Defects Dimensionality
Examples
Point
0
Vacancy
Line
1
Dislocations
Plane
2
Grain boundary,
Twinning,
Tilt/Twist
grain boundary
Interstitial
impurity
vacancy
Substitutional
impurity
Interstitial solid solution applies to carbon in α-iron.
The carbon atom is small enough to fit with some
strain in the interstice (or opening) among adjacent
Fe atoms in this important steel structure
But the interstitial solubility is quite low since the size mismatch of the site to the radius of
a carbon atom is only about 1/4
Defects in ionic solids
Frenkel
defect
Cation vacancy
+
cation interstitial
Schottky
defect
Cation vacancy
+
anion vacancy
POINT DEFECTS
• The simplest of the point defect is a vacancy, or vacant lattice site.
• All crystalline solids contain vacancies.
• Principles of thermodynamics is used explain the necessity of the
existence of vacancies in crystalline solids.
• The presence of vacancies increases the entropy (randomness) of
the crystal.
• The equilibrium number of vacancies for a given quantity of
material depends on and increases with temperature as
follows: (an Arrhenius model)
Total no. of atomic sites
Energy required to form vacancy
Equilibrium no. of vacancies
Nv= N exp(-Qv/kT)
T = absolute temperature in Kelvin
k = gas or Boltzmann’s constant
DISLOCATIONS
 Edge
dislocation
 Screw dislocation
DISLOCATIONS
EDGE
MIXED
SCREW
 Usually dislocations have a mixed character and Edge and Screw
dislocations are the ideal extremes
DISLOCATIONS
Random
Structural
 Geometrically necessary dislocations
A dislocation has associated with it two vectors:

t  A unit tange nt vector along the dislocatio n line

b  The Burgers vector
Burgers Vector
Edge dislocation
Crystal with edge dislocation
Perfect crystal
RHFS:
Right Hand Finish to Start
convention
Edge dislocation

Direction of tt
vector
dislocation line vector

Direction of b
b vector
Dislocation Motion
• Dislocation motion leads to plastic deformation.
• An edge dislocation moves in response to a shear stress applied in a
direction perpendicular to its line.
• Extra half-plane at A is forced to the right; this pushes the top halves
of planes B, C, D in the same direction.
• By discrete steps, the extra 1/2-plane moves from L to R by
successive breaking of bonds and shifting of upper 1/2-planes.
• A step forms on the surface of the crystal as the extra 1/2-plane
exits.
19
 Dislocation is a boundary between the slipped and the unslipped parts
of the crystal lying over a slip plane
 The intersection of the extra half-plane of atoms with the slip plane
defines the dislocation line (for an edge dislocation)
 Direction and magnitude of slip is characterized by the Burgers vector
of the dislocation (A dislocation is born with a Burgers vector)
 The Burgers vector is determined by the Burgers Circuit
 Right hand screw (finish to start) convention is used for determining
the direction of the Burgers vector
 As the periodic force field of a crystal requires that atoms must move
from one equilibrium position to another  b must connect one
lattice position to another (for a full dislocation)
 Dislocations tend to have as small a Burgers vector as possible
Compressive stress
field
Tensile stress
field
Positive edge dislocation
Negative edge dislocation
ATTRACTION
REPULSION
Can come together and cancel
one another
Edge Dislocation Glide
Shear stress
Surface
step
Screw dislocation
[1]
[1] Bryan Baker
chemed.chem.purdue.edu/genchem/ topicreview/bp/materials/defects3.html -
Screw dislocation
Another type of dislocation, called a screw dislocation, exists, which may be
thought of as being formed by a shear stress that is applied to produce the distortion
shown in Figure 4.4a: the upper front region of the crystal is shifted one atomic
distance to the right relative to the bottom portion. The atomic distortion associated
with a screw dislocation is also linear and along a dislocation line. Sometimes the
symbol is used to designate a screw dislocation.
Formation
of a step
on the
surface of
a crystal by
the motion
of (a) edge
dislocation
and (b)
screw
dislocation.
26
Slip Systems
• Dislocations move more easily on specific planes and in
specific directions.
• Ordinarily, there is a preferred plane (slip plane), and
specific directions (slip direction) along which dislocations
move.
• The combination of slip plane and slip direction is called
the slip system.
• The slip system depends on the crystal structure of the
metal.
• The slip plane is the plane that has the most dense
atomic packing (the greatest planar density).
• The slip direction is most closely packed with atoms
(highest linear density).
27
t
b || t
b
1
2
3
If b || t
Then parallel planes  to the dislocation line
lose their distinct identity and become one
continuous spiral ramp
Hence the name SCREW DISLOCATION
Burgers vector
Johannes Martinus
BURGERS
Burger’s vector
Burgers vector
Positive
Edge
Dislocation
Screw
Dislocation
Extra half
plane above
the slip plane
Left-handed
spiral ramp
b parallel to t
Negative
Extra half
plane below
the slip plane
Right-handed
spiral ramp
b antiparallel to t
Grain Boundaries
Grain boundary, was introduced as the boundary separating two small grains or
crystals having different crystallographic orientations in polycrystalline materials.
Within the boundary region, which is probably just several atom distances wide,
there is some atomic mismatch in a transition from the crystalline orientation of
one grain to that of an adjacent one.
Figure 16.2. At the grain boundary, there is a disturbance in the
atomic packing.
A pure tilt boundary causes a constant
angle of tilt between lattice planes of the
same type in adjacent regions of the
sample. It is composed of a regular array
of edge dislocations of the same sign in the
plane of the boundary. If the Burgers vector
of the dislocations is, b, and their spacing
is, D, then the angle of tilt is given by q =
b/D.
A twist boundary causes a pure rotation
between two crystals of the same
structure. The boundary is composed of a
regular two-dimensional array of screw
dislocations of the same sign in the
boundary plane. If all the dislocations have
a Burgers vector, b, and their spacing in
the array is D, the twist angle is q = b/D
Figure 16.4. Low-angle twist boundary.
Low angle tilt grain boundary
~8º TILT BOUNDARY IN SrTiO3 POLYCRYSTAL
2.761 Å
No visible
Grain
Boundary
Fourier filtered image
Dislocation
structures at
the Grain
boundary
Twin Boundary
 The atomic arrangement on one side of the twin boundary is related to
the other side by a symmetry operation (usually a mirror)
 Twin boundaries usually occur in pairs such that the orientation
difference introduced by one is restored by the other
 The region between the regions is called the twinned region
Annealing twins (formed during recrystallization)
Twin
Deformation twins (formed during plastic deformation)
Twin boundary in Fe doped SrTiO3 bicrystals (artificially prepared)
High-resolution micrograph
Mirror related
variants
Twin plane
[1] S. Hutt, O. Kienzle, F. Ernst and M. Rühle, Z Metallkd, 92 (2001) 2
Stacking Fault
 Error in the sequence of stacking atomic planes → Stacking fault
 Defined by a shift vector
FCC stacking
FCC stacking
with a stacking fault
…ABC ABC ABC ABC…
…ABC AB AB ABC…
Thin region of HCP type of stacking
 In above the number of nearest neighbours remains the same
but next-nearest neighbours are different than that in FCC
 Stacking fault energy ~ 0.01 – 0.05 J/m2
 Stacking fault in HCP can lead to thin region of FCC kind of stacking