Achieving high d 33 and d 33* simultaneously through the synergy of internal bias fields and multiphase coexistence in (Bi 0.5 Na 0.5 ) 0.76 Sr 0.24 TiO 3 ceramics

(Bi _0.5 Na _0.5 )TiO ₃ -based lead-free piezoelectric ceramics face a central challenge: the difficulty in simultaneously achieving a high piezoelectric constant ( d ₃₃ ) and a large-signal piezoelectric constant ( d ₃₃ *), which limits their application in actuators and transducers. This study proposes a synergistic strategy of constructing a three-phase coexistence region and introducing an internal bias field in (Bi _0.5 Na _0.5 ) _0.76 Sr _0.24 TiO ₃ ceramics through Li ⁺ doping to coordinate the trade-off between d ₃₃ and d ₃₃ *. Through this strategy, the (Bi _0.5 Na _0.5 ) _0.76 Sr _0.24 TiO ₃ - x wt% Li ₂ CO ₃ (BNSTL- x ) ceramics with x  = 1.00 simultaneously achieve outstanding piezoelectric properties: d ₃₃  = 281 pC/N and d ₃₃ * = 1250 pm/V. The rhombohedral-tetragonal-pseudocubic (R3c-P4bm-Pm\(\:\stackrel{-}{3}\)m) three-phase coexistence structure, combined with an optimized grain size, contributes to the high piezoelectric response. Furthermore, the superposition of the internal bias field induced by defect dipoles and the external electric field generates highly asymmetric bipolar strain curves, thereby significantly enhancing d ₃₃ *. This work provides a novel material design strategy for developing high-performance lead-free piezoelectric ceramics.