Elastic properties of cubic and rhombohedralBiFeO3from first-principles calculations

Abstract

First-principles elastic constants c ij 's of BiFeO 3 with cubic nonmagnetic ͑NM͒/ferromagnetic ͑FM͒ structures and rhombohedral antiferromagnetic ͑AFM͒ structure have been calculated within the generalized gradient approximation ͑GGA͒ 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 pressure͒ 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 eV͒, and the cubic NM phase is mechanical unstable at high temperatures. The presently predicted c ij 's of BiFeO 3 provide helpful guidance for future measurements, and make the stress estimation and elastic energy calculation in BiFeO 3 thin films possible.

Photoexcitation of gigahertz longitudinal and shear acoustic waves in BiFeO3 multiferroic single crystal

“…The elastic constants C ij have been calculated for the rhombohedral structure and for various unit cell volumes. 19 At room temperature, x-ray diffraction experiments give a mean volume per atom of 0.0125 nm 3 . Therefore at this unit cell volume, we can extract from Shang et al 19 .…”

“…19 At room temperature, x-ray diffraction experiments give a mean volume per atom of 0.0125 nm 3 . Therefore at this unit cell volume, we can extract from Shang et al 19 . These values are in good agreement with the measurement data, even if the TA1 mode value is slightly out of the range determined experimentally.…”

“…These experimental values, which are very desired for BFO integration in micro-nanoelectronic devices, are in very good agreement with recent theoretical findings. 19 At room temperature, the bulk BFO structure is described by a rhombohedral R3c space group with a perovskite pseudocubic unit cell elongated along the [111] polarization direction. For the purpose of this study, bulk BFO crystal was grown using flux method.…”

“…Using the BFO density of q ¼ 8340 kgm À3 , longitudinal acoustic mode leads to a value of C 11 ¼ 205À255 GPa which is in a very good agreement with the theoretical predictions C 11 ¼ 220 GPa. 19 From Eqs. (3) and (4), a single experimental measurement of V TA1 and V TA2 cannot allow the determination of the full set of the additional elastic constants because there are three unknown constants against two experimental inputs.…”

“…Despite uncertainties of the order of 10% or less, arising from the experimental refractive index evaluation, these results are in good agreement with theoretical predictions based on first-principle calculations. 19 From the relationships between the three differently polarized sound velocities in rhombohedral crystal and the elastic coefficients that follow 28…”