First-principles investigation of hydrogen interaction with TiC precipitates in $\alpha$-Fe

A correct description of hydrogen diffusion and trapping is the prerequisite for an understanding of the phenomenon of hydrogen embrittlement. In this study, we carried out extensive first-principles calculations based on density functional theory to investigate the interaction of H with TiC precipitates that are assumed to be efficient trapping agents mitigating HE in advanced high-strength steels. We found that there exists a large variety of possible trapping sites for H associated with different types of interfaces between the TiC particle and the Fe matrix, with misfit dislocations and other defects at these interfaces, and with carbon vacancies in TiC. The most efficient trapping by more than 1 eV occurs at carbon vacancies in the interior of TiC particles. However, these traps are difficult to populate at ambient temperatures since the energy barrier for H entering the particles is high. H trapping at the semicoherent interfaces between the TiC particles and the Fe matrix is moderate, ranging from 0.3 to 0.5 eV. However, a sufficiently large concentration of the carbide particles can significantly reduce the amount of H segregated at dislocation cores in the Fe matrix. A systematic comparison of the obtained theoretical results with available experimental observations reveals a consistent picture of hydrogen trapping at the TiC particles that is expected to be qualitatively valid also for other carbide precipitates with the rock-salt crystal structure.

Figure 1

Schematic representation of the semicoherent interface.

Figure 2

Schematic diagram of energy profile associated with H trapping at a Fe/TiC interfaces and in the interior of an TiC precipitate containing a vacancy.

Figure 3

Atomic structure of bulk TiC (Ti: white spheres, C: grey spheres) with marked trigonal (T) and saddle point $\left({\mathrm{S}}_{1-3}\right)$ sites.

Figure 4

A schematic representation of three investigated translation states for the ${\left(001\right)}_{\text{Fe}}/{\left(001\right)}_{\text{TiC}}$ interface obtained by different relative shifts of the two crystals. Top and bottom panels represent the ${\left(001\right)}_{\text{Fe}}$ and the ${\left(001\right)}_{\text{TiC}}$ interface planes, respectively.

Figure 5

Atomic structures of the three investigated configurations of the ${\left(001\right)}_{\text{Fe}}/{\left(001\right)}_{\text{TiC}}$ interface (see Fig. 4) after a complete relaxation of all degrees of freedom. Black, grey, and white spheres represent Fe, C, and Ti atoms, respectively.

Figure 6

Schematic representation of the two adjoining Fe and TiC planes across the ${\left(011\right)}_{\text{Fe}}/{\left(001\right)}_{\text{TiC}}$ interface. Black, grey, and white spheres represent Fe, C, and Ti atoms, respectively.

Figure 7

Atomic structure of the ${\left(011\right)}_{\text{Fe}}/{\left(001\right)}_{\text{TiC}}$ supercell after a complete relaxation of all degrees of freedom. Black, grey, and white sphere represent Fe, C, and Ti atoms, respectively.

Figure 8

Schematic representation of the stable positions for H at the Fe-on-Ti, bridge, and Fe-on-Ti configurations of the ${\left(001\right)}_{\text{Fe}}/{\left(001\right)}_{\text{TiC}}$ interface. The black, grey, and white circles represent Fe, C, and Ti atoms, respectively. Only one Fe and one TiC planes directly adjacent to the interface are displayed.

Figure 9

A representative example of H (red sphere) segregated at the ${\left(110\right)}_{\text{Fe}}/{\left(001\right)}_{\text{TiC}}$ interface. In the left panel, only the Fe and TiC interfacial planes are shown.

Figure 10

Illustration of the different C vacancies positions considered in the vicinity of the ${\left(001\right)}_{\text{Fe}}/{\left(001\right)}_{\text{TiC}}$ coherent interface.

Figure 11

Energy profiles experienced by H atoms at (a) the perfect coherent ${\left(001\right)}_{\text{Fe}}/{\left(001\right)}_{\text{TiC}}$ interface (red curve) and the misfit dislocation core therein (black curve); (b) coherent ${\left(001\right)}_{\text{Fe}}/{\left(001\right)}_{\text{TiC}}$ interface with single C vacancies at the interface and in the interior of the carbide (black curve), connected vacancies (dashed black curve), and single C vacancy in the interior of the carbide with double H occupancy (red dashed curve); and (c) ${\left(110\right)}_{\text{Fe}}/{\left(001\right)}_{\text{TiC}}$ interface with (black curve) and without (red curve) C vacancies at the interface, and with C vacancies in the interior of the carbide (grey line).

Figure 12

(Left) Trap escape energies [calculated according to Eqs. (4) and (5)] as a function of the source of traps (coherent interface, semicoherent interface, C vacancies at the interface, and C vacancies inside the TiC precipitate). The labels refer to those in Table 6. In addition, the escape energy from a percolating network of C vacancies is labeled as “Vs-net.” (Right) H desorption energies extracted from various experimental studies (see the text) as a function of the average size of the particles. The left dark-grey region of the plot indicates the size range of coherent TiC particles, the middle white and light-grey regions indicate the size range of semicoherent TiC particles, and the dark-grey region on the right indicates the size range of incoherent particles. Note that since Pressouyre and Bernstein carried out electrochemical permeation measurements (not TDS), the reported values are not strictly desorption energies. For comparison, the most relevant trap escape energies are marked in red.

Figure 13

Reduction of the H occupancy at Fe screw dislocation cores due to the presence of different concentrations of semicoherent carbide precipitates at $T=300$ K.

Figure 14

Different supercell sizes used for monitoring the convergence of the segregation energies; both the lateral dimension of the supercell and the number of atomic layers perpendicular to the interface were varied.