Fig. 4.

Schematic of two representative grains in poled BiFeO₃. a The diffraction planes and orientations of 71° domain walls, occurring on (011)_pc planes, in {100}_pc and {111}_pc grains. In {100}_pc grain (top grain), the 71° domain wall (solid blue lines) is perpendicular to the 100_pc diffracting planes (black dashed line). In the {111}_pc grain, the 71° domain walls separate 111_pc and 11$\overline{1}$_pc diffracting planes and form an angle of 35.26°. The angle between 71° domain walls in {100}_pc and {111}_pc grains is 54.74°; b charge distribution on conductive domain walls under applied external electric field, E_app = E₀sin(ωt). Charge redistribution rate is different for grains with different crystallographic orientations, i.e., {100}_pc and {111}_pc. Their dielectric permittivities, electrical conductivities and piezoelectric coefficients are thus different, represented by κ₁₀₀ and κ₁₁₁, σ₁₀₀ and σ₁₁₁, and d₁₀₀ and d₁₁₁, respectively. This will result in different effective fields in individual grains, represented by E₁₀₀ and E₁₁₁. The grain elongations upon field application, indicated by the solid black shapes, are due to the piezoelectric effect in the {100}_pc grain and non-180° domain wall motion in the {111}_pc grain