1. Crystallographic Aspects of Dislocations

2. Outline Slip Systems Cross Slip Partial Dislocations Stacking Faults
BCC, FCC, HCP
Cross Slip
Partial Dislocations
Stacking Faults
The Thompson Tetrahedron
Fancy Stuff
Frank rule, Frank loop, Lomer lock, Lomer-Cotrell dislocations, prismatic dislocations
22.71: Physical Metallurgy

3. Different views of FCC supercell
Slip Systems
Systems of planes and directions that make dislocation movement easy
Different views of FCC supercell
22.71: Physical Metallurgy

4. Different views of FCC supercell
Slip Systems
Systems of planes and directions that make dislocation movement easy
Different views of FCC supercell
22.71: Physical Metallurgy

5. Different views of FCC supercell
Slip Systems
Systems of planes and directions that make dislocation movement easy
Different views of FCC supercell
22.71: Physical Metallurgy

6. Counting Slip Systems Multiply: Number of non-parallel planes
Number of close packed directions per plane l k h
Same slip planes!
22.71: Physical Metallurgy

7. Draw primary slip systems for FCC, BCC, and HCP crystal systems
In Class
Draw primary slip systems for FCC, BCC, and HCP crystal systems
22.71: Physical Metallurgy

8. Evidence of Slip Systems
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9. Annealing twins in brass
Side Note: Twinning
Bands can “flip” to mirror image of surrounding crystal
Annealing twins in brass
22.71: Physical Metallurgy

10. Side Note: Twinning Alternate plastic deformation mechanism
Twinning observed in irradiated reactor pressure vessel steel
22.71: Physical Metallurgy

11. Twinning
Differently oriented dislocations inside/outside twin boundary!
MIT Dept. of Nuclear Science & Engineering : Radiation Damage & Effects in Nuclear Materials
Prof. Michael P. Short
Page 11
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12. Evidence of Slip Systems
A scanning electron micrograph of a single crystal of cadmium deforming by dislocation slip on 100 planes, forming steps on the surface
22.71: Physical Metallurgy

13. Evidence of Slip Systems
N. Friedman et al. Phys. Rev. Lett. 109, (2012)
Nanopillar compression tests using a diamond flat punch
Clear 45 degree angles observed
Slip systems activated by shear
22.71: Physical Metallurgy

14. Evidence of Slip Systems
S. Brinckmann et al. Phys. Rev. Lett. 100, (2008)
Nanopillar compression tests using a diamond flat punch
Clear 45 degree angles observed
Slip systems activated by shear
22.71: Physical Metallurgy

15. Secondary Slip Systems
When something blocks a primary slip system, a secondary slip system may activate
Only if it is energetically favorable to continue deforming
What happens if a secondary system can’t activate?
22.71: Physical Metallurgy

16. Cross Slip Dislocation switches slip systems if it get stuck
Derek Hull and David J. Bacon, Introduction to dislocations, 4th ed. (Butterworth-Heinemann, Oxford, 2001).
Dislocation switches slip systems if it get stuck
Example: pinned screw dislocation
time
22.71: Physical Metallurgy

17. Cross Slip Allen & Thomas, p. 100 [101] l k h
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18. Slip Systems Slip directions partially or fully enclose slip planes
Allen & Thomas, “The Structure of Materials,” p. 116
Slip directions partially or fully enclose slip planes
22.71: Physical Metallurgy

19. HCP Slip Systems { } { } { } Ideal c/a = 1.63299 11 2 4 c 10 1 1 11 2
[0001] { } 10 1 1 { } 11 2 2 a2 { } 11 2 4 a 1
22.71: Physical Metallurgy

20. Partial Dislocations Look carefully at the (111) plane in FCC
How many ways can atom A move to location B? B B A A
22.71: Physical Metallurgy

21. Partial Dislocations Look carefully at the (111) plane in FCC
How many ways can atom A move to location B? B B A A
22.71: Physical Metallurgy

22. Partial Dislocations
Allen & Thomas, p. 119
A “perfect” dislocation can split into two “partials”
These move in unison
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23. Partial Dislocations
Allen & Thomas, p. 117
A “perfect” dislocation can split into two “partials”
22.71: Physical Metallurgy

24. Partial Dislocation Separation
After formation, the two partials repel each other
Why?
Opposite screw parts attract
Parallel edge parts repel
22.71: Physical Metallurgy

25. Stacking Faults
The shifted portion of the partial dislocation is a “stacking fault”
Atomic stacking order into the screen has changed
Was ABCA / BCABCABC …
Now it is ABCA / CABCABC …
22.71: Physical Metallurgy

26. Stacking Fault Energy (SFE)
Energy needed to create a stacking fault
High SFE materials deform by full dislocation glide
Cross slip is easier
Low SFE materials deform by SF creation and glide
Cross slip is harder
What is the cutoff threshold? Frank’s Rule!
If 𝑏 1 2 ≥ 𝑏 𝑏 1− 2 , then splitting is energetically favorable
22.71: Physical Metallurgy

27. The Thompson Tetrahedron
22.71: Physical Metallurgy

28. Lomer-Cottrell Dislocation
Two partials hit at 60 degree angles
Each consists of a leading and trailing partial
Leading partial intersections will form a new full edge dislocation
22.71: Physical Metallurgy

29. Lomer-Cottrell Dislocation
Lomer-Cottrell Dislocation Determination
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30. Lomer Lock Both original dislocations (BC and DB) were in slip planes
Is the new dislocation in any slip planes?
What happens next?
22.71: Physical Metallurgy

31. What Happens When Dislocations Get Stuck?
When bits get pinned, they can bow out… creating Frank-Read sources
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32. Dislocation Loops Loops have mixed edge/screw character
May be circular planes of atoms between two planes
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33. Frank-Read Loop Sources
Come from sessile sections of dislocations
Old strain direction
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34. Frank-Read Loop Sources
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35. Forces Between Dislocations
X & Y forces, no Z-force
Peach-Kohler Equation
Burgers vector of dislocation (2) transposed
Line vector of dislocation (2) transposed
Force vector on dislocation (2)
Stress tensor induced by dislocation (1)
22.71: Physical Metallurgy

36. Forces Lead to Pileup
Dislocations moving & piling up in Inconel 617 (Ni-based alloy) under in-situ straining in the TEM
22.71: Physical Metallurgy

37. Forces Lead to Grain Boundaries
Tilt grain boundary in Al
22.71: Physical Metallurgy