Original paper
Ab initio (DFT) calculations of corundum (α-Al2O3) oxygen isotope fractionation
Krylov, Dmitry P.; Evarestov, Robert A.
European Journal of Mineralogy Volume 30 Number 6 (2018), p. 1063 - 1070
29 references
published: Dec 20, 2018
published online: Sep 7, 2018
manuscript accepted: Mar 26, 2018
manuscript revision received: Feb 25, 2018
manuscript received: Dec 11, 2017
Abstract
Equilibrium oxygen isotope (18O/16O) fractionations (β-factors) for corundum are predicted from first principles using the “frozen phonon” technique within the density functional theory (DFT). Calculations of the phonon frequencies and the isotopic frequency shifts were consequently performed over 1, 3, 8, and 27 wave vectors using the supercell approach, with the Gaussian-type all-electron basis sets and hybrid functional B3LYP. The presented phonon frequencies agree with experimental infra-red and Raman data. The results of β-factor calculations are presented in terms of the logarithmic functions, 1000lnβ crn, computed for temperatures from 0 to 2000 °C with a computational step of 20 °C and then fitted by the conventional cubic polynomial Ax + Bx 2 + Cx 3, with x = 106/T(K)2. The following expressions corrected for incomplete Brillouin-zone sampling quantify oxygen isotope fractionation of corundum. Within the harmonic approximation: 1000 ln β crn = 9.2657 x - 0.12110 x 2 + 0.00175 x 3 0 < T ° C < 2000 . Accounting for thermal expansion (the quasi-harmonic approximation): 1000 ln β crn = 9.03363 x - 0.08912 x 2 + 0.00036 x 3 ( 0 < T ° C < 1570 ) The pressure effect on corundum β-factors is found to be negligible below ca. 25 kbar at temperatures exceeding 500 °C. At ultra-high pressures the correction can be made using the expression (∂(1000lnβ)/∂P)T (kbar) = 0.00967 × 106/T(K)2.
Keywords
corundum •
oxygen isotopes •
18O/16O fractionation •
β-factors •
first principles •
density functional theory