Document

Download Report

Transcript Document 

Crystallographic
Aspects of Dislocations
Outline
• Slip Systems
• 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
Prof. Michael P. Short, P. 2
Slip Systems
http://ilan.schnell-web.net/physics/fcc/
• Systems of planes and directions that make
dislocation movement easy
Different views
of FCC supercell
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 3
Slip Systems
http://ilan.schnell-web.net/physics/fcc/
• Systems of planes and directions that make
dislocation movement easy
Different views
of FCC supercell
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 4
Slip Systems
http://ilan.schnell-web.net/physics/fcc/
• Systems of planes and directions that make
dislocation movement easy
Different views
of FCC supercell
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 5
Counting Slip Systems
• Multiply:
• Number of non-parallel planes
• Number of close packed directions per plane
l
h
k
Same slip planes!
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 6
In Class
Draw primary slip systems for
FCC, BCC, and HCP crystal systems
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 7
Evidence of Slip Systems
http://www.doitpoms.ac.uk/tlplib/slip/printall.php
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 8
Side Note: Twinning
http://www.doitpoms.ac.uk/tlplib/miller_indices/printall.php
• Bands can “flip” to
mirror image of
surrounding crystal
Annealing twins in brass
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 9
Side Note: Twinning
• Alternate plastic deformation mechanism
http://moisespinedacaf.blogspot.com/
http://dcg.materials.drexel.edu/?page_id=14#nuclear
Twinning observed in irradiated
reactor pressure vessel steel
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 10
http://dcg.materials.drexel.edu/?page_id=14#nuclear
Twinning
Differently oriented dislocations
inside/outside twin boundary!
MIT Dept. of Nuclear Science & Engineering
22.74:
& Effects in Nuclear Materials
22.71:Radiation
Physical Damage
Metallurgy
Prof. Michael P. Short
PageP.1111
Prof. Michael P. Short,
Evidence of Slip Systems
http://www.doitpoms.ac.uk/tlplib/miller_indices/printall.php
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
Prof. Michael P. Short, P. 12
Evidence of Slip Systems
N. Friedman et al. Phys. Rev. Lett. 109, 095507 (2012)
• Nanopillar compression
tests using a diamond
flat punch
• Clear 45 degree angles
observed
• Slip systems
activated by shear
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 13
Evidence of Slip Systems
S. Brinckmann et al. Phys. Rev. Lett. 100, 155502 (2008)
• Nanopillar compression
tests using a diamond
flat punch
• Clear 45 degree angles
observed
• Slip systems
activated by shear
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 14
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
Prof. Michael P. Short, P. 15
Cross Slip
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
Prof. Michael P. Short, P. 16
Cross Slip
Allen & Thomas, p. 100
[101]
l
h
22.71: Physical Metallurgy
k
Prof. Michael P. Short, P. 17
Slip Systems
Allen & Thomas, “The Structure of Materials,” p. 116
• Slip directions partially or fully enclose slip planes
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 18
HCP Slip Systems
Ideal c/a = 1.63299
c
[0001]
{1011}
{1122}
a2
a1
22.71: Physical Metallurgy
{1124}
Prof. Michael P. Short, P. 19
Partial Dislocations
• Look carefully at the (111) plane in FCC
• How many ways can atom A move to location B?
B
B
A
22.71: Physical Metallurgy
A
Prof. Michael P. Short, P. 20
Partial Dislocations
• Look carefully at the (111) plane in FCC
• How many ways can atom A move to location B?
B
B
A
22.71: Physical Metallurgy
A
Prof. Michael P. Short, P. 21
Partial Dislocations
Allen & Thomas, p. 119
• A “perfect” dislocation can split into two “partials”
These move in unison
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 22
Partial Dislocations
Allen & Thomas, p. 117
• A “perfect” dislocation can split into two “partials”
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 23
Partial Dislocation
Separation
• After formation, the two partials repel each other
• Why?
Opposite screw
parts attract
Parallel edge parts repel
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 24
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
Prof. Michael P. Short, P. 25
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!
2
2
• If 𝑏12 ≥ 𝑏1+
+ 𝑏1−
, then splitting is energetically
favorable
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 26
The Thompson Tetrahedron
http://imechanica.org/files/Partial%20Dislocation%20Tutorial%20for%20FCC%20Metals.pdf
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 27
Lomer-Cottrell Dislocation
http://imechanica.org/files/Partial%20Dislocation%20Tutorial%20for%20FCC%20Metals.pdf
• 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
Prof. Michael P. Short, P. 28
Lomer-Cottrell Dislocation
http://imechanica.org/files/Partial%20Dislocation%20Tutorial%20for%20FCC%20Metals.pdf
Lomer-Cottrell Dislocation Determination
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 29
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
Prof. Michael P. Short, P. 30
What Happens When
Dislocations Get Stuck?
• When bits get pinned, they can bow out… creating
Frank-Read sources
http://youtu.be/Db85wOCWJkU
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 31
Dislocation Loops
• Loops have mixed edge/screw character
• May be circular planes of atoms between two planes
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 32
Frank-Read Loop Sources
• Come from sessile sections of dislocations
Old strain direction
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 33
Frank-Read Loop Sources
http://virtualexplorer.com.au/special/meansvolume/contribs/wilson/Generation.html
http://www.numodis.fr/tridis/TEM/recordings/FR_loin_53.mpg
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 34
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
Prof. Michael P. Short, P. 35
Forces Lead to Pileup
Dislocations
moving & piling
up in Inconel
617 (Ni-based
alloy) under insitu straining in
the TEM
http://youtu.be/r-geDwE8Z5Y
22.71: Physical Metallurgy
Prof. Michael P. Short, P. 36
Forces Lead to Grain
Boundaries
http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_7/backbone/r7_2_1.html
Tilt grain boundary in Al
22.71: Physical Metallurgy
http://moisespinedacaf.blogspot.com/
Prof. Michael P. Short, P. 37