What is Vacancy Defects

First-principles calculations are performed by taking into account the strong correlation effects on ceria. To obtain an accurate description including f electrons, the authors optimized the Coulomb U parameter for use in Local-Density Approximation (LDA) and Generalized Gradient Approximation (GGA) calculation. A good agreement with experimental data is obtained within the GGA+U (Wu-Cohen scheme). Elastic stiffness constants are found in correct agreement with the available experimental results. Born effective charge, dielectric permittivity, and the phonon-dispersion curves are computed using density functional perturbation theory. The origin of magnetism in undoped ceria with intrinsic defects is investigated. The authors show that both of Ce and O vacancies induce local moments and ferromagnetism without doping ceria by magnetic impurities in this chapter.