First-principles computational tensile test of γ-Fe grain boundaries considering the effect of magnetism: Electronic origin of grain boundary embrittlement due to Zn segregation

The development of high-strength steels requires detailed understanding of the effect of solute elements on γ-Fe grain boundaries (GBs). In this study, first-principles computational tensile tests (FPCTT) were conducted on γ-Fe GBs to elucidate the mechanism of GB embrittlement due to Zn segregation. The paramagnetic γ-Fe GB was simulated by the $\mathrm{\Sigma }5\left(310\right)$ GB in the antiferromagnetic double-layer (AFMD) configuration. The FPCTTs revealed that the fracture stress and fracture energy of the γ-Fe GB were reduced by Zn segregation, which is consistent with experimental results. Crystal orbital Hamilton population analysis was also performed to investigate the change in electronic states during the tensile process, and the enhancement of GB fracture by Zn segregation is caused by the breaking of the covalent-like bonds between Fe and Zn at a relatively small strain compared to the Fe–Fe bonds. This behavior is attributed to the localized nature of the $3d$ orbitals of Zn in γ-Fe. The FPCTTs of γ-Fe GBs using the AFMD properly consider the effect of magnetism in paramagnetic γ-Fe under tensile strain and is useful for investigating the effects of various solute elements on GB fracture and for the development of high-strength steels.

Figure 1

Σ5(310) GB model from (a) [001] and (b) [1$\overline{3}$0] axial directions. (c) Bulk model viewed along the [001] axis. The colors indicate the size of the coordinates along the [001] axis, and the numbers 1–4 are the indices of the equivalent GB sites. The red and pink atoms with the index $u$ have positive magnetic moments, and the blue and light blue atoms with the index $d$ have negative magnetic moments. $B$ in the bulk model represents a site substituted for Zn.

Figure 2

(a) Energy vs strain and (b) stress vs strain for the clean GB and the GB with Zn.

Figure 3

Changes in atomic structure of (a) the clean GB and (b) the GB with Zn during FPCTTs. The atomic structure of the clean GB during the structural relaxation at 31.7% strain is also shown in (a). The atomic structure of the GB with Zn during the structural relaxation at 26.7% strain is also shown in (b).

Figure 4

Variation of bond length with strain between atoms near the GB center. The black plots represent the bonds in the clean GB, and the red plots represent the bonds in the GB with Zn. The black and red vertical dashed lines represent the strains at which GB fracture occurs in the clean GB and the GB with Zn, respectively.

Figure 5

Variation of -ICOHP between atoms near the GB center with strain. The black and red plot shows the -ICOHP of bonds in the clean GB and in the GB with Zn, respectively. The black and red vertical dashed lines represent the strains at which GB fracture occurs in the clean GB and the GB with Zn, respectively.

Figure 6

(a) COHPs of Fe ($1u$)–Fe ($4d$) and Zn ($1u$)–Fe ($4d$) at strains of 0.0, 18.3, 20.0, 21.7, and 25.0%. (b) -ICOHPs obtained by integrating the COHPs up to the corresponding energy on the horizontal axis at 0.0, 18.3, 20.0, 21.7, and 25.0% strain. The black and red lines show the bond in the clean GB and in the GB with Zn, respectively.

Figure 7

Difference in -ICOHP obtained by integrating the difference between the COHP of Fe ($1u$)–Fe ($4d$) and Zn ($1u$)–Fe ($4d$) up to the corresponding energy on the horizontal axis. Positive values mean that the -ICOHP of Zn ($1u$)–Fe ($4d$) is larger than that of Fe ($1u$)–Fe ($4d$).

Figure 8

(a) COHPs between Fe ($1u$)–Fe ($4d$) and (b) LDOSs of Fe ($1u$) and (c) Fe ($4d$) in the clean GB at 0, 20.0, 21.7, and 25.0% strain.

Figure 9

(a) COHPs between Zn ($1u$)–Fe ($4d$) and (b) LDOSs of Zn ($1u$) and (c) Fe ($4d$) in the GB with Zn at 0, 20.0, 21.7, and 25.0% strain.

Figure 10

Strain dependence of the magnetic moment of Fe atoms near the GB center.