3.1.2. H-Charged Grain Boundaries

The most frequently used strategy to identify the preferred lattice sites for segregation of the hydrogen atoms is usually based on considering several energetically favorable positions (selected with the help of intuition or former experience) at each GB and finding the most favorable one. In the present study, we tested another possible strategy—taking the advantage of the first principles molecular dynamics simulations (FP-MD)—that allowed us to simulate elevated temperatures and to observe a migration of hydrogen atom across the GB. The main advantage of this strategy is the possibility of also finding energetically favorable positions that are not dictated by symmetry and might thus be overlooked in static approaches. Although this approach is more convenient for less-symmetrical GBs than those considered in our study, we decided to test its predictive potential. Moreover, this approach can also indicate positions that can be stabilized by entropy terms at elevated temperatures.

For the present FP-MD simulations, we used a special version of the VASP code compiled for the gamma point only. We enlarged the simulation supercells, repeating those described in Table 2 in the *z*-direction (in the case of Σ3 GB, also in the *y*-direction) to avoid artificial atomic interactions due to the limited supercell size. Thus, the numbers of Ni atoms in the enlarged supercells were increased to 144, 180, and 180 for Σ3, Σ5, and Σ11 GBs, respectively. To make the simulations feasible, the convergence criterion was reduced to 10−<sup>5</sup> eV, the cutoff energy was set to 200 eV, and symmetrization of the charge density was switched off. The time step was set to 2 fs. Let us note that lattice parameters of the enlarged supercells were multiplied by the factor of 1.0065 (the atomic positions were set in fractional coordinates), which corresponded to the thermal expansion of a pure nickel from 0 K to 500 K. Then, we introduced a hydrogen atom to the GB and started the FP-MD calculations by a gradual increase in temperature from 0 K to 500 K within the 10,000 time steps, and proceeded with another 10,000 time steps at constant temperature of 500 K.

Hydrogen positions recorded during the constant-temperature range were subjected to a statistical analysis to identify the positions most frequently occupied by the H atom. Results for the Σ5 GB (with the highest energy and void space) can be seen from the histogram in Figure 3 displaying the frequency of occurrence of hydrogen atom in positions described by their coordinates (fractional coordinates with respect to the supercell dimensions). The interval on the horizontal axis for a construction of the histogram was set to 1 × <sup>10</sup><sup>−</sup>3. The histogram contains only the data for *<sup>y</sup>* and *<sup>z</sup>* coordinates since the data for the *x*-coordinate exhibited only one sharp peak at 0.5. To label the preferred segregation sites, we use the same nomenclature (S*x*) as Di Stefano et al. [7]. These positions are also marked in Figure 4, displaying the atomic configurations of all GBs. The peaks in Figure 3 reveal the preferred segregation sites labeled S0 and S2.

**Figure 3.** The histogram for the Σ5 GB. The solid and dashed lines correspond to frequencies of occurrence of the H atom along the *y*- and *z*-coordinates, respectively. The *x*-coordinate is not shown because there is only one strong peak at 0.5 which corresponds to the GB located in the middle of the supercell. The coordinates are in fractional units of the first principles molecular dynamics simulation (FP-MD) supercell (corresponding to that in Figure 2 repeated three times along *z*), and the positions S0 and S2 are defined in Figure 4.

**Figure 4.** Details of the grain boundary configuration with indicated positions of the preferred segregation sites for hydrogen atoms. S0 and S2 are the preferred segregation positions found in the FP-MD simulations, and S1 is another position considered in Reference [7].

Results for other GBs (though not included in Figure 3) were obtained the same way. Such established hydrogen positions and corresponding segregation energies were compared with those already published by Di Stefano et al. [7]. Since the present nomenclature is consistent, the S2 positions in both studies are identical. However, instead of the position S1 reported in [7], we found another position marked S0. The segregation energy of −247 meV (−228 meV) obtained for S0 (S2) in the present work is close to the value of −230 meV calculated for S1 in Reference [7]. Alvaro et al. [10] studied preferable hydrogen positions in the Σ5 GB and suggested that hydrogen atoms prefer the octahedral-like positions similar to those in the Ni bulk. However, according to our results—as well as the work of Di Stefano et al. [7] (where these positions were marked as S6 and S7)—their segregation energies are higher than the energies of S1 and S2.

The hydrogen segregation for the remaining GBs of a smaller energy and void space is significantly reduced when compared to Σ5. According to the FP-MD results obtained for Σ3 and Σ11 GBs, the hydrogen atoms tend to segregate only at octahedral sites near the GB planes. These positions are depicted in Figure 4 and marked by small (blue) spheres representing the segregated hydrogen atoms. This figure shows the hydrogen occupation sites for all three studied GB supercells that were used for the determination of cohesive strengths.
