Detailed structural investigations on the substitution-induced structural phase transition from the rhombohedral phase to an orthorhombic phase in (Bi,RE)FeO3 epitaxial thin films (RE = La, Sm, and Dy) grown on (100) SrTiO3 substrates are presented. X ray diffraction reveals that the unit cell dimensions of the orthorhombic phase are strongly dependent on the type of the RE dopant. For RE = La3+ ion, which has an ionic size comparable to the Bi3+ ion, the unit cell is found to be a(0) x a(0) x 2a(0), where a(0) is the pseudo-cubic lattice parameter. This is in contrast with the root 2a(0) x root 2a(0) x 2a(0) unit cell for the case of smaller ionic radius RE (= Sm and Dy) elements. While clear double-hysteresis loops in the polarization versus electric-field curves due to fieldinduced transitions are observed for smaller ionic radius RE (= Sm and Dy), no signature of the double hysteresis loops is observed for the RE = La case across the structural boundary. We have also performed systematic tracking of the structural phases as functions of the RE composition and temperature, based on which we propose a phase diagram. This work reveals that the ionic size of the RE element plays a critical role in the evolution of the structural and functional properties of RE-substituted BiFeO3 thin film materials systems. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3605492]