251. Nonmetal Doping at Octahedral Vacancy Sites in Rutile: A Quantum Mechanical Study
- Author
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C. Wilson, Nicholas, E. Grey, Ian, and P. Russo, Salvy
- Abstract
The stability of boron and carbon dopants (D) at vacant octahedral sites in rutile has been investigated using density functional theory quantum mechanical (QM) modeling. Three different types of sites were considered: 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 from the QM total energies of the relaxed defect and host structures, combined with chemical potentials of the reservoir components that were corrected for both temperature and gas partial pressure variations. The contribution of vibrational free energy to Edas a function of temperature was evaluated for the BFrenkelmodel using ab initio phonon density of states calculations. The calculated vibrational and configurational free energy terms were of opposite sign and partially cancelled, giving a relatively small (0.3 eV at 700 K) combined contribution to Ed. Under strongly reducing conditions at 1500 K, boron incorporation at interstitial and Frenkel sites is favored, with Edvalues of 0.53 and 0.8 eV respectively, whereas the Edvalues for carbon doping were high (>4 eV) for all three models under high-temperature reducing conditions. Under oxygen-rich conditions relevant to sol−gel processing, the Dvacmodel was favored for both boron and carbon. Further stabilization of the Dvacmodel for boron was obtained at a protonated vacancy site, giving Ed1.16 eV for (BH)vacat 700 K.
- Published
- 2007
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