Imaging Dislocations Technology for a better society 1

Linear defects Edge dislocation Dislocations 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 occur https: //www. ndeed. org/Education. Resources/Community. College/Materials/Structur e/linear_defects. htm MENA 3100: Diff Technology for a better society 2

Edge dislocation Visualized 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. MENA 3100: Diff Technology for a better society 3

Edge dislocation u b MENA 3100: Diff Technology for a better society 4

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(u) Technology for a better society 6

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FCC Slip plane: Slip direction: Burger vector: BCC Slip plane: Slip direction: Burger vector: Technology for a better society 8

FCC Slip plane: Slip direction: Burger vector: BCC {111} <110> ao/2[110] Slip plane: Slip direction: Burger vector: {110} <111> a 0/2[111] Technology for a better society 9

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Important 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)? Technology for a better society 11

Howie-Whelan equations Modify the Howie-Whelan equations to include a lattice distortion R. So for the imperfect crystal Adding lattice displacement α = 2πg·R Defects are visible when α ≠ 0 Intensity of the scattered beam Technology for a better society 12

Contrast from a dislocation: Isotropic elasticity theory, the lattice displacement R due to a straight dislocation in the u-direction is: 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 Technology for a better society 13

g · R / g · b analysis Screw: be = 0 b || u b x u = 0 Edge: b = be b ˔ u Invisibility criterion: Technology for a better society 14

Cindy Smith Technology for a better society 15

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Screw dislocation g·b = 2 g·b = 1 Important to know the value of S Technology for a better society 18

Edge dislocation • Always 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 g · b = +1 g · b = +2 Gives invisibility Gives one intensity dip Gives two intensity dips close to s=0 Usually 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 Technology for a better society 19

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Example: B=1/2[101] ? U Technology for a better society 22

Imaging dislocations with Two-beam technique Technology for a better society 23

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Imaging dislocations with Weak-beam technique Technology for a better society 26

$Intensity of the diffracted beam in a perfect crystal (two-beam): Effective excitation error Thickness$

Intensity of the diffracted beam in a perfect crystal (two-beam): Effective excitation error Thickness Technology for a better society 27

Weak beam: Increase S to 0. 2 nm-1 to increase Seff Technology for a better society 28

Seff increases Decreases rapidly The contrast of a dislocations are quite wide (~ ξgeff/3) Characteristic length of the diffraction vector S >> ξg-2 ξgeff small Narrow image of most defects Technology for a better society 29