An ab initio perturbed ion study of structural properties of TiO2, SnO2, and GeO2 rutile lattices

This work describes a theoretical quantum mechanical study on TiO2, SnO2 and GeO2 rutile structures in order to characterize the geometric, mechanical, thermodynamic and electronic properties of these systems. The doping processes of V4+ at the sixfold-coordinated site have been studied with the aim of determining the relative stability of pure and doped structures. Ab initio perturbed ion calculations with Slater-type orbitals for representing atomic centers and large cluster models have been used. Local geometry optimizations have been performed to determine the lattice energy, lattice parameters and bulk modulus, as well as the force constant and vibrational frequencies (nu) of the breathing vibrational modes, a(1g), in the sixfold-coordinated site. Numerical results are analyzed and compared with experimental data, the geometrical distances obtained by computer simulation being in agreement with the reported experimental values. The difference in energy for the substitution of Ti4+, Sn4+ and Ge4+ for V4+ in TiO2, SnO2 and GeO2, respectively is very dependent on the method used to represent these doping processes. The TiO2, SnO2 lattices show a decrease in the nu value from the pure to the doped structure while a opposite trend is obtained for the GeO2 structure. The validity of the methodology is discussed.