RESUMO
First principles studies of multiferroic materials, such as bismuth ferrite (BFO), require methods that extend beyond standard density functional theory (DFT). The DFT + U method is one such extension that is widely used in the study of BFO. We present a systematic study of the effects of the U parameter on the structural, ferroelectric and electronic properties of BFO. We find that the structural and ferroelectric properties change negligibly in the range of U typically considered for BFO (3-5 eV). In contrast, the electronic structure varies significantly with U. In particular, we see large changes to the character and curvature of the valence band maximum and conduction band minimum, in addition to the expected increase in band gap, as U increases. Most significantly, we find that the [Formula: see text]/[Formula: see text] ordering at the conduction band minimum inverts for U values larger than 4 eV. We therefore recommend a U value of at most 4 eV to be applied to the Fe d orbitals in BFO. More generally, this study emphasises the need for systematic investigations of the effects of the U parameter not merely on band gaps but on the electronic structure as a whole, especially for strongly correlated materials.
RESUMO
Natural materials such as nacre exhibit a high resistance to crack propagation, inspiring the development of artificial composites imitating the structure of these biological composites. We use a phase field approach to study the role played by the elastic modulus mismatch between stiff and soft layers on crack propagation in such bioinspired composites. Our simulations show that the introduction of a thin layer of a soft phase in a stiff matrix can lead to arrest of a propagating crack and can also lead to crack branching. The crack branching observed in the phase field model is analyzed using a cohesive zone approach. Further, we show that the toughness of such a composite can be substantially higher than that of its constituents.
