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 β_zrn(¹⁸O/¹⁶O) = 9.83055x – 0.19499x² + 0.00388x³ and 1000 ln β_zrn(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 β_zrn values and isotope fractionation factors between quartz and zircon (1000 ln β_qtz – 1000 ln β_zrn) are significantly different from those obtained by previous experimental, empirical, and semiempirical calibrations of isotope equilibria.