The three-dimensional orientation of polarization vectors at the surface of ferroelectric barium–titanate (BaTiO3) ceramics is evaluated using voltage-modulated scanning force microscopy (SFM). By applying an ac voltage to the conductive SFM tip, we measure the relative amount of the three orthogonal components Px, Py, and Pz, of the polarization vector at any surface point. The measured polarization orientation together with the actual domain-wall orientation allows a precise reconstruction of the crystallographic orientation of the investigated grains down to a 40 nm resolution. Excellent agreement is obtained when comparing this orientation with the crystallographic reconstruction revealed by etch patterns from the sample surface topography. We show that the surface topography manifests a domain structure, which was present in the past, while the actual ferroelectric domain configuration is revealed by the modulation technique.

Piezoresponse force microscopy (PFM) is applied to image ferroelastic formed c domains in a single crystal ferroelectric barium titanate bulk material. A simple model and an analytical approach are presented, which provides a basis to understand the complex tip-surface interactions responsible for the image contrast in PFM. In particular, the measured amplitude of the piezoresponse out-of-plane surface displacements of a $C^{-}$ domain is compared with theoretical results based upon a three-dimensional Green’s function solution. The electric field distribution in the tip-surface contact is determined using image-charge calculations for a spherical tip separated by a thin water layer from a mechanically isotropic and electrically anisotropic dielectric half plane.