Intrinsic Piezoelectric Response in Perovskite Alloys: PMN-PT versus PZT

First-principles supercell calculations and the modern theory of polarization are used to compute the e₃₃ piezoelectric coefficients of Pb(Zr0.5Ti0.5O₃) (PZT) and 0.60Pb(Mg1/3Nb2/3)O₃+0.40PbTiO₃ (PMN-PT) alloys. A drastic enhancement by a factor of 2.7 is found for e₃₃ when going from PZT to PMN-PT. The huge value of e₃₃ in PMN-PT comes from the large response of the internal coordinates of Pb, Ti, Nb, and O atoms to a macroscopic strain. On the other hand, the Mg atoms contribute little to the piezoelectricity for dielectric and elastic reasons.