Contributions to the Measurement of Absolute Isotope Ratios of Carbon Dioxide by the Gravimetric Mixture Approach

Carbon dioxide is together with water vapour, methane and nitrous oxide one of the major
contributors to the atmospheric greenhouse gas concentration. The atmospheric concentration of carbon dioxide is heavily and continuously increasing since the beginning of the
industrialization, and its contribution to the global warming is commonly accepted. Due
to the roll of carbon dioxide in the global carbon cycle and its global warming potential
the isotopic composition of carbon dioxide is of great interest since it is an important
analytical tool. This tool helps to understand the global carbon flux and to discriminate
between anthropogenic and natural sources and thus it also helps to verify and control
emission regulations and in the end to reduce the emission.
The isotopic composition of carbon dioxide is measured with the highest achievable accuracy by mass spectrometry. With mass spectrometers only the measured ion intensity
ratios are directly available. These measured ion intensity ratios differ from the actual
isotope ratios and correction is needed. This difference is commonly known as mass bias,
which is a collective term for all the effects that lead to this difference. Unfortunately, mass
bias cannot be avoided completely, it can only be reduced. As mass bias is inevitable, it
is common praxis to use a certified isotopic reference material. By comparing the certified
isotope ratios with the measured ratios, mass bias correction factors (K-factors) can be determined. With these correction factors also the measured intensity ratios of the unknown
sample can be corrected, provided both the reference and the sample were measured in
the same sequence and under the same conditions.
In the case of the isotopic variations of carbon dioxide, this reference is NBS19, which is
used to report relative differences between a virtual calcite (called VPDB) and the sample.
These differences are reported on the international VPDB δ scale. There are two major
problems with this scale. The first problem is that the absolute isotope ratios of NBS19
(and hence VPDB) are not known in a way that they are traceable to the base unit mole.
This is the reason for the usage of the relative differences. The lack of traceability to the
mole can lead to comparability issues between different laboratories and makes the whole
reference scale vulnerable to drifts of the defining material, NBS19.
The second major problem is, that NBS19 is out of stock and cannot be ordered any
more, this endangers the whole scale and makes it difficult to continue the scale without
increasing uncertainties by introducing a new reference material. For these reasons the
knowledge of absolute isotope ratios of carbon dioxide is urgently needed, since then the
above mentioned problems would be solved.
VII
In this cumulative thesis it is presented for the first time how K-factors can be calculated
analytically for systems with more than three isotopes. In addition to the calculation
of the K-factors it is presented how the uncertainties associated with the K-factors can
be calculated, in order to consider their contribution to the uncertainty associated with
the absolute isotope ratios and render the traceability-chain to the mole unbroken. The
knowledge gained about the calculation of the K-factors for atomic systems served as the
base for the adaption of the approach to molecular systems.
In the fourth section of this thesis, it is shown how the gravimetric mixture approach must
be adapted for carbon dioxide, since a statistical isotope distribution must be considered.
A new mathematical approach is presented which considers the statistical distribution and
allows to calculate the correct K-factors. This approach has also been generalized so that
in future it can be applied also to other isotopologue systems. A buoyancy correction
scheme for masses of gases in closed gas vessels was developed for this study and is also
presented. First blends of isotopically altered parent materials were prepared and the
results applying the newly developed mathematical scheme are presented. In a critical
discussion possible reasons for not achieving absolute isotope ratios are given, for example
measurement limitations of the mass spectrometer used in this study or deviation from a
statistical isotopic distribution. In a simulation using a reasonable data set the validity
and the performance (in terms of achievable uncertainties) of the approach was assessed
and discussed. Further applications and improvements of the method are presented.