Point Defects in Insulators

crystal structure of alumina Alumina, Al2O3, is a prototypical large band gap refractory ceramic that is widely used in both single crystal and polycrystalline form. Like most materials, the properties of alumina, and hence its industrial value, are defect sensitive. The concentration of point defects such as vacancies, interstitials, and substitutional impurities controls the transport of matter and hence the rates of creep and sintering. Impurity levels also control such diverse properties as the colour of ruby and sapphire (naturally doped α-Al2O3 single crystals) and the oxidation rate of Al-containing alloys. Up to now, theories of the rates of defect diffusion and matter transport have failed to explain measured data, in particular the effect of impurities. We have used quantum mechanical calculations based on density-functional theory combined with classical thermodynamics in a mass-action framework to determine:

  1. Point defect concentrations in undoped crystals.
  2. The effects of aliovalent solutes (Mg, Ti) on the defect populations.
  3. The concentrations of defect complexes, and how the interplay of temperature, Fermi level and the partial pressure of oxygen affects the defect populations.
  4. Migration barriers for oxygen and Al point defects.

These results of these calculations are combined to yield oxygen and aluminium diffusivities, for which the agreement with experiment is now satisfactory. In particular, the "buffering" mechanism that limits the sensitivity of the oxygen diffusivity to impurity levels is explained.

Our approach adapts the Zhang-Northrup formalism originally developed for use in semiconductors. This has been little used in ceramics to date, but the success of its application to alumina suggests that it may play a larger role in future.

Concentrations of point defects in alumina as functions of the impurity concentration at 1750K

Concentrations of Al and O vacancies and of the principal dopant and cluster species as functions of Mg concentration (right-hand side) and Ti concentration (left-hand side) at T=1750K and pO2/p0 = 0.2.

Migration pathways of the split Al vacancy and Al interstitial in alumina

(a) Initial configuration and (b) migration pathway of the VAl split vacancy, and (c) initial configuration and (d) migration pathway of the Ali interstitial. Red spheres represent O2- ions, and blue spheres Al3+ ions. Crosses are vacant sites on the cation lattice, blue squares are Al3+ ions on such sites, and crossed circles are the initial positions of the moving atoms. r indicates relaxation after the initial atomic jump, an integral part of the correlated motion.