| Abstract
| - The stability of boron and carbon dopants (D) at vacant octahedral sites in rutile has been investigated usingdensity functional theory quantum mechanical (QM) modeling. Three different types of sites wereconsidered: vacant Ti lattice site (Dvac), vacant Ti site + Ti interstitial (DFrenkel), and interstitial site (Dint).The defect formation energies, Ed, at different temperatures and gas partial pressures were calculated fromthe QM total energies of the relaxed defect and host structures, combined with chemical potentials of thereservoir components that were corrected for both temperature and gas partial pressure variations. Thecontribution of vibrational free energy to Ed as a function of temperature was evaluated for the BFrenkel modelusing ab initio phonon density of states calculations. The calculated vibrational and configurational free energyterms were of opposite sign and partially cancelled, giving a relatively small (0.3 eV at 700 K) combinedcontribution to Ed. Under strongly reducing conditions at 1500 K, boron incorporation at interstitial and Frenkelsites is favored, with Ed values of 0.53 and 0.8 eV respectively, whereas the Ed values for carbon dopingwere high (>4 eV) for all three models under high-temperature reducing conditions. Under oxygen-richconditions relevant to sol−gel processing, the Dvac model was favored for both boron and carbon. Furtherstabilization of the Dvac model for boron was obtained at a protonated vacancy site, giving Ed = 1.16 eV for(B+H)vac at 700 K.
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