Calculation of oxygen isotope fractionation in quartz-water system with special reference to the low temperature fractionation

Abstract

Reduced partition function ratios for α and β-quartz have been calculated at various temperatures using the modified Urey-Bradley force field and Debye and Einstein functions. The error estimation for the reduced partition function ratios has also been made with the use of the standard deviations of force constants calculated by a least squares procedure. Theoretical values for the oxygen isotope fractionation factor between quartz and water vapor up to 1000°C have been calculated. The oxygen isotope fractionation factor between quartz and liquid water below 100°C has been obtained by combining the theoretical reduced partition function ratios for α-quartz and water vapor and experimental data on the liquid-vapor frationation of water. The obtained quartz-liquid water fractionations can be expressed as 10 3 lnα qtz−H 2 O(1) = −18.977 + 8.582( 10 10 T ) + 1.9189( 10 10 T ) 2 It was also found that the theoretical calculation was inevitably accompanied by a relatively large error. The isotopic temperature scales obtained by other workers for the pair of quartz and liquid water lie within the error range of the present calculation. Although the slopes of all scales including the present one on a plot of 10 3 ln α vs 10 6 T 2 are almost identical, the empirical scale by Knauth and Epstein is the one that is closest to the present result.