Relative energetics and structural properties of zirconia using a self-consistent tight-binding model

We describe an empirical, self-consistent, orthogonal tight-binding model for zirconia, which allows for the polarizability of the anions at dipole and quadrupole levels and for crystal field splitting of the cation d orbitals, This is achieved by mixing the orbitals of different symmetry on a site with coupling coefficients driven by the Coulomb potentials up to octapole level. The additional forces on atoms due to the self-consistency and polarizabilities are exactly obtained by straightforward electrostatics, by analogy with the Hellmann-Feynman theorem as applied in first-principles calculations. The model correctly orders the zero temperature energies of all zirconia polymorphs. The Zr-O matrix elements of the Hamiltonian, which measure covalency, make a greater contribution than the polarizability to the energy differences between phases. Results for elastic constants of the cubic and tetragonal phases and phonon frequencies of the cubic phase are also presented and compared with some experimental data and first-principles calculations. We suggest that the model will be useful for studying finite temperature effects by means of molecular dynamics.

Proton ordering energetics in ice phases

Results from first-principles calculations on the subtle energetics of proton ordering in ice phases are shown only to depend on the electrostatic components of the total energy. Proton ordered ice phases can therefore be predicted using electronic structure methods or a tailored potential model. However, analysis of the electron density reveals that high order multipole components, up to hexadecapole, are needed to adequately capture total energy differences between proton ordered and disordered phases. This suggests that current potential models may be unable to reproduce the position of proton ordered ice phases in the phase diagram without extensions to describe high order electrostatics. (c) 2006 Elsevier B.V. All rights reserved.