Order–disorder character of PbTiO3

We report the displacive and order–disorder characters of PbTiO3 analyzed using a classical atomic model which was developed under the inverse relation between the bond length and the bond valence. The ferroelectric phase changes to the paraelectric phase around 700 K, and the histograms of Ti–O and Pb–O bond lengths have three peaks which become a single peak above the phase transition temperature. The order–disorder character of this material was clearly shown by analyzing the ion displacement magnitudes. (Some figures in this article are in colour only in the electronic version) Ferroelectricity in perovskites has been widely investigated due to applications like nonvolatile random access memory [1–3]. Comes et al used x-ray scattering to study the structural disorder of BaTiO3 and KNbO3 [4]. Starting from the work of Comes et al the n-site model was developed and studied with first-principles calculations [5, 6]. PbTiO3 has a simple structural phase transition compared to the other perovskites such as BaTiO3. While PbTiO3 has been believed to be a typical displacive ferroelectric, some experimental evidence reveals an order–disorder behavior in this material [7–9]. The evidence suggests that the Pb ions are disordered over six sites along the cubic principal axes. Unfortunately, despite the evidence that supports the notion of an order–disorder behavior in PbTiO3, there is difficulty in interpreting experimental results. First-principles calculations have been used for studying and understanding ferroelectrics. Differences in the ferroelectric phase transition (including the effect of tetragonal strain) between BaTiO3 and PbTiO3 were studied with the first-principles calculations [10], and a few atomic potential models based on the density functional theory have been developed [11–15]. In the case of BaTiO3, the order–disorder and displacive characters during the phase transitions were examined with an effective Hamiltonian approach specified by the first-principles pseudopotential calculations [16, 17]. In order to study the displacive and order–disorder characters of PbTiO3, we use a classical model potential based on the inverse relation between the bond valence and the bond length. The parameters of this potential model were fit to the reference structures obtained from first-principles calculations developed for ionic systems [13]. The total interatomic potential of the bond-valence model is given by: Ebv = Ec + Er + Eb + Ea, (1) where Ec is a Coulombic potential, Er is a short-range repulsive potential, Eb is a potential for the bond-valence relation, and Ea is an angle potential which is required for correcting the octahedral tilt. The form of the Coulombic potential Ec is