Polarization rotation dynamics and path-dependent piezoelectricity in relaxor ferroelectric single crystals: A three-dimensional phase-field study

Relaxor ferroelectric single crystals, such as PMN − 0.3 PT , exhibit exceptional piezoelectric performance, widely attributed to polarization rotation through intermediate phase structures. However, the dynamic pathways of polarization rotation under external fields and their influence on piezoelectricity remain unclear. In this work, a three-dimensional phase-field model is developed with a novel displacement-based periodic boundary condition capable of describing non-zero strain states. Using a staggered scheme, we systematically investigate the evolution of phase structures, polarization rotation paths, and path-dependent piezoelectric responses under mechanical, electrical, and combined electromechanical loading. Results reveal that compressive stress transforms the rotation path from R → M b → M → M c → T to R → M b → O → M c → T, while tensile stress and electric fields maintain a stable R → M a → T path. Under coupled loading with a small sinusoidal electric perturbation, the effective d 33 exhibits a pronounced “increase–decrease” trend with stress, consistent with experimental observations. The study elucidates how rotation-path topology and intermediate phases govern piezoelectric performance, providing guidance for tailoring high-performance relaxor ferroelectric devices. Three-dimensional phase-field simulations reveal external fields-induced polarization rotation paths in PMN-0.3PT single crystals, highlighting the strong correlation between intermediate monoclinic phases and path-dependent piezoelectric enhancement.