Transferable potentials for the Ti–O system

Transferable potentials have been derived by computer modelling of the series of higher titanium oxides, from Ti 2 O 3 (with Ti 3+ ions) to TiO 2 (with Ti 4+ ions), and including the lower members of the series of phases, Ti n O 2n-1 , which have mixed oxidation states; some of these are described as crystallographic shear phases. Two potential models have been developed: one comprises coulombic interactions between charge centres, a core–shell model for the oxygen anions, repulsive exponential anion–cation interactions and, in addition, primary antiferromagnetic interactions between Ti 3+ –Ti 3+ ions at short distances (r ij <2.6 Å), and secondary repulsive ferromagnetic interactions at longer distances; the second potential differs only in that it uses oxygen anions which are rigid. The potentials more-or-less successfully model the static crystal structures and their corresponding lattice energies for the full group of oxides included in the modelling, as well as for two independent test structures, and are expected to be equally effective in modelling still higher members of the shear phases, Ti n O 2n-1 . Modelling of the dynamic properties (elastic constant and relative permittivity) is not reliable. The shell model oxide potential has a large (‘hard’) spring constant, and largely mimics the rigid potential, but at the expense of slight instabilities in the modelled structures.