Solubility and Anisotropic Migration Behaviors of Helium in bcc Iron Under Strain

doi:10.1007/s40195-017-0590-7

Abstract

Abstract:

The different solution and migration behaviors of tetrahedral and octahedral interstitial helium in bcc iron have been investigated by using first principles calculations. We showed that the tetrahedral site has less charge transfer and less redistribution of the density of states but stronger bonding and a lower solution energy. This is due to the coupling between the symmetrical facts of the two interstitial atoms and the 3d orbitals of Fe atoms. The solution energies of both sites are not significantly influenced by applied normal strains of 2% and 4%. In contrast, the migration barriers have the reverse trends for different migration directions under strain, which can be explained by an anisotropic elastic energy change and charge transfer. The lower migration energy along certain directions under strain can facilitate the segregation of helium and the formation of helium bubbles.

Key words: Strain, Point defects, Migration, Density functional theory (DFT), Iron, Helium embrittlement

Yue Yu, Ben Xu, Hao Chen, Zhi-Gang Yang, Chi Zhang. Solubility and Anisotropic Migration Behaviors of Helium in bcc Iron Under Strain[J]. Acta Metallurgica Sinica (English Letters), 2018, 31(2): 199-207.

Figures/Tables 15

Table 1 Solution energies of tetrahedral and octahedral interstitial sites in a 2 × 2 × 2 supercell (without strain)

E _sol (eV)	Our calculation	Literature values [23] by VASP	Literature values [24] by VASP	Literature values [20] by SIESTA
Tetrahedral site	4.46	4.37	4.56	4.38
Octahedral site	4.65	4.60	4.76	4.55

Table 2 Strain induced by helium in supercells with different interstitials

Interstitial site	x (%)	y (%)	z (%)
Tetrahedral	1.65	1.65	2.04
Octahedral	1.08	1.08	3.29

Table 3 Stress induced by helium in supercells with different interstitials

Interstitial site	x (GPa)	y (GPa)	z (GPa)
Tetrahedral	9.95	9.95	10.3
Octahedral	9.62	9.62	11.6

Table 4 Elastic part and electronic part of the interstitial solution energy

Interstitial site	Tetrahedral	Octahedral
E _sol (eV)	4.46	4.65
E _d (eV)	0.92	1.01
E_e (eV)	3.54	3.64

Table 5 Solution energies of T and O sites for different strains applied

Strain	\(E_{\text{sol}}^{\text{tetra}}\) (eV)	\(E_{\text{sol}}^{\text{octa}}\) (eV)
-4% (compressive)	4.433	4.629
-2% (compressive)	4.456	4.649
0 (none)	4.458	4.652
2% (tensile)	4.446	4.650
4% (tensile)	4.447	4.639

Fig. 1 Charge density difference around interstitial helium atom and its nearest iron atoms: a, b charge density difference of the octahedral site; c, d charge density difference of the tetrahedral site. a, c Cross-sectional surface containing the helium atom and the nearest iron atoms corresponding to b, d, respectively. The color red means the highest charge density difference, while blue means the lowest. The contour surfaces above 0 are shown by black lines separated by 0.003 eV/?3, while those below 0 are shown by white lines. In c, d, the blue part suggests a loss of charge density, while yellow suggests an increase in charge density. Helium lies in the center of the red part, while the positions of the iron atoms are shown by the white crosses

Table 6 Bader charge analysis for Fe and He atoms in a 2 × 2 × 2 lattice. (e = 1.6 × 10-19 C)

	Tetrahedral	Octahedral
Atom	Bader charge (e)	Bader charge (e)
Fe_1nn	13.9552	13.8575
He	2.1819	2.2142
Fe_2nn	13.9906	13.9547
Bond	Bond distance (?)	Bond distance (?)
Fe_1nn-He	1.6367	1.5021
Fe_2nn-He	2.3146	2.1243

Fig. 2 Total densities of states for Fe and He atoms. The Fe atoms are at the nearest neighboring sites for both the octahedral and tetrahedral interstitials

Fig. 3 Projected density of states over Fe and He atoms. The Fe atoms are at the nearest neighboring site for both octahedral and tetrahedral interstitials

Fig. 4 Projected densities of states of \(d_{{x^{2} - y^{2} }} /d_{{z^{2} }}\) orbitals for a atoms from pure Fe; b the nearest neighboring atoms of the tetrahedral interstitial; c the nearest neighboring atoms of the octahedral interstitial

Fig. 5 Migration paths along different directions: a [011] (∥y-z plane); b [101] (∥x-z plane); c [-110] (∥x-y plane)

Fig. 6 a Migration barrier for direction [011] with data points of small strain ranging from 0.2% compressive to 0.2% tensile, b migration barrier as a function of the applied uniaxial strain for three different migration directions

Table 7 Stress of the starting, transition and ending states for migration along different directions when no strain applied

Direction		Start		Transition		End
[011]	Direction	xx (yy)	zz	yy (zz)	xx	zz (xx)	yy
	Stress (GPa)	-0.099	-0.15	0.33	-0.53	-0.10	-0.16
	σ _? (GPa)	-0.0015		-0.79		-0.0020
[101]	Direction	xx (yy)	zz	xx (zz)	yy	yy (zz)	xx
	Stress (GPa)	-0.096	-0.15	0.34	-0.54	-0.10	-0.15
	σ _? (GPa)	-0.00050		0.42		-0.074
[-110]	Direction	yy (zz)	xx	xx (yy)	zz	xx (zz)	yy
	Stress (GPa)	-0.10	-0.15	0.35	-0.51	-0.096	-0.15
	σ _? (GPa)	-0.074		0.41		-0.00050

Fig. 7 Differential charge densities at the transition state for three different migration directions: a [011]; b [101]; c [-110]

Fig. 8 Charge densities of the transition state of migration [110] under different strains (cross section, separated by 0.005 eV/?3): a 4% tensile strain, b no strain, c 4% compressive strain. The red and blue mean the highest and lowest charge density difference, respectively. The contour surfaces above 0 are shown by black solid lines, while contour surfaces below 0 are shown by black dashed lines (around the blue parts). The positions of the iron atoms are indicated with white crosses, and the helium lies in the center of the red part. (The difference of length in the x direction is caused by the compressive strain applied)

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