MENA 3100 Diff Linear defects https wwwndeedorgEducationResourcesCommunityCollegeMaterialsStructurelineardefectshtm Dislocations are areas were the atoms are out of position in the crystal structure ID: 1030245
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1. 1Imaging Dislocations
2. 2MENA 3100: DiffLinear defectshttps://www.ndeed.org/EducationResources/CommunityCollege/Materials/Structure/linear_defects.htmDislocations are areas were the atoms are out of position in the crystal structure. Dislocations are generated and move when a stress is applied. The motion of dislocations allows slip – plastic deformation to occurEdge dislocation
3. 3MENA 3100: DiffEdge dislocationVisualized as an extra half-plane of atoms in a lattice.Defective points produced in the lattice by the dislocation lie along a line. This line runs along the top of the extra half-plane. The inter-atomic bonds are significantly distorted only in the immediate vicinity of the dislocation line.
4. 4Edge dislocationMENA 3100: Diffbu
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6. 6(u)
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8. 8FCCBCCSlip plane:Slip direction:Burger vector: Slip plane:Slip direction:Burger vector:
9. 9FCCBCCSlip plane: {111}Slip direction: <110>Burger vector: ao/2[110]Slip plane: {110}Slip direction: <111>Burger vector: a0/2[111]
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11. 11Important questions to answer:Is the dislocation interacting with other dislocations, or with other lattice defects?Is the dislocation jogged, kinked, or straight?What is the density of dislocations in that region of the specimen (and what was it before we prepared the specimen)?
12. 12Howie-Whelan equationsModify the Howie-Whelan equations to include a lattice distortion R. So for the imperfect crystalAdding lattice displacementα = 2πg·RDefects are visible when α ≠ 0 Intensity of the scattered beam
13. 13Isotropic elasticity theory, the lattice displacement R due to a straight dislocation in the u-direction is:Contrast from a dislocation:b is the Burgers vector, be is the edge component of the Burgers vector, u is a unit vector along the dislocation line (the line direction), and ν is Poisson’s ratio.g·R causes the contrast and for a dislocation
14. 14g · R / g · b analysisScrew: Edge: be = 0b || u b x u = 0 b = be b ˔ u Invisibility criterion: Invisibility criterion:
15. 15Cindy Smith
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18. 18g·b = 1g·b = 2Screw dislocationImportant to know the value of S
19. 19Edge dislocationAlways remember: g·R causes the contrast and for a dislocation, R changes with z.We say that g·b = n. If we know g and we determine n, then we know b.g · b = 0 Gives invisibilityg · b = +1 Gives one intensity dipg · b = +2 Gives two intensity dips close to s=0Usually set s > 0 for g when imaging a dislocation in two-beam conditions. Then the dislocation can appear dark against a bright background in a BF image
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22. 22Example:B=1/2[101] ?U
23. 23Imaging dislocations with Two-beam technique
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26. 26Imaging dislocations with Weak-beam technique
27. 27Intensity of the diffracted beam in a perfect crystal (two-beam):ThicknessEffective excitation error
28. 28Increase S to 0.2 nm-1 to increase SeffWeak beam: -2
29. 29Seff increasesDecreases rapidlyThe contrast of a dislocations are quite wide (~ ξgeff/3)Narrow image of most defects Characteristic length of the diffraction vectorS >> ξg-2ξgeff small
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31. 31The contrast in the WB image depend on the value of S:How to determine this:
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33. 33Images
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