Structural properties of PbTiO₃ and PbZr_xTi_1−xO₃: A quantum‐chemical study

Abstract

ABSTRACT:We investigate the structural and electronic properties of pure and Zr-doped PbTiO 3 crystals. The nature of atomic relaxation around the Zr impurity is studied through quantum-chemical simulations based on the Hartree-Fock theory and a periodic large unit cell model adopted within the so-called intermediate neglect of differential overlap approximation. The most stable defect configurations are predicted for different impurity concentrations. The results obtained are compared with those from other theoretical studies and a number of experimental measurements carried out on this technologically important perovskite-type crystal.

A quantum mechanical study of La-doped Pb(Zr,Ti)O3

“…The details of parametrization are described elsewhere [19], however, we can briefly state that the main results obtained on pure PbTiO 3 crystals were in concordance with the other available studies [20] and reproduced some important features of the electronic band structure, e.g. density of states (DOS) and composition of the energetic bands.…”

Quantum chemical investigation of lanthanum doping effects in tetragonal and rhombohedral PZT materials

“…We also managed to reproduce the hybridization between the Ti 3d and O 2p AOs for the tetragonal phase of the PbTiO 3 crystal in accordance with the expectations [26], as well as quite strong Zr 4d-O 2p hybridization effect in the PbZrO 3 crystal [27], and a subsequent significant covalent contribution into the chemical bonding between the Zr and O atoms. This covalency appeared to be even more important as the corresponding Ti-O covalency in the PbTiO 3 crystal [25]. In previous studies of the PZT crystals considering different zirconium concentrations [28], some interesting tendencies were confirmed.…”

“…Because the chemical bonding between the Ti and O atoms as well as that between the Zr and O atoms consists of both covalent and ionic contributions, the Ti and Zr atoms try (i) to adjust to the aforementioned O movements and (ii) to take into account the changes produced upon the Coulomb interaction in the Ti-La and Zr-La pairs. The obtained results of relaxation for the positively charged Ti and Zr atoms, thus, are following: the Ti(21) and Ti (22) atoms move by 0.21 Å, the Ti(23) and Ti(24) atoms displace themselves by 0.23 Å, and finally the Ti (25) and Ti(26) atoms change their initial positions by ϳ0.14 Å with respect to the closest impurity atom (see Fig. 2).…”

“…Thus, obtained atomic parameters for the PZT crystals can be found in Ref. 25, whereas the numerical parameters for the La atom were obtained by reproducing (i) the ground state 2 …”

“…The atomic parametrization for the PZT was done by one of us (A.S.) earlier and took into consideration the composition of energetic bands, density of states, and reproduction of crystalline lattice parameters [25]. We also managed to reproduce the hybridization between the Ti 3d and O 2p AOs for the tetragonal phase of the PbTiO 3 crystal in accordance with the expectations [26], as well as quite strong Zr 4d-O 2p hybridization effect in the PbZrO 3 crystal [27], and a subsequent significant covalent contribution into the chemical bonding between the Zr and O atoms.…”