Recently, nanoparticles based on rare earth fluorides have been widely investigated due to their possible medical and spintronic applications, where it is desirable to know the magnetic moment volume distribution. However, this feature is hard to find out from the experiments, so we employ ab initio spin-polarized calculations for this purpose in order to find out the tendencies and common features in three different compounds. In the present work, the nanoparticles of dipole magnets with different sizes, namely TbF₃, DyF₃ and HoF₃, were simulated, and optimized structures were found. We present the optimized structures for the particles with various sizes, as well as for slabs constructed from same compounds. Lastly, for optimized geometries, the analysis of magnetic moments’ distribution over the nanoparticles and slabs volume was performed.

The development of thin, wear-resistant coatings is a relevant area in the field of surface engineering, especially given the increasing demand for resource efficiency and reliability of machine elements. In this study, we investigate the structural and phase composition, tribological characteristics, and physical and mechanical properties of zirconium carbonitride (ZrCN) coatings deposited by high-velocity oxygen-fuel spraying (HVOF) on U8G carbon steel substrates. Particular attention is paid to the influence of spraying parameters, in particular air pressure, on the formation of coatings and their performance properties. X-ray phase analysis methods revealed the formation of Zr₂CN, ZrC, ZrN, ZrO₂, and Fe₃O₄ phases, with the dominance of the cubic phase ZrN(C) with a lattice parameter of a = 4.6360 Å. Tribological tests have shown that at an air pressure of 0.38 MPa, the minimum friction coefficient is achieved, presumably due to the formation of an amorphous CN_x phase with a self-lubricating effect. The wear mechanism is predominantly abrasive in nature; the width of wear tracks is 329–759 μm. The coatings demonstrate a significant increase in microhardness—up to 1512–1857 HV, which is 4–4.5 times higher than the substrate. The results of adhesion tests carried out in accordance with ASTM D4541-22 showed a maximum adhesion strength of 14.56 MPa. The results obtained confirm the high efficiency of thin ZrCN coatings obtained by the HVOF method as a promising solution for protecting metal surfaces subject to intense wear in tribological systems.