Size effects in ferroics

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Abstract
Ferroic crystals have domain walls which can be moved by electric field (ferroelectrics), magnetic fields (ferromagnets), mechanical stress (ferroelastics) or a higher order phenomenon involving a combination of the three (secondary ferroics). Because of the large contribution movable domain walls make to piezoelectricity, permittivity, permeability, and to elastic compliance, these materials are used as transducers, capacitors, transformers, sensors and actuators. A basic understanding of size effects is critical to the development of these devices, which are being made in smaller and smaller sizes in the form of thin films, fiber-filled composites, and multilayer ceramics with submicron grain sizes. Four regimes are observed when the particle size is made smaller: (1) crystals or large grains in ceramics contain many domain walls, but the number of walls, and the number of types of walls, grows smaller as grain size is reduced. (2) When the size is decreased sufficiently, the particles become single domain. The properties of single domain particles are quite different from those of multi-domain particles. (3) At yet smaller grain size, the particles exhibit diffuse phase transformations, nonlinear physical properties, and glass-like behavior. (4) The fourth regime is in the nanometer range where ferroic behavior disappears as surface effects begin to dominate.

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