Piezoelectric effects and electromechanical theories at the nanoscale.

Considerable effort has been made to study the piezoelectric effect on the nanoscale, which serves as a physical basis for a wide range of smart nanodevices and nanoelectronics. This paper reviews recent progress in the research on the piezoelectric properties and electromechanical effects of piezoelectric nanomaterials (PNs). The review begins with an introduction to existing PNs which exhibit a diverse range of atomic structures and configurations. The nanoscale measurement of their effective piezoelectric coefficients (EPCs) is summarised with an emphasis on the major factors determining the piezoelectric properties of PNs. The paper concludes with a review of the electromechanical theories that are able to capture the small-scale effects on PNs, which include the surface piezoelectricity, flexoelectricity and Eringen's nonlocal theory. In contrast to the classical theories, two types of EPCs are defined, which were found to be size-dependent and loading condition-selective.