Oxygen and silicon β-factors of zircon estimated from first principles
Zircon β-factors have been calibrated against temperature for isotopic substitutions of 18O/16O and 30Si/28Si. Calculations were performed using the density functional theory (DFT) with the “frozen phonon” approach. The deduced geometric parameters of the zircon unit cell, and the phonon frequencies calculated, agree well with the experimental data. The results are expressed by the cubic polynomials on x = 106/T(K)2: 1000lnβzrn(18O/16O) = 9.83055x – 0.19499x2 + 0.00388x3; 1000lnβzrn(30Si/28Si) = 7.89907x – 0.17978x2 + 0.00377x3. The expressions deduced can be utilized to construct geothermometers if combined with β-factors of coexisting phases. New calibrations of quartz-zircon are given. The new values of 1000lnβzrn and the estimated isotope fractionation factors between quartz and zircon (1000lnβqtz–1000lnβzrn) deviate considerably from previously used experimental, empirical, and semi-empirical calibration of the isotopic equilibrium.