Elastic properties of cubic and rhombohedral BiFeO3 from first-principles calculations

First-principles elastic constants c(ij)'s of BiFeO3 with cubic nonmagnetic (NM)/ferromagnetic (FM) structures and rhombohedral antiferromagnetic (AFM) structure have been calculated within the generalized gradient approximation (GGA) and the GGA+U approach. In addition, the elastic properties of polycrystalline aggregates including bulk modulus and shear modulus are also determined and compared with experiments. It is found that the predicted c(ij)'s decrease with increasing volume (or decreasing pressure) except for the c(14) of the rhombohedral AFM phase. The cubic NM and FM phases are predicted to be harder than the rhombohedral AFM one, indicated by their smaller equilibrium volumes and larger bulk moduli. Additionally, the cubic FM phase is found nearly isotropy (by GGA and GGA+U with U-eff=6 eV), and the cubic NM phase is mechanical unstable at high temperatures. The presently predicted c(ij)'s of BiFeO3 provide helpful guidance for future measurements, and make the stress estimation and elastic energy calculation in BiFeO3 thin films possible.