Figure 4: Temperature-dependent microstructure and dielectric response for [100]-poled PNR-ferroelectric composites.

(a,b) Temperature-dependent microstructures and dielectric permittivities, respectively. In a, the colour bar denotes the angle between the polar vector of the grids and the [100] direction. Here an example of specific PNRs’ transformation to the ‘collinear’ state is given with increasing temperature from 100 to 150 K, as marked by the black dashed circles. In b, the intrinsic dielectric permittivities of the ferroelectric matrix and the PNR are given for comparison. The error bars represent the s.d.’s and are obtained from five different random distributions of PNRs with a volume fraction of 7.5%. For calculation of the dielectric permittivities, the magnitude and period of the a.c. E-field were 10⁴ V m⁻¹ and 10⁵ time steps, respectively. The corresponding three-dimensional simulations, given in Supplementary Figs 13 and 14, show similar results to the two-dimensional simulations.