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Publication Figures

Publication Date:
2019-04-24

First Author:
Pui-Wai Ma

Title:
Symmetry-broken self-interstitial defects in chromium, molybdenum and tungsten

Paper Identifier:
CP/19/7

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Figure Reference Title Description Number of Figure Data Items Identifier Download Figure Details
2D-diffusion.png FIG. 1. Sketch illustrating a two-dimensional transition path-ways of migration of a?110?dumbbell proposed by Jacquesand Robrock 0 CF/19/8 Download
Group6_110_to_111_PBE.eps FIG. 2. (Color online) Results of nudged elastic band calcu-lations illustrating how the formation energy of a SIA dumb-bell varies as a function of the orientation of the axis of thedefect. The orientation changes from being collinear to the[110] direction (the left edge of the diagram) to being collinearto the [111] direction (the right edge of the diagram). Thecurves were computed taking into account the elastic correc-tion associated with the use of periodic boundary conditions[12, 31, 32]. Note that the only curve in the Figure that ismonotonic refers to Nb, which is a group 5 metal. 1 CF/19/9 Download
Group6_110_to_111_Eint_PBE.eps FIG. 3. (Color online) The elastic correctionEcorrelpart ofthe formation energy of defects corresponding to the curvesshown in Fig. 2. 1 CF/19/11 Download
Mo_11x_Vesta.png FIG. 4. (Color online) Atomic structure of a symmetry-broken?11??SIA dumbbell defect in Mo, simulated using a supercellcontaining 5×5×5 BCC unit cells. Symmetry breaking in the core of the defect gives rise to buckling of the central [111]atomic string containing an extra atom. Buckling can occurs in one of the three{110}atomic planes equivalent by symmetrywith respect to the straight linear?111?configuration of the defect. 1 CF/19/13 Download
LDOS_11x_111_atom85.eps FIG. 5. (Color online) The local density of states (DOS) forone of the two atoms at the center of?111?and?11??dumbbellconfigurations in Mo. A plot showing the DOS computed forperfect BCC lattice is shown for comparison. The position ofthe Fermi energy for all the three structures corresponds tothe origin of the horizontal axis and is indicated by a dashedvertical line. 1 CF/19/15 Download
PBE_111d_string_distance FIG. 6. (Color online) Distances between successive atomsiandj=i+ 1 in a?111?atomic string containing an extraatom. (Top) data for a?111?dumbbell and (bottom) datafor a?11??configuration in Cr/AFM, Cr/NM, Mo and W.Positions of atoms were computed using the GGA-PBE func-tional. 1 CF/19/17 Download
PBE_11xd_string_distance FIG. 6. (Color online) Distances between successive atomsiandj=i+ 1 in a?111?atomic string containing an extraatom. (Top) data for a?111?dumbbell and (bottom) datafor a?11??configuration in Cr/AFM, Cr/NM, Mo and W.Positions of atoms were computed using the GGA-PBE func-tional. 1 CF/19/19 Download
PBE_111d_string_volume FIG. 7. (Color online) Voronoi volumes of atoms belonging toa?111?atomic string containing an extra atom. (Top) datafor a?111?dumbbell and (bottom) data for a?11??configu-ration of a defect in Cr/AFM, Cr/NM, Mo and W. All thecalculations were performed using the GGA-PBE functional. 1 CF/19/21 Download
PBE_11xd_string_volume FIG. 7. (Color online) Voronoi volumes of atoms belonging toa?111?atomic string containing an extra atom. (Top) datafor a?111?dumbbell and (bottom) data for a?11??configu-ration of a defect in Cr/AFM, Cr/NM, Mo and W. All thecalculations were performed using the GGA-PBE functional. 1 CF/19/23 Download
Cr_11x_total_dden FIG. 8. (Color online) Two-dimensional plots of electron charge density difference computed for a?11??dumbbell configurationin the (1 ?10) plane in Cr/AFM, Cr/NM, Mo and W. Calculations were performed using the GGA-PBE functional. Electroncharge density difference is defined as the self-consistent electron density minus a superposition of atomic charge densities. 1 CF/19/25 Download
Cr_NM_11x_dden FIG. 8. (Color online) Two-dimensional plots of electron charge density difference computed for a?11??dumbbell configurationin the (1 ?10) plane in Cr/AFM, Cr/NM, Mo and W. Calculations were performed using the GGA-PBE functional. Electroncharge density difference is defined as the self-consistent electron density minus a superposition of atomic charge densities. 1 CF/19/26 Download
Mo_11x_dden FIG. 8. (Color online) Two-dimensional plots of electron charge density difference computed for a?11??dumbbell configurationin the (1 ?10) plane in Cr/AFM, Cr/NM, Mo and W. Calculations were performed using the GGA-PBE functional. Electroncharge density difference is defined as the self-consistent electron density minus a superposition of atomic charge densities. 1 CF/19/27 Download
W_11x_dden FIG. 8. (Color online) Two-dimensional plots of electron charge density difference computed for a?11??dumbbell configurationin the (1 ?10) plane in Cr/AFM, Cr/NM, Mo and W. Calculations were performed using the GGA-PBE functional. Electroncharge density difference is defined as the self-consistent electron density minus a superposition of atomic charge densities. 1 CF/19/31 Download
Cr_111_total_dden FIG. 9. (Color online) Two-dimensional plots of electron charge density difference computed for a?111?dumbbell configurationin the (1 ?10) plane in Cr/AFM, Cr/NM, Mo and W. Calculations were performed using the GGA-PBE functional. Electroncharge density difference is defined as the self-consistent electron density minus a superposition of atomic charge densities. 1 CF/19/33 Download
Cr_NM_111_dden FIG. 9. (Color online) Two-dimensional plots of electron charge density difference computed for a?111?dumbbell configurationin the (1 ?10) plane in Cr/AFM, Cr/NM, Mo and W. Calculations were performed using the GGA-PBE functional. Electroncharge density difference is defined as the self-consistent electron density minus a superposition of atomic charge densities. 1 CF/19/35 Download
Mo_111_dden FIG. 9. (Color online) Two-dimensional plots of electron charge density difference computed for a?111?dumbbell configurationin the (1 ?10) plane in Cr/AFM, Cr/NM, Mo and W. Calculations were performed using the GGA-PBE functional. Electroncharge density difference is defined as the self-consistent electron density minus a superposition of atomic charge densities. 1 CF/19/37 Download
W_111_dden FIG. 9. (Color online) Two-dimensional plots of electron charge density difference computed for a?111?dumbbell configurationin the (1 ?10) plane in Cr/AFM, Cr/NM, Mo and W. Calculations were performed using the GGA-PBE functional. Electroncharge density difference is defined as the self-consistent electron density minus a superposition of atomic charge densities. 1 CF/19/39 Download
schematic_11x_to_x11 FIG. 10. Schematic diagram illustrating the migration path-way of an SIA defect from a [11?] to a [?11] dumbbell config-uration. Values of parameter?for Group 6 metals are listedin Table II and III. Note that the initial and final configu-rations of the defect are associated with symmetry-breakingoccurring in twodifferent{110}planes. 0 CF/19/41 Download
Group6_11x_to_x11_PBE.eps FIG. 11. (Color online) Migration energy barriers computedusing the nudged elastic band method, and correspondingto the trajectory of migration of a symmetry-broken [11?]SIA dumbbell to an adjacent cell, as illustrated in Fig. 10.Calculations were performed using the GGA-PBE exchange-correlation functional. 1 CF/19/42 Download
Group6_11x_to_x11_Eint_PBE.eps FIG. 12. (Color online) Energy contribution due to the elasticcorrectionEcorrelcorresponding to the trajectory of migrationshown in Figs. 10 and 11. 1 CF/19/44 Download
Fig. 13 to 17 FIG. 13. Patterns of Huang diffuse scattering produced by an ensemble of randomly distributed and average over equivalentcrystallographic orientations?100?dumbbells. FIG. 14. Patterns of Huang diffuse scattering produced by randomly distributed and average over equivalent crystallographicorientations?111?dumbbells. FIG. 15. Patterns of Huang diffuse scattering produced by randomly distributed and average over equivalent crystallographicorientations?110?dumbbells. FIG. 16. Patterns of Huang diffuse scattering produced by randomly distributed and average over equivalent crystallographicorientations?11??SIA dumbbells. FIG. 17. Patterns of Huang diffuse scattering by?111?,?110?and?11??randomly distributed and average over the equiv-alent crystallographic orientations dumbbell configurationscomputed for a [022] reflection in the (100) plane in recip-rocal space. Only the?111?dumbbell configurations producezero intensity lines parallel to the [0 ?11] direction in reciprocalspace. 1 CF/19/46 Download