Charged point defect in rutile titanium dioxide: From defect charge distribution to defect phonon free energy

The dominant charged point defects in transition metal oxides can change with temperature (T) and oxygen partial pressure (PO2) to control the electrical properties of the materials. Thus it is important to understand how the defect formation energies (DFEs) of all the defects are changed with T and PO2, which is not easily measured experimentally. Density Functional Theory (DFT) is combined with thermodynamics to construct a new methodology to calculate the DFEs ab initio. Rutile TiO 2 is chosen as a model material because it is a relatively simple binary system and there is a wealth of existing macroscopic experimental data, such as its dependence of the electrical conductivity on T and PO2, temperature dependent thermal expansion coefficient, etc.;Chapter 1 introduces the general method to calculate DFEs, which combines DFT with thermodynamics, including the supercell method to calculate the total energies of defective and pure supercells; the use of Bader analysis to analyze the real space charge distribution, which helps choose a potential alignment method to correct for the artificial interaction caused by periodic boundary conditions, and a thermodynamic approach to extrapolate DFEs to any T and PO2.;Chapter 2 discusses the temperature-dependent defect-induced phonon free energy in the harmonic approximation, which gives nontrivial contributions to the DFEs. The temperature dependences of the defect-induced phonon free energies are different from the pure rutile structure, and more importantly they are different for differently charged defects. The physical origin is largely associated with the soft phonon mode at low frequencies for titanium interstitials, while for oxygen vacancies and titanium vacancies the differences in the phonon free energies are caused by the collective contribution from all phonon modes influenced by the introduction of the charged defects.;Chapter 3 points out the necessity of considering the thermal expansion of the materials in the DFE calculation. The differences between harmonic and qusi-harmonic approximations for the phonon free energy and Gibbs free energy calculations are discussed. Defect phase diagrams are constructed in the PO2-T-Ef spaces to explain how the dominant defect types change with environmental conditions.