Design-oriented synergistic optimization of piezoelectric coefficient and coercive field in piezoceramics for the electrostrain enhancement

Large electrostrains in piezoceramics are highly desirable for actuators and precision positioning systems. The reported high strains are commonly achieved under disparate electric-field conditions, hindering the establishment of general design principles for strain enhancement. Here, a design-oriented framework correlating the piezoelectric coefficient ( d 33 ) and coercive field ( E c ) with strain evolution through a Gaussian differential unipolar strain model (d S uni /d E ) is developed. The model reveals that electrostrain is governed by the d 33 -related initial response amplitude and E c -defined peak transient piezoelectric coefficient ( d 33 ˆ T ), while the overall electrostrain evolution is intrinsically constrained by the fundamental d 33 – E c trade-off. These correlations provide a mechanistic basis for electrostrain optimization. A synergistic d 33 – E c optimization strategy is demonstrated by incorporating a relaxor end component together with acceptor-donor co-doping. This approach simultaneously increases both d 33 and E c , expanding the d S uni /d E profile and yielding an enhanced strain of 0.19% under 2 kV/mm. The rise in E c results from strengthened tetragonality, while the improved d 33 stems from reinforced relaxor behavior that facilitates reversible domain switching, as corroborated by refined static domain structure and dynamic ferroelectric scaling analysis. This work establishes a differential strain-based design paradigm, offering fundamental insights into electrostrain regulation through d 33 – E c synergy in piezoceramics.