Rhombohedral ␣-Fe 2 O 3 has been studied by using density-functional theory ͑DFT͒ and the generalized gradient approximation ͑GGA͒. For the chosen supercell all possible magnetic configurations have been taken into account. We find an antiferromagnetic ground state at the experimental volume. This state is 388 meV/͑Fe atom͒ below the ferromagnetic solution. For the magnetic moments of the iron atoms we obtain 3.4 B , which is about 1.5 B below the experimentally observed value. The insulating nature of ␣-Fe 2 O 3 is reproduced, with a band gap of 0.32 eV, compared to an experimental value of about 2.0 eV. Analysis of the density of states confirms the strong hybridization between Fe 3d and O 2p states in ␣-Fe 2 O 3 . When we consider lower volumes, we observe a transition to a metallic, ferromagnetic low-spin phase, together with a structural transition at a pressure of 14 GPa, which is not seen in experiment. In order to take into account the strong on-site Coulomb interaction U present in Fe 2 O 3 we also performed DFTϩU calculations. We find that with increasing U the size of the band gap and the magnetic moments increase, while other quantities such as equilibrium volume and Fe-Fe distances do not show a monotonic behavior. The transition observed in the GGA calculations is shifted to higher pressures and eventually vanishes for high values of U. Best overall agreement, also with respect to experimental photoemission and inverse photoemission spectra of hematite, is achieved for Uϭ4 eV. The strength of the on-site interactions is sufficient to change the character of the gap from d-d to O-p-Fe-d.

Based on large-scale density functional theory calculations we provide a systematic overview of the size dependence of the energetic order and magnetic properties of various morphologies of FePt and CoPt clusters with diameters of up to 2.5 nm. For FePt, ordered multiply twinned icosahedra and decahedra are more favorable than the L1_(0) phase throughout the investigated size range. For CoPt, segregated morphologies predominate with considerably increased energy differences to the L1_(0) structure. The compositional trends are traced back to differences between the morphologies in the partial electronic density of states associated with the 3d element.

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Structure and magnetism of iron clusters with up to 641 atoms have been investigated by means of density functional theory calculations including full geometric optimizations. Body-centered cubic (bcc) isomers are found to be lowest in energy when the clusters contain more than about 100 atoms. In addition, another stable conformation has been identified for magic-number clusters, which lies well within the range of thermal energies as compared to the bcc isomers. Its structure is characterized by a close-packed particle core and an icosahedral surface, while intermediate shells are partially transformed along the Mackay path between icosahedral and cuboctahedral geometry. The gradual transformation results in a favorable bcc environment for the subsurface atoms. For Fe55, the shellwise Mackay-transformed morphology is a promising candidate for the ground state.

Fatigue life of components or test specimens often exhibit a significant scatter. Furthermore, size effects have a non-negligible influence on fatigue life of parts with different geometries. We present a new probabilistic model for low-cycle fatigue (LCF) in the context of polycrystalline metal. The model takes size effects and inhomogeneous strain fields into account by means of the Poisson point process (PPP). This approach is based on the assumption of independently occurring LCF cracks and the Coffin-Manson-Basquin (CMB) equation. Within the probabilistic model, we give a new and more physical interpretation of the CMB parameters which are in the original approach no material parameters in a strict sense, as they depend on the specimen geometry. Calibration and validation of the proposed model is performed using results of strain controlled LCF tests of specimens with different surface areas. The test specimens are made of the nickel base superalloy RENE 80.