Atomic formulation of nano-piezoelectricity in barium titanate

Atomistic Field Theory (AFT) is used to determine nano-piezoelectricity of barium titanate. The computational method, Generalized Finite Element Method (GFEM), is utilized to formulate a nanocube made of cubic phase barium titanate (BaTiO₃) under a simple tensile loading. The results show how the mechanical displacement induces the polarization and the electric potential. Our simulation predicts how mechanical loading generates the voltage distribution at the nanoscale. This study also shows at nanoscale, a 6 nm×6 nm×6 nm cube can generate ̃27.2 volts, which can be a significant energy source. The effective d₃₃ is ̃3×10^-10 m/V. This theory and numerical scheme can serve as a possible design tool for Nanogenerator, nano-piezoelectronics and nano-energy harvesting.