Materials Contrast in Piezoresponse Force Microscopy
  Piezoresponse Force Microscopy contrast in transversally isotropic material corresponding to the case of c+ - c- domains in tetragonal ferroelectrics is analyzed using Green's function theory by Felten et al. [J. Appl. Phys. 96, 563 (2004)]. A simplified expression for PFM signal as a linear combination of relevant piezoelectric constant are obtained. This analysis is extended to piezoelectric material of arbitrary symmetry with weak elastic and dielectric anisotropies. This result provides a framework for interpretation of PFM signals for systems with unknown or poorly known local elastic and dielectric properties, including nanocrystalline materials, ferroelectric polymers, and biopolymers. 
Sergei V. Kalinin, Eugene A. Eliseev, and Anna N. Morozovska