Nonmetal Doping at Octahedral Vacancy Sites in Rutile: A Quantum Mechanical Study

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• 作者：Nicholas C. Wilson ; Ian E. Grey ; Salvy P. Russo
• 刊名：Journal of Physical Chemistry C
• 出版年：2007
• 出版时间：July 26, 2007
• 年：2007
• 卷：111
• 期：29
• 页码：10915 - 10922
• 全文大小：200K
• 年卷期：v.111,no.29(July 26, 2007)
• ISSN：1932-7455

文摘

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 (D_vac), vacant Ti site + Ti interstitial (D_Frenkel), and interstitial site (D_int).The defect formation energies, E_d, 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 E_d as a function of temperature was evaluated for the B_Frenkel 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 E_d. Under strongly reducing conditions at 1500 K, boron incorporation at interstitial and Frenkelsites is favored, with E_d values of 0.53 and 0.8 eV respectively, whereas the E_d 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 D_vac model was favored for both boron and carbon. Furtherstabilization of the D_vac model for boron was obtained at a protonated vacancy site, giving E_d = 1.16 eV for(B+H)_vac at 700 K.