  Metals exhibit a size-dependent hardening when subject to indentation.
Mechanisms for this phenomenon have been intensely researched in recent times.
Does such a size-effect also exist in the electromechanical behavior of
ferroelectrics?--if yes, what are the operative mechanisms? Our experiments on
BaTiO3 indeed suggest an electromechanical size-effect. We argue, through
theoretical calculations and differential experiments on another
non-ferroelectric piezoelectric (Quartz), that the phenomenon of
flexoelectricity(as opposed to dislocation activity) is responsible for our
observations. Flexoelectricity is the coupling of strain gradients to
polarization and exists in both ordinary and piezoelectric dielectrics. In
particular, ferroelectrics exhibit an unusually large flexoelectric response.
