spontaneous polarization, dynamical charges (Z*), and the full piezoelectric stress tensor of
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 C/m 2, e 31=− 0.93 C/m 2, and e 33= 3.23 C/m 2, agree well with …