Multiscale modeling of ferroelectrics with stochastic grain size distribution

Macroscopic properties of ferroelectrics are controlled by processes on the microscale, in particular the switching of crystal unit cells and the movement of domain walls, respectively. Besides these microscopic levels, the grains of a polycrystalline material constitute the mesoscopic scale. Interactions of grains with statistically distributed orientations, as a consequence of mechanical and electrostatic mismatch, give rise to for example, residual stress which in turn affects domain switching. A multiscale modeling thus has to incorporate at least three interacting scales. In this context, the condensed method has recently been elaborated as an efficient tool with low computational cost and effort of implementation. It is extended toward statistical distributions of grain sizes in a representative material volume element and amended with regard to the modeling of domain evolution. Each of the few parameters of the constitutive approach has a unique physical meaning and is adapted to available experimental values of macroscopic quantities of barium titanate taken from various sources.

As-Grown Domain Structure in Calcium Orthovanadate Crystals

An as-grown domain structure in nominally pure and Mn-doped calcium orthovanadate (CVO) crystals was studied by several methods of domain imaging: optical microscopy, piezoelectric force microscopy, and Cherenkov-type second harmonic generation. The combination of imaging methods provided an opportunity for comprehensive study of the domain structure on the polar surface and in the bulk of the samples. It was shown that, in nominally pure CVO crystals, an irregular 3D maze of rounded domains, with charged walls, essentially tilted from the polar direction, was present. It was proposed that the domain structure was formed just below the phase transition temperature and persisted during subsequent cooling. Such behavior is due to effective bulk screening of the depolarization field and a low value of the pyroelectric field which appears during cooling. The revealed formation of triangular domains and flat fragments of domain walls in Mn-doped CVO was attributed to polarization reversal under the action of the polar component of the pyroelectric field, above the threshold value for domain switching. This fact represents the first observation of the domain switching in CVO crystals.