Factors of 18O/16O fractionation in corundum estimated from the calculation of isotopic shifts on vibration frequencies

The β-factors of corundum were estimated on the basis of DFT calculations of vibrational frequency changes due to 16O–18O isotope substitution in a harmonic approximation using an all-electron Gaussian-type basis set and the B3LYP hybrid functional (the CRYSTAL program). Calculations were performed accounting for eight phonon wave vectors within the first Brillouin zone. The results are approximated by the relation 1000ln βcrn = 9.19874x–0.12326x2 + 0.00213x3 (x = 106/T(K)2, 400 < T(K) < 1300), which can be used in isotope geochemical studies in combination with the known temperature effects on the β-factors of other phases.