  In this work, we explore the origin and type of charge carriers, and their
transport mechanism in polycrystalline barium-iron-niobate (BFN,
BaFe$_{0.5}$Nb$_{0.5}$O$_3$) ceramics, at lower temperatures between 20K and
300K. The observed point defects at grain andsurface defects at grain boundary
region are responsible for the electronic conductivity, whereas dipoles at
grain boundary region are responsible for the ionic conductivity, these
independent electronic and ionic conductivity were responsible for the total
conductivity of our BFN sample. The required activation energy for conduction
of electrons in grain boundary region and ions in grain region were calculated
to be 317 meV and 17 meV respectively. The electronic conductivity of grain
region obey Jonscher's power law. Analysis of the temperature dependent
frequency exponent suggest that the electronic conductivity of grain follows
the overlapping large polaron tunneling (OLP) model. The temperature dependent
conductivity follows the Mott variable range hopping model(VRH), showing
hopping range increases with decreasing temeprature. The defect density of the
grain obtained to be $3.17 \times 10^{17}$ eV/cm$^3$. The contribution of
phonon to the conductivity understood by considering Schankenberg model,
activation energy of 110 meV corresponds to the multiphonon (both optical and
acoustic) and 1.6 meV corresponds to acoustic phonon only. Our systematic study
provides in-depth understanding of the low temperature conductivity mechanism
of polycrystalline BFN ceramics.
