  The presence of superlattice reflections and detailed analyses of the powder
neutron and x-ray diffraction data reveal that La rich
(BF$_{0.50}$-LF$_{0.50}$)$_{0.50}$-(PT)$_{0.50}$ (BF-LF-PT) has ferroelectric
rhombohedral crystal structure with space group \textit{$R3c$} at ambient
conditions. The temperature dependence of lattice parameters, tilt angle,
calculated polarization $(P_{s})$, volume, and integrated intensity of
superlattice and magnetic reflections show an anomaly around 170 K. Impedance
spectroscopy, dielectric and ac conductivity measurements were performed in
temperature range $473K \leq T \leq 573K$ to probe the origin of large remnant
polarization and frequency dependent broad transitions with large dielectric
constant near $T_c^{FE}$. Results of impedance spectroscopy measurements
clearly show contributions of both grain and grain boundaries throughout the
frequency range ($10^{3}$ Hz$\leq f\leq 10^{7} $ Hz). It could be concluded
that the grain boundaries are more resistive and capacitive as compared to the
grains, resulting in inhomogeneities in the sample causing broad frequency
dependent dielectric anomalies. Enhancement in dielectric constant and remnant
polarization values are possibly due to space charge polarization caused by
piling of charges at the interface of grains and grain boundaries. The
imaginary parts of dielectric constant ($\epsilon^{\prime\prime}$) Vs frequency
data were fitted using Maxwell-Wagner model at $T_c^{FE}(\sim 523$K) and model
fits very well with the data up to $10^{5}$ Hz. Magnetodielectric measurements
prove that the sample starts exhibiting magnetoelectric coupling at $\sim 170$
K, which is also validated by neutron diffraction data.
