Size and scaling effects in ferroelectric ceramics. A tribute to Paolo Nanni

The change in properties with decreasing the physical dimensions of the system is commonly referred to as "size effect". Ferroelectrics are particularly prone to show strong size effects as ferroelectricity arises from a long-range ordering phenomenon. Barium titanate (BaTiO3), the prototype ferroelectric perovskites, exhibits long-range ordering of the electrical dipoles related to the cooperative off-center displacement of the Ti4+ ions in the TiO6 octahedra, determining the appearance of a spontaneous polarization and lattice strain. The confinement of the system in a small volume and any other obstacle (dislocations, grain boundaries, pores, etc.) which disrupt the long-range ferroelectric order will have an impact on ferroelectricity-related properties, such as polarization, dielectric permittivity, tunability and piezoelectric coefficients. The modification of the domain structure and domain mobility with decreasing grain size also greatly contributes to the alteration of properties in comparison to the bulk reference values. In the case of BaTiO3 ceramics, the dielectric permittivity and the piezoelectric coefficients are maximized for a grain size of ?1 micron. Below this value, a progressive suppression of the properties is observed. Size and scaling effects in ferroelectric materials have received significant interest over the last decades from a fundamental point of view, i.e. the determination of the critical size below which ferroelectricity eventually disappears, and the practical implications related to the continuous miniaturization of active and passive devices utilizing ferroelectric materials. For example, the thickness of the dielectric layers in BaTiO3-based multilayer ceramic capacitors (MLCCs) has decreased in twenty years from about 10 micron to half a micron with grains smaller than 100 nm while the number of layers has increased to 1000. One of the main contributions of Prof. Paolo Nanni and his group to the field of ferroelectric materials is the work on the size effect in barium titanate ceramics. He realized that a better understanding of the relationships between processing and microstructure was essential for obtaining dense materials with homogeneous grains over a wide range of sizes and thus systematically investigate the size effect. The fabrication of dense ceramics with grain size down to 30 nm was made possible by (i) using fine powders with narrow particle size distribution synthesized by a hydrothermal-like method, and (ii) adopting advanced rapid sintering techniques such as spark plasma sintering. The evolution of properties with decreasing grain size revealed the importance of both intrinsic and extrinsic effects. Intrinsic effects are mainly determined by the suppression of the spontaneous lattice strain. Important extrinsic contributions come from the dilution effect of the grain boundaries on the dielectric permittivity, determined by the distribution of the electric field inside the ceramic, and the blocking effect of the grain boundaries on the motion of the domain walls. In this talk we will present an overview on the current state of understanding of size and scaling effects in ferroelectric ceramics with particular emphasis on barium titanate, mentioning the contribution of Paolo Nanni and his group to the specific field.