Hydrogen Trapping in bcc Iron

Abstract

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.

Keywords: bcc iron; first principles calculations; hydrogen embrittlement; trapping energies.

Figure 1

Possible sites for H in the bulk of bcc Fe. The red spheres correspond to the interstitial positions (OS, TS correspond to the octahedral and tetrahedral sites) and the blue sphere corresponds to the substitutional site (SS).

Figure 2

Schematic structures of (a) the coincident site lattice (CSL) Σ3(111) [1,2,3,4,5,6,7,8,9,10] grain boundary (GB) and (111) free surface (FS); (b) the CSL Σ5 (012) [100] GB and (012) FS; (c) the CSL Σ5 (100) [001] GB and (001) FS used in this work. Capital/not capital letters of the numbers of layers and H positions refer to GB/FS, respectively. The red spheres correspond to H interstitial sites located in the GB plane. The green spheres correspond to H interstitial sites located outside the GB plane. The view is normal to the GB planes; and no labels are used for the demonstration of the possible tetrahedral and octahedral sites of H in the I0 and I0´ layers for the case of Σ3(111) [1,2,3,4,5,6,7,8,9,10] and no labels for the H positions in the cases of Σ5 (012) [100] and Σ5 (100) [001]. I0 and I0´ labels are referred to the first layer of H located directly at the GB layer and the next to GB layer, which correspond to the octahedral and tetrahedral sites in the case of Σ3(111) [1,2,3,4,5,6,7,8,9,10]. The blue spheres correspond to the GB layers.

Figure 3

(a) ½<111> screw and (b) M111 mixed dislocations. The location of the dislocation core is marked as a purple triangle. Initial H atom positons are marked with the red spheres. The digits −2, −1, 0, 1, 2 are the numbers of H positions and correspond to Figure 7. 0´ H position is additionally considered one in the dislocation core, but it was found to be less energetically preferable during the atomic relaxation procedure and therefore is not shown in the H profile in Figure 7.

Figure 4

(a) ½<111> screw and (b) M111 mixed dislocations. The location of the dislocation core is marked as a purple triangle. The [111] (screw) component of the relative displacement of the neighboring atoms produced by the dislocation is depicted as an arrow between them.

Figure 5

Dependence of the TS-H-interstitial formation energy on the supercell size at constant volume (blue line, blue squares) and at constant pressure (red line, red squares). The results of the present calculations are compared to other theoretical [62,78,107,113] data marked as triangles and experimental data extrapolated to 0 K (ZPE corrected) [110,111,112] and marked as circles.

Figure 6

(a) Dependence of the H-trapping energy on the number of H atoms ($n$) in the $n$H-V cluster. The results of the present calculations are compared to other theoretical data [12,24,114] and experimental results [115,116]. (b) Structures of H-vacancy clusters are shown in the bottom panel. The vacancy is marked as a blue circle. Hydrogen atoms are shown with small red circles.

Figure 7

Hydrogen trapping profiles for Σ 3 (111) GB, (111) FS, mixed 111 dislocation and a vacancy. The trapping energies are presented relative to the geometrical centre of each defect indicated by 0. The considered trapping sites are located at the first, second and third atomic planes away from the corresponding defects, as indicated in Figure 2a and Figure 3b. In the case of a vacancy, the next nearest neighbour TS positions are shown. Minus signs refer either to mirrored or to compressed (in the case of M111 dislocation) crystallographic directions.

Figure 8

The locations of H sites (a) in the computational cell with two ½<111> screw dislocations, (b–f) corresponding to the sites from −2 to 2 from Figure 3b in the cell with two mixed 111 dislocations. The location of the dislocation core is marked as a purple triangle; the final positions of H after the optimisation are shown as the red circles. The [111] component of the relative displacement of the neighboring atoms produced by the dislocation is depicted as an arrow between them.

Figure 9

The temperature dependence of the H concentration at Σ3 (111) GB, M111 dislocation and a vacancy (a) for H bulk concentration 100 ppm, (b) for H bulk concentration 1 ppm.