PSI - Issue 13

Eunan J. McEniry et al. / Procedia Structural Integrity 13 (2018) 1099–1104 Author name / Structural Integrity Procedia 00 (2018) 000 – 000 3 where + is the total energy of the grain boundary with a carbon atom situated at the chosen site, is the total energy of the grain boundary without C, and is the chemical potential of C (here chosen to be the energy of C in an octahedral site in α -Fe). With the present sign convention, positive values of indicate a preference to segregation. We first consider the set of twist {110} GBs in α -Fe. Such grain boundaries are a family of low-energy boundaries, where the grain boundary energy is relatively independent of the angle of twist. In total we have considered the four boundaries, shown in Figure 1. In all cases, we find that the preferential position for C in the interface plane is the same as that for H. For the bulk- like Σ3 boundary, this is a four -fold coordinated site, with a weak segregation energy Σ 3 ~0.1 eV. For the other b oundaries considered, namely the Σ9, Σ11 and Σ17 boundaries, the preferential site for C is five-fold coordinated, with much larger segregation energies (Table 1). For the case of H, deep traps for the non-bulk-like boundaries are found; however, the density of such traps is small, so that the ability of this class of boundaries to effectively trap significant quantities of H and C is limited. We find that the segregation energy for carbon is larger than that of H fo r all boundaries other than Σ3, resulting primarily from the very low solubility of carbon in the bulk of the material. 1101

Figure 1 : Images of the {110} twist GBs considered in the simulations. As the twist angle φ changes, the coincidence site lattice (denoted by Σ) changes. We next consider a set of symmetric tilt GBs (Figure 2) which are formed from tilting perfect {011} surfaces with respect to one another. The boundaries are defined by { 1 11} surfaces with n an integer, and where the habit plane of these boundaries remains [01̅ 1] in all cases. Increasing the value of n corresponds to a lowering of the tilt angle, and the structure moves from a high-angle low- Σ boundary to a low -angle grain boundary, with edge dislocation character. The critical structural motif is a five-fold coordinated “void - like” site (circled in the right -hand image in Figure 2) which one would anticipate being a likely site for segregation. In the case of H, this void-like site is indeed the most favourable for H. Interestingly the segregation energies ( ~0.3 eV) are essentially independent of the angle of tilt and are hence characteristic of this structural motif. In the case of C, the situation is more complex. Much larger segregation energies for C at the void ( ~ 1.8eV) are found, again with no particular correlations with respect to the tilt angle. However, and in contrast to the H scenario, a number of additional sites in the plane of the grain boundaries are found to be favourable for C segregation ( ~ 0.3-0.5eV). For these sites, there is a much stronger dependence of the segregation energy on the degree of tilt, with the segregation lowered for smaller tilt angles, a consequence of the lowered available excess volume. Table 1. Summary of calculated segregation and co-segregation energies for the complete set of grain boundaries considered in the present work. Boundary (eV) (eV) − (meV) − (meV) − (meV) Σ3{110} twist 0.26 0.13 -11 -110 35 Σ9{110} twist 0.68 1.06 -10 30 9 Σ11{110} twist 0.83 1.23 -13 -20 4 Σ17{110} twist 0.95 1.45 -9 -19 11 Σ9 { 1 2 11} [11̅ 0] 0.29 1.78 -212 (edge) -24 (GB plane) -981 (edge) -154 (GB plane) -150 (edge) 36 (GB plane) Σ13 { 1 3 11} [11̅ 0] 0.27 1.85 -232 (edge) -19 (GB plane) -934 (edge) -135 (GB plane) -172 (edge) 73 (GB plane) Σ17 { 1 4 11} [11̅ 0] 0.32 1.83 -218 (edge) -14 (GB plane) -970 (edge) -124 (GB plane) -154 (edge) 53 (GB plane)