Fundamental understanding of H localization in steel is an important step towards theoretical descriptions of hydrogen embrittlement mechanisms at the atomic level. In this paper, we investigate the interaction between atomic H and defects in ferromagnetic body-centered cubic (bcc) iron using density functional theory (DFT) calculations. Hydrogen trapping profiles in the bulk lattice, at vacancies, dislocations and grain boundaries (GBs) are calculated and used to evaluate the concentrations of H at these defects as a function of temperature. The results on H-trapping at GBs enable further investigating H-enhanced decohesion at GBs in Fe. A hierarchy map of trapping energies associated with the most common crystal lattice defects is presented and the most attractive H-trapping sites are identified.

High-temperature properties of ceria surfaces are important for many applications. Here, we report the temperature dependencies of surface energy for (111) and (110) ${\mathrm{CeO}}_2$ obtained in the framework of the extended two-stage up-sampled thermodynamic integration using Langevin dynamics. The method was used together with machine-learning potentials called moment tensor potentials (MTPs), which were fitted to the results of the ab initio molecular dynamics calculations for (111) and (110) ${\mathrm{CeO}}_2$ at different temperatures. The parameters of MTP training and fitting were tested, and the optimal algorithm for the ceria systems was proposed. We found that the temperature increases from 0 to 2100 K led to the decrease of the Helmholtz free energy of (111) ${\mathrm{CeO}}_2$ from 0.78 to 0.64 $\mathrm{J}/{\mathrm{m}}^2$. The energy of (110) ${\mathrm{CeO}}_2$ dropped from 1.19 $\mathrm{J}/{\mathrm{m}}^2$ at 0 K to 0.92 $\mathrm{J}/{\mathrm{m}}^2$ at 1800 K. We show that it is important to consider anharmonicity, as simple consideration of volume expansion gives the wrong temperature dependencies of the surface energies.

High temperature properties of ceria surfaces are important for many applications. Here we report the temperature dependences of surface energy for the (111) and (110) CeO2 obtained in the framework of the extended two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD). The method was used together with machinelearning potentials called moment tensor potentials (MTPs), which were fitted to the results of the ab initio MD calculations for (111) and (110) CeO2 at different temperatures. The parameters of MTPs training and fitting were tested and the optimal algorithm for the ceria systems was proposed. We found that the temperature increases from 0 K to 2100 K led to the decrease of the Helmholtz free energy of (111) CeO2 from 0.78 J/m2 to 0.64 J/m2. The energy of (110) CeO2 dropped from 1.19 J/m2 at 0 K to 0.92 J/m2 at 1800 K. We show that it is important to take anharmonicity into account as simple consideration of volume expansion gives wrong temperature dependences of the surface energies.