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.
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