Fig. 4: Phase-field simulation, breakdown strength and impedance spectrum analysis of ceramics.

a, b The out of plane phase image of pure BSN (a) and BSTN-0.1Ta (b) after a writing voltage of ±12 V; (c–e) Phase-field simulations on dielectric breakdown of the BSN (c) and BSTN-Ta (d), corresponding nominal electric field-charge-density relation (e); (f) Weibull distribution of experimental breakdown strength; (g) Impedance spectra of BSTN-0.1Ta ceramics at a temperature region of 460–560 °C; (h) The fitted activation energy of grains and grain boundaries.