Imaging Dislocations Technology for a better society 1

Imaging Dislocations Technology for a better society 1 Linear defects Edge dislocation

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 https://www.ndeed.org/EducationResources/CommunityCollege/Materials/ Structure/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 Technology for a better society

5 (u) Technology for a better society 6 Technology for a better society

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

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

Slip plane: {111} Slip direction: <110> Burger vector: ao/2[110] BCC Slip plane: {110} Slip direction: <111>

Burger vector: a0/2[111] Technology for a better society 9 Technology for a better society 10

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 = 2gRgR

= 2 Defects are visible when 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: = 1 1 ( + + (2 (1 2 ) + 2 ) }) {

2 4 (1 ) 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 is Poissons ratio. gR causes the contrast and for a dislocation Technology for a better society

13 g R / g b analysis = Screw: be = 0 b || u

1 1 ( + + (2 (1 2 ) + 2 ) }) { 2 4 (1 ) bxu=0

Edge: b = be bu = =

Invisibility criterion: 1 = ( ) 2 2

=0 1 1 ( + { + (2 ( 1 2 ) + 2 ) }) 2 4 (1 )

Invisibility criterion: =0 Technology for a better society 14 Cindy Smith Technology for a better society

15 Technology for a better society 16 Technology for a better society 17

Screw dislocation gb = 2 gb = 1 Important to know the value of S Technology for a better society

18 Edge dislocation Always remember: gR causes the contrast and for a dislocation, R changes with z. We say that gb = n. If we know g and we determine n, then we know b. gb=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 Technology for a better society 20 Technology for a better society 21

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

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

24 Technology for a better society 25 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 Technology for a better society

27 Weak beam: Increase S to 0.2 nm-1 to increase Seff -2

= 1+ 2 2 Technology for a better society

28 Seff increases Decreases rapidly The contrast of a dislocations are quite wide (~ geff/3) Characteristic length of the diffraction vector S >> g-2

= geff

1+ 2 2 small Narrow image of most defects Technology for a better society 29 Technology for a better society

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

Technology for a better society 32 Images Technology for a better society 33 Technology for a better society

34 Technology for a better society 35 Technology for a better society 36

Technology for a better society 37 Technology for a better society 38 Technology for a better society

39 Technology for a better society 40

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