Morphotropic phase boundary structures of relaxor ferroelectrics

Relaxor based ferroelectric crystals such as PZN-xPT and PMN-xPT have drawn a great attention due to an obervation of a huge piezoelectric coefficient and an ultrahigh strain level in the system. Although the first principles theoretical calculations attempt to explain the observations on the basis of a single perovskite unit cell, recent observations of a complex mesoscopic ordering process and a heterogeneous domain structure tend to support a more complex supercell of many perovskite unit cells. Since correct stoichiometry of PZN-xPT(or PMN-xPT) does not allow Fm3m and polarized Raman scattering data forbids P (3) over bar m1 lattice structures we may assume a simple pile-up structure of supercells without any specific superlattice translational symmetry. Our random pile-up structure requires a supercell of 27 perovskite unit cells to satisfy the boundary conditions of structural and compositional variations. Using this supercell model of mesoscopic structural modifications we calculate specific mixing concentrations at MPB of various ferroelectric relaxors to be compared with observed values.