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Dislocations—Linear Defects
Dislocations are abrupt changes in the regular ordering of atoms,
along a line (dislocation line) in the solid. They occur in high density
and are very important in mechanical properties of material.
They are characterized by the Burgers vector, found by doing a loop
around the dislocation line and noticing the extra interatomic spacing
needed to close the loop. The Burgers vector in metals points in a
close packed direction.
Edge dislocations occur when an extra plane is inserted. The
dislocation line is at the end of the plane. In an edge dislocation, the
Burgers vector is perpendicular to the dislocation line.
Screw dislocations result when displacing planes relative to each
other through shear. In this case, the Burgers vector is parallel to the
dislocation line.
Burgers vector b. It help us to describe the size and the direction
of the main lattice distortion caused by a dislocation.
Dislocations shown above have Burgers vector directed
perpendicular to the dislocation line. These dislocations are called
edge dislocations.
There is a second
basic type of
dislocation, called
screw dislocation.
The screw dislocation
is parallel to the
direction in which the
crystal is being
displaced (Burgers
vector is parallel to the
dislocation line).
DislocationsDislocations
Edge dislocation
Screw dislocation
Burgers vector b
Dislocation
line ζζζζ
bζζζζb//
ζζζζ⊥b
Mixed/partial dislocations: The
exact structure of dislocations in
real crystals is usually more
complicated than the ones shown.
Edge and screw dislocations are
just extreme forms of the possible
dislocation structures. Most
dislocations have mixed edge/screw
character. To add to the complexity
of real defect structures, dislocation
are often split in "partial“
dislocations that have their cores
spread out over a larger area.
Interfacial Defects
External Surfaces :
The environment of an atom at a surface differs from that of an atom
in the bulk, in that the number of neighbors (coordination) decreases.
This introduces unbalanced forces which result in relaxation (the
lattice spacing is decreased) or reconstruction (the crystal structure
changes).
Surface atoms have unsatisfied atomic bonds, and higher energies
than the bulk atoms ⇒ Surface energy, γ (J/m2)
• Surface areas tend to minimize (e.g. liquid drop)
• Solid surfaces can “reconstruct” to satisfy atomic bonds at
surfaces.
External SurfaceExternal Surface
Free surface can be modeled as a simple termination of the bulk
crystal on low-index planes (those having the lowest energy). The
resultant picture is the so-called terrace-ledge-kink (TLK) model.
Surfaces and interfaces are very
reactive and it is usual that impurities
segregate there. Since energy is
required to form a surface, grains tend
to grow in size at the expense of
smaller grains to minimize energy.
This occurs by diffusion, which is
accelerated at high temperatures.
Grain Boundaries :
Polycrystalline material comprised of many small crystals or
grains. The grains have different crystallographic orientation.
There exist atomic mismatch within the regions where grains
meet. These regions are called grain boundaries.
Surfaces and interfaces are reactive and impurities tend to
segregate there. Since energy is associated with interfaces,
grains tend to grow in size at the expense of smaller grains to
minimize energy. This is accelerated at high temperatures.
The density of atoms in the region including the grain boundary
is smaller than the bulk value, since void space occurs in the
interface.
Interfacial defects
• Interfacial defects form either between different phases, or
between different crystals.
Interfaces between
crystals are grain
boundaries, as
discussed earlier.
Microscopy
Visible light: 0.4~0.7m
Resolution limit ~ 0.5λλλλ~ 0.3µµµµ
Brass (annealing twins)
FCC - Cu/Zn alloy
Bronze (Cu/Sn alloy)
Examined by the
optical properties
of the surface: need etching
Depth of field is important:
needs a flat surface
(polishing) Up to 2000x
Grain Size
100x
3.5”
ASTM (American Society for Testing
And Materials)
grain size number n
12 −= nN
N = no. of grains/in2
46 grains + 22 on circumference
= 46 + 22/2 =57 grains
N=57 / π (3.5/2)2 = 6 grains/in2
6=2n-1, n=3.6 n N
With
Scanning Electron Microscope
Electron gun
Condenser
lens
Scan coils
Objective
lens
Specimen Detector
Display &
storage
Display &
storage
Scan generator
High depth of
field !!!
2000x
Modes: Emissive, reflective,
absorptive, X-ray, etc..
10~50,000x
Transmission Electron Microscope - TEM
Electron gun
Condenser
lens
Objective
lens
Specimen
Camera
Magnifying
lenses
In TEM, sample thickness < 1000A for electron transmission
Diffraction, Microscopy, Spectroscopy are all possible
in the same column. Applications: determine
dislocation, defects, micro-precipitates, etc..
Up to
1,000,000x