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, 1000lnβcrn, computed for temperatures from 0 to 2000 °C with a computational step of 20 °C and then fitted by the conventional cubic polynomial Ax + Bx2 + Cx3, 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 lnβcrn=9.2657x - 0.12110x2+ 0.00175x3 0 <T °C< 2000.
Accounting for thermal expansion (the quasi-harmonic approximation): 
1000lnβcrn= 9.03363x-0.08912x2 + 0.00036x3 (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.

You do not currently have access to this article.