Local Fe and Nb contributions to the intrinsic polarization of Pb(Fe0.5Nb0.5)O3 revealed by the geometrical polarization approach

In this paper, the spontaneous polarization of the Pb(Fe 0 . 5 Nb 0 . 5 )O 3 (PFN) multiferroic compound is determined by using the Geometrical Polarization Approach (GPA), a semi-empirical method to obtain spontaneous polarization from refined crystallographic data. Two distinct unit cells were analyzed: a conventional tetragonal unit cell ( P 4 mm ) with statistical Fe/Nb occupancy at the perovskite B-site, and an expanded supercell composed of eight stacked unit cells refined in the triclinic P 1 space group, allowing an explicit description of Fe and Nb atomic positions within the supercell. While both approaches yield comparable Rietveld refinement quality, the conventional unit cell significantly underestimated the spontaneous polarization (∼2.3 μC/cm 2 ). In contrast, the supercell revealed distinct local polarization contributions from Fe and Nb. The global polarization calculated from the supercell structure (∼2.9 μC/cm 2 ) differs from that obtained using the statistically averaged conventional cell, indicating the importance of the structural details in the polarization determination. Electron-density mapping further revealed distinct local electronic environments around Fe and Nb, suggesting different dipole asymmetries that are consistent with their different polarization contributions. These results support the GPA as an effective tool to resolve intrinsic structural polarization features in chemically disordered perovskites and offer insights into the structure–property relationships in multifunctional ferroelectric materials.