This paper presents simulation predictions of electric field gradients (EFGs) and binding energies for two phases of ZrO 2 , cubic and tetragonal, when doped with small concentrations of Cd, Y, Y + Nb, and Y + Ta. The creation of oxygen vacancies in bulk is elucidated through ab-initio calculations. The focus is on EFGs as a function of the concentration of free oxygen vacancies with high accuracy. EFGs decrease as the oxygen vacancy trapping probability increases, dependent on vacancy concentration. The crucial factors are point defects. Radiation induced defects, which are traps of charge carriers are discussed. Trivalent Y 3+ ions induce an increase in the concentration of oxygen vacancies in ZrO 2 , while Cd, Y + Ta, and Y + Nb dopants induce a decrease in the concentration of oxygen vacancies. A convenient polynomial dependence of the energy on inverse super -cell size, where wave -function overlap and electrostatic interactions bring about more complex dependencies on super -cell access, is presented here. We demonstrate that this complexity can be resolved using Chebyshev polynomials, which may include electron -phonon coupling.
