First-Principles Determination of Oxygen and Silicon β-Factors for Zircon

Abstract

The temperature dependence of the β-factors of zircon was determined for 18O/16O and 30Si/28Si isotopic substitutions. Calculations were performed on the basis of the density functional theory (DFT) using the frozen phonon approach. The obtained geometric parameters of the zircon crystal lattice and vibrational frequencies are in good agreement with experimental data. The results were approximated by the following cubic polynomials in x = 106/T(K)2: 1000 ln βzrn(18O/16O) = 9.83055x – 0.19499x2 + 0.00388x3 and 1000 ln βzrn(30Si/28Si) = 7.89907x – 0.17978x2 + 0.00377x3. The obtained relations can be used in combination with the β-factors of other phases for the construction of geothermometers. New calibrations of the quartz–zircon isotope geothermometer were proposed. The obtained 1000 ln βzrn values and isotope fractionation factors between quartz and zircon (1000 ln βqtz – 1000 ln βzrn) are significantly different from those obtained by previous experimental, empirical, and semiempirical calibrations of isotope equilibria.