William F Defliese
email: w.defliese@uq.edu.au

Aradhna Tripati

Analytical effects on clumped isotope thermometry: Comparison of a common sample set analyzed using multiple instruments, types of standards, and standardization windows

Rationale: Carbonate clumped isotope geothermometry is being increasingly applied in multiple disciplines in the geosciences. However, there are potential interlaboratory issues arising from different standardization procedures that may contribute to the multiple Δ 47 -temperature calibrations reported in the literature. We investigate this issue by comparing a common temperature calibration sample set across three different mass spectrometers, using multiple standardization methods.

Methods

The same temperature calibration sample set was analyzed on three different mass spectrometers. Several standardization methods were utilized, including the use of carbonate versus gas standards, and different types of background correction were applied to the raw data.

Introduction

Carbonate clumped isotope geothermometry is a promising isotopic technique that is being applied to fundamental problems in earth and atmospheric sciences [START_REF] Eiler | Paleoclimate reconstruction using carbonate clumped isotope thermometry[END_REF] . The measurement of the organization of multiple rare isotopes within a molecule opens up avenues of scientific inquiry that are not accessible with single isotope systems, such as the longstanding problem of determining the respective influences of water isotopic values and carbonate growth temperatures on the oxygen isotope composition of carbonate minerals. The carbonate clumped isotope thermometer has been deployed in a growing number of applications, such as paleoclimatology [START_REF] Finnigan | The Magnitude and Duration of Late Ordivician-Early Silurian Glaciation[END_REF][START_REF] Henkes | Temperature evolution and the oxygen isotope composition of Phanerozoic oceans from carbonate clumped isotope thermometry[END_REF][START_REF] Horton | Evaporation induced 18 O and 13 C enrichment in lake systems: A global perspective on hydrologic balance effects[END_REF] , sedimentology and basin analysis [START_REF] Bergman | Tracing paleofluid sources using clumped isotope thermometry of diagenetic cements along the Moab fault, Utah[END_REF][6][7] , and tectonics [START_REF] Carrapa | Uplift of the Central Andes of NW Argentina associated with upper crustal shortening, revealed by multiproxy isotopic analyses[END_REF][START_REF] Huntington | Carbonate clumped isotope thermometry in continental tectonics[END_REF][START_REF] Huntington | High late Miocene-Pliocene elevation of the Zhada Basin, southwestern Tibetan Plateau, from carbonate clumped isotope thermometry[END_REF] because it is completely independent of the sample's bulk isotopic composition, and allows temperatures to be measured directly without knowledge of the isotopic composition of water. In this application, the overexpression of [START_REF] Ghosh | 13 C-18 O bonds in carbonate minerals: A new kind of paleothermometer[END_REF] C- [START_REF] Schmid | An automated method for 'clumped-isotope' measurements on small carbonate samples[END_REF] O bonds within the carbonate lattice relative to a randomized mixture of isotopes (denoted Δ 47 ) is controlled by the formation temperature of the carbonate mineral, assuming that it formed at equilibrium 11,[START_REF] Schauble | Preferential formation of 13 C-18 O bonds in carbonate minerals, estimated using first-principles lattice dynamics[END_REF] .

However, measurement of multiple rare isotopes within a molecule requires very high precision, making analytical requirements a challenge compared with single rare isotope systems such as carbon ( 13 C/ 12 C) or oxygen ( 18 O/ [START_REF] Dennis | Defining an absolute reference frame for 'clumped' isotope studies of CO 2[END_REF] O). The target analytes are very rare in abundance, so high amplification of signals along with very long integration times are required. The standard procedure for carbonate samples involves liberating CO 2 from solid carbonate using >100 weight percent phosphoric acid, multiple steps of cryogenic separation to remove water, and purification to remove organics and overlapping m/z contaminants via gas chromatography or use of a molecular resin trap [START_REF] Ghosh | 13 C-18 O bonds in carbonate minerals: A new kind of paleothermometer[END_REF] . Measurements of many sample/working gas cycles and/or multiple sample replicates may be necessary in order to achieve meaningful instrumental errors that approach shot noise limits [START_REF] Huntington | Methods and limitations of 'clumped' CO 2 isotope (Δ 47 ) analysis by gas-source isotope ratio mass spectrometry[END_REF] .

Standardization of Δ 47 data is a complex process requiring multiple steps, and several procedures have been proposed to both provide a common reference frame between labs and to account for instrumental effects in measurement. The first effect to be recognized was a mass spectrometric correction for non-linearity, where measured m/z 47 values show a dependence on m/z 44 ions, as expressed in a plot of Δ 47 versus δ 47 values [START_REF] Ghosh | 13 C-18 O bonds in carbonate minerals: A new kind of paleothermometer[END_REF][START_REF] Huntington | Methods and limitations of 'clumped' CO 2 isotope (Δ 47 ) analysis by gas-source isotope ratio mass spectrometry[END_REF][START_REF] Bernasconi | Background effects on Faraday collectors in gas-source mass spectrometry and implications for clumped isotope measurements[END_REF][START_REF] Dennis | Defining an absolute reference frame for 'clumped' isotope studies of CO 2[END_REF][START_REF] He | Pressure baseline correction and high-precision CO 2 clumped-isotope (Δ 47 ) measurements in bellows and micro-volume modes[END_REF][START_REF] Schmid | An automated method for 'clumped-isotope' measurements on small carbonate samples[END_REF] . This effect is related to instrumental design and is caused by a secondary scattering of ions as they travel through the flight tube creating negative currents on the Faraday collectors, and the magnitude of the effect is variable through time, depending on filament age, source tuning, and other instrument specific parameters. Three different types of correction schemes have been used. An initial correction scheme for this non-linearity involves the measuring CO 2 gases of varying bulk isotopic composition which have been heated at 1000 °C for several hours to create a randomized distribution of isotopes (originally proposed by Ghosh et al) [START_REF] Ghosh | 13 C-18 O bonds in carbonate minerals: A new kind of paleothermometer[END_REF] . A suite of these gases would be measured, the non-linearity measured, and subtracted out of the final sample Δ 47 values as, by definition, samples that have been equilibrated at the same temperature have the same Δ 47 value, even if they have different bulk isotopic ratios. This procedure must be done continually throughout the measurement period to account for changes in the non-linearity correction.

A variant of this approach replaces the equilibrated gases with two carbonate standards of differing bulk isotopic ratios that have been heated to a high temperature and then rapidly quenched, ensuring similar Δ 47 values despite differing δ 47 values [START_REF] Schmid | An automated method for 'clumped-isotope' measurements on small carbonate samples[END_REF] . A more recent approach termed the pressure baseline (PBL) correction involves analyzing the peak shape produced during a slow magnet scan at various gas pressures (corresponding to different signal sizes), identifying the magnitude of negative currents impacting the peak shapes, and subtracting these currents from future measurements [START_REF] Bernasconi | Background effects on Faraday collectors in gas-source mass spectrometry and implications for clumped isotope measurements[END_REF][START_REF] He | Pressure baseline correction and high-precision CO 2 clumped-isotope (Δ 47 ) measurements in bellows and micro-volume modes[END_REF][START_REF] Fiebig | Slight pressure imbalances can affect accuracy and precision of dual inlet-based clumped isotope analysis[END_REF] . This procedure has the benefit of being less time consuming to implement; however, it must be performed daily. Many labs use some combination of the above approaches, and often a PBL is applied in addition to equilibrated gases or paired carbonate standards.

The second issue realized was that the non-linearity correction did not fully account for inter-lab differences in Δ 47 . Specifically, the non-linearity correction did not fully anchor the Δ 47 scale, with scale compression or stretching observed. To provide a more complete standardization scheme, Dennis et al [START_REF] Dennis | Defining an absolute reference frame for 'clumped' isotope studies of CO 2[END_REF] proposed that gas or carbonate standard values be defined absolutely to create an absolute reference frame [START_REF] Dennis | Defining an absolute reference frame for 'clumped' isotope studies of CO 2[END_REF] , using one of two methods. The first approach is to equilibrate CO 2 gases at variable temperatures. In addition to heated gas standards, equilibrated CO 2 gas standards could be produced at different temperatures with variable bulk composition by taking advantage of isotopic exchange that occurs with water in the H 2 O + CO 2 ↔ H 2 CO 3 reaction. These gases, equilibrated at different temperatures, are used for the nonlinearity correction, and then each assigned an absolute Δ 47 value based on theoretical predictions of values given the temperature of equilibrium [START_REF] Wang | Equilibrium thermodynamics of multiply substituted isotopologues of molecular gases[END_REF] , so that an absolute reference frame (ARF) can be built to account for scale compression or stretching of Δ 47 values. A carbonate standard-based method of standardization was also proposed [START_REF] Dennis | Defining an absolute reference frame for 'clumped' isotope studies of CO 2[END_REF][START_REF] Schmid | An automated method for 'clumped-isotope' measurements on small carbonate samples[END_REF] that involves the use of in-house carbonate standards of varying bulk isotopic composition and Δ 47 values to build the ARF. Carbonate standards can be used alone without the use of supplementary equilibrated gases [START_REF] Bernasconi | Reducing Uncertainties in Carbonate Clumped Isotope Analysis Through Consistent Carbonate-Based Standardization[END_REF][START_REF] Meckler | Long-term performance of the Kiel carbonate device with a new correction scheme for clumped isotope measurements[END_REF] , or can be used as an additional correction (secondary transfer function, or STF) on top of the use of equilibrated gases. The carbonate standards approach has the benefit that it does not require the time-consuming step of manufacturing equilibrated gases, and furthermore treats all standards identically to samples (which may or may not be the case with equilibrated gases, depending on lab group and procedure), but it still requires analyzing multiple standards during the run, reducing sample throughput.

The identification of different potential sources of inter-laboratory offsets has led to new methods being proposed for standardization, as described above. However, the impact of the lack of a consistent practice in standardization is unclear. It is uncertain whether different labs need to use the same standardization methods to achieve consistency, or whether there are multiple valid methods of standardization. Thus, consensus on best practice has not yet been reached. Yet quantifying the impacts of standardization method on resultant Δ 47 values is critical for resolving why there are still discrepancies in Δ 47 -temperature calibrations, and for quantifying the magnitude of equilibrium and kinetic isotope effects. There are three end-member hypotheses for the origin of discrepancies in reported calibrations: 1) there are measurable equilibrium and kinetic isotope effects that give rise to the range of values observed in the literature 11,23-27 , 2) inter-laboratory differences in sample digestion give rise to the variation observed in Δ 47 [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF][START_REF] Kelson | Toward a universal carbonate clumped isotope calibration: Diverse synthesis and preparatory methods suggest a single temperature relationship[END_REF][START_REF] Murray | Determining the Δ 47 acid fractionation in dolomites[END_REF][START_REF] Swart | Oxygen Isotopic Exchange Between CO 2 and Phosphoric Acid: Implications for the Measurement of Clumped Isotopes in Carbonates[END_REF] , and 3) inter-laboratory differences in Δ 47 measurement and/or standardization give rise to the variation observed in Δ 47 [START_REF] Olack | Modeling the Measurement: Δ 47 , Corrections, and Absolute Ratios for Reference Materials[END_REF][START_REF] Petersen | Effects of Improved 17 O Correction on Interlaboratory Agreement in Clumped Isotope Calibrations, Estimates of Mineral-Specific Offsets, and Temperature Dependence of Acid Digestion Fractionation[END_REF] .

This paper represents a contribution to partially testing hypotheses 2 and 3, with the caveat that all three hypotheses may in fact be true. Here we report the results of a multi-year study where we quantify the differences that can be caused by the use of different standardization techniques. We achieve this by analyzing a common set of synthetic calcite and aragonite samples on two different mass spectrometers and reanalyzing results from a published dataset [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] from a third mass spectrometer. The three mass spectrometers each have a different preparation line. Further, we analyze the effects of different standardization methods, including using gas standards only, carbonate standards only, and a mixture of gas and carbonate standards for corrections, and we explore the impact of using different standardization intervals for corrections. We report the consequent impacts on calculated Δ 47 -temperature calibrations, and show that carefully chosen measurement windows yield results for the same set of samples that are largely comparable across multiple instruments.

Methods

Samples

Calcite and aragonite samples synthesized and measured in the Lohmann Stable Isotope Lab at the University of Michigan (Ann Arbor, MI, USA) were reported in Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] , and these data were reanalyzed for this study. In the case of the 5 °C calcite sample, we used a parallel precipitate that was grown at using the same apparatus and methods as the sample reported in Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] ; however; this sample was not used for that study. We measured splits of these samples on multiple instruments in the Tripati Stable Isotope Lab at UCLA (Los Angeles, CA, USA). These carbonates consist of calcite and aragonite that were grown at controlled temperatures using the 'passive degassing' technique. Samples were grown in a 4-L beaker at 5, 25, 50, and 70 °C, while being allowed to exchange freely with atmosphere. Some of the samples used in Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] were exhausted, including all replicates at 50 °C, so they were not included in this study. The mineralogy of each sample used is given in Table 1. For full details on the synthesis of these materials, please refer to Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] .

Mass spectrometers and operating procedures

For this study, we used data from three mass spectrometers, two of which are housed in the Tripati Lab at UCLA, and one of which is located in the Lohmann Lab at the University of Michigan (UMich). Details of sample digestion and mass spectrometric analysis are described below.

University of Michigan, Ann Arbor

Sample Digestion

Carbonate samples and standard materials (equilibrated gases) were prepared through use of a custom-built offline manual prep line. Briefly, carbonates were digested in 105 weight percent H 3 PO 4 in a common acid bath apparatus, held at 75 °C using an enclosed circulating water bath. CO 2 and the co-produced H 2 O were frozen in a U-trap simultaneous with digestion to avoid potential equilibration with H 2 O and scrambling of [START_REF] Ghosh | 13 C-18 O bonds in carbonate minerals: A new kind of paleothermometer[END_REF] C-18 O bonds. CO 2 gases were subject to two stages of cryogenic separation using a liquid nitrogen/1-propanol slush held at -90 °C to remove CO 2 . Dehydrated CO 2 gas was further cleaned to remove organic and other potentially overlapping contaminants by use of a gas chromatograph (Supelco Supel-Q PLOT, 30m x 0.53 mm; Sigma-Aldrich, MO, USA; for samples prior to July 2011) or U-trap filled with PoraPak Q resin (Waters Corp., Milford. MA, USA; 50-80 mesh, for samples in July 2011 and after). Samples cleaned using the gas chromatograph were carried using an ultra-high-purity He stream at 7 mL/min at a temperature of -20°C, and collected downstream of the gas chromatograph in a multi-loop trap immersed in liquid N 2 . Samples cleaned using the PoraPak were frozen into a cold finger upstream of the PoraPak U-trap, and allowed to warm to room temperature. CO 2 was equilibrated with the PoraPak for 5 minutes at -30 °C, and then liquid nitrogen was placed on a cold finger downstream of the PoraPak U-trap to draw the CO 2 through the trap. Yields were checked by manometer before and after cleaning to ensure complete transfer; any sample that was incomplete was discarded. Cleaned CO 2 was transferred to a glass cold finger for storage, and was analyzed on the mass spectrometer within 24 hours of cleaning.

Mass spectrometry

The UMich instrument is a Thermo Fisher Scientific (Bremen, Germany) MAT 253 isotope ratio mass spectrometer. It has been modified to simultaneously collect masses 44-49 [START_REF] Huntington | Methods and limitations of 'clumped' CO 2 isotope (Δ 47 ) analysis by gas-source isotope ratio mass spectrometry[END_REF] , with the following resistors on each Faraday cup: 3 x 10 8 , 3 x 10 10 , and 10 11 Ω for masses 44, 45, and 46, and 10 12 Ω resistors for masses 47-49. Analyses were performed in dual inlet mode using standard stainless-steel capillaries, and the pressure was balanced between each acquisition to achieve a signal of 16V on the mass 44 cup for both sample and standard bellows. Each replicate measurement had 8 acquisitions, with each acquisition consisting of 10 sample-standard comparisons, with an 8 second integration time and 16 second changeover delay. Each acquisition was also preceded by peak centering and a 120 second background delay. The total integration time for each replicate was 640 seconds.

Types of standards run

The Δ 47 results for the UMich instrument were standardized to the Absolute Reference Frame [START_REF] Dennis | Defining an absolute reference frame for 'clumped' isotope studies of CO 2[END_REF] by comparison with CO 2 gases of varying bulk isotopic composition which were equilibrated at 25 °C and 50 °C by exchange with water, and at 1000 °C by heating in an oven for a minimum of 2 hours. In typical operation, two equilibrated gases were run per day. All equilibrated gases were subject to the same cleaning and handling procedure as carbonate samples, as discussed above, except that they were not reacted with phosphoric acid.

University of California, Los Angeles

Sample Digestion

Both instruments at UCLA are coupled to custom-built automatic reaction and prep lines, which operate identically, though they differ slightly in dimension and layout. Each line uses a common acid bath reaction chamber held at 90 °C by use of a heating element and thermocouple. The resultant CO 2 and H 2 O pass through a water trap held at ~-50 °C by a mixture of ethanol and dry ice, and are frozen into a U-trap by liquid nitrogen throughout the duration of the reaction. CO 2 is then entrained in a stream of ultra-high-purity He, and cleaned by use of a gas chromatograph filled with PoraPak Q (50-80 mesh) held at -20 °C. The cleaned CO 2 is collected downstream of the gas chromatograph and passed through a second water trap before being frozen in a multi-loop trap by liquid nitrogen. CO 2 is cryogenically cleaned an additional time with a dry ice/ethanol slush to remove water, and passed to the mass spectrometer for analysis. Equilibrated gases were introduced by use of an external port that bypassed the common acid bath; otherwise they were cleaned and processed in an identical manner to carbonate samples and standards.

Mass spectrometry

The two instruments at UCLA are a Thermo Fisher Scientific MAT 253 mass spectrometer and a Nu Instruments (Wrexham, UK) Perspective IS mass spectrometer. The MAT 253 has been modified to simultaneously collect masses 44-49, as described in Huntington et al [START_REF] Huntington | Methods and limitations of 'clumped' CO 2 isotope (Δ 47 ) analysis by gas-source isotope ratio mass spectrometry[END_REF] . The signal is passed through resistors of 3 x 10 8 , 3 x 10 10 , and 10 11 Ω for masses 44, 45, and 46, while 10 12 Ω resistors are used for masses 47-49. Analyses were performed in dual inlet mode using nickel capillaries, and the pressure was balanced between each acquisition to achieve a signal of 16V on the mass 44 cup for both sample and standard bellows. Each replicate measurement had 9 acquisitions, with each acquisition consisting of 10 sample-standard comparisons, with an 8 second integration time and 16 second changeover delay. The total integration time for each replicate was 720 seconds.

The Nu Instruments Perspective IS mass spectrometer at UCLA is a relatively new design, with several differences from the MAT 253. It has a Nier-type ion source and magnetic sector; however, it features a pair of quadratic lenses after the magnetic sector, and cups 47, 48, and 49 are shielded by small electrostatic sector analyzers, which can be tuned to screen out secondary background ions. The resistors are the same as for the MAT 253. Analyses were performed in dual inlet mode using stainless steel capillaries. Measurement of each replicate consisted of 80 cycles of sample-standard comparison, each with 20 seconds integration time and a 6 second changeover delay, for a total integration time of 1600 seconds per replicate. The pressure on the bellows was continuously adjusted after each changeover using the previous acquisition as feedback using a Newtonian zeroing technique, and balanced to achieve a signal of 16V on the mass 44 cup for both sample and standard bellows. This is a key difference from the MAT 253, which only pressure balances after every 10 changeovers as part of a separate routine that is not part of the acquisition cycle.

Types of standards run

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The Δ 47 results for both UCLA instruments were standardized to the Absolute Reference Frame 16 by comparison with CO 2 gases of varying bulk isotopic composition which were equilibrated at 25 °C by exchange with water, and at 1000 °C by heating in an oven for a minimum of 2 hours, and by the use of carbonate standards (ETH 1-4, as well as in-house standards Carrara Marble, Carmel Chalk, Veinstrom, and TV03). In typical operation, one equilibrated gas and two carbonate standards were run per day. All equilibrated gases were subject to the same cleaning and handling procedure as carbonate samples/standards, as discussed above, except that they were not reacted with phosphoric acid.

Data Processing and Standardization

University of Michigan

We reprocessed the UMich data that was previously published in Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] . With the exception of one variation, exactle the same data processing techniques have been used. Following recent suggestions [START_REF] Daëron | Absolute isotopic abundance ratios and the accuracy of Δ 47 measurements[END_REF][START_REF] Schauer | Choice of 17 O correction affects clumped isotope (Δ 47 ) values of CO 2 measured with mass spectrometry[END_REF] , we recalculated isotope ratios using the isotope parameter set of Brand et al [START_REF] Brand | Correction for the 17 O interference in δ 13 C measurements when analyzing CO 2 with stable isotope mass spectrometry (IUPAC Technical Report)[END_REF] , in contrast to using Gonfiantini et al 37 which was originally used in Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] . Data was placed on the Absolute Reference Frame by use of equilibrated gases prepared at 25, 50, and 1000 °C, as described previously. No pressure baseline corrections were carried out on this instrument. In typical operation, one 1000 °C gas and one 25 or 50 °C gas were run daily, for a total of two equilibrated gases analyzed each day. The Absolute Reference Frame was then calculated daily, using a moving window of the previous 14 analyzed equilibrated gases, which approximated a one-week window. We did not calculate the effects of a longer standardization window for the UMich instrument, as this instrument is not a dedicated clumped isotope device, and clumped isotope measurements were conducted for two-to three-week periods every 4-6 months. We found that the reference frame calibrations were unstable and required constant monitoring to provide a stable standardization to the ARF. All samples were treated with an acid fractionation factor of 0.062 ‰, following Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] , and acid digestion at 75 °C. Stable isotope ratios for these samples are listed in Table 1.

University of California, Los Angeles

At UCLA, data was acquired over a period of six months on each instrument. We then constructed reference frames using 10 different standardization techniques, using aliquots of the same set of samples and standards, as described below. All isotope ratios were calculated using the isotope parameters of Brand et al [START_REF] Brand | Correction for the 17 O interference in δ 13 C measurements when analyzing CO 2 with stable isotope mass spectrometry (IUPAC Technical Report)[END_REF] , and an acid fractionation factor of 0.082 ‰ was applied to all samples, following Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] , and acid digestion at 90 °C. We used a mixture of the ETH standards provided by Stefano Bernasconi (ETH, Zurich, Switzerland) and in-house UCLA standards Carrara Marble, Carmel Chalk, Veinstrom, and TV03 as carbonate standards for this exercise. For the purpose of this exercise, we used the values for the ETH standards published in Müller et al [START_REF] Müller | Carbonate clumped isotope analyses with the long-integration dual-inlet (LIDI) workflow: scratching at the lower sample weight boundaries[END_REF] . The accepted values of the in-house standards are listed in the supporting information.

Historically what has been done at UCLA is to monitor standard drift and choose standardization intervals that reflect instrument stability, by constantly monitoring the reference frame. Typically, standardization windows range from several weeks to months in time. For this study, we chose two end-member standardization intervals to construct the Absolute Reference Frame, with each type of standardization window applied to both instruments. The first type of standardization interval consisted of approximately one-month intervals, where all data collected within each month were binned together and used to construct the ARF. The second type used a 6-month window, where all data collected within the entire 6 months were binned together to construct the ARF. This allowed us to assess the stability of the reference frame through time.

Five different methods were used to construct the Absolute Reference Frame (ARF) for each instrument and standardization window at UCLA. It should be noted that we did not perform pressure baseline corrections for any of these standardization methods. The first method used only the equilibrated gas data to create non-linearity correction and the ARF, as described in Dennis et al [START_REF] Dennis | Defining an absolute reference frame for 'clumped' isotope studies of CO 2[END_REF] . All carbonate standards are ignored in the analysis. The second method used equilibrated gases to construct the non-linearity correction, and used equilibrated gases and carbonate standards to create the ARF. The third method used the equilibrated gases to do the non-linearity correction, and then used carbonate standards for the ARF. The fourth method ignored the non-linearity correction, and used the carbonate standards alone to construct the ARF. The fifth method used the assigned values of ETH 1 and 2 to do the non-linearity correction, and used all the carbonate standards to create the ARF. We note for the MAT 253 at UCLA, there were not enough carbonate ETH standards run in the latter half of the 6-month acquisition window to robustly determine the fifth type of standardization for the shorter time intervals. Therefore, the last method has not been applied in the 1-month standardization series, resulting in 9 standardization techniques. A summary of each technique used is listed in Table 2, with a numerical code given for each unique combination of ARF construction and correction window length. We will refer to this code in the text, where appropriate.

Results

A Table with all samples and standards used in this study is available in the supporting information. Four of the original samples from Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] The various temperature-versus-Δ 47 regressions produced are listed in Table 3 (for the 253 instrument at UCLA) and Table 4 (for the Perspective IS instrument at UCLA). These regressions are compared with the data originally analyzed at the University of Michigan, where new regressions for the Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] data are generated using only the subset of samples concurrently analyzed at UCLA. Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] originally reported the following calibration, using the Gonfiantini et al 37 parameter set and standardization using equilibrated gases only (method 6 in our Notably, the addition or subtraction of various data points slightly affects the slope, intercept, and error of each regression, although they all overlap. This is not surprising, as they were all produced and analyzed in the same manner using the same equipment, and it shows that the original work of Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] is internally consistent. These serve as useful comparisons with the regressions calculated using the various standardization techniques, and allow a comparison with the data generated at UCLA.

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Discussion

Effects of Different Standardization Techniques

The different standardization techniques employed in this study reveal that Δ 47 values are sensitive to standardization practices. However, our analysis reveals that while there are changes with different techniques, the majority of them produce temperature regressions that are statistically identical to each other. To analyze this, for each instrument we performed ANCOVA analysis of each regression compared with every other regression on that instrument. The resulting p-values are presented in Tables 5 and6 for the Perspective IS and MAT 253, respectively. Critically, the majority of standardization techniques produced regressions that were statistically identical (p-value for differences in slope/intercept of greater than 0.10, reject separate regression hypothesis), with some exceptions that warrant further discussion.

The regressions produced using the Perspective IS instrument are remarkably similar to each other, regardless of the standardization technique used. In fact, all 10 techniques are statistically identical (all p-values greater than 0.1, reject separate regression hypothesis), as shown in Table 5. Most standardization techniques also yield results that are statistically identical to the reprocessed Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] data, with all slopes statistically indistinguishable, and only the intercepts significantly different at the 95% level (Figure 1). These differences in intercept are of the order of the differences reported for the error on acid digestion [START_REF] Müller | Calibration of the oxygen and clumped isotope thermometers for (proto-) dolomite based on synthetic and natural carbonates[END_REF][START_REF] Petersen | Effects of Improved 17 O Correction on Interlaboratory Agreement in Clumped Isotope Calibrations, Estimates of Mineral-Specific Offsets, and Temperature Dependence of Acid Digestion Fractionation[END_REF] with an average offset of 0.022‰ in this dataset, and may reflect slight differences in acid temperature and/or other measurement discrepancies. It should be noted that these discrepancies are only detectable at the 95% confidence level because the reproducibilities of the Perspective IS and UMich 253 instruments are quite high, as evidenced by the low measurement error for each. The Perspective IS instrument is very stable throughout the whole study interval, as shown by the fact that there is no significant difference between any of the internally generated regressions, regardless of the standardization window (i.e., stability on a timescale of 6 months) or technique employed. It should be noted that this was a very stable time in the instrument's performance, with no downtime due to repairs or maintenance.

The regressions produced using the MAT 253 instrument are not as similar to each other as the Perspective IS, as shown in Table 6. It should be noted that the data on the MAT 253 shows much more scatter in general (as evidenced by much larger errors on temperature regressions) than either the Perspective IS or the University of Michigan MAT 253, which may be due to having analyzed only 4 samples on this instrument compared with 5 on the Perspective IS. As the missing sample is one of the cold end-members in our comparison (5 °C calcite) it may have a large influence on the final results.

There are two regressions that are statistically different from the other 7 produced, and both of them are ARF constructions that ignore the non-linearity correction (methods 4 and 9 in Table 2). There is also a difference between the intercept of the Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] data and the regressions produced on the UCLA MAT 253 (Figure 2), although the slopes of the regressions are statistically identical, as long as the non-linearity correction is performed in some manner. Similar to the Perspective IS, the MAT 253 produces internally consistent regressions when nonlinearity corrections are preformed, regardless of the time window (i.e., 1-month versus 6-month window) for standardization.

We also compared the two UCLA instruments with each other, focusing on the 1-month standardization windows (methods 6-9) as this is more reflective of real-world practices than using a 6-month window. For this exercise we only used the 4 samples analyzed in common between the MAT 253 and Perspective IS, excluding the 5 th sample (5 °C calcite) analyzed on the Perspective IS. The resulting regressions produce slopes that are statistically identical (Table 7), except when non-linearity is ignored on the MAT 253 (method 9), although the intercepts are often different between the two instruments. The cause of this discrepancy is difficult to identify, as each instrument was standardized in an identical manner, using exactly the same standards and procedures for each. There are physical differences between the two extraction lines and mass spectrometers, but both operate on the same principles and should produce similar results when properly standardized. A possible cause of this discrepancy could be related to the phosphoric acid digestions on each instrument -any difference in acid temperature/density/volume could cause an offset in intercept due to raising or lowering the Δ 47 value of each sample and carbonate standards, but would not affect the slopes of the resulting calibrations, assuming that the acid is at a constant temperature/density/volume through time.

If it is in fact somehow related to the acid digestion process, the standardization techniques that rely on carbonate standards will produce regressions that are more in agreement with each other across the two instruments, which is exactly what our data reveals. The MAT 253 standardization technique, which relies on equilibrated gases to do the non-linearity correction but carbonate standards for the ARF (method #8), produces a regression that is most similar to the Perspective IS regressions, producing statistically identical regressions, compared with all other standardization techniques that produce regressions differing at 95% (or higher) confidence. This shows that using carbonate standards can improve the reproducibility between different instrumentation as carbonate standards are treated identically to sample unknowns [START_REF] Schmid | An automated method for 'clumped-isotope' measurements on small carbonate samples[END_REF][START_REF] Bernasconi | Reducing Uncertainties in Carbonate Clumped Isotope Analysis Through Consistent Carbonate-Based Standardization[END_REF][START_REF] Meckler | Long-term performance of the Kiel carbonate device with a new correction scheme for clumped isotope measurements[END_REF] , whereas equilibrated gases are not digested by phosphoric acid, leaving an additional variable that is not accounted for in the standardization process.

Our results also show the importance of the approach used to correct for non-linearity, as our standardization schemes that did not address non-linearity produced the most divergent This article is protected by copyright. All rights reserved. results, similar to Fiebig et al [START_REF] Fiebig | Slight pressure imbalances can affect accuracy and precision of dual inlet-based clumped isotope analysis[END_REF] . Correcting for non-linearity can be done in one of three ways: 1) using equilibrated gases, following Dennis et al [START_REF] Dennis | Defining an absolute reference frame for 'clumped' isotope studies of CO 2[END_REF] ; 2) using two (or more) carbonate standards than have differing bulk isotopic ratios, but identical Δ 47 values such as ETH-1 and ETH-2 [START_REF] Meckler | Long-term performance of the Kiel carbonate device with a new correction scheme for clumped isotope measurements[END_REF][START_REF] Müller | Carbonate clumped isotope analyses with the long-integration dual-inlet (LIDI) workflow: scratching at the lower sample weight boundaries[END_REF] ; and 3) performing a pressure baseline correction [START_REF] Bernasconi | Background effects on Faraday collectors in gas-source mass spectrometry and implications for clumped isotope measurements[END_REF][START_REF] He | Pressure baseline correction and high-precision CO 2 clumped-isotope (Δ 47 ) measurements in bellows and micro-volume modes[END_REF] . In this study, we used both the 1 st and 2 nd methods, which produced results that were statistically identical to each other for both instruments. It should be noted that we observed the greatest agreement between regressions when we used equilibrated gases alone to perform the non-linearity correction, and then carbonate standards alone to build the remaining portion of the ARF (method 8 in Table 2). We suspect that this may reflect the more limited isotopic range encompassed by ETH-1 and ETH-2 versus equilibrated gases, which can potentially cover a much larger range of δ 13 C and δ [START_REF] Schmid | An automated method for 'clumped-isotope' measurements on small carbonate samples[END_REF] O values when calculating the non-linearity correction slope, although we emphasize that either method is adequate per our analysis.

Our data shows the importance of performing this correction, as our standardization procedures that intentionally disregarded the correction (methods 4 and 9 in Table 2) produced regressions that were statistically different from all others, being the only ones that produced a steeper 'Ghosh' style slope similar to that reported in Ghosh et al [START_REF] Ghosh | 13 C-18 O bonds in carbonate minerals: A new kind of paleothermometer[END_REF] . The version of the MAT 253 used at UCLA (and University of Michigan) has been shown to be particularly susceptible to these issues [START_REF] Huntington | Methods and limitations of 'clumped' CO 2 isotope (Δ 47 ) analysis by gas-source isotope ratio mass spectrometry[END_REF] , although it should be noted that they are easily resolved with proper procedures and care during operation and standardization. Newer versions of the MAT 253 (such as the 253+, not evaluated here) have features designed to minimize scattering and background effects. The Perspective IS does not seem to suffer anywhere near as much from scattering effects as shown by the fact that all standardization techniques produced similar regressions, which is due to the different geometry and use of electrostatic analyzers to 'shield' the Faraday cups from background ions. Although the non-linearity correction is already a standard part of clumped isotope procedures, we emphasize that the non-linearity correction is of critical importance for clumped isotope measurements, and is easy to implement using any of the three methods listed above.

We did not find a significant influence of calibration window (1-month versus 6-month) on regression slope for either UCLA instrument (MAT 253 or Perspective IS), although we did observe offsets in intercept. This surprised us to some degree, as typically instruments do not display such high stability through time, as exemplified by the common slope. Typically, some instrumental conditions will change over the period of several months (downtime for maintenance, power outages, aging of filament, retune focus parameters, etc.) which necessitate the use of a new calibration window. The choice of calibration window can vary significantly from instrument to instrument depending on operating conditions [START_REF] Ghosh | 13 C-18 O bonds in carbonate minerals: A new kind of paleothermometer[END_REF][START_REF] Huntington | Methods and limitations of 'clumped' CO 2 isotope (Δ 47 ) analysis by gas-source isotope ratio mass spectrometry[END_REF] , and as such all laboratories should regularly monitor the calibration by continuing to analyze standards, regardless of apparent stability. Instrumental stability can only be assessed in hindsight, as conditions could change at any moment during a run period. We emphasize this, as while our 6-month calibration window produced results that were fairly similar to the UM regression, the shorter 1-month windows produced better agreement.

Implications for Prior Work and Multiple Temperature Calibrations

One of the most puzzling issues in the clumped isotope literature has been the problem of multiple Δ 47 -temperature calibrations, which display a wide range in temperature sensitivity. The first two published calibrations [START_REF] Ghosh | 13 C-18 O bonds in carbonate minerals: A new kind of paleothermometer[END_REF][START_REF] Dennis | Clumped isotope thermometry of carbonatites as an indicator of diagenetic alteration[END_REF] had almost a 50% difference from each other, and this has been referred to as the 'two slope' or "steep and shallow slope" problem. Many studies have attempted to address the underlying cause of these discrepancies, investigating factors such as mineralogy [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF][START_REF] Kelson | Toward a universal carbonate clumped isotope calibration: Diverse synthesis and preparatory methods suggest a single temperature relationship[END_REF][START_REF] Murray | Determining the Δ 47 acid fractionation in dolomites[END_REF][START_REF] Petersen | Effects of Improved 17 O Correction on Interlaboratory Agreement in Clumped Isotope Calibrations, Estimates of Mineral-Specific Offsets, and Temperature Dependence of Acid Digestion Fractionation[END_REF][START_REF] Bonifacie | Calibration of the dolomite clumped isotope thermometer from 25 to 350 °C, and implications for a universal calibration for all (Ca, Mg, Fe)CO 3 carbonates[END_REF][START_REF] Eagle | The influence of temperature and seawater carbonate saturation state on 13 C-18 O bond ordering in bivalve mollusks[END_REF][START_REF] Fernandez | Siderite 'clumped' isotope thermometry: a new paleoclimate proxy for humid continental environments[END_REF][START_REF] Henkes | Carbonate clumped isotope compositions of modern marine mollusk and brachiopod shells[END_REF][START_REF] Kluge | Effects of brine chemistry and polymorphism on clumped isotopes revealed by laboratory precipitation of mono and multiphase calcium carbonates[END_REF] , precipitation rate [START_REF] Tang | Evaluation of kinetic effects on clumped isotope fractionation (Δ 47 ) during inorganic calcite precipitation[END_REF][START_REF] Kelson | Toward a universal carbonate clumped isotope calibration: Diverse synthesis and preparatory methods suggest a single temperature relationship[END_REF] , acid digestion temperature [START_REF] Müller | Calibration of the oxygen and clumped isotope thermometers for (proto-) dolomite based on synthetic and natural carbonates[END_REF][START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF][START_REF] Kelson | Toward a universal carbonate clumped isotope calibration: Diverse synthesis and preparatory methods suggest a single temperature relationship[END_REF][START_REF] Murray | Determining the Δ 47 acid fractionation in dolomites[END_REF][START_REF] Petersen | Effects of Improved 17 O Correction on Interlaboratory Agreement in Clumped Isotope Calibrations, Estimates of Mineral-Specific Offsets, and Temperature Dependence of Acid Digestion Fractionation[END_REF][START_REF] Müller | Carbonate clumped isotope analyses with the long-integration dual-inlet (LIDI) workflow: scratching at the lower sample weight boundaries[END_REF] , the use of varying isotopic constants [START_REF] Olack | Modeling the Measurement: Δ 47 , Corrections, and Absolute Ratios for Reference Materials[END_REF][START_REF] Petersen | Effects of Improved 17 O Correction on Interlaboratory Agreement in Clumped Isotope Calibrations, Estimates of Mineral-Specific Offsets, and Temperature Dependence of Acid Digestion Fractionation[END_REF][START_REF] Daëron | Absolute isotopic abundance ratios and the accuracy of Δ 47 measurements[END_REF][START_REF] Schauer | Choice of 17 O correction affects clumped isotope (Δ 47 ) values of CO 2 measured with mass spectrometry[END_REF] , and the use of natural versus synthetic materials [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] , in addition to other procedural and methodological issues. No single factor has yet been found as the cause of this historical discrepancy in the literature. It is important to note that the 'two slope' problem represents the outliers, and recently published calibrations show much better alignment with each other (i.e., Petersen et al [START_REF] Petersen | Effects of Improved 17 O Correction on Interlaboratory Agreement in Clumped Isotope Calibrations, Estimates of Mineral-Specific Offsets, and Temperature Dependence of Acid Digestion Fractionation[END_REF] , and references within), perhaps due to better standardization and methodological improvements. The emerging consensus on a 'true' Δ 47 -temperature is a major achievement for clumped isotope thermometry, although there remains work to be done. This study does not present a solution for a 'true' Δ 47 -temperature relationship; however, it does allow us to offer some insight into the nature of the historical 'two slope' problem. Our results show that even when vastly different standardization procedures and instrumentation are used, the same sample materials generate statistically identical Δ 47 -temperature slopes, with the important exception of procedures that ignore the non-linearity correction. Given that the nonlinearity correction has been a standard part of clumped isotope practice for some time [START_REF] Huntington | Methods and limitations of 'clumped' CO 2 isotope (Δ 47 ) analysis by gas-source isotope ratio mass spectrometry[END_REF][START_REF] Dennis | Defining an absolute reference frame for 'clumped' isotope studies of CO 2[END_REF] , this should not result in any changes to current practices for the vast majority of labs worldwide. This work suggests that as long as labs are following a rigorous standardization procedure to construct a proper reference frame [START_REF] Huntington | Methods and limitations of 'clumped' CO 2 isotope (Δ 47 ) analysis by gas-source isotope ratio mass spectrometry[END_REF][START_REF] Dennis | Defining an absolute reference frame for 'clumped' isotope studies of CO 2[END_REF][START_REF] Bernasconi | Reducing Uncertainties in Carbonate Clumped Isotope Analysis Through Consistent Carbonate-Based Standardization[END_REF][START_REF] Fernandez | A Reassessment of the Precision of Carbonate Clumped Isotope Measurements: Implications for Calibrations and Paleoclimate Reconstructions[END_REF] and other lab protocols, differences in measured Δ 47temperature slopes probably reflect real differences in the samples themselves [START_REF] Tripati | Beyond temperature: Clumped isotope signatures in dissolved inorganic carbon species and the influence of solution chemistry on carbonate mineral composition[END_REF][START_REF] Kimball | Carbonate "clumped" isotope signatures in aragonitic scleractinian and calcitic gorgonian deep-sea corals[END_REF] , and are largely not affected by laboratory practices.

Our data also shows it may be possible to 'steepen' or 'shallow' the slope of a Δ 47temperature regression by undercorrecting or overcorrecting for non-linearity. This is particularly the case if there is a linear relationship between the sample's δ 47 value (related to δ 13 C and δ 18 O values) and Δ 47 value, i.e. if higher temperature samples have more negative δ 47 values. This can result in a situation where all the calibration samples, even when uncorrected for non-linearity, form a linear relationship with respect to formation temperature and Δ 47 value, as exemplified by the carbonates produced by Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] and used in this study. As such, the slope of the non-linearity correction plays a very important role in determining the slope of the final Δ 47 -temperature relationship, and under-or overcorrecting will affect the final slope. In the case of this study, as the non-linearity slope is positive, when uncorrected it results in a 'steepening' of the calculated temperature relationship. This relationship arises because the same sources of bicarbonate and deionized water were used to precipitate the Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] carbonates, so the δ 47 values (and particularly the δ 18 O values) become more negative at higher temperatures. Any laboratory-grown samples that use the same carbon and water sources for all temperatures could be sensitive to the same effects, and this phenomenon may be a possible explanation for the origin of the historical 'two slope' problem.

Update to Defliese et al (2015) Temperature Calibration

As part of this work, we recalculated the original data presented in Defliese et al [START_REF] Defliese | Compositional and temperature effects of phosphoric acid fractionation on Δ 47 analysis and implications for discrepant calibrations[END_REF] using the Brand et al [START_REF] Brand | Correction for the 17 O interference in δ 13 C measurements when analyzing CO 2 with stable isotope mass spectrometry (IUPAC Technical Report)[END_REF] isotopic parameters as recommended [START_REF] Daëron | Absolute isotopic abundance ratios and the accuracy of Δ 47 measurements[END_REF][START_REF] Schauer | Choice of 17 O correction affects clumped isotope (Δ 47 ) values of CO 2 measured with mass spectrometry[END_REF] . We can combine those results with measurements of those same samples from UCLA used in this study to present updated Δ 47temperature calibrations (Figure 3). We used the Δ 47 values produced by standardization with equilibrated gases and short time intervals for data from the University of Michigan (method 6 in Table 2), as carbonate standards were not analyzed at the University of Michigan. For the data from UCLA, we used the data standardized with both equilibrated gases and carbonate standards, and short time intervals (method 7 in Table 2). This analysis produced the following calibrations: All three of these calibrations are within error of each other, and are generally slightly steeper in slope (but still within error) than the calibration produced solely using data from the University of Michigan. Notably, recently published calibration studies [START_REF] Müller | Calibration of the oxygen and clumped isotope thermometers for (proto-) dolomite based on synthetic and natural carbonates[END_REF][START_REF] Kelson | Toward a universal carbonate clumped isotope calibration: Diverse synthesis and preparatory methods suggest a single temperature relationship[END_REF][START_REF] Petersen | Effects of Improved 17 O Correction on Interlaboratory Agreement in Clumped Isotope Calibrations, Estimates of Mineral-Specific Offsets, and Temperature Dependence of Acid Digestion Fractionation[END_REF][START_REF] Bonifacie | Calibration of the dolomite clumped isotope thermometer from 25 to 350 °C, and implications for a universal calibration for all (Ca, Mg, Fe)CO 3 carbonates[END_REF] have steeper slopes and smaller intercepts that do not overlap with these calibrations, suggesting that there are probably real differences in the absolute Δ 47 -temperature relationships among these carbonates, given that the Perspective IS (which should be immune to issues arising from the non-linearity correction) shows the same result as the UMich MAT 253 (Figure 3). If there is a universal calibration, it is likely that calibration studies encompassing a larger number of samples, measurements, and range of temperatures, such as Petersen et al [START_REF] Petersen | Effects of Improved 17 O Correction on Interlaboratory Agreement in Clumped Isotope Calibrations, Estimates of Mineral-Specific Offsets, and Temperature Dependence of Acid Digestion Fractionation[END_REF] , better capture the true Δ 47temperature relationship [START_REF] Fernandez | A Reassessment of the Precision of Carbonate Clumped Isotope Measurements: Implications for Calibrations and Paleoclimate Reconstructions[END_REF] .

Recommendations for Future Work

Carbonate clumped isotope measurements are in the process of becoming a mature technique, with new laboratories opening worldwide, each with slightly varying instrumental setup and procedures. Our results show that convergent results can be achieved using a variety of instrumentation and standardization procedures, which bears good news for the future application of the technique. However, our results do highlight that rigorous standardization is necessary to produce accurate data. Carefully chosen measurement windows using carbonate standards or a mix of carbonate and gas standards are ideal, and can yield results for the same set of samples that are comparable across multiple instruments.

In particular, the non-linearity correction must be monitored and corrected for, via one of the three techniques discussed above, and the ARF carefully constructed with reference frame variability characterized. In this analysis, conditions were typically more stable over a one month time frame (UCLA) than a 6 month time frame. The new generation of instruments improve long-term stability of the reference frame.

Our data also shows that the use of carbonate standards may offer an improvement in interlaboratory standardization (in our case, intralaboratory) versus the use of equilibrated gases alone, as demonstrated by the improvement in regression significance when using carbonate standards to build the ARF. This will probably vary depending on the skill of the worker making the equilibrated gases, as well as the physical setup of laboratory apparatus and instrumentation. As such, carbonate standards offer the advantage of being processed in a manner identical to sample materials, eliminating the unknown effect of phosphoric acid digestion, and limiting the 'human factor' associated with making equilibrated gases on manual vacuum lines. They are also much easier to transport and provide direct comparison across laboratories compared to equilibrated gases, which require a separate specialized vacuum line to prepare. As such, in step with other recent proposals [START_REF] Bernasconi | Reducing Uncertainties in Carbonate Clumped Isotope Analysis Through Consistent Carbonate-Based Standardization[END_REF] , we recommend the frequent use of carbonate standards within each laboratory's standardization scheme, whether in conjunction with equilibrated gases or replacing them entirely.

Conclusions

As clumped isotope geochemistry has evolved over time, and the number of users has expanded, there have been many different standardization techniques applied. We evaluated the effects of several of these different techniques on a common set of synthetic carbonates, and find that there can be significant effects caused by the use of different standardization techniques. Specifically, the non-linearity correction must be performed accurately when using a MAT 253 instrument, whether via equilibrated gases, carbonate standards, or the use of a pressure baseline correction. Our results show that undercorrecting for non-linearity can cause an apparent steepening in the slope of Δ 47 -temperature calibrations, and hypothetically a shallowing if overcorrected. In addition, our analysis suggests that the use of carbonate standards to place Δ 47 data in the absolute reference frame can improve interlaboratory data comparisons, as carbonate standards are not subject to the same types of human influences as equilibrated gases, while also capturing variability in acid digestion that is not recognized by equilibrated gases. Fortunately, the majority of standardization procedures that we investigated produced results that were comparable with one another, showing that prior data utilizing these methods with careful monitoring of reference frame variability is robust. This article is protected by copyright. All rights reserved. 2) versus equilibrated gases and carbonate standards (method 7 in Table 2). Note that all University of Michigan data uses method 6 (equilibrated gases only) in all figures. Dashed lines are 95% confidence intervals.

Red line: Data from the University of Michigan (all 8 samples). Grey line: Data from the UCLA Perspective IS (5 samples). Blue line: Data from the UCLA MAT 253 (4 samples). Black line: All combined data. A: Equilibrated gases only ARF (method 6), calculated using the Brand [START_REF] He | Pressure baseline correction and high-precision CO 2 clumped-isotope (Δ 47 ) measurements in bellows and micro-volume modes[END_REF] O correction.

  were analyzed on the 253This article is protected by copyright. All rights reserved.

  instrument at UCLA (25 °C calcite, and 5, 25, and 70 °C aragonite), versus 5 on the Perspective IS (5 and 25 °C calcite, and 5, 25, and 70 °C aragonite).

  3038 ± 0.0376 (All Data)

Table 6 :

 6 ANCOVA analysis of the regressions produced via the different standardization techniques on the UCLA MAT 253 mass spectrometer (denoted T in this table), plus the equivalent regression at the University of Michigan 253. A: P-values for each regression pair are listed in the matrix, with -for boxes that are self-comparison. Color coding indicates significance, green boxes produced statistically identical values (p-values > 0.1, reject different slope/intercept), yellow boxes are borderline different (0.1 > p-value > 0.05, statistically different at 90% confidence), and red boxes indicate significantly different values (p-value < 0.05, statistically different at 95% or greater confidence). *Indicates that the regression pair produces a statistically identical slope, but not a statistically identical intercept, with pvalues for common slope listed in part B. B: For regression pairs that are statistically different (p-value < 0.05), p-values of a test to determine common slope (i.e., temperature dependence), with same color coding as A.

Figure 1 :

 1 Figure 1: Plot the various Δ 47 -Temperature regressions from the UCLA Perspective IS instrument as well as the recalculated 5-point line from the University of Michigan. Temperature is in degrees Kelvin.Dashed lines are 95% confidence intervals. A: Regressions produced using a 6-month standardization window (methods 1-5). B: Regressions produced using a shorter, 1-month standardization window (methods 6-9).

Figure 2 :Figure 3 :

 23 Figure 2: Plot of the various Δ 47 -Temperature regressions from the UCLA MAT 253 instrument as well as the recalculated 4-point line from the University of Michigan. Temperature is in degrees Kelvin. Dashed lines are 95% confidence intervals. A: Regressions produced using a 6-month standardization window (methods 1-5). B: Regressions produced using a shorter, 1-month standardization 6-

Table 2 )

 2 : the temperature in Kelvin. Using the parameter set of Brand et al[START_REF] Brand | Correction for the 17 O interference in δ 13 C measurements when analyzing CO 2 with stable isotope mass spectrometry (IUPAC Technical Report)[END_REF] and equilibrated gases (method 6), the calculated regression for the University of Michigan MAT 253 is slightly different, though not at a statistically significant level (p = 0.4579):Subsetting only the four data points analyzed on the UCLA MAT 253 with the Brand et al[START_REF] Brand | Correction for the 17 O interference in δ 13 C measurements when analyzing CO 2 with stable isotope mass spectrometry (IUPAC Technical Report)[END_REF] parameter set and equilibrated gases (method 6), the calculated regression is also statistically identical (p = 0.931) to the original UM calibration:

	∆ 47 =	34841 ± 2293 𝑇 2	+ 0.3031 ± 0.0244
	where T is ∆ 47 = 34283 ± 1774 𝑇 2	+ 0.2870 ± 0.0189
	∆ 47 =	36693 ± 2899 𝑇 2	+ 0.2612 ± 0.0322
	Subsetting only the five data points analyzed on the UCLA Perspective IS with the Brand et al 36
	parameter set and equilibrated gases (method 6), the calculated regression is similarly
	statistically identical (p = 0.7753):
	∆ 47 =	35254 ± 2476 𝑇 2	+ 0.2751 ± 0.0284

Table 2 :

 2 Numbering scheme for the different standardization techniques used in this study. In future Tables, the institution and instrument used are identified followed by the numeric code for standardization technique, i.e. 'UCLA T 4' for the 6-month, no non-linearity correction, carbonate standards only ARF method using samples/standards analyzed on the UCLA Thermo MAT 253. Method 10 was not applied to the UCLA MAT 253 as we did not analyze enough ETH standards to perform the non-linearity correction in 2 out of 6 months.This article is protected by copyright. All rights reserved.

	Set	Slope 1 SE Intercept	1 SE
	University of	35254 2476 0.2751 0.0284
	Michigan MAT 253 (5
	point)
	UCLA Perspective 1	36720 4049 0.2757 0.0461
	UCLA Perspective 2	37310 4114 0.2624 0.0470
	UCLA Perspective 3	38730 4270 0.2486 0.0486
	UCLA Perspective 4	37300 4238 0.2652 0.0482
	UCLA Perspective 5	39250 4284 0.2426 0.0490
	UCLA Perspective 6	36360 3757 0.2865 0.0428
	UCLA Perspective 7	36690 3829 0.2794 0.0436
	UCLA Perspective 8	37980 3990 0.2680 0.0454
	UCLA Perspective 9	37210 3992 0.2768 0.0454

Table 4 :

 4 Slopes and intercepts for the ten different regressions calculated on the Perspective IS mass spectrometer at UCLA, plus the equivalent regression at the University of Michigan for the MAT 253. The equation solved is Δ 47 = Slope/T 2 + Intercept, where T is in Kelvin.

		UCLA	UCLA	UCLA	UCLA	UCLA	UCLA	UCLA	UCLA	UCLA
	UM 253	P1	P2	P3	P4	P5	P6	P7	P8	P9

Table 5 :

 5 ANCOVA analysis of the regressions produced via the different standardization techniques on the UCLA Perspective IS mass spectrometer (denoted P in this table), plus the equivalent regression at the University of Michigan 253. A: P-values for each regression pair are listed in the matrix, with -for boxes that are self-comparison.

	Color coding indicates significance, green boxes produced statistically
	identical values (p-values > 0.1, reject different slope/intercept), yellow boxes are borderline different
	(0.1 > p-value > 0.05, statistically different at 90% confidence), and red boxes indicate significantly
	different values (p-value < 0.05, statistically different at 95% or greater confidence). *Indicates that the
	regression pair produces a statistically identical slope, but not a statistically identical intercept, with p-
	values for common slope listed in part B. B: For regression pairs that are statistically different (p-value
	< 0.05), p-values of a test to determine common slope (i.e., temperature dependence), with same color
	coding as A. All regression pairs show a common slope, indicating statistical differences only in the
	intercepts.

This article is protected by copyright. All rights reserved.

Table 7 :

 7 Comparison of the ANCOVA analysis of the Perspective IS (abbreviated as P) and MAT 253 (abbreviated as T) instruments at UCLA. Only the standardization techniques utilizing 1-month windows are considered, as this is more representative of real-world practices. For this analysis, only the four samples measured on both instruments were considered. A: P-values for each regression pair are listed in the matrix, with -for boxes that are self-comparison. Color coding indicates significance, green boxes produced statistically identical values (p-values > 0.1, reject different slope/intercept), yellow boxes are borderline different (0.1 > p-value > 0.05, statistically different at 90% confidence), and red boxes indicate significantly different values (p-value < 0.05, statistically different at 95% or greater confidence). *Indicates that the regression pair produces a statistically identical slope, but not a statistically identical intercept, with p-values for common slope listed in part B. B: For regression pairs that are statistically different (p-value < 0.05), p-values of a test to determine common slope (i.e., temperature dependence), with the same color coding as A.

This article is protected by copyright. All rights reserved.

Acknowledgements

The work was funded by the Department of Energy through BES grant DE-FG02-13ER16402. Travel to present this work at a conference was partially supported by the "Laboratoire d'Excellence" LabexMER (ANR-10-LABX-19) and co-funded by a grant from the French government under the program "Investissements d'Avenir".


Jieli Lyu

Valérie Geertsen

Cyrille Hamon
email: cyrille.hamon@universite-paris-saclay.fr

Doru Constantin
email: doru.constantin@universite-paris-saclay.fr

Determining the morphology and concentration of core-shell Au/Ag nanoparticles *

Accurately measuring the shape, structure and concentration of nanoparticles (NPs) is a crucial step towards understanding their formation and a prerequisite for any applications. While determining these parameters for single-metal NPs is by now rather routine, reliably characterizing bimetallic NPs is still a challenge. Using four complementary techniques: transmission electron microscopy (TEM), light absorbance spectroscopy (AS), small-angle x-ray scattering (SAXS) and inductively coupled plasma mass spectrometry (ICP-MS) we study bimetallic nanoparticles obtained by growing a silver shell on top of a gold seed. The initial quasi-spherical objects become faceted and grow into a rounded cube as the molar silver-to-gold ratio K increases. The shape evolution is well described by SAXS and TEM. The shell thickness, overall size polydispersity and number particle concentration obtained by the various methods are in good agreement, validating the use of non-invasive in situ techniques such as AS and SAXS for the study of bimetallic NPs. * Electronic Supplementary Information (ESI) available: TEM images and associated histograms of particle sizes, calculations of the SAXS form factor, calculations of the UV-Vis extinction spectra of core-shell objects in the LWA approximation and BEM simulations of the UV-Vis extinction spectra.

Introduction

Synthesizing nanoparticles with carefully chosen properties (optical, magnetic, catalytical etc.) is one of the main goals of materials science. These properties depend on the shape and composition of the particles, and measuring these parameters accurately is an essential prerequisite to developing a reliable formulation process.

Noble metal nanoparticles are particularly interesting due to their optical properties, related to the presence of plasmon resonance (very sensitive to the particle shape) and due to the richness of synthesis methods that can yield a large variety of shapes and sizes, with very good yield and relatively low polydispersity. Bimetallic particles consisting of a gold core covered with a silver shell offer further control over the optical properties and exhibit lower dissipation in the visible range. [1][2][3][4][5] Before any application, it is indispensable to determine the particle concentration, as well as their average morphology (size, shape, rounding) and their distribution. Ideally, these parameters should be determined by non-invasive techniques, directly applicable in the reaction medium and time-resolved. The typical example is UV-Vis-IR absorbance spectroscopy (AS) c , but several groups have shown that small-angle X-ray scattering (SAXS) can also provide valuable information [6][7][8][9][10] . Although the presence of two constituents complicates the application of these methods to bimetallic objects, recent studies point the way towards a deeper understanding of their structure and evolution 5,11 . An important source of progress over the last decade has been the improvement in synthesis protocols, yielding particle populations with better size and shape monodispersity, and allowing the extraction of more information using the various characterization techniques. In turn, this information can be used to further improve the synthesis protocols.

1 Our goal in this paper is to apply AS and SAXS to a series of samples where the particle morphology is modified systematically by changing a reaction parameter and to validate the information by cross-checking the results and by comparing them with two other methods: transmission electron microscopy (TEM) and inductively coupled plasma mass spectrometry (ICP-MS) that require extracting the particles from their environment. More specifically, we synthesize core-shell Au/Ag nanoparticles by growing a silver shell on top of a spherical gold seed, for various values of the molar ratio K between silver precursor and gold. At low K, the shell is quasi-spherical (probably rhombicuboctahedral 11 ), while at higher K it becomes cubic. We measure the size and shape of the objects by SAXS and TEM and their concentration by SAXS, AS and ICP-MS and compare the results of the various techniques.

Materials and Methods

Particle synthesis

Materials:

All the reactants were purchased from Sigma-Aldrich and used without further purification: hexadecyltrimethylammonium bromide (CTAB, ≥ 99%), hexadecyltrimethylammonium chloride (CTAC, 25 wt% in H2O), hydrogen tetrachloroaurate trihydrate (HAuCl 4 • 3H 2 O, ≥ 99.9%), silver nitrate (AgNO 3 , ≥ 99%), L-ascorbic acid (AA, ≥ 99%), sodium borohydride (NaBH 4 , 99%). Water purified by reverse osmosis with a resistivity (> 15 MΩ.cm) was used in all experiments.

Gold sphere synthesis:

Gold spheres (AuSph) were prepared by seed-mediated growth involving two overgrowth steps:

• Seeds were prepared by mixing 50 µL of a 0.025 M HAuCl 4 solution with 4.7 mL of a 0.1 M CTAB solution in a 20 mL scintillation vial at 30 • C; 300 µL of a freshly prepared 0.01 M NaBH 4 solution was then injected under vigorous stirring. The mixture was left undisturbed at 30 • C for at least 1h.

• S1 spheres: In a 20 mL scintillation vial, a growth solution was prepared by mixing 120 µL of a 0.025 M HAuCl 4 solution with 10.5 mL of a 0.094 M CTAC solution. Then, 4.5 mL of AA at 0.1 M and 300 µL of the seed solution were added in sequence under vigorous stirring. The mixture was left undisturbed at room temperature for at least 1h.

• S2 spheres: In a 200 mL Erlenmeyer flask, a growth solution was prepared by mixing 1200 µL of a 0.025 M HAuCl 4 solution with 100.5 mL of a 0.094 M CTAC solution. Then, 40.5 mL of AA at 0.1 M and 300 µL of S1 solution was added in sequence under vigorous stirring. The mixture was left undisturbed at room temperature for at least 1h. The AuSph were centrifuged and redispersed in 10 mM CTAC before further use.

Silver shell growth:

Overgrowth was performed according to recently published protocols 4,5 . The purified S2 described above were centrifuged at 8500 g for 30 min and redispersed in a 10 mM CTAC solution at a final gold concentration of 0.25 mM in all samples. Silver and ascorbic acid were added in sequence to avoid silver particle formation. The molar ratio between the AA and the Ag precursor was fixed to 4 in all experiments. The silver-to-gold molar ratio K (Ag ions per Au atoms in the AuSph, at the beginning of the process) was varied between 0.1 and 8. For instance, in the case of K = 2, 50 µL of a 0.1 M AgNO 3 solution was injected in 10 mL S2 suspension. After brief shaking, the solution was supplemented with 50 µL of a 0.4 M AA solution, shaken again and kept at 60 • C for 3h.

Particle geometry

The particles are described as gold spheres with radius R centered within silver shells of thickness t, and hence with outer radius R + t (sphere-in-sphere model), or within cubes of size a (sphere-in-cube model). In the latter situation we define the thickness t = a/2 -R. We denote by K = ν Ag ν Au the molar Ag/Au ratio for the individual particles. The corresponding volume ratio is given by f K, with f =

M Ag M Au ρ Au ρ Ag = 1.008. If K is known, t is given by: t = R (1 + f K) 1/3 -1 (1a)
for a sphere in sphere and by:

t = R (1 + f K) 1/3 (π/6) 1/3 -1 , for f K > (6/π -1) (1b)
for a sphere in cube. Note that, in Eq. ( 1b), the sphere-in-cube model is only defined above a minimal Ag/Au ratio K min = f -1 (6/π -1) 0.903 below which the Ag amount is not enough to form a complete cubic shell around the core sphere.

Transmission electron microscopy

The solutions were concentrated by slow centrifugation to a final Au 0 concentration of 0.75 mM in 0.55 mM CTAB. 10 µL of this solution was then dropped on a carbon-coated grid and dried at 70 • C. Transmission electron microscopy (TEM) images were obtained with a JEOL 1400 microscope, operating at an acceleration voltage of 120 kV. To extract the particle size, we analyzed the images using the ImageAnalyzeParticles operation in Igor Pro 7.0. The individual particles were modeled as ellipses with half-axes a and b and their equivalent radius was computed as R = √ ab. Due to the low relative contrast between gold and silver only the outer boundary of the particles was detected, so R corresponds to the radius of the complete object. The quadraticity parameter Q (area ratio of circumscribed square to particle) was extracted using the minboundrect function 12 implemented in MATLAB.

Small-angle x-ray scattering

The SAXS measurements were performed on the SWING beamline of the SOLEIL synchrotron (Saint-Aubin, France.) The sample-to-detector distance was 6.5 m and the beam energy E = 12 keV, covering a scattering vector range 0.0015 < q < 0.2 Å -1

. The beam size was approximately 500 × 200 µm 2 (H ×V ). The solutions were filled into round glass capillaries, with an outer diameter of 1.4 mm and 10 micron-thick walls, purchased from WJM-Glas (Berlin, Germany), placed vertically in a motorized holder. The capillaries were filled with the sample solution and sealed at the top using a glue gun to prevent evaporation. All measurements were performed at room temperature (22 • C).

The scattered signal was recorded by an Eiger 4M detector (Dectris Ltd., Switzerland) with pixel size 75 µm. Preliminary data treatment (angular averaging and normalization) was done using the software Foxtrot developed at the beamline and yielded the intensity as a function of the scattering vector I(q) in absolute units. Subsequent data modeling was done in Igor Pro 7.0 using functions available in the NCNR SANS package [START_REF] Kline | [END_REF] (SchulzSpheres used to model the initial Au particles, before Ag addition and PolyCoreShellRatio used for the sphere-in-sphere model) and a model developed in-house for the sphere in cube (see the ESI † for the details.) The latter is a simplified version of the algorithm presented in Ref 14.

UV-Vis absorbance spectroscopy

The solutions were shaken and pipetted into polystyrene cuvettes with 1 cm optical path. We used a Cary 5000 spectrometer (Agilent) to measure the extinction spectrum between 200 and 1200 nm, in a dual-beam configuration with a water-filled cuvette in the reference path.

BEM simulations

Simulated extinction spectra were calculated by the boundary element method (BEM), using the MNPBEM toolbox developed in the MATLAB environment. 15 . This numerical technique allows a very detailed description of the particle shape and the use of the full Maxwell equations, including retardation effects. It is however very demanding in computation time (tens of minutes for a given particle) and thus cannot be included in a fitting routine.

Analytical model for the extinction

Rigorous analytical solutions exist for homogeneous and core-shell spherical particles in the framework of Mie theory 16,17 . While computationally tractable, the full Mie theory is not always necessary for objects much smaller than the wavelength. Furthermore, using the complete formalism can sometimes obscure the role of the various parameters in the evolution of the spectra.

We therefore start from the Rayleigh (or quasistatic) approximation, corresponding to the first term of Mie theory. This model yields very simple formulas for the extinction spectrum of homogeneous and core-shell spherical particles [START_REF] Bohren | Absorption and Scattering of Light by Small Particles[END_REF] . For larger particle sizes, the deviation from the Rayleigh regime is accounted for in the long-wavelength approximation (LWA) [START_REF] Meier | [END_REF] , as applied to a core-shell object by Chung et al. [START_REF] Chung | [END_REF][START_REF] Chung | [END_REF] . We validate the model by comparing it to BEM simulations. The full calculation details and the comparison to the BEM spectra are presented in the ESI †.

Inductively coupled plasma mass spectrometry

Inductively coupled plasma mass spectrometry (ICP-MS) yields the elemental concentration in solution, with very few assumptions. It is therefore a very robust technique, but it provides no information as to the size and shape of the objects. The gold and silver concentrations were determined using an iCAP Q Thermo Electron instrument after external calibration by dilution of multi-element standard solutions (SPEX, MS3 for gold and MS2 for silver). Measurements were repeated six times before averaging. All dilutions (samples and standards) were prepared by weight. Gold determination was performed at mass 198 in hydrochloric media. Silver was measured at mass 107 and 109 and before averaging. The silver determination is performed in nitric media. Sample dilutions were performed as follows: samples were heated in a bath at a temperature of 30 • C to avoid CTAB solidification. A 10 µL aliquot of sample was added to a polypropylene vial. On the aliquot was poured 10 µL of aqua regia saturated with NH 4 Cl to dissolve both gold and silver [START_REF] Pollard | [END_REF] . Sample dilution was then realized by addition of diluted hydrochloric or nitric acid. Both hydrochloric acid and nitric acid were purified previously by distillation. The same protocol was repeated for standards except that stock standard solutions were not heated. 3 Particle size and shape

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Transmission electron microscopy

We performed TEM measurements on nine samples, with K = 0, 0.4, 0.7, 0.9, 1.2, 1.4, 2, 4, and 8. Some representative image selections are shown in Figure 1. More images are shown in the ESI †.

The size of the gold core was extracted from the initial population, before the addition of silver (molar ratio K = 0), yielding a radius R 0 = 13.0 nm. The shell thickness for each K > 0 was obtained by subtracting R 0 from the mean equivalent particle radius R K at that given K. The polydispersity is computed as the standard deviation of the radius distribution divided by its mean: p K = σ K / R K . These parameters are compared to the SAXS data (see below.)

The shape of the particles can be assessed using the quadraticity Q, defined as the ratio between the area of the smallest circumscribed square and that of the particle projection. This parameter is 1 for a perfect square, 4/π for a perfect circle and can be even larger for anisotropic or irregular shapes.

The mean quadraticity Q is shown in Figure 2 (left panel): at first glance, it seems to decrease linearly with K, as shown by the fit. However, the large standard deviations call for a more refined analysis. To this end, we plot in the same Figure (right panel) the histograms of Q for each K value. We can separate three regimes, identified by line color: At low K ≤ 0.7 (black line), the distributions are monomodal, relatively narrow and centered around the 4/π value corresponding to a perfect circle. Almost all particles are spherical. At intermediate K (blue line) the distributions are wide and possibly bimodal, with one spherical subpopulation and one with Q 1.15. At high K ≥ 2.0 (red line) the distributions are once again monomodal, with a decreasing mode but with a substantial contribution at higher Q. This contribution is almost absent for K = 8.0, as shown by the reduced std. dev. The cubes become predominant at K = 2.0, so we can locate the shape transition between 1.4 and 2.0.

Small-angle x-ray scattering

We recorded the azimuthally averaged scattered intensity I(q) as a function of the scattering vector q for all samples in dilute solutions. The data is shown in Figure 3, along with fits using both sphere-in-sphere and sphere-in-cube models (Eqs. (1a) and (1b), respectively.) For coherence, the latter model was only used for molar Ag/Au ratios above K min 0.903; attempts to fit curves at lower ratios yield unphysical results (cube sizes a < 2R.) We fixed throughout the core radius R = 12.4 nm, value obtained by fitting the data for K = 0.

The goodness-of-fit function χ 2 divided by the number of experimental points N pts is shown in Figure 4 for Figure 3 Scattered intensity I as a function of the scattering vector q for all solutions (dots, various colors). The spectra were shifted vertically for clarity. The molar Ag/Au ratio K is indicated above each curve. Fits with the sphere-in-sphere model (solid lines) and with the sphere-in-cube model (dashed lines) are displayed for each curve. all the fits displayed in Figure 3. The fit quality is better for the sphere-in-sphere model below K = 1.4 and for the sphere-in-cube model above K = 2, in agreement with the visual inspection of Figure 3. The oscillations between 0.03 and 0.1

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are very revealing: they are deep for spheres and shallow for cubes and are very well described by the corresponding model at low and high K, respectively. In the intermediate range (0.9 ≤ K ≤ 1.6) both models are unsatisfactory due to the shape polydispersity illustrated in Figure 2.

In Figure 5 we plot the thickness t extracted from the fits in Figure 3 (solid squares for sphere-in-sphere and open dots for sphere-in-cube) and the TEM values (diamonds). We also plot the thickness values predicted by Eqs. (1a) and (1b) (solid and dashed line, respectively) assuming that the Ag/Au ratio for each particle is the experimental one K in the reaction medium (i.e. that all the Ag ions are used to form shells and that all particles have the same morphology.)

Both SAXS models include a homothetical polydispersity, plotted in Figure 6, alongside the TEM values. The latter are in good agreement with the sphere-in-sphere model up to K = 2 and with the sphere-in-cube model above this value.

Silver-to-gold ratio

Using ICP-MS we can determine the Ag/Au ratio within the particles; we plot it against their ratio in solution, K, in Figure 7. The diagonal line is the expected value if the reaction proceeded to completion and the two parameters are equal. The same line corresponds to the solid/dashed curve in Figure 5 for the spherical/cubical shell model. The experimental values follow K with considerable variability: their ratio fluctuates between 0.74 and 1.74.

Particle concentration

The concentration of particles in solution is of course a very important parameter; it can be obtained from full-curve fitting of the AS 23 or SAXS 24 curves or, for homogeneous gold nanoparticles, in an easier manner from the near-UV extinction 25,26 or from the integrated invariant, respectively 27 . ICP-MS gives access to the molar concentration of Au and Ag separately (in different measurements.) Each of these techniques uses a completely different principle. A full analysis of the SAXS data gives access to both the size and the number density of the particles, while the other techniques only yield their product, i.e. the volume concentration. For bimetallic objects, no simple method exists, either in SAXS or AS; it is therefore necessary to model the entire experimental curve. Since the scattered intensity I(q) is measured in absolute units, it is directly proportional to the number density n. In Figure 8 we plot (as solid squares) this parameter as a function of the molar ratio K for the sphere-in-sphere model (the results of the sphere-in-cube model are within 9% of these values.)

The number density also appears in the model for the extinction spectra. We fit the experimental data with the sphere-in-sphere model, where only n and a constant background are adjustable parameters: the core radius R and the shell thickness t are fixed at the values obtained from the SAXS data using the same model. The SAXS values for n are more scattered than the AS ones and some points (circled in Figure 8) are very low. The ICP-MS results are close to the SAXS ones at low K ≤ 1 and above the AS at K ≥ 2.

Conclusions

The particle populations have excellent monodispersity p (between 5 and 10 %) as measured by SAXS and TEM (see Figure 6) and confirmed by the agreement between the calculated and predicted shell thickness (see Figure 5). Analysis of the TEM images (see Figure 2) shows a transition between quasi-spherical and cubic shapes between K = 1.4 and 2, while the quality of the SAXS fits finds the transition at about K = 2: the two techniques are in very good agreement! The values for the particle concentration n obtained by three techniques are in good agreement (within 40% of their average), except for some low-value SAXS points. The systematic difference between the techniques is lower than the spread of values for each technique, highlighting the importance of careful sampling protocols: sample agitation to ensure homogeneity and avoid the appearance of concentration gradients, temperature control to prevent surfactant crystallization, weighing the aliquots rather than relying on pipetting volumes (which are not always accurate for surfactant solutions.)

Among the four methods used, SAXS yields the most information about the particles: the size, polydispersity, shape and concentration are accurately determined, as shown by very good agreement with the other techniques. This result validates the use of SAXS for studying complex (bimetallic and aspherical) nano-objects, statically or during their growth. However, the particles must be reasonably monodisperse in order to take full advantage of this technique. Of course, scattering methods only yield indirect information and imaging techniques remain essential for identifying the particle shapes and choosing the appropriate model, so TEM should always be used as a complement.

Figure 1

 1 Figure 1 TEM images for different values of the molar ratio K.

Figure 2

 2 Figure 2 Quadraticity parameter Q. Left: average value Q as a function of K (mean and standard deviation, solid dots and error bars) with linear fit (solid line). The limiting values for a perfect circle and square are shown as dashed lines. Right: Histograms of Q for each K value (shifted vertically for clarity.) The mean and std. dev. from the left panel are shown under each curve. Colors (black, blue and red) distinguish three types of curves (see text.)

Figure 4

 4 Figure4 Goodness-of-fit function for the SAXS models in Figure3, shown as solid squares (for the sphere-in-sphere model) and as open circles (for the sphere-in-cube model) as a function of the Ag/Au ratio K.

Figure 5 Figure 6 Figure 7

 567 Figure 5 Shell thickness extracted from the fits in Figure 3 for the two models and corresponding geometrical predictions (see the text for more details.) The TEM values are shown as red diamonds.

  The results are plotted in Figure 8 as open dots. From the mass gold concentration c Au measured via ICP-MS we determine n = c Au ρ Au 3 4πR 3 (where R = 12.4 nm is the radius determined by SAXS) and plot it in Figure 8 as diamonds.

Figure 8

 8 Figure 8 Number particle density n as a function of the Ag/Au ratio K, extracted from fitting the SAXS data in Figure 3 (solid black squares), from the UV-Vis absorbance data (open red dots) and from ICP-MS (blue diamonds). Anomalously low SAXS values are circled.

Acknowledgements

JL acknowledges financial support by the China Scholarship Council (CSC). The SOLEIL synchrotron is acknowledged for the provision of beamtime and Thomas Bizien for his support. We thank Claire Goldmann for the preparation of some nanoparticle batches and for continuous experimental support.

Conflicts of interest

There are no conflicts to declare.