Size and scaling effects in barium titanate. An overview

Ferroelectric perovskites such as BaTiO₃ and Pb(Zr,Ti)O₃ are well-suited for a variety of applications including piezoelectric transducers and actuators, multilayer ceramic capacitors, thermistors with positive temperature coefficient, ultrasonic and electro-optical devices. Ferroelectricity arises from the long-range ordering of elemental dipoles which determines the appearance of a macroscopic polarization and a spontaneous lattice strain. The confinement of a ferroelectric system in a small volume produces a perturbation of the polar order because of the high fraction of surface atoms and ferroelectricity vanishes when the size of the material is reduced below a critical dimension. This critical size is of a few nanometres in the case of epitaxial thin films and of 10−20 nm for nanoparticles and nanoceramics. The change in properties with decreasing physical dimensions is usually referred to as size effect. Thin films and ceramics are particularly prone to show size effects. A progressive variation of dielectric, elastic and piezoelectric properties of ferroelectric ceramics is already observed when the grain size is reduced below ≈10 μm, i.e. at a length scale much larger than the critical size. In this case it is more appropriate to refer to scaling effects as they are not related to material confinement. The aim of this contribution is to review the current understanding of size and scaling effects in perovskite ferroelectric ceramics and, in particular, in BaTiO₃. After a short survey on the intrinsic limits of ferroelectricity and on the impact of particle/grain size on phase transitions, the role of interfaces such as ferroelectric/ferroelastic domain walls and grain boundaries in scaling of dielectric and piezoelectric properties will be discussed in detail. Multiple mechanisms combine to produce the observed scaling effects and the maximization of the dielectric constant and piezoelectric properties exhibited by BaTiO₃ ceramics for an intermediate grain size of ≈1 μm. The broad dispersion of experimental data is determined by spurious effects related to synthesis, processing and variation of Ba/Ti ratio. Furthermore, we will consider these size effects, and other properties in relation to the downsizing the modern multilayer BaTiO₃ based capacitors.