Acta Metallurgica Sinica (English Letters) ›› 2018, Vol. 31 ›› Issue (2): 199-207.DOI: 10.1007/s40195-017-0590-7
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Yue Yu1, Ben Xu1(), Hao Chen1, Zhi-Gang Yang1, Chi Zhang1
Received:
2017-05-09
Revised:
2017-05-09
Online:
2018-02-20
Published:
2018-03-20
About author:
About author:Lin Lv and Feng-Qing Wang have contributed equally to this work.
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.
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E sol (eV) | Our calculation | Literature values [ | Literature values [ | Literature values [ |
---|---|---|---|---|
Tetrahedral site | 4.46 | 4.37 | 4.56 | 4.38 |
Octahedral site | 4.65 | 4.60 | 4.76 | 4.55 |
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 [ | Literature values [ | Literature values [ |
---|---|---|---|---|
Tetrahedral site | 4.46 | 4.37 | 4.56 | 4.38 |
Octahedral site | 4.65 | 4.60 | 4.76 | 4.55 |
Interstitial site | x (%) | y (%) | z (%) |
---|---|---|---|
Tetrahedral | 1.65 | 1.65 | 2.04 |
Octahedral | 1.08 | 1.08 | 3.29 |
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 |
Interstitial site | x (GPa) | y (GPa) | z (GPa) |
---|---|---|---|
Tetrahedral | 9.95 | 9.95 | 10.3 |
Octahedral | 9.62 | 9.62 | 11.6 |
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 |
Interstitial site | Tetrahedral | Octahedral |
---|---|---|
E sol (eV) | 4.46 | 4.65 |
E d (eV) | 0.92 | 1.01 |
Ee (eV) | 3.54 | 3.64 |
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 |
Ee (eV) | 3.54 | 3.64 |
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 |
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
Tetrahedral | Octahedral | |
---|---|---|
Atom | Bader charge (e) | Bader charge (e) |
Fe1nn | 13.9552 | 13.8575 |
He | 2.1819 | 2.2142 |
Fe2nn | 13.9906 | 13.9547 |
Bond | Bond distance (?) | Bond distance (?) |
Fe1nn-He | 1.6367 | 1.5021 |
Fe2nn-He | 2.3146 | 2.1243 |
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) |
Fe1nn | 13.9552 | 13.8575 |
He | 2.1819 | 2.2142 |
Fe2nn | 13.9906 | 13.9547 |
Bond | Bond distance (?) | Bond distance (?) |
Fe1nn-He | 1.6367 | 1.5021 |
Fe2nn-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. 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
Direction | Start | Transition | End | ||||
---|---|---|---|---|---|---|---|
[ | 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 | ||||
[ | 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 | ||||
[- | 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 |
Table 7 Stress of the starting, transition and ending states for migration along different directions when no strain applied
Direction | Start | Transition | End | ||||
---|---|---|---|---|---|---|---|
[ | 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 | ||||
[ | 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 | ||||
[- | 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. 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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