Calculation of the Reduced Partition Function Ratios of α-, β-Quartzs and Calcite

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The reduced partition function ratios (r.p.f.r.) of α,β-quartz and calcite were calculated for oxygen isotopic substitution, using the force fields. Optical vibrations are represented by factor group mode (<I>k</I>=0) and acoustic contributions were approximated by the Debye mode of vibration. The theoretical calculation predicts that the r.p.f.r. of quartz could have a discrete gap of about 0.8% at the α-β-transition temperature (573°C), the r.p.f.r. of α-quartz being larger in magnitude and in temperature-dependency. This implies that the isotopic fractionation factors between quartz and other materials such as water, could be significantly affected by the transition. A comparison of the calculated r.p.f.r. of quartz and calcite with the experimental fractionation factors between these minerals and water yields a fairly consistent value of the r.p.f.r. of water, supporting the force field models used for calculations. The comparison also revealed that the r.p.f.r. of water in the temperature interval 300–800°C and under a hydrostatic pressure of 2 Kb should deviate from those of ideal water vapor at the same temperatures by as much as 1% due to the non-ideality of the compressed water fluid.
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