The use of heat capacity data to calculate carbon isotope fractionation between graphite, diamond, and carbon dioxide: a new approach

Abstract

A new approach for calculating the β-factors of elements (substances consisting of single-element atoms) from calorimetric data on the specific heat capacities has been established. The approach is based on first order thermodynamic perturbation theory and harmonic approximation. It has been applied to calculate the β-factors of graphite and diamond. The polynomial expansions for them have been evaluated: ▪ A comparison with values of the β-factors obtained by Bottinga (1969b) has shown a disagreement that seems to be essential for carbon isotope geothermometry. The carbon dioxide β-factors have been calculated in the harmonic approximation from spectroscopic data on fundamental frequencies. The method of calculation is based on the group theory technique. The calculated equilibrium isotope fractionation factors between carbon dioxide and graphite are significantly lower than those obtained from partial exchange experiments by Scheele and Hoefs (1992). Combining the Chacko (1991) data on the calcite β-factors with the present data on the β-factors of graphite, the isotope equilibrium fractionation curve between calcite and graphite has been evaluated. This curve shows somewhat better coincidence with the Valley and O'Neil (1981) empirical fractionation curve than the curve obtained by Chacko (1991). The excellent agreement between the theoretical and the empirical calibrated isotope fractionation curves has been achieved by taking into account a pressure effect on the calcite-graphite equilibrium isotope fractionation factor. Nevertheless, significant disagreement with appropriate data of Scheele and Hoefs (1992) is observed.