Domain geometry engineering and domain average engineering of ferroics

Multidomain samples of ferroics (ferroelectrics, ferroelastics, and related materials) with fixed geometrical distribution of domains can offer new macroscopic properties required for particular applications. Two extreme cases of such applications are defined. In domain-geometry-engineered samples of ferroic crystals, the spatial distribution of domains and thus the spatial distribution of tensorial properties is tuned to correspond to the k-vectors of applied electric, optical or acoustic fields. For a given wavelength, the size, geometry, and distribution of domains give rise to a qualitatively new kind of response specified by the symmetry of the multidomain system. In domain-average-engineered samples of ferroic crystals, the specimen is subdivided into a very large number of domains, representing mu domain states where mu is smaller than the theoretically allowed maximum number, and forming a regular or irregular pattern, Its response to external fields is roughly described by tensorial properties averaged over all of the domain states involved. The effective symmetry of the domain-average-engineered system is given by a point group H and we show how it can be determined. As an example, all groups H are specified for domain-average-engineered samples which can arise in a material undergoing the phase transition with symmetry change from m(3) over bar m to 3m.