The origins of electromechanical indentation size effect in ferroelectrics

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.