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Geochemical Journal
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Lattice dynamical aspect of oxygen isotope partition function ratio for alpha quartz

Iwao Kawabe
Geochemical Journal, Vol. 13, No. 2, P. 57-67, 1979

ABSTRACT

A full lattice dynamical method has been applied to the calculation of the oxygen isotopic partition function ratio for α-quartz in order to examine the result of the Debye-Einstein model calculation. The modified Urey-Bradley force field was used as a force field model of α-quartz. The phonon dispersion curves and elastic constants of α-quartz have also been calculated. These calculated values are in fairly good agreement with the available experimental data. The agreement gives additional grounds for the use of the modified Urey-Bradley force field. The wave vector-dependence of Infqtz(q) has been examined along the x, y, and z directions in the Brillouin zone. It has been found that the Infqtz(q) little changes with the wave vector. The changes of the Infqtz(q) along the three directions are only less than 0.5% at 0°C, although the value of Infqtz(q) becomes a minimum at the Brillouin zone center. By virtue of the small wave-vector dependence of Inqtz(q), the reduced partition function ratio for α-quartz given by the direct summation technique converges very rapidly. The reduced partition function ratio for α-quartz has been evaluated in the temperature range between 0 and 550°C by means of the direct summation technique combined with the perturbation method. The obtained values of the oxygen isotope fractionation factor between α-quartz and liquid water below 100°C can be expressed as 103Inαqtz-H2O(1) = -17.287+8.6913(103/T) + 1.8459(103/T)2. This temperature scale gives only 1-1.5 ‰ higher fractionations than that of the earlier Debye-Einstein model calculation. When the small differences of the fractionations between the present and earlier calculations and the error associated with the theoretical calculation are taken into consideration, the Debye-Einstein approximation in evaluating the isotopic partition function ratio for α-quartz can be concluded not to bias seriously the result.

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