Structural, cohesive, and magnetic properties of two symmetric $\Sigma${}3(111) and $\Sigma${}5(210) tilt grain boundaries (GBs) in pure bcc Fe and in dilute FeCr alloys are studied from first principles. Different concentrations and positions of Cr solute atoms are considered. We found that Cr atoms placed in the GB interstice enhance the cohesion by 0.5\char21{}1.2$\hskip0.3em${}J/m2. Substitutional Cr in the layers adjacent to the boundary shows anisotropic effect on the GB cohesion: it is neutral when placed in the (111) oriented Fe grains and enhances cohesion by 0.5$\hskip0.3em${}J/m2 when substituted in the boundary layer of the (210) grains. The strengthening effect of the Cr solute is dominated by the chemical component of the adhesive binding energy. Our calculations show that unlike the free iron surfaces, Cr impurities segregate to the boundaries of the Fe grains. The magnetic moments on GB atoms are substantially changed and their variation correlates with the corresponding relaxation pattern of the GB planes. The moments on Cr additions are two to four times enhanced in comparison with that in a Cr crystal and are antiparallel to the moments on the Fe atoms.

The spin-density-functional theory (DFT) and DFT+U with the Hubbard U term accounting for on-site Coulomb interactions were applied to investigate structure, stability, and electronic properties of different terminations of the Fe3O4(111) surface. All terminations of the ferrimagnetic Fe3O4(111) surface exhibit very large (up to 90%) relaxations of the first four interlayer distances, decreasing with the oxide layer depth. Our calculations predict the iron-terminated surface to be most stable in a wide range of the accessible values of the oxygen chemical potential. The adsorption of Au and Pd on two stable Fe- and O-terminated surfaces is studied. Our results show that Pd binds stronger than Au both to the Fe- and O-terminated surface. DFT+U gives stronger bonding than DFT. The bonding of both adsorbates to the O-terminated magnetite surface is by 1.5\char21{}2.5~eV stronger than to the Fe-terminated surface.

Structural and physical properties of the high-entropy alloy ${\left(\mathrm{NbTa}\right)}_{0.67}{\left(\mathrm{MoHfW}\right)}_{0.33}$ were studied by x-ray powder diffraction, energy dispersive x-ray spectroscopy, magnetization, electrical resistivity, and specific heat measurements. The experimental results were supported by theoretical calculations using two complementary approaches for electronic structure calculations: the Korringa-Kohn-Rostoker method with the coherent potential approximation (KKR-CPA) and projector augmented wave (PAW) within the density functional theory. It was found that the alloy forms with a cubic, body-centered structure (space group $Im\overline{3}m$, W-type structure) with a lattice parameter $a=3.287\left(1\right)$ Å and a random (but microscopically homogeneous) distribution of the constituent elements. At high temperature the alloy exhibits simple metallic behavior, while at low temperature it becomes a type-II superconductor with the critical temperature $T_{\mathrm{c}}\approx 4.3$ K and the upper critical field ${\mu }_0{H}_{\mathrm{c}2}\approx 1.45$ T. The electron-phonon coupling constant calculated from the PAW data, ${\lambda }_{\mathrm{el}-\mathrm{ph}}^{\mathrm{th}-\mathrm{PAW}}=0.63$, is in perfect agreement with the experimental results.