First-principles study of piezoelectricity in tetragonal PbTiO3

The e 33 component of the piezoelectric strain tensor in tetragonal PbTiO3 was studied by an allelectron ab initio method, and was found to be in good agreement with the experimental piezoelectric stress constant of high quality twin-free single PbTiO3 crystals. Equations of the density functional theory were solved within the general gradient approximation (GGA) using the general potential linearized augmented plane-wave local orbital (LAPW + LO) method. Macroscopic polarization values necessary to calculate the piezoelectric coefficient and elements of the Born effective charge tensors were determined via finite differences using the geometric phase formulation. In this approach, bulk quantities are expressed as the property of the phase of the wavefunction in terms of a Berry connection. The e 33 component of the piezoelectric tensor, i.e. the change in polarization with strain, was extracted from results of groundstate Berry's phase calculations performed on units cells of different strains and volumes. We found that in PbTiO3 the large intrinsic piezoelectric response is mainly due to strong coupling between macroscopic strain and internal microscopic strain, giving the value of 3.23 C/m2 for the e 33 modulus.