Interatomic Potentials: Ferroelectrics

Abstract

The success of the atomistic approach is evident from the large number of investigations on complex oxides crystals. Regardingferroelectric perovskites, we note the early work of Lewis and Catlow, who derived empirical shellmodel potential parametersfor the study of defect energies in cubic BaTiO3 [5, 18]. Thismodelwas subsequently used formore refined ab initio embeddedcluster calculations of impurities, as well as for the simulation of surface properties. For lattice dynamical properties,the most successful approach has been carried out in the framework of the nonlinear oxygen polarizability model [6]. In thisshell model an anisotropic core–shell interaction is considered at the O2- ions, with a fourth-order core–shell interaction along the B–O bond. The potential parameters were obtained by fitting experimentalphonon dispersion curves of the cubic phase. The main achievement of this model was the description of the soft mode temperaturedependence (TO-phonon softening which is related with the ferroelectric transition). However, neither of these models, wasable to simulate the ferroelectric phase behavior of the perovskites. Besides the traditional empirical approach, in whichpotentials are obtained by suitable fitting procedures to macroscopic physical properties, there is increasing interest inderiving pair potentials from first-principles calculations. In 1994, Donnerberg and Exner developed a shell model for KNbO3, deriving the Nb–O short-range pair potential from Hartree–Fock calculations performed on a cluster of ions [7]. They showedthat this ab initio pair potential was in good agreement with a corresponding empirical potential obtained from fitting procedures to macroscopicproperties. Their model, however, was not able to simulate the structural phase transition sequence of KNbO3 either. They argued that the consideration of additional many-body potential contributions would enable them to model structuralphase transitions. However, as we will see, it is in fact possible to simulate ferroelectric phase transitions just by usingclassical pairwise interatomic potentials fitted to first-principles calculations. Ab initio methods provide underlying potential surfaces and phonon dispersion curves at T =OK, thereby exposing the presence of structuralinstabilities in the full Bril-louin zone, and this information is indeed very useful for parameterizing classical potentialswhich can then be used in molecular dynamics simulations. In this way, finite-temperature simulations of ABO3 perovskites and the properties of chemically and microstructurally more complex systems can be addressed at the atomic level.