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 Inf_qtz(q) has been examined along the x, y, and z directions in the Brillouin zone. It has been found that the Inf_qtz(q) little changes with the wave vector. The changes of the Inf_qtz(q) along the three directions are only less than 0.5% at 0°C, although the value of Inf_qtz(q) becomes a minimum at the Brillouin zone center. By virtue of the small wave-vector dependence of In_qtz(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 10³Inα_qtz-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.