1：Experimental Design and Method Selection:

The study uses composition engineering and sintering process regulation to control grain sizes and internal stress, employing conventional solid-state reaction for ceramic fabrication. Theoretical models include polarization coupling and internal stress models to explain electro-strain behaviors.

2：Sample Selection and Data Sources:

Polycrystalline {Bi0.5[(Na0.80K0.20)1-xLix]0.5}1-ySryTiO3 ceramic samples were fabricated with specific compositions, selected based on prior studies to exhibit critical relaxor-ferroelectric behavior.

3：5[(Na80K20)1-xLix]5}1-ySryTiO3 ceramic samples were fabricated with specific compositions, selected based on prior studies to exhibit critical relaxor-ferroelectric behavior. List of Experimental Equipment and Materials:

3. List of Experimental Equipment and Materials: Raw chemicals (Bi2O3, Na2CO3, K2CO3, Li2CO3, SrCO3, TiO2) from Sinopharm Chemical Reagent Co., Ltd.; equipment includes ball mill, sintering furnace, ferroelectric tester (aixACCT TF Analyzer 1000), LCR analyzers (Tonghui 2816A, HP 4980), AFM/PFM (MFP-3D), FE-SEM (JSM-7500), EDS (FEI Titan 80-300), XRD (Bruker D8 Advanced), and synchrotron XRD (Shanghai Synchrotron Radiation Facility).

4：Experimental Procedures and Operational Workflow:

Powders were ball-milled, calcined, pressed into disks, sintered at 1090–1190 °C for 0.5-12 h, and electrodes applied. Electrical properties were measured under unipolar and bipolar electric fields, with fatigue tests at 90 kV/cm. Structural and domain analyses were performed using XRD, SEM, PFM, and in situ techniques.

5：5-12 h, and electrodes applied. Electrical properties were measured under unipolar and bipolar electric fields, with fatigue tests at 90 kV/cm. Structural and domain analyses were performed using XRD, SEM, PFM, and in situ techniques. Data Analysis Methods:

5. Data Analysis Methods: Data were analyzed using statistical methods and software associated with the equipment, focusing on strain, polarization, dielectric constant, and structural parameters to interpret electro-strain mechanisms.