Fig. 4: Domain structure and polarization property of the materials simulated by the phase-field method.

a Strain-electric field (S-E) loops of the AFE MLCCs (out-of-plane direction). b Schematic of interlaminar strain at the dielectric layer interfaces induced by the electrostriction effect. c, d Phase-field simulated dipole orientation and domain structure in the dielectric layers without and with the interlaminar strain (E = 400 kV cm⁻¹). e P_z distribution (dashed boxes of Fig. 4c, d) across the out-of-plane direction of each dielectric layer. For simplicity, P_z values are fitted with a high-order polynomial. f Three-dimensional free energy density surface diagram under zero strain, in-plane tensile strain, and in-plane compressive strain.