Introduction
Multiply substituted isotopologues are molecules, formula units and other moieties in which there are two or more isotopic substitutions by rare heavy isotopes. In geochemistry they are commonly referred to as clumped isotopes, and over the past 13 years there has been considerable progress in the development of analytical techniques that can measure with sufficient accuracy and precision their variability in naturally occuring gases and solids \cite{Eiler_2004,Eiler_2007,Huntington_2009,Rosenheim_2013,Yoshida_2012}\cite{Eiler_2004}\cite{Eiler_2004,Huntington_2009}\cite{Eiler_2004} . The most widely developed application has been Isotope thermometers of carbonate minerals, particularly those that are characteristic of conditions at the surface and in the upper crust of Earth and even Mars \cite{Came_2007,Affek_2008,Da_ron_2011,Swanson_2012,Halevy_2011}
Not-with-standing this progress there are a number of unresolved issues relating to both sample preparation and analysis. These include mass spectrometer sensitivity, non-linearity, scale compression and the algorithm and constants for correction of the \(^{17}\)O contribution to the m/z = 45 signal and hence the \(\)\(\delta^{13}\)C value \cite{Huntington_2009,Dennis_2011,Bernasconi_2013,Rosenheim_2013,Da_ron_2016} and the effects of contamination of the analyte gas on measured clumped isotope compositions \cite{Eiler_2004,Huntington_2009,Petersen_2015}.
With systematic and careful calibration of mass spectrometer characteristics using gases equilibrated at high and low temperatures it is possible to translate data onto an absolute reference frame in which the data are scaled according to the theoretical value of \(\Delta_{47}\) assigned to CO2 equilibrated at both 1000o and 25o C \cite{Dennis_2011}. Dennis et al. (2011) convincingly demonstrate that for carbonates used in an inter-laboratory comparison the data from different laboratories are in agreement when transferred to the absolute reference frame. It is then somewhat surprising that attempts to calibrate the clumped isotope thermometer by different groups, albeit using different methods and samples (collection of natural biogenic and inorganic samples from well characterised environments, laboratory inorganic precipitation experiments etc.) yields a range of absolute clumped isotope values and temperature sensitivities. \cite{Sawaki_2010}
A key factor limiting the accuracy and precision of clumped isotope measurements and one that may be critical in understanding the range of published calibrations is the purity of the analyte gas. The major multiply substituted isotopologue in CO2 derived from carbonates by reaction with phosphoric acid is 18O13C16O which is present at a nominal abundance of approximately 44 × 10-6. Its abundance relative to the theoretical stochastic abundance in a sample is represented by the Δ value, defined as \cite{Wang_2004}:
\(\Delta_{47}=\left(\frac{R_{47}}{R_{47}^{\cdot}}-1\right)\)