S. Fabris et al., Relative energetics and structural properties of zirconia using a self-consistent tight-binding model, PHYS REV B, 61(10), 2000, pp. 6617-6630
We describe an empirical, self-consistent, orthogonal tight-binding model f
or zirconia, which allows for the polarizability of the anions at dipole an
d quadrupole levels and for crystal field splitting of the cation d orbital
s, 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 polar
izabilities are exactly obtained by straightforward electrostatics, by anal
ogy with the Hellmann-Feynman theorem as applied in first-principles calcul
ations. The model correctly orders the zero temperature energies of all zir
conia polymorphs. The Zr-O matrix elements of the Hamiltonian, which measur
e covalency, make a greater contribution than the polarizability to the ene
rgy differences between phases. Results for elastic constants of the cubic
and tetragonal phases and phonon frequencies of the cubic phase are also pr
esented and compared with some experimental data and first-principles calcu
lations. We suggest that the model will be useful for studying finite tempe
rature effects by means of molecular dynamics.