Mode oxygen isotopes

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. 

In the Slater-type mode, oxygen atoms oscillate with the largest relative amplitude. As a result, we find that the criterion of the FE lattice instability in totally oxygen isotope-exchanged STO and KTO is ... 

Calculations of 180 EIEs upon reactions of natural abundance O2 require the normal mode stretching frequencies for the 160—160 and 180—160 isotopologues (16 16j/ and 18 16, ). These values can often be obtained directly from the literature or estimated from known force constants. DFT calculations can be used to obtain full sets of vibrational frequencies for complex molecules. Such calculations are actually needed to satisfy the requirements of the Redlich-Teller product rule. In the event that the full set of frequencies is not employed, the oxygen isotope effects upon the partition functions change and are redistributed in a manner that does not produce a physically reasonable result. 

In the achiral species 19, 20 and 21 the (R)- and (S)-1,2-propanediol binding modes are equivalent and no preferred retention or loss of the heavy oxygen isotope should be expected, even upon stereospedfic migration. This has been confirmed experimentally, i.e., about 50% of the 18O was retained in all three cases. In the chiral specimens 22, 23, 24 and 25, however, stereospecific migration of the unlabelled hydroxyl group should lead to chirally labelled geminal diols. Such a process should be preferred by the substrates 23 and 25 (Fig. 18). 

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). 

They found that the order for the M—0 stretching modes (M—0 force constants) was (02)Pd(02) > Pd(Oj) and (02)Ni(02) > Ni(02), and since the 0-0 force constant increased as the M-0 force constant decreased, reversibility could not be equated with shorter 0—0 bond length. To test the proposed isosceles model they predicted the various absorptions that would be expected on the basis of the symmetrical structure (a) and unsymmetrical structure (c), Fig. 8. If the isotopic ratio of 0 0 is 1 1, then three bands would be expected for structure (a), with relative intensities 1 2 1, and four bands would be expected for structure (c), with relative intensities 1 1 1 1, the two oxygen atoms now being in different environments. These workers 189) then obtained the IR spectrum for the cocondensation product from the reaction between nickel and O2 (4.2—10°K), in isotopic ratio 0 =1 1, and found three bands with relative inten-... 

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