Fig. 1: Long-range average symmetry evolution.

a ABO3 perovskite structure showing the surrounding oxygen cage of A-site and B-site cations. b Stereographic projection of a pseudocubic perovskite viewed along the [001]p direction based on the direction of polar vector. MA, MB and MC denote different monoclinic structures. T, R, and O specify tetragonal, rhombohedral, and orthorhombic structures, respectively. c Structural phase diagram for PMN–xPT with defined symmetries and morphotropic phase boundary. The dots mark the analyzed compositions at room temperature. d The results of Rietveld-refinement based on high-resolution synchrotron X-ray diffraction patterns. The circle point and solid line indicate the observed and fitted data, respectively. For 35PT, the blue and pink line show the individual peaks from T and MC, respectively.