The giant piezoelectric effect: electric field induced monoclinic phase or piezoelectric distortion of the rhombohedral parent?

Lead zinc niobate-lead titanate (PZN-PT) single crystals show very large piezoelectric strains for electric fields applied a long the unit cell edges e.g. [001](R). It has been widely reported that this effect is caused by an electric field induced phase transition from rhombohedral (R3m) to monoclinic (Cm or Pm) symmetry in an essentially continuous manner. Group theoretical analysis using the computer program ISOTROPY indicates phase transitions between R3m and Cm (or Pm) must be discontinuous under Landau theory. An analysis of the symmetry of a strained unit cell in R3m and a simple expansion of the piezoelectric strain equation indicate that the piezoelectric distortion due to an electric field along a cell edge in rhombohedral perovskite-based ferroelectrics is intrinsically monoclinic (Cm), even for infinitesimal electric fields. PZN-PT crystals have up to nine times the elastic compliance of other piezoelectric perovskites and it might be expected that the piezoelectric strains are also very large. A field induced phase transition is therefore indistinguishable from the piezoelectric distortion and is neither sufficient nor necessary to understand the large piezoelectric response of PZN-PT.