Technology for a better society 1 Imaging Dislocations

Technology for a better society 2 MENA 3100: Diff Linear defects e/linear_defects.htm Dislocations 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 occur Edge dislocation

Technology for a better society 3 MENA 3100: Diff 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.

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

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6 (u)

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8 FCC BCC Slip plane: Slip direction: Burger vector: Slip plane: Slip direction: Burger vector:

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

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Technology for a better society 11 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 12 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 13 Isotropic 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, b e 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 14 g · R / g · b analysis Screw: Edge: b e = 0 b || u b x u = 0 b = b e b ˔ u Invisibility criterion:

Technology for a better society 15 Cindy Smith

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

Technology for a better society 19 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 = 0Gives invisibility g · b = +1Gives one intensity dip g · b = +2Gives 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

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

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

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

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

Technology for a better society 28 Increase S to 0.2 nm -1 to increase S eff Weak beam:

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

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Technology for a better society 31 The contrast in the WB image depend on the value of S: How to determine this:

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Technology for a better society 33 Images

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