Spatial variations of polarization in ferroelectrics and related materials

Electron microscopy studies in lanthanum doped lead titanate reveals the evolution of a spatial modulation in the magnitude of the spontaneous polarization with the increase of the lanthanum dopant. On the incorporation of -25 atom percent lanthanum, the conventional domain structure becomes ill-defined, and tweed microstructures are observed. The structural information can be associated with the change from normal ferroelectric to diffuse ferroelectric phase transition behavior. Different from twin structures, these modulated structures represent a new type of polarization variation existing within a single domain. Further understanding of the observed spatial variation in polarization requires structural analysis at the atomic scale. Holographic electron microscopy is proposed as a potential tool to study various polarization gradients in ferroelectric materials. Understanding the spatial variations in polarization is essential to better comprehend the extrinsic contributions to the elasto-dielectric properties in ferroelectrics.