Fundamental formulations and recent achievements in piezoelectric nano-structures: a review.

Piezoelectric nano-structures have been regarded as the next-generation piezoelectric material due to their inherent nano-sized piezoelectricity. This review summarizes the recent theoretical and experimental findings in piezoelectric nano-structures, including piezoelectric nanowires, nanoplates, nanobeams, nanofilms, nanoparticles, and piezoelectric heterogeneous materials containing piezoelectric nano-inhomogeneities. To begin, the types of piezoelectric nano-structured materials and the wide application of piezoelectric nano-structures in recent years are delineated. Next, the theoretical foundations including the definition of surface stress and electric displacement, the surface constitutive relations, the surface equilibrium equations, and nonlocal piezoelectricity, and their applications, are illustrated. Then, the effective mechanical and piezoelectric properties are depicted. Furthermore, the experimental investigations are classified, and some important observations are discussed. Finally, the perspectives and challenges for the future development of piezoelectric nano-structures are pointed out.