First-Principles Study of Piezoelectricity inPbTiO3

The first self-consistent computations of piezoelectricity in a ferroelectric are presented. Bulk spontaneous polarization, dynamical charges ( $Z^{*}$), and the full piezoelectric stress tensor of ${\mathrm{PbTiO}}_3$ were determined from ground-state Berry's phase calculations using the all-electron linearized augmented plane wave method. Both the proper and total piezoelectric moduli were computed and were found to be significantly different. The theoretical piezoelectric stress moduli, $e_{15}=3.15\mathrm{}\mathrm{C}/{\mathrm{m}}^2$, $e_{31}=-0.93\mathrm{}\mathrm{C}/{\mathrm{m}}^2$, and $e_{33}=3.23\mathrm{}\mathrm{C}/{\mathrm{m}}^2$, agree well with single crystal experimental data.