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Dislocations – Linear Defects
– Two-dimensional or line defect
– Line around which atoms are misaligned – related to slip
• Edge dislocation:
– extra half-plane of atoms inserted in a crystal structure
– Or – think of it as a partially slipped crystal
– b  to dislocation line
• Screw dislocation:
– spiral planar ramp resulting from shear deformation
– b  to dislocation line
Burger’s vector, b: measure of lattice distortion or the
amount of displacement. Burger’s vector is equal in
magnitude to interatomic spacing.
Edge Dislocation
• This is a crystal that is slipping
• Slip has occurred in the direction of
slip vector over the area ABCD
• Boundary between portion that has
slipped and not slipped is AD
• AD is the edge dislocation
• The Burger’s vector b is
 = magnitude to the amount of slip
 Is acting in the direction of slip
 Note that b is ┴ dislocation line
Source: G. Dieter, Mechanical Metallurgy, McGraw Hill, 1986.
Dislocations – Linear Defects
Edge Dislocation
Fig. 4.3, Callister 7e.
Motion of Edge Dislocation
• 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.
(Courtesy P.M. Anderson)
Dislocations – Linear Defects
Screw Dislocation
b
Dislocation
line
Burgers vector b
(b)
(a)
Adapted from Fig. 4.4, Callister 7e.
Edge, Screw, and Mixed Dislocations
Mixed
Edge
Adapted from Fig. 4.5, Callister 7e.
Screw
Dislocations – Linear Defects
Dislocations are visible in electron micrographs
Transmission Electron Micrograph
of Titanium Alloy. Dark lines are
dislocations. 51450X
Adapted from Fig. 4.6, Callister 7e.
Interfacial - Planar Defects
Surfaces
–
–
–
–
Atoms do not have the same coordination number
Therefore are in higher energy state
Surface energy, g [=] J/m2
Materials always try to reduce surface energy – tendency
towards spherical shapes
Grain Boundaries – Interfacial Defects
Solidification- result of casting of molten material
– 2 steps
• Nuclei form
• Nuclei grow to form crystals – grain structure
• Start with a molten material – all liquid
nuclei
liquid
crystals growing
grain structure
• Crystals grow until they meet each other
Grain Boundaries
Grain Boundaries
• regions between crystals
• transition from lattice of
one region to that of the
other
• slightly disordered
• low density in grain
boundaries
– high mobility
– high diffusivity
– high chemical reactivity
High energy locations where impurities tend to segregate to
Planar Defects in Solids
• One case is a twin boundary (plane)
– Special kind of grain boundary
– Mirror lattice symmetry
– Essentially a reflection of atom positions across the twin plane.
Brass at 60X
Figure4.13c
Adapted from Fig. 4.9, Callister 7e.
• Stacking faults
– For FCC metals an error in ABCABC packing sequence
– Ex: ABCABABC
Diffusion
Diffusion - Mass transport by atomic motion
Mechanisms
• Gases & Liquids – random (Brownian) motion
• Solids – vacancy diffusion or interstitial diffusion
Diffusion
• Interdiffusion: In an alloy, atoms tend to migrate from regions of
high conc. to regions of low conc.
Initially
After some time
Adapted from
Figs. 5.1 and
5.2, Callister
7e.
Diffusion
• Self-diffusion: In an elemental solid, atoms also migrate.
Label some atoms
After some time
C
C
A
D
B
D
A
B
Diffusion Mechanisms
Vacancy Diffusion:
• atoms exchange with vacancies
• applies to substitutional impurity atoms
• rate depends on:
--number of vacancies
--activation energy to exchange.
increasing elapsed time
Diffusion Simulation
• Simulation of
interdiffusion
across an interface:
• Rate of substitutional
diffusion depends on:
--vacancy concentration
--frequency of jumping.
(Courtesy P.M. Anderson)
Diffusion Mechanisms
Interstitial diffusion – smaller atoms can diffuse between atoms
in lattice positions.
Adapted from Fig. 5.3 (b), Callister 7e.
Which will be faster – vacancy diffusion or interstitial diffusion?
Processing Using Diffusion
Case Hardening:
• Diffuse carbon atoms into the
host iron atoms at the surface.
• Use a controlled atmosphere
with a specific carbon potential
(effective concentration)
• Elevated Temperature
• Example of interstitial diffusion
is a case hardened gear.
Result: The higher concentration of C atoms near the
surface increases the local hardness of steel.