  Relaxor ferroelectrics, which can exhibit exceptional electromechanical
coupling are some of the most important functional materials with applications
ranging from ultrasound imaging to actuators and sensors in
microelectromechanical devices. Since their discovery nearly 60 years ago, the
complexity of nanoscale chemical and structural heterogeneity in these systems
has made understanding the origins of their unique electromechanical properties
a seemingly intractable problem. A full accounting of the mechanisms that
connect local structure and chemistry with nanoscale fluctuations in
polarization has, however, remained a need and a challenge. Here, we employ
aberration-corrected scanning transmission electron microscopy (STEM) to
quantify various types of nanoscale heterogeneity and their connection to local
polarization in the prototypical relaxor ferroelectric system
Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$-PbTiO3 (PMN-PT). We identify three main
contributions that each depend on Ti content: chemical order, oxygen octahedral
tilt, and oxygen octahedral distortion. These heterogeneities are found to be
spatially correlated with low angle polar domain walls, indicating their role
in disrupting long-range polarization. Specifically, these heterogeneities lead
to nanoscale domain formation and the relaxor response. We further locate
nanoscale regions of monoclinic distortion that correlate directly with Ti
content and the electromechanical performance. Through this approach, the
elusive connection between chemical heterogeneity, structural heterogeneity and
local polarization is revealed, and the results validate models needed to
develop the next generation of relaxor ferroelectric materials.
