Strain-driven phase transitions and related intrinsic polarization, dielectric, and piezoelectric properties for single-domain films were studied for BiFeO ₃ using phenomenological Landau–Devonshire theory. A stable and mixed structure between tetragonal and rhombohedral-like (monoclinic) phases is predicted at a compressive misfit strain of u_m=-0.0382 without an energy barrier. For a tensile misfit strain of u_m=0.0272 , another phase transition between the monoclinic and orthorhombic phases was predicted with sharply high dielectric and piezoelectric responses.