Three intrinsic relationships of lattice parameters between intermediate monoclinic M-C and tetragonal phases in ferroelectric Pb (Mg1/3Nb2/3)(1-x)Ti-x O-3 and Pb (Zn1/3Nb2/3)(1-x)Ti-x O-3 near morphotropic phase boundaries

Systematic analysis of extensive experimental data confirms the theoretical prediction of three intrinsic relationships of lattice parameters between the recently discovered intermediate monoclinic M-C phase and the conventional tetragonal phase in ferroelectric Pb[(Mg1/3Nb2/3)(1-x)Ti-x]O-3 and Pb[(Zn1/3Nb2/3)(1-x)Ti-x]O-3 near the morphotropic phase boundaries. These intrinsic relationships of lattice parameters are fulfilled by experimental data reported in the literature for different temperatures, compositions, and electric fields. They present quantitative evidence that the intermediate monoclinic M-C phase is a mixed state of nanometer-sized twin-related domains of the conventional ferroelectric tetragonal phase. The analysis supports the concept recently proposed by Khachaturyan and co-workers [Phys. Rev. Lett. 91, 197601 (2003)] that the intermediate monoclinic M-C phase is adaptive ferroelectric and ferroelastic phase, which is homogeneous only on the macroscale while inhomogeneous on the nanoscale. Due to the small domain size and small ferroelastic strain, the conventional diffraction measurement does not resolve the lattice of individual nanodomains rather instead only perceives the average diffraction effect of nanotwins, yielding the experimentally observed monoclinic symmetry. The result indicates that the electric-field-induced domain-wall movement plays an essential role in the ultrahigh electromechanical responses of Pb[(Mg1/3Nb2/3)(1-x)Ti-x]O-3 and Pb[(Zn1/3Nb2/3)(1-x)Ti-x]O-3, and the high-density domain walls associated with the nanotwins have a significant contribution to the peculiar material properties near the morphotropic phase boundaries.