Length Scale
of Imperfections
Line Defects:
Dislocations and their Scale
point, line, planar, and volumetric defects
Vacancies,
impurities
dislocations
Grain and twin
boundaries
Voids
Inclusions
precipitates
From Chawla and Meyers, Mechanical Behavior of Materials
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Line Defects: Dislocations
Dislocations:
• are line defects,
• cause slip between crystal plane when they move,
• produce permanent (plastic) deformation.
Schematic of a Zinc (HCP):
• before deformation
• after tensile elongation
slip steps
Adapted from Fig.
7.9, Callister 6e.
Actual strained
hcp Zn
2
Incremental Slip and Bond Breaking
• Dislocations slip planes incrementally...
• Dislocation motion requires the successive bumping
of a half plane of atoms (from left to right here).
• Bonds across the slipping planes are broken and
remade in succession.
Atomic view of edge dislocation motion
from left to right as a crystal is sheared.
Shear stress
QuickTime™ and a
Cinepak decompressor
are needed to see this picture.
(Courtesy P.M. Anderson)
Snapshot midway in shear
3
Edge Dislocations Exiting Crystal Form Steps
Burger’s
Vector = b
Shear stress
The caterpillar or rug-moving analogy
4
• Dislocations are line defects that
separate Slipped vs Not Slipped.
• They form loops inside crystal,
having screw, edge and mixed
character.
• Dislocation moves perpendicular to
line direction along each segment.
• Top of crystal moves in direction of
b (Burger’s vector).
• Same surface steps created.
Hayden, Moffatt, Wulff, “The Structure and Properties of Materials,” Vol III (1965)
5
6
Formation of Steps from Screw and Edge Dislocations
Shear stress
Edge
Shear stress
Screw
Both screw and edge motion create same steps!
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The Edge Dislocations and Burger’s Vector
Looking along line direction of edge
Burger’s vector = extra step
• Edge looks like extra plane of atoms.
• Burger’s vector is perpendicular to line.
• Positive Edge (upper half plane)
Stress fields
at an Edge
dislocation
• Is there a Negative Edge?
• Where is it?
• What happens when edge gets to
surface of crystal?
• What are the stresses near edge?
Like trying to zip up those old jeans.
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Burger’s vectors mostly on the
most close-packed planes in the most closed-packed direction
What are the most close-packed PLANES AND DIRECTIONS fcc, bcc, and sc?
b
9
Dislocations Can Create Vacancies and Interstitials
All defects cost energy (J/m2 or erg/cm2)
• But getting rid of defects, like large dislocations, does lower energy
(but not to perfect crystal).
Dislocations can annihilate one another!
• Non-overlapping edges create vacancies.
• Overlapping edges create interstitials.
Almost complete
plane of atoms


Slip plane

vacancies
Non-overlapping
Slip plane

Slip plane
Overalapping

Slip plane

Extra atoms
go into interstitial
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Planar Defects: Surfaces
All defects cost energy (energy is higher than perfect crystal)
Surfaces, grain, interphase and twin boundaries, stacking faults
Planar Defect Energy is Energy per Unit Area (J/m2 or erg/cm2)
• Surfaces: missing or fewer number of optimal or preferred bonds.
surface
11
Planar Defects: Grain Boundary
All defects cost Energy per Unit Area (J/m2 or erg/cm2)
• Grain boundary: fewer and/or missing optimal bonds.
- low-angle GB and high-angle GB.
high-angle
Grain
boundaries
surface
low-angle
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Relative Energies of Grain Boundaries
high-angle
• The grains affect properties
• mechanical,
• electrical, …
Grain 2
• Recall they affect diffraction so you
know they’re there.
• What should happen to grains
as temperature increases?
Hint:
surfaces (interfaces) cost energy.
Grain I
Grain 3
low-angle
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Dislocation Interactions Can Create Planar Defects!
Small-Angle Grain Boundaries: a tilt and a twist
All defects cost energy (J/m2 or erg/cm2)
• Tilt Grain boundary:
- from array of edge dislocations
- misorientation of crystal planes = 
• Twist Grain boundary
- when  is parallel to boundary
b
Tilt
C
T
d
Should energy of GB depend on ?
If dislocation cost energy, how are they there?
Twist

sin~ =b/d
Bi-crystals are made by twist boundaries

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Twin Boundaries: an atomic mirror plane
original atomic positions
before twinning
• There has to be another opposite twin nearby to get back to perfect crystal,
because all defects cost energy (J/m2 or erg/cm2) and to much defect costly.
• Stress twins can be created (e.g., Tin) in which case the atoms must move
at the speed of sound.
What happens when something moves at speed of sound?
15
Twin Boundaries: Load drop in F vs %EL
Stress twins are created and work to create them lead to load drop.
Cu-8.0at.%Al
Sudden load drop
accompanies twinning
f

normal
twinning
direction
twin
plane
F
m  cos cos f
Schmid factor
M. S. Szczerba, T. Bajor, T. Tokarski Phil. Mag. 84 (2004) 481-502.
fcc
twin
fcc
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Stacking Faults: Messed up stacking
FCC
HCP
or C
slip
or C
• All defects cost energy (J/m2 or erg/cm2).
• Stress, dislocation motion can create Stacking Faults.
• What is stacking of FCC and HCP in terms of A,B, and C positions in (111) planes?
hcp
…ABCABCABC…
...ABCACABABCABC...
…….fcc
fcc ………..
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Optical Microscopy
• Useful up to 2000X magnification.
• Polishing removes surface features (e.g., scratches)
• Etching changes reflectance, depending on crystal
orientation.
close-packed planes
Adapted from Fig. 4.11(b) and (c),
Callister 6e. (Fig. 4.11(c) is courtesy
of J.E. Burke, General Electric Co.
micrograph of
Brass (Cu and Zn)
0.75mm
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Optical Microscopy
Grain boundaries...
• are imperfections,
• are more susceptible
to etching,
• may be revealed as
dark lines,
• change direction in a
polycrystal.
Adapted from Fig. 4.12(a)
and (b), Callister 6e.
(Fig. 4.12(b) is courtesy
of L.C. Smith and C.
Brady, the National
Bureau of Standards,
Washington, DC [now the
National Institute of
Standards and
Technology, Gaithersburg,
MD].)
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Polymer, too: Colloidal Epitaxy via Focused Ion Beam Lithography
SEM of patterned cover slip
Silica (f=1.18mm, 0.5vol%)
Zirconia (f~ 3nm, 0.03vol%)
From Prof. Braun’s group.
On cover of Langmuir (2004)
Objective
lens
Sedimented growth: dislocations and SF
In 37th layer: GB and SF
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Use Microscopy to see defects:
contrast using optical, electron, scanning probe
Poly-xtal Pb ~1x
Poly-xtal Cu-Zn 60x
• Optical ~ 2x103 x
• Scanning EM ~ 5x104 x
• High-resolution TEM ~106 x
• Scanning probe ~109 x topo-map)
Fe-Cr GB 100x
Dislocation in Ti alloy
~50,000 x
Old brass door knobs have been etched by acid
in your sweat and you can see with your eyes
the grains and their different orientations.
Move w/  and
change w/ T
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TEM Image of Dislocations in Ti Alloy
• Why are dislocations not loops?
• Dislocations are formed
-solidification
- plastic deformation
- thermal stresses from cooling
In focus
51,450 x
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SUMMARY
• Defect materials responsible for most desired properties useful to
engineering, e.g., mechanical, thermal, and electrical.
• They occur in metals, ceramics, polymers, and semiconductors.
• Defect can be categorized in terms of Point, Line, or Planar defects.
• Point: vacancies, interstitials, substitutional, …
• Line: dislocations (mostly for metals, but not exclusively).
• Planar: surfaces, grain boundaries, boundaries (twin, antiphase,
domain, tilt … ), stacking faults, …
• Defects can be observed by eye or various microscopies.
• Defects can be created or affected by temperature, stress, etc.,
requiring or leading to other defects, as with dislocations.
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