The surface energy, particularly for nanoparticles, is one of the most important quantities in understanding the thermodynamics of particles. Therefore, it is astonishing that there is still great uncertainty about its value. The uncertainty increases if one questions its dependence on particle size. Different approaches, such as classical thermodynamics calculations, molecular dynamics simulations, and ab initio calculations, exist to predict this quantity. Generally, considerations based on classical thermodynamics lead to the prediction of decreasing values of the surface energy with decreasing particle size. This phenomenon is caused by the reduced number of next neighbors of surface atoms with decreasing particle size, a phenomenon that is partly compensated by the reduction of the binding energy between the atoms with decreasing particle size. Furthermore, this compensating effect may be expected by the formation of a disordered or quasi-liquid layer at the surface. The atomistic approach, based either on molecular dynamics simulations or ab initio calculations, generally leads to values with an opposite tendency. However, it is shown that this result is based on an insufficient definition of the particle size. A more realistic definition of the particle size is possible only by a detailed analysis of the electronic structure obtained from initio calculations. Except for minor variations caused by changes in the structure, only a minor dependence of the surface energy on the particle size is found. The main conclusion of this work is that surface energy values for the equivalent bulk materials should be used if detailed data for nanoparticles are not available.

Sc-based III-nitride alloys were studied using density functional theory with special quasi-random structure methodology. ScxAl1−xN and ScxGa1−xN alloys are found to be stable in hexagonal phases up to x ≈ 0.56 and x ≈ 0.66, respectively, above which rock-salt structures are more stable. Epitaxial strain stabilization can prevent spinodal decomposition up to x ≈ 0.4 (ScxAl1−xN on AlN or GaN) and x = 0.27 (ScxGa1−xN on GaN). The increase in Sc content expands the in-plane lattice parameter of ScxAl1−xN and ScxGa1−xN alloys, leads to composition- and strain-tunable band gaps and polarization, and ultimately introduces ferroelectric functionality in ScxGa1−xN at x ≈ 0.625. A modified Becke-Johnson exchange-correlation potential was applied to study the electronic structures, which yielded band gaps comparable to those from hybrid functional calculations, yet in a much shorter computational time. The alloys were found to retain wide band gaps, which stay direct up to x = 0.25 (ScxAl1−xN) and x = 0.5 (ScxGa1−xN). The band gaps decrease with increasing x for ScxAl1−xN, in which the Sc-3d states dominate at the conduction band minimum and lead to flat electron dispersion at the Γ point. Conversely, the band gaps increase with increasing x for ScxGa1−xN (up to x = 0.5), in which Sc-3d states do not contribute to the conduction band minimum at the Γ point.

The ability to increase the thermal stability of protective coatings under work load gives rise to scientific and industrial interest in age hardening of complex nitride coating systems such as ceramic-like Ti_1−xAl_xN. However, the decomposition pathway of these systems from single-phase cubic to the thermodynamically stable binary nitrides (cubic TiN and wurtzite AlN), which are essential for age hardening, are not yet fully understood. In particular, the role of decomposition kinetics still requires more detailed investigation. In the present work, the combined effect of annealing time and temperature upon the nano-structural development of Ti_0.46Al_0.54N thin films is studied, with a thermal exposure of either 1 min or 120 min in 100 °C steps from 500 °C to 1400 °C. The impact of chemical changes at the atomic scale on the development of micro-strain and mechanical properties is studied by post-annealing investigations using X-ray diffraction, nanoindentation, 3D-atom probe tomography and high-resolution transmission electron microscopy. The results clearly demonstrate that the spinodal decomposition process, triggering the increase of micro-strain and hardness, although taking place throughout the entire volume, is enhanced at high diffusivity paths such as grain or column boundaries and followed within the grains. Ab initio calculations further show that the early stages of wurtzite AlN precipitation are connected with increased strain formation, which is in excellent agreement with experimental observations.

We present experimental data showing that the equiatomic CrMnFeCoNi high-entropy alloy undergoes two magnetic transformations at temperatures below 100 K while maintaining its fcc structure down to 3 K. The first transition, paramagnetic to spin glass, was detected at 93 K and the second transition of the ferromagnetic type occurred at 38 K. Field-assisted cooling below 38 K resulted in a systematic vertical shift of the hysteresis curves. Strength and direction of the associated magnetization bias was proportional to the strength and direction of the cooling field and shows a linear dependence with a slope of $0.006\pm 0.001 \mathrm{emu}\mathrm{T}$. The local magnetic moments of individual atoms in the CrMnFeCoNi quinary fcc random solid solution were investigated by ab initio (electronic density functional theory) calculations. Results of the numerical analysis suggest that, irrespective of the initial configuration of local magnetic moments, the magnetic moments associated with Cr atoms align antiferromagnetically with respect to a cumulative magnetic moment of their first coordination shell. The ab initio calculations further showed that the magnetic moments of Fe and Mn atoms remain strong (between 1.5 and $2{\mu }_{\mathrm{B}}$), while the local moments of Ni atoms effectively vanish. These results indicate that interactions of Mn- and/or Fe-located moments with the surrounding magnetic structure account for the observed macroscopic magnetization bias.