Nonstoichiometry of zirconia

Abstract

Phenomenological equations are suggested for describing the processes of disordering in electron and ion subsystems. Dependences of the concentration of point defects on the partial pressure of oxygen for each kind of defect are obtained in the course of the solution of the equations of defect formation due to the Schottky, Frenkel, and anti-Frenkel mechanisms. Equilibria of zirconia with the ambient at high temperatures are considered together with the processes of defect ionization in an electron subsystem. To the obtained systems of quasichemical equations a chosen condition for electric neutrality is added and the system is transformed into systems of algebraic equations. Linearization of these equations and their solution made it possible to describe the number densities of electrons, holes, vacancies, and interstices in terms of known constants and the partial pressure of oxygen in the general form. The solutions to these systems were chosen in the form of the product of the equilibrium constant of the investigated reaction of defect formation and the exponential function of the partial pressure of oxygen.