First-Principles Determination of Oxygen and Silicon β-Factors for Zircon
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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.
The author thanks V.B. Polyakov (Institute of Experimental Mineralogy, Russian Academy of Sciences) for carefully reviewing the manuscript and helpful comments. Calculations of β-factors from inelastic neutron scattering data were conducted using a program of the reviewer.
This study was financially supported by the Russian Foundation for Basic Research, project no. 19-05-00175. Computer resources were provided by the Resource Center “Computer Center of the St. Petersburg State University” (http://cc.spbu.ru).
CONFLICT OF INTEREST
The authors declare that they have no conflict of interest.
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