Mode oxygen isotope fractionation

The theory developed for perfect gases could be extended to solids, if the partition functions of crystals could be expressed in terms of a set of vibrational frequencies that correspond to its various fundamental modes of vibration (O Neil 1986). By estimating thermodynamic properties from elastic, structural, and spectroscopic data, Kieffer (1982) and subsequently Clayton and Kieffer (1991) calculated oxygen isotope partition function ratios and from these calculations derived a set of fractionation factors for silicate minerals. The calculations have no inherent temperature limitations and can be applied to any phase for which adequate spectroscopic and mechanical data are available. They are, however, limited in accuracy as a consequence of the approximations needed to carry out the calculations and the limited accuracy of the spectroscopic data. 

Elcombe and Hulston 1975 Kawabe 1978). Kieffer (1982) took a less detailed approach in calculating oxygen isotope partition function ratios for 11 silicate minerals, calcite and rutile. As input for her calculations, Kieffer used the measured spectra for the forms of minerals, divided the vibrational modes for these minerals into four groups, and then developed a set of rules for estimating the frequency shift associated with each group on substitution. Importantly, she applied the same rules to each mineral considered in her study, which resulted in an internally consistent set of partition function ratios. Most of Kieffer s calculated fractionation factors are in excellent agreement with experimental data (Clayton and Kieffer 1991). 

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