Symmetry of piezoelectric (1-x)Pb(Mg_1/3Nb_2/3)O ₃-xPbTiO₃ (x=0.31) single crystal at different length scales in the morphotropic phase boundary region

We use probes of three different length scales to examine symmetry of (1-x)Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ (PMN-xPT) single crystals in the morphotropic phase boundary (MPB) region at composition x = 0.31 (PMN-31% PT). On the macroscopic scale, x-ray diffraction (XRD) shows a mixture of strong and weak diffraction peaks of different widths. The closest match to XRD peak data is made with monoclinic Pm (M_C) symmetry. On the local scale of a few nanometers, convergent beam electron diffraction (CBED) studies, with a 1.6-nm electron probe, reveal no obvious symmetry. These CBED experimental patterns can be approximately matched with simulations based on monoclinic symmetry, which suggests locally distorted monoclinic structure. A monoclinic Cm (M_A or M_B)-like symmetry could also be obtained from certain regions of the crystal by using a larger electron probe size of several tens of nanometers in diameter. Thus the monoclinic symmetry of single crystal PMN-31%PT is developed only in parts of the crystal by averaging over locally distorted structure on the scale of few tens of nanometers. The macroscopic symmetry observed by XRD is a result of averaging from the local structure in PMN-31%PT single crystal. The lack of local symmetry at a few nanometers scale suggests that the polarization switching results from a change in local displacements, which are not restricted to specific symmetry planes or directions.