’s and demonstrated that good long- and

short-term reproducibility can be achieved using only carbonates for data

correction. Bernasconi et al. (

2018

) discussed in detail these standards

and postulated, based on a limited interlaboratory data set, that carbonate

standardization should generally improve interlaboratory data compara

bility. This claim seems arguably strengthened by the results of Meinicke

et al. (

2020

), Peral et al. (

2018

), Piasecki et al. (

2019

), Kele et al. (

2015

)

as recalculated by Bernasconi et al. (

2018

), and Jautzy et al. (

2020

). The

first three studies produced independent foraminifera-based the fourth a

travertine and the fifth a synthetic carbonate-based Δ

-temperature cali

bration anchored to the same set of carbonate standards. These studies

yielded statistically indistinguishable slopes and intercepts despite the use of independent sample sets and

in the case of Peral et al. (

2018

), a different analytical system. In addition, a reanalysis of samples from five

previous calibrations by Anderson et al. (

2021

) using carbonate standardization revealed no significant dif

ferences in temperature dependence of Δ

between the different sample sets. This, solved a long standing

debate about variations in slope among calibrations

A possible limitation of carbonate standardization is that available carbonates have a smaller range in δ

and, perhaps more importantly, a smaller range in Δ

values than what is achievable with heated and

equilibrated gases. In some specific cases, standardization procedures require extrapolation to compositions

that are not within the δ

–Δ

space created by carbonate standards (Figure

). In addition, the range of Δ

values for carbonates is only on the order of 0.5‰ between 0 and 1000 °C. The smaller range in Δ

com

pared to HG’s and EG’s requires higher precision and also a larger number of replicates of both standards

and samples. Daëron (

2021

) and Kocken et al. (

2019

) suggest

∼

50:50 ratio of standard to sample replicates

to keep standardization errors small.

1.2.

InterCarb Goals and Design

InterCarb was designed with the aim to carefully evaluate the potential of carbonates to serve as a standard

ization scheme that improves interlaboratory agreement for “unknown” carbonates both inside and outside

of the δ

–Δ

space defined by the anchor samples (Figure

). The main questions posed are:

Is it possible to produce consistent carbonate clumped isotope measurements across laboratories using

carbonate reference materials exclusively? In other words, does the observed interlaboratory scatter in

values match that expected from intralaboratory analytical precision?

BERNASCONI ET AL.

10.1029/2020GC009588

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Figure 1.

The δ

versus Δ

values of carbonate standards (Δ

the I-CDES scale proposed here) and heated and equilibrated gases in

comparison to the compositional ranges of typical natural carbonates.

The observed range in measured clumped isotope compositions in natural

carbonates can be completely bracketed by heated and equilibrated

standard gases from which δ

values have been chosen by the

user. The δ

values for the anchor samples used in InterCarb (red) and

the unknowns (black) are reported for a theoretical working gas with

stochastic isotope distribution, derived from VPDB. Actual δ

values will

vary by laboratory depending on the composition of the working gas.

Note the smaller achievable range in both δ

and Δ

values when using

carbonate standards compared to heated and equilibrated gases and the

large extrapolation necessary for the determination of the composition

for MERCK. Heated and equilibrated CO

standard gases have a larger

range, allowing for more robust stretching calculations with identical

numbers of standard:sample analyses. I-CDES, Intercarb-Carbon Dioxide

Equilibrium Scale.

-6

-4

-20

-10

MERCK

IAEA-C2

IAEA-C1

ETH-4

ETH-3

ETH-1

ETH-2

heated

gases

equilibrated

gases

(‰)

vs.

stochastic

VPDB-CO

(‰)

0.2

0.4

0.6

0.8

methane

seep

carbonates

terrestrial

carbonates

marine

carbonates

diagenetic

carbonates

marbles

pressure

baselin

"non-linearity")

effects

scale

compression

effects

Geochemistry, Geophysics, Geosystems

How well does the carbonate standardization approach perform when extrapolating beyond the δ

–Δ

compositional space sampled by a set of carbonate reference materials?

Do carbonate reference materials fully correct effects arising from different reaction temperatures, sam

ple preparation protocols, and analytical equipment?

Can we define a self-consistent set of widely available reference materials with community-agreed com

positions accurately anchored to the CDES scale?

Does the use of carbonate reference materials for standardization improve the interlaboratory reproduc

ibility compared to using HG’s and EG’s?

1.3.

Approach

Seven carbonate standards with a large range of δ

and Δ

values (Figure

) were distributed among par

ticipating laboratories and analyzed, treating three carbonates as “anchors” (whose Δ

values are assigned

a priori) and the remaining four as “unknowns” (whose Δ

values are unknown, to be determined by

comparison with the anchors). Due to their relatively widespread use in different laboratories, the three

reference materials ETH-1, ETH-2, and ETH-3 (Bernasconi et al.,

2018

; Meckler et al.,

2014

) were chosen as

anchors. They are still available today in relatively large quantities (>600 g), have been in use at ETH since

2013 and in many other laboratories for several years. Importantly, they have been thoroughly tested for

homogeneity based on thousands of measurements in 80–150 μg aliquot sizes in different laboratories and

no changes in composition have been noticed at ETH in the 7 years they have been in use.

The “unknown” InterCarb reference materials were chosen to cover a wide natural range in δ

and Δ

values. These samples had to be available in large quantities, inexpensive, and if possible distributed by

an organization with a long-term perspective in order to ensure future data quality and availability for the

increasing number of laboratories globally.

Materials and Methods

2.1.

Sample Description

The anchor samples ETH-1 (Carrara marble heated at 600 °C), ETH-2 (synthetic carbonate heated at 600 °C)

and ETH-3 (Upper cretaceous chalk) are described in detail in Bernasconi et al. (

2018

IAEA-C1 (marble from Carrara, Italy) is distributed by the International Atomic Energy Agency (IAEA) as

a mechanically crushed and milled product with grains ranging from 1.6 to 5 mm. All 50 g provided were

ground and thoroughly homogenized in a ball mill at ETH Zürich to a grain size of less than 100 μm and

transferred in 0.5 g aliquots to plastic vials for distribution. Nishida and Ishimura (

2017

) found that IAEA

603, which was produced from the same coarse marble as IAEA C-1, was isotopically inhomogeneous.

Whitish grains (1–2 per 100 grains; grain weight, 8–63 μg) were significantly depleted in

O and

C com

pared to translucent grains. In this study we found no evidence of inhomogeneity in Δ

for sample aliquots

of 80–110 μg after the original material was ground in the ball mill.

IAEA-C2 is a freshwater travertine from Bavaria distributed by IAEA as a powder which was treated identi

cally to IAEA-C1. XRD analysis shows it to be calcite (Figure

ETH-4 is a commercially available synthetic calcium carbonate (Riedel-De Haën; calcium carbonate Puriss.

p.a.; Lot No. 30800) determined to be calcite by XRD (Figure

with intermediate formation temperature

and the same bulk isotope composition as ETH-2 (see Bernasconi et al.,

2018

for details).

MERCK (Catalog No. 1.02059.0050; lot no. B1164559 515) is an ultra-pure, commercially available synthetic

calcium carbonate determined to be calcite by XRD (Müller et al.,

2019

) and was chosen for its very low

C and δ

O values of approximately −42.2‰ and −15.5‰ (VPDB), respectively. This sample represents

an extreme case of extrapolation from the δ

–Δ

space defined by the anchor materials (Figure

). The

same product was recently used to prepare the carbon isotope reference material USGS44 by Qi et al. (

2021

)

which, after careful determination of its Δ

could be used as a substitute for the aliquots of MERCK dis

tributed for this study.

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Geochemistry, Geophysics, Geosystems

2.2.

Instrumentation

The reported data were produced with a variety of preparation systems including custom built (13 labora

tories) and commercial systems (11 laboratories; Protium MS IBEX, ThermoFisher Scientific Kiel IV de

vice and Nu Instruments Nucarb). Reaction temperatures were generally 90 °C for “large-sample” custom

preparation systems and 70 °C for the Kiel and the NuCarb. Four mass spectrometer types were used: Ther

mo Fisher Scientific MAT253 and 253Plus, Nu Instruments Perspective, and Elementar Isoprime 100. All

participants contributed results they considered to be of “publication-grade” quality, based on their existing

quality-control procedures.

2.3.

Clumped Isotope Compositions of the ETH Anchor Materials

The clumped isotope compositions of the four ETH reference materials relative to the CO

reference frame

CDES were first reassessed based on new data provided by 10 laboratories that also provided HG and EG

data measured during the same sessions as the ETH reference materials. The data were processed with the

same Python script used for the carbonate data in order to avoid any differences in data processing (see

Section

2.4

Although, strictly speaking,

C-

O clumping in carbonate represents a mass-63 anomaly, the clumped iso

tope composition of carbonate minerals is reported as Δ

, that is, as the mass-47 excess in the CO

produced

by acid digestion of these minerals, including the respective temperature-dependent isotopic fractionation.

As initially all reactions were carried out at 25 °C (Ghosh, Adkins, et al.,

2006

), the Δ

values have tradi

tionally been reported for a 25 °C acid temperature. With the advent of automated extraction lines, reaction

temperatures have been increased to 70 °C or 90 °C. To account for the temperature dependence of the

acid fractionation factor (Guo et al.,

2009

; Petersen et al.,

2019

) and to project these results back to the orig

inal 25 °C acid reactions, various acid temperature correction values have been reported over time, based

on experimental observations and/or theoretical predictions. Given that here seven out of 10 laboratories

reacted carbonates at 90 °C, two at 70 °C, and only one at 25 °C, our redetermination of the Δ

values of

ETH-1/2/3/4 relative to the CDES projected to 25 °C would rely substantially on the accuracy of these acid

temperature corrections (which typically range between 60 and 90 ppm). For this reason, we report the Δ

values of CO

produced by reacting ETH-1/2/3/4 at 90 °C. With this choice the numerical effect of poorly

known acid corrections is minimized because the data from 70 °C and 25 °C reactions have relatively lit

tle influence on the final, error-weighted average Δ

values (cf. statistical weights in Figure

). We thus

propose to break with tradition and define the nominal Δ

values of the anchor standards as those of CO

produced at 90 °C, providing the most robust relationship to the CDES.

2.4.

Data Processing, Correction, and Error Assessment

It should be stressed that the InterCarb experiment, by design, is not intended to grade the analytical per

formance of individual laboratories. Each participating laboratory (or mass spectrometer, in the case of lab

oratories with several instruments) was thus randomly assigned an anonymous identifying number. Within

each laboratory, analyses were grouped in different analytical sessions defined by the participants them

selves. An analytical session is generally defined by a time in which the behavior of the analytical system

(preparation system, source tuning, backgrounds, isotope scrambling in the source) is considered to be sim

ilar. The database record of each analysis consists of a laboratory identifier, a session identifier, an analysis

identifier, the name of the analyzed sample, the mass spectrometer model, the acid reaction temperature,

the mass of the reacted carbonate, and background-corrected δ

, δ

, and δ

values.

The only instrumental corrections to the raw data applied independently by each participating laboratory

were background corrections (“Pressure Baseline Correction” or PBL) to the ion currents/voltages (Bernas

coni et al.,

2013

; Fiebig et al.,

2016

2019

; He et al.,

2012

). The PBL is strongly dependent on instrument de

sign (it is not observed in some instruments) and configuration, and varies temporally depending on many

factors. This correction, therefore, can only be carried out by each participating laboratory according to its

own established procedures and monitoring.

BERNASCONI ET AL.

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Geochemistry, Geophysics, Geosystems

To avoid artifacts arising from different calculation/standardization procedures, rounding errors, and

correction parameters, raw data from all laboratories were processed by a single Python script (

http://doi.

org/10.5281/zenodo.4314448

) based on data reduction, standardization and error propagation methods de

scribed in detail in the companion paper (Daëron,

2021

). Here we briefly summarize these calculations.

Session-averaged, background-corrected δ

and δ

values for each of the three anchor samples were first

used to calculate the bulk isotope composition of the working gas used in each session, based on (a) previ

ously reported δ

VPDB

and δ

VPDB

values of ETH-1, ETH-2, and ETH-3 (Bernasconi et al.,

2018

), (b) the

IUPAC

O correction parameters of Brand et al. (

2010

), and (c) a temperature-dependent oxygen-18 acid

fractionation factor between CO

and calcite of Kim et al. (

2015

). This recalculation of working gas bulk

compositions avoids (small) discrepancies potentially introduced by inaccuracies in the nominal composi

tions of the working gases.

Raw Δ

values were computed according to:







raw

Δ /1

RR

where

is the measured ratio and

* the calculated stochastic ratio of mass 47 over mass 44 of CO

assuming perfectly linear IRMS measurements and a stochastic working gas. Values are then normalized

to “absolute” Δ

values (noted

abs

in the equation below, and simply Δ

thereafter) using session-specific

relationships of the form:

 

rawabs47

4747

ΔΔδ

abc

For each session, the best-fit standardization parameters (a,

, c) are computed from an unweighted least

squares regression, treating

raw

as the response variable, only considering the three anchor samples ETH-

1, ETH-2, and ETH-3. Note the advantage of this form over that in Dennis et al. (

2011

) is the ability to

have three standards with distinct Δ

values whilst being able to solve for

(compositional nonlinearity)

(Daëron et al.,

2016

). Absolute Δ

values are then computed for all replicates within that session. Standard

ization parameters for all sessions are listed in Table

Throughout this study, the analytical error assigned to each individual raw Δ

analysis is equal to the

pooled “external” repeatability of raw Δ

measurements of anchors and unknowns within each session.

In the figures and tables, final measurement uncertainties are reported as standard errors and/or 95% con

fidence limits, considering fully propagated errors taking into account reference frame corrections. In Fig

ures

and

, different types of error bars are used to represent analytical errors only considering uncertain

ties in the analyses of a given sample or the full uncertainty considering standardization uncertainties (the

“autogenic” errors of Daëron,

2021

). In both cases, the analytical error assigned to each individual raw Δ

analysis is equal to the pooled “external” repeatability of raw Δ

measurements for all samples (anchors

and unknowns) within each session. This treatment of error is a new approach that more fully accounts for

error in both the sample measurement and reference frame.

Results and Discussion

3.1.

Redetermination of Nominal Δ

Values for the ETH Standards Relative to Heated and

Equilibrated CO

Gases

The weighted averages of the four standards (projected to 90 °C for the reactions at 25 and 70 °C using the

acid temperature correction suggested by Petersen et al.,

2019

), comprising 873 analyses of the carbonate

standards and 946 heated and equilibrated gases from 10 different laboratories, are reported in Table

and

Figure

. The large number of analyses and the appropriate consideration of the errors on the anchors (CO

gas analyses) distinguishes this effort from previous work and allow a robust redetermination of the accept

ed values of the ETH reference materials with 1SE uncertainties of 2 ppm or less.

When compared with Bernasconi et al. (

2018

), the average Δ

values ETH-1 and ETH-2, projected back to

25 °C (+0.088‰), are respectively 0.035 and 0.040‰ more positive than the original values, whereas ETH-3

BERNASCONI ET AL.

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Geochemistry, Geophysics, Geosystems

increases by 0.010 and ETH-4 by 0.031‰. A similar positive offset of Δ

compared to the values reported

in Bernasconi et al. (

2018

) has also been reported in Fiebig et al. (

2019

), Bajnai et al. (

2020

), and Thaler

et al. (

2020

The observation that these changes in nominal values decrease as Δ

increases suggests a simple hypoth

esis to explain this discrepancy: in the original study of Meckler et al. (

2014

), the carbonate samples and

the heated/equilibrated CO

gases experienced different analytical procedures. The HGs were measured

as large samples at constant beam intensity through a different capillary than the carbonates, which were

measured using the microvolume and a decreasing beam. The potential effects of partial re-equilibration

for the heated gases in the gas preparation line or in the capillaries of the mass spectrometer could be sig

nificant whereas it would be minuscule for the gases equilibrated at 25°, leading to an overestimation of Δ

scale compression and thus of the stretching applied to the Δ

scale toward theoretical values. The observed

changes in apparent ETH-1 and ETH-2 Δ

values may therefore simply reflect partial re-equilibration of

heated gases at the time of measurements at ETH (and reported in Meckler et al.,

2014

), increasing their

values in the original study by about 0.05‰ (Figure

It has been suggested previously that ETH-1 and ETH-2 should be indistinguishable in Δ

and close to

stochastic distribution (Müller, Violay, et al.,

2017

). This is because Δ

values of ETH-1 and ETH-2, origi

nally heated to 600 °C, were found to be higher by only around 0.006‰ from the same carbonates heated at

1000 °C to achieve stochastic distribution of the isotopes. However, additional test measurements in multi

ple laboratories of samples heated at >1000 °C are necessary to confirm this observation.

One laboratory (Laboratory F) did however observe a large difference in the value for ETH-1 and ETH-2,

although their values of ETH-3 and ETH-4 are similar to other laboratories. The reason for these incon

sistencies is probably due to the fact that ETH-1 was only measured four times with a limited number of

HG/EG, and ETH-2 and ETH-4 were not measured in the same session. In addition, the laboratories with

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Laboratory

All

of sessions

of H/E CO

946

193

257

192

ETH-1

of analyses

232

(‰; 90 °C acid)

0.2052

0.2016

0.1926

0.2108

0.1940

0.1601

0.2013

0.2143

0.1932

0.2183

0.2152

±1SE

0.0016

0.0046

0.0058

0.0069

0.0042

0.0245

0.0107

0.0032

0.0045

0.0109

0.0036

Statistical weight

0.118

0.074

0.053

0.146

0.004

0.022

0.241

0.124

0.021

0.197

ETH-2

of analyses

215

(‰; 90 °C acid)

0.2085

0.2077

0.1840

0.2225

0.1978

0.1374

0.1650

0.2141

0.1968

0.2172

0.2170

±1SE

0.0015

0.0047

0.0070

0.0046

0.0050

0.0233

0.0101

0.0029

0.0043

0.0154

0.0033

Statistical weight

0.105

0.047

0.108

0.092

0.004

0.023

0.272

0.125

0.010

0.213

ETH-3

of analyses

264

(‰; 90 °C acid)

0.6132

0.6156

0.5975

0.6169

0.6102

0.5950

0.6143

0.6159

0.6094

0.6428

0.6124

±1SE

0.0014

0.0037

0.0056

0.0033

0.0038

0.0237

0.0099

0.0033

0.0042

0.0103

0.0035

Statistical weight

0.140

0.062

0.175

0.134

0.003

0.020

0.179

0.110

0.018

0.158

ETH-4

of analyses

162

(‰; 90 °C acid)

0.4505

0.4438

0.4230

0.4624

0.4506

0.4230

0.4454

0.4560

0.4414

0.4831

0.4646

±1SE

0.0018

0.0058

0.0071

0.0068

0.0049

0.0226

0.0095

0.0032

0.0042

0.0161

0.0057

Statistical weight

–

0.093

0.064

0.068

0.133

0.006

0.035

0.314

0.177

0.012

0.097

Note

. Reported standard errors represent analytical uncertainties associated both with reference frame errors (HG/EG) and carbonate sample reproducibility

(Daëron,

2021

Table 1

Newly Determined Nominal Δ

Values of the ETH Standards Projected to 90 °C Acid Reaction Using Acid Correction Factors of −0.088‰ and −0.022‰ for 25 °C

and 70 °C Reactions, Respectively (Petersen et al.,

2019

)

Geochemistry, Geophysics, Geosystems

the smallest number of replicate measurements have uncertainties that are systematically larger (Table

These results highlight the importance of strict correction procedures in clumped isotope analysis. Suffi

cient replication of both standards and samples is critical and, if insufficient, offsets can arise when com

paring results from different sessions. Due to these difficulties it is good practice to spread replicates of the

same sample in different sessions over longer periods of time to obtain accurate results and follow a

∼

50:50

standard to sample replicate ratio.

Based on the results above, the difference between the average of ETH1/2 and ETH-3 is reduced by 0.028‰,

thus leading to a compression of the scale by about 5.8% compared to the values reported by Bernasconi

et al. (

2018

). As a consequence, the slopes of published temperature calibrations produced with carbonate

standardization (Bernasconi et al.,

2018

; Jautzy et al.,

2020

; Kele et al.,

2015

; Meinicke et al.,

2020

; Peral

et al.,

2018

; Piasecki et al.,

2019

) will become slightly shallower, with more positive

-intercepts. If Δ

results

from previous publications are also recalculated with the new standard values (see Section

3.4

), however,

changes in calculated formation temperatures will be negligible. For this reason, when comparing data from

publications using old accepted values of the ETH standards for standardization (either those published by

Meckler et al.,

2014

or those recalculated with the IUPAC parameters by Bernasconi et al.,

2018

) to newer

data, it is recommended to directly compare the reconstructed temperatures rather than recalculating Δ

Full recalculation of old measurements usually requires the availability of the entire data set including

standards and the same correction procedures (e.g., averaging methods) used in the original publications

(but see Appendix

for an alternative calculation method).

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Figure 2.

New determination of Δ

values for the four ETH standards relative to the CDES using updated CO

equilibrium values. These measurements, using

acid reaction temperatures of 90 °C, 70 °C, or 25 °C, are projected to 90 °C using acid corrections of −0.088‰ and −0.022‰ for 25 °C and 70 °C reactions,

respectively (Petersen et al.,

2019

). Error bars correspond to 95% confidence limits taking into account fully propagated errors (i.e., taking into account errors in

both unknown and anchor analyses). Boxes correspond to 95% confidence limits not accounting for normalization errors (i.e., only taking into account errors

in unknown analyses). Red numbers are the error-weighted average values (with statistical weights summarized in upper-left corners). All plots have the same

horizontal scales for the different samples. CDES, Carbon Dioxide Equilibrium Scale.

Geochemistry, Geophysics, Geosystems

3.2.

InterCarb Results

Results for the unknown carbonate samples were obtained from 25 mass

spectrometers in 22 laboratories. The Δ

values of the four unknown

samples were normalized to the new community-derived values of ETH-

1, ETH-2, and ETH-3 of Table

, then averaged per individual analytical

session and mass spectrometer (Tables

and

). Mean Δ

values ob

tained for each sample in each mass spectrometer are shown in Figure

The details of each analytical session, including the number of samples

and standards measured, the isotopic composition of the working stand

ard, the scaling parameters and the internal reproducibilities (as 1SD) of

the individual sessions are listed in Table

. Some laboratories reported

data for only a subset of the unknown samples, and both replication level

and analytical reproducibility vary greatly from laboratory to laboratory

(Table

To clearly distinguish Δ

values normalized to the CDES using car

bonates rather than heated and equilibrated gases, we propose the new

acronym (I-CDES), short for InterCarb-CDES, to reflect the use of the

proposed InterCarb reference materials for data standardization (see Sec

tion

3.5

for more details).

The laboratory averages for the four unknowns show standard deviations

of 0.011‰ for ETH-4 and IAEA-C1, 0.018‰ for IAEA-C2 and 0.024‰ for

MERCK, the most extreme case of extrapolation (Table

). Qualitatively,

laboratories with stronger analytical constraints (i.e., better intralabora

tory repeatability of Δ

measurements and/or greater number of analy

ses) generally converge toward the overall mean value for each sample

(Figure

). This suggests that the observed interlaboratory variability is

largely due to random errors that can be alleviated by replication, even for laboratories with relatively large

analytical errors on individual measurements. It is also notable that fully propagated analytical errors that

take into account uncertainties in the standardization procedure can be substantially larger than the errors

based on the uncertainty associated with sample analyses alone, which is what is generally reported in the

literature. The increase in error is also related to intralaboratory repeatability and the number of standards

measured. In addition, the error increases for unknown samples whose compositions lie outside the “an

chor triangle” defined by ETH-1/2/3. This is illustrated by the increased scatter and errors associated with

MERCK, the carbonate farthest from the “anchor triangle,” consistent with the models of Daëron (

2021

)

(see also Kocken et al.,

2019

As seen in Table

, there are stark differences in the total number of replicate analyses and the typical Δ

reproducibility achieved in different laboratories. As a result, final uncertainties in the average Δ

values

of unknown samples vary considerably (Figure

). Interlaboratory variability is smaller among laboratories

with small analytical uncertainties, and larger among laboratories with few replicate analyses and/or poor

analytical repeatability. If we chose only laboratories that have provided data with average standard errors

below 0.01‰ (Table

), which is within the shot-noise limits of modern IRMS instruments, interlaboratory

standard deviation (1SD) becomes

≤

9 ppm for ETH-4 (

= 22), IAEA-C1(

= 15), and IAEA-C2 (

= 13)

and

≤

0.015‰ for MERCK (

= 11; with SE < 0.0135). We note that this does not significantly change the

average value of the unknowns, and highlights the importance of sufficient sample replication to obtain

accurate results.

Next we may assess whether interlaboratory discrepancies are significantly larger than expected from intral

aboratory analytical uncertainties, that is, whether we can detect the effects of hypothetical unrecognized

sources of scatter beyond known analytical errors.

In order to do so, we compute the “number-of-sigma” deviation obtained by each laboratory for each un

known sample, relative to that sample’s overall weighted average value. For example, the sigma-deviation

for sample ETH-4 and Lab01 is equal to (0.4477–0.4511)/0.0052 = −0.66 and that for MERCK and Lab13 is

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Figure 3.

New nominal Δ

values for the ETH standards compared

to previously reported ones. The dashed gray line is a linear regression

through the new versus old values of ETH-1/2/3/4, whose extrapolation

coincides with 25 °C equilibrated CO

but not with heated gases.

Apparent changes in the ETH-1/2/3/4 values thus scale linearly with

the Δ

difference between carbonate samples and 25 °C equilibrated

, suggesting that Δ

values of heated gases in the original study may

have been biased by

∼

+0.05‰ through partial re-equilibration at room

temperature between the quenching of heated CO

and its ionization in

the isotope-ratio mass spectrometer source.

Geochemistry, Geophysics, Geosystems

BERNASCONI ET AL.

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12 of 25

Number of analyses

Working gas

Standardization parameters

Reproducibility (ppm)

Lab

Session

VPDB

VSMOW

VPDB

VSMOW

−3.58

25.38

0.91

(6.0 × l0

−4

)

−0.893

31.5

−3.52

25.58

0.89

−2.1 × 10

−3

−0.765

22.8

150

146

488

−3.63

25.22

0.98

(−2.9 × 10

−5

)

−0.965

33.5

−36.89

8.76

0.99

−5.6 × 10

−4

−0.955

13.0

−36 0.88

8.83

0.98

(−5.5 × 10

−4

)

−0.931

16.1

−10.44

31.64

0.98

(−1.6 × 10

−4

)

−0.917

27.9

121

−3.65

25.28

1.00

(−1.7 × 10

−4

)

−0.917

25.2

–

−6.57

27.18

0.97

5.0 × 10

−3

−1.022

259

562

40.6

−10 0.43

31.31

0.95

l.7 × 10

−3

−0.970

8.6

−3.62

25.05

0.99

(3.8 × 10

−4

)

−0.968

20.9

−3.63

25.06

0.90

1.1 × 10

−3

−0.901

113

17.3

−2.95

25.52

0.83

(−3.8 × 10

−4

)

−0.920

21.0

−2.98

24.93

0.92

(−9.9 × 10

−5

)

−0.920

13.3

−3.01

24.90

0.88

(3.6 × 10

−4

)

−0.932

9.4

−2.95

25.28

0.90

(−l.4 × 10

−4

)

−0.926

17.3

–

−11.64

35.75

0.87

3.5 × 10

−3

)

−0.836

303

23.9

−2.68

25.86

0.94

(−9.2 × 10

−4

)

−0.686

28.4

−2.64

25.96

0.94

(8.6 × 10

−4

)

−0.741

33.2

−2.64

25.91

0.93

(−1.7 × 10

−4

)

−0.728

33.2

−2.67

25.85

0.85

(1.3 × 10

−4

)

−0.629

44.5

−2 0.70

25.79

0.87

(1.3 × 10

−3

)

−0.660

43.3

−2.63

25.90

0.92

(3.9 × 10

−4

)

−0.693

37.8

−2.66

25.90

0.96

(−1.9 × 10

−3

)

−0.709

48.8

−2.66

25.89

1.03

(3.9 × 10

−5

)

−0.806

42.7

−2.67

25.84

0.92

(1.6 × 10

−4

)

−0.722

46.7

−2.63

25.91

0.97

(4.4 × 10

−4

)

−0.767

40.5

−2.67

25.87

0.97

(2.5 × 10

−4

)

−0.760

49.5

−2.66

25.86

1.02

(7.9 × 10

−4

)

−0.767

61.3

−2.63

25.93

0.89

(1.3 × 10

−3

)

−0.685

41.0

−2.59

25.90

0.90

(−3.6 × 10

−4

)

−0.665

104

27.4

−2.68

25.79

0.95

−2.0 × 10

−3

−0.685

36.0

−2.63

25.89

0.96

(−5.4 × 10

−4

)

−0.765

38.8

−3.60

25.36

0.89

3.8 × 10

−3

−0.856

28.3

−3.36

19.94

0.90

5.2 × 10

−3

−0.928

18.4

−3.53

24.49

0.92

−l.0 × 10

−2

−0.968

1667

22.4

−3.60

25.27

0.98

−9.6 × 10

−3

−0.994

16.0

−7.43

32.38

0.98

l.9 × 10

−3

−1.077

35.1

101

−7.41

32.42

0.93

(−2.0 × 10

−4

)

−0.877

23.0

135

−7.43

32.37

0.96

(−2.8 × 10

−4

)

−0.900

30.0

Table 2

Summary of All InterCarb Analyses

Geochemistry, Geophysics, Geosystems

BERNASCONI ET AL.

10.1029/2020GC009588

13 of 25

Table 2

Continued

Number of analyses

Working gas

Standardization parameters

Reproducibility (ppm)

Lab

Session

VPDB

VSMOW

VPDB

VSMOW

100

−3.63

25.37

0.99

(−8.1 × 10

−5

)

−0.974

19.1

−3.60

25.53

0.98

(3.5 × 10

−4

)

−0.996

270

28.9

298

−3.02

24.99

0.91

(−2.2 × 10

−4

)

−1.065

25.0

150

−3.01

25.08

1.00

(−3.l ×10

−4

)

−1.088

210

33.7

367

−2.76

25.78

0.98

(−5.0 × 10

−4

)

−1.088

317

19.3

−3.75

25.15

0.89

3.7 × 10

−3

−0.904

10.2

−3.74

25.18

0.87

4.6 × 10

−3

−0.897

9.3

−3.74

25.17

0.88

5.5 × 10

−3

−0.909

9.7

−3.74

25.17

0.88

5.3 × 10

−3

−0.908

8.7

235

−10.29

33 0.18

0.98

−3.7 × 10

−4

−0.993

176

239

26.8

−3.63

24.95

0.93

(1.3 × 10

−4

)

−0.972

159

19.3

−3.61

25.04

0.97

(5.8 × 10

−4

)

−1.021

128

30.0

−10.38

31.93

0.84

−1.7 × 10

−3

−0.747

20.5

−10 0.40

31.92

0.86

−l.0 × 10

−3

−0.794

9.2

−10 0.40

31.92

0.91

−l.6 × 10

−3

−0.807

11.0

−10.43

31.84

0.99

(1.3 × 10

−4

)

−0.908

22.4

−10 0.41

31.85

0.97

(−1.7 × 10

−4

)

−0.877

12.8

−10.47

31.66

0.94

−7.8 × 10

−4

−0.920

23.4

−10 0.43

31.82

0.95

(−4.8 × 10

−4

)

−0.907

12.0

−10.49

31.73

0.99

(1.7 × 10

−4

)

−0.926

13.3

−32 0.89

36 0.92

0.96

−2.5 × 10

−3

−0.887

14.6

−3.72

24.98

1.02

4.6 × 10

−3

−1.027

14.0

–

−10.49

31.56

0.99

−4.1 × 10

−3

−0.979

109

10.1

–

−9.73

23.81

0.81

(6.3 × 10

−4

)

−0.940

204

29.3

168

147

172

169

714

−3.45

25.25

0.81

(1.5 × 10

−4

)

−0.722

11 0

37 0.7

0 2

- 3 0.4 1

25 0.4 2

0.83

(1.6 × 10

−5

)

−0.761

45.7

−3.52

25.12

0.96

(6.0 × 10

−4

) 1

−0.835

40.5

−24.48

25.66

0.99

(2.0 × 10

−4

)

−0.970

193

23.4

5.03

38.66

0.99

(2.0 × 10

−4

)

−0.962

164

416

22.5

−3.63

28.89

0.93

−2.1 × 10

−3

−0.921

14.3

–

−3.62

25.20

0.90

l.0 × 10

−3

−0.886

139

11.4

–

−3.54

25.37

0.98

9.9 × 10

−3

−0.951

155

443

20.5

–

−10 0.77

31.02

1.00

4.4 × 10

−3

−0.948

20.5

−4.40

25.32

0.98

(2.1 × 10

−4

)

−0.955

107

9.9

–

−40.04

5.51

0.89

(2.2 × 10

−4

)

−0.998

14 5

15.0

–

−40 0.03

5.40

0.92

(−1.1 × 10–4)

−1.014

8.7

Notes

. Nf is the number of degrees of freedom when estimating pooled analytical repeatabilities and standardization model uncertainties. Standardization

parameters

, and

refer to the scrambling factor in the source, the compositional slope due to positive or negative backgrounds in the collectors and the

working gas offset, respectively (see Section

2.4

and Daëron,

2021

). Values of standardization parameter

which are statistically indistinguishable from zero at

95% confidence level are reported in parenthesis. Reproducibility is reported as 1 SD.

Geochemistry, Geophysics, Geosystems

equal to (0.5470–0.5135)/0.0135 = +2.48. If the analytical errors reported in Table

are reasonably accu

rate, we expect the population of sigma-deviations among all laboratories to be distributed as the canonical

Gaussian distribution (

= 0;

= 1), and we can test this prediction using established statistical methods

such as a Kolmogorov-Smirnov test of normality (Massey,

1951

). We carried out this test for two cases: only

considering the error of sample replication (Figure

, upper row) and second including the normalization

error (i.e., the fully propagated error (Figure

, lower row). If we neglect uncertainties arising from stand

ardization (the “allogenic” errors of Daëron,

2021

), the sigma-deviations are no longer normally distributed

(

= 0.003, Figure

upper-left panel). When considering fully propagated analytical errors, as shown in

the lower-left panel of Figure

, the distribution of sigma-deviations for all laboratories and all samples is

statistically indistinguishable from the expected normal distribution (

= 0.19). Figure

also illustrates that

neglecting standardization errors does not strongly affect the normality of sigma-deviations for IAEA-C1,

which has δ

and Δ

values within the range covered by the three anchor samples. By contrast, sigma-devi

BERNASCONI ET AL.

10.1029/2020GC009588

14 of 25

ETH-4

IAEA-C1

IAEA-C2

MERCK

47(I-CDES

(‰ ± 1SE)

47(I-CDES

(‰ ± 1SE)

47(I-CDES

(‰ ± 1SE)

47(I-CDES

(‰ ± 1SE)

0.4477 ± 0.0052

0.2773 ± 0.0080

0.6275 ± 0.0088

0.4991 ± 0.0105

0.4499 ± 0.0044

0.3086 ± 0.0060

0.6299 ± 0.0061

0.5025 ± 0.0089

0.4430 ± 0.0074

0.3114 ± 0.0073

0.6427 ± 0.0112

0.5235 ± 0.0152

0.4841 ± 0.0248

0.2959 ± 0.0215

0.6368 ± 0.0291

–

0.4734 ± 0.0055

0.2916 ± 0.0044

0.6378 ± 0.0057

0.4987 ± 0.0094

0.4545 ± 0.0060

0.3004 ± 0.0051

0.6471 ± 0.0069

0.5229 ± 0.0116

0.4607 ± 0.0066

0.3099 ± 0.0042

0.6520 ± 0.0052

0.5231 ± 0.0098

0.4442 ± 0.0072

0.3099 ± 0.0060

0.6383 ± 0.0071

0.5159 ± 0.0127

0.4505 ± 0.0041

0.2926 ± 0.0064

0.6309 ± 0.0078

0.5630 ± 0.0158

0.4416 ± 0.0075

0.2987 ± 0.0060

0.6348 ± 0.0065

0.4954 ± 0.0130

0.4468 ± 0.0025

222

0.3085 ± 0.0043

0.6354 ± 0.0050

0.5175 ± 0.0066

0.4521 ± 0.0032

0.3015 ± 0.0026

0.6479 ± 0.0032

0.5064 ± 0.0054

0.4484 ± 0.0062

0.3048 ± 0.0113

0.6376 ± 0.0091

0.5470 ± 0.0135

0.4548 ± 0.0041

–

0.4480 ± 0.0083

0.3016 ± 0.0090

0.6217 ± 0.0116

0.4642 ± 0.0195

0.4627 ± 0.0076

0.2962 ± 0.0063

0.6563 ± 0.0084

0.5176 ± 0.0136

0.4634 ± 0.0250

0.3254 ± 0.0181

0.6971 ± 0.0314

0.4623 ± 0.0429

0.4510 ± 0.0046

196

0.3060 ± 0.0079

0.6386 ± 0.0084

0.5317 ± 0.0104

0.4460 ± 0.0106

0.2851 ± 0.0142

0.6015 ± 0.0183

0.5256 ± 0.0339

0.4627 ± 0.0095

–

0.4470 ± 0.0108

–

0.4639 ± 0.0124

–

0.5269 ± 0.0213

0.4453 ± 0.0137

–

0.4544 ± 0.0042

–

0.4378 ± 0.0058

0.3008 ± 0.0051

0.6396 ± 0.0062

0.5152 ± 0.0095

w. avg

0.4511 ± 0.0011

945

0.3018 ± 0.0013

310

0.6409 ± 0.0016

333

0.5135 ± 0.0024

286

0.011

–

0.011

–

0.018

–

0.024

–

Notes

. Note the larger standard deviation for the samples further from the calibration triangle defined by the anchors.

The average Δ

values for individual analytical sessions are reported in Table

Table 3

Average Δ

Values (±1SE, Fully Propagated Uncertainties) Obtained by Each Mass Spectrometer From the 22

Laboratories