Lead-free (1-$x$)K$_{0.5}$Bi$_{0.5}$TiO$_3$-$x$BiFeO$_3$ ceramics with $x = 0.1$-0.4 were prepared by a conventional solid-state reaction. X-ray diffraction coupled with Rietveld refinement confirmed main perovskite phase with pseudo-cubic structure. Temperature-dependent dielectric measurements revealed broad dielectric anomalies and frequency dispersion, indicating relaxor behaviour. At 100 kHz, the highest room-temperature relative permittivity of 925 was obtained at $x = 0.2$. The highest maximum and remanent polarisation were obtained at $x = 0.3$ with 30 and 16 $\mu$C cm$^{-2}$, respectively. This work demonstrates a new lead-free solid solution for dielectric and ferroelectric applica... More >