Abstract

# Abstract

Rationale: Clumped isotope geochemistry is concerned with measuring the natural abundance of isotopic molecules, unit cells and other moieties that contain two or more rare stable isotopes. Accurate measurement of the abundance of such multiply substituted species using isotope ratio mass spectrometry (IRMS) techniques imposes stringent requirements on instrument performance in terms of overall sensitivity, linearity etc. that are difficult to achieve. To meet these requirements we have designed, constructed and evaluated the performance of a new IRMS that is optimised for clumped isotope ratio measurements of CO$$_{2}$$.

Methods: Following an analysis of the factors that limit the performance of existing IRMS instrument designs for clumped isotope measurements we determined an optimum instrument/magnet geometry using ion optic transfer matrix methods, and considering aberrations up to second order. Before the final engineering design the individual component ion optics (source and faraday collectors) were modelled using SIMION. The instrument has a 120$$^{o}$$, symmetric extended geometry with a gas dual-inlet. Construction is based on standard UHV principles. Instrument control and data acquisition is based on National Instruments compactRIO hardware and LabVIEW software.

Results: We demonstrate that the MIRA mass spectrometer has excellent sensitivity (<500 CO$$_{2}$$ molecules.ion$$^{-1}$$) combined with high abundance sensitivity and a linear response in terms of measured $$\Delta_{47}$$ over a 100‰ range in measured absolute isotope composition ($$\delta^{47}$$) with respect to the working reference gas of the mass spectrometer. Precision of measured $$\Delta_{47}$$ is at the shot noise limit of <0.01‰ for a standard measurement cycle of 80 minutes duration. Long term stability of the instrument and measurements is excellent.

Conclusions: The MIRA instrument can measure CO$$_{2}$$ isotopologues to a high precision (0.01‰ for $$\Delta_{47}$$). The instrument is linear and has sufficient sensitivity for both high sample throughputs (12 measurements per 24 hour cycle) and the analysis of gas samples down to 10$$^{-5}$$ moles in size.

# Introduction

Multiply substituted isotopologues are molecules, formula units and other moieties in which there are two or more isotopic substitutions by rare, usually heavy isotopes. In geochemistry they are commonly referred to as clumped isotopes and over the past ten years there has been a growing interest in measuring the variability of their abundance in naturally occurring materials (Wang 2004)(Eiler 2007). The most widely developed application has been the isotope thermometry of carbonate minerals, particularly those that are characteristic of conditions at the surface and in the upper crust of Earth and even Mars (Came 2007)(Affek 2008)(Daëron 2011)(Swanson 2012)(Halevy 2011). However clumped isotope studies in other systems, including tropospheric and stratospheric CO$$_{2}$$ (Eiler 2004)(Affek 2006)(Affek 2007) and stratospheric O$$_{2}$$ (Yeung 2012) point to potentially important applications across a wide range of problems in the atmosphere, biosphere and solid earth.

To date virtually all published measurements have been made using commercially available Thermo-Finnigan 253 gas source isotope ratio mass spectrometers that have been modified to include a six faraday cup collector array with amplifier gains optimised for measurement of isotopologues of CO$$_{2}$$ and O$$_{2}$$ ( see (Huntington 2009)). In addition there are a small but increasing number of published studies using smaller radius sector instruments such as the Thermo-Finnigan Delta XP IRMS ((Yoshida 2012)Yoshida:2013kw ) and the Elementar IsoPRIME (Rosenheim 2013)(Tang 2014). These studies demonstrate that it is possible to make measurements of multiply substituted isotopologues in the analyte gases CO$$_{2}$$ and O$$_{2}$$ at sufficient precision for geochemical studies. This is despite the low nominal abundance of multiply substituted isotopologues. For example the variability in abundance of the mass 47 isotopologue in CO$$_{2}$$ (dominated by $$^{18}$$O$$^{13}$$C$$^{16}$$O) can be determined to a precision of better than 0.01‰ despite its low nominal concentration of approximately 44ppm (Huntington 2009) and references therein).

The abundance of an isotopologue is expressed as an excess value determined with respect to the theoretical stochastic abundance (Wang 2004):

${\Delta _{47}} = \left( {\frac{{{R_i}}}{{R_i^*}} - 1} \right) \times 1000$

where R$$_{i}$$ represents the measured abundance ratio of isotopologue i relative to that of the non-isotopically substituted isotopologue, and R$$^*$$ represents the abundance ratio for the isotopologue when all the isotopes are randomly distributed. This stochastic abundance ratio is calculated from the measured bulk isotopic composition of the sample.

Not-with-standing the fact that high precision measurements of $$\Delta_{47}$$ in CO$$_{2}$$ can be made the procedure requires careful calibration to correct for instrument dependent analytical artefacts. The two most important of these are: (i) so called ’non-linearity’ of the measured $$\Delta_{47}$$ value as a function of the bulk isotopic composition of the sample, and (ii) scrambling of the clumped isotope signal resulting in scale compression.

Non-linearity refers to a divergence between the measured and true $$\Delta_{47}$$ value with increasing difference in bulk isotopic composition between the sample and instrument working reference gas. This is characterized as a linear trend with positive slope in plots of apparent $$\Delta_{47}$$ versus $$\delta^{47}_{(sam-wrg)}$$ for gas samples that have the same $$\Delta_{47}$$ value. The trends are best observed using gas samples that have been heated to 1000$$^{\circ}$$C in order to randomize the isotope distribution (the so-called heated gas line). The cause of the dispersion in $$\Delta_{47}$$ values is not fully understood. Careful observation shows the non-linearity is associated with a negative offset in the baselines of the minor isotopologue peaks when analyte gas is introduced to the mass spectrometer ((He 2012)(Bernasconi 2013)). The magnitude of the offset increases with the analyte gas pressure within the analyser and is termed the Pressure Base Line (PBL) effect. The offset is widely thought to be associated with a negative current to the faraday cups. Whilst this can result from a flux of positive secondary ions away from individual faraday cups it is more likely to be due to insufficient screening of secondary electrons that arrive at the faraday cup assemblies ((Huntington 2010)(He 2012)(Bernasconi 2013)). He et al. (2013) speculate that the secondary electrons result from interaction between the major ion beam and the flight tube of the instrument after the beam has passed through the deflecting field of the magnet.

The magnitude of the non-linearity effect varies from instrument to instrument and is also observed to change in a secular fashion with both slow drift and step changes. Gradients in plots of $$\Delta_{47}$$ *versus* $$\delta^47$$ vary between 0.006 to 0.05 (e.g. (Huntington 2009)(Rosenheim 2013)) to a near neutral response of 0.0011 ((Yoshida 2012)). Given that the $$\delta^{47}_{(sam-wrg)}$$ value is approximately the sum of the $$\delta^13C_{(sam-wrg)}$$ and $$\delta^{18}O_{(sam-wrg)}$$ values then $$\delta^{47}_{(sam-wrg)}$$ values of $$\pm$$10 to $$\pm$$ 20 ‰ are regularly observed during analysis of natural carbonates assuming a working reference gas close in composition to CO$$_{2}$$ derived from a typical marine carbonate. Thus corrections of as much as 0.5 to 1‰ in $$\Delta_{47}$$ are not uncommon for those instruments that are markedly non-linear.

Several different procedures for correction of non-linearity have been proposed including: (i) a simple transfer function involving extrapolation of measured $$\Delta_{47}$$ values parallel to the heated gas line towards a zero $$\delta^{47}_{sam-wrg}$$ value ((Huntington 2009)), and; (ii) correction of peak intensities with explicit compensation for the PBL effect by measurement of the magnitude of the baseline shift ((He 2012)(Bernasconi 2013)(Rosenheim 2013)). That we still don’t have a full understanding of the PBL effect and it’s causes is shown by the fact that different results are obtained when directly comparing both correction methods using the same heated gas data ((Rosenheim 2013)).

Scrambling in the ion source results from ion-molecule interactions with ion induced dissociation and recombination of CO$$_{2}$$ ion fragments resulting in a degree of randomization of the isotope distributions. The net effect of this is a scale compression of the clumped isotope signal with measured $$\Delta_{47}$$ values being smaller than predicted from thermodynamic considerations (Dennis 2011). The degree of scale compression appears to be a function of source pressure, gas and ion residence time within the ion source, and possibly electron current and energy (Huntington 2009) with values ranging from close to 1 to as low as 0.7. Since one is wanting to measure to high precision small excess values on rare clumped isotopes it is advantageous to maximize the signal by using high source pressures and electron currents. Thus whilst the full details of the electron-molecule/ion interactions in the source are not fully understood it is important that they are subject to detailed investigation. In the absence of a phenomenological or constitutive description of the scrambling effects a protocol for normalizing analytical data to a theoretical reference frame scaled according to statistical mechanical calculations of the expected isotopologue distributions based on spectroscopic data for CO$$_{2}$$ has been proposed and implemented by most laboratories (Dennis 2011). The method is based on measuring gases that have a varying degree of isotope ordering as a result of equilibration at different temperatures and comparing the measured excess to theoretically calculated values. When results obtained from different instruments and laboratories are scaled according to this scheme data are found to be in good agreement (Dennis 2011).

Given the rapidly growing interest in clumped isotope measurements and the known instrumental effects that are characteristic of current commercially available instruments we have designed a new isotope ratio mass spectrometer that has excellent performance particularly with respect to linearity and sensitivity. The MIRA (Multi Isotopologue Ratio Analyser) employs a symmetric 120$$^{\circ}$$ extended geometry that optimizes beam transmission and beam quality. In this paper we describe the ion optics design, basic construction details and analytic performance of MIRA. In particular we demonstrate that the MIRA design is linear with no dispersion of the measured $$\Delta_{47}$$ value with bulk isotopic composition. A secondary aim was for an engineering and electronics design that was accessible to typical university mechanical and electronic workshops. The overall construction is based on standard UHV principles employing readily available CF fittings etc.