Download L6-Imperfections

IMPERFECTIONS FOR
BENEFIT
Sub-topics
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Point defects
Linear defects – dislocations
Plastic deformation through dislocations
motion
Surface
IDEAL STRENGTH
Ideally, the strength
of a material is the
force necessary to
break inter-atomic
bonds
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DEFECTS IN CRYSTALLINE STRUCTURES
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CRYSTALS ALWAYS CONTAIN DEFECTS
A vacancy is a site at which an
atom is missing –
while vacancies play a role in
diffusion, creep, and
sintering, they do not influence
strength
Total number of atomic sites
Energy required
for the formation of a
vacancy
Point defects: 0.1 nm (10-10 m)
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Temperature
SOLUTE ATOMS
Substitutional solid solution –
dissolved
atoms replace those of the host
Interstitial solid solution – dissolved
atoms squeeze into spaces or
“interstices” between the host atoms
Dissolved atoms rarely have the same
size as the host material, so the
surrounding
lattice is distorted
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
SELF-INTERSTITIAL DEFECT
Large distortions in the surrounding
lattice because the atom is substantially
larger than the interstitial position in
which it is situated
The formation of this defect is not highly probable, and it exists in
very small concentrations, which are significantly lower than for
vacancies.
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IMPURITY ATOMS
substitutional
impurity atom
interstitial
impurity atom
Material properties can be altered significantly
through the addition of impurity atoms
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INTERSTITIAL DEFECTS
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SUBSTITUTIONAL DEFECTS
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POINT DEFECTS IN CERAMICS
cation
interstitial
cation
vacancy
a cation vacancy–
anion vacancy pair
anion
vacancy
Schottky defect
a cation–vacancy and a
cation– interstitial pair.
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Frenkel defect
SUMMARY OF POINT DEFECTS
(c) 2003 Brooks/Cole Publishing / Thomson Learning
vacancy
interstitial atom
large substitutional atom
small substitutional atom
Frenkel defect
a cation–vacancy and a
cation– interstitial pair.
Schottky defect
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a cation vacancy– anion vacancy pair
DEFECTS FOR PLASTICITY
Crystals all contain line defects known as
dislocations
“Dislocated” = “out of joint”
Dislocations act
as
the main
source of
plastic
deformation in
crystalline
materials
A dislocation is an extra half-plane of atoms in the crystal –
in the figure, the upper part of the crystal has one more
double-layer of atoms than the lower part – dislocations
distort the lattice and make metals soft and ductile
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ENERGY OF DISLOCATIONS
Dislocations distort the lattice
The magnitude of distortion
decreases with distance away
from the dislocation line
Elastic energy associated with them
If they cost energy, why are they there?
All metals initially contain an
appreciable number of dislocations
produced from the growth of the crystal
from the melt or vapour phase.
Irregular grain boundaries are believed to be responsible for
emitting dislocations.
Dislocation can be formed by aggregation and collapse of
vacancies.
Heterogeneous nucleation of dislocations is possible from high
local stresses at second-phase particles or as a result of phase
transformation.
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STRESSES AROUND DISLOCATION CORE
The atoms above the dislocation line are
squeezed together
The free energy of a
dislocation is the sum of a
number of terms:
(i) the core energy (within a
radius of about three lattice
planes from the dislocation
core);
(ii) the elastic strain energy
outside the core and
extending to the boundaries
of the crystal, and
(iii) the free energy arising from
the entropy contributions
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The atoms below are pulled apart
CHARACTERISTICS OF DISLOCATIONS
The magnitude and direction of the
lattice distortion is expressed in
terms of a Burgers vector
For metallic materials, the Burgers
vector is in a close-packed
crystallographic direction and is of
magnitude equal to the interatomic
spacing.
edge dislocation
The Burgers vector is significant in
determining the yield strength of a material
by affecting solute hardening, precipitation
hardening and work hardening.
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BURGERS VECTOR
To determine the Burgers vector of a dislocation in a two-dimensional
primitive square lattice, proceed as follows:
Trace around the end of the dislocation
plane to form a closed loop. Record the
number of lattice vectors travelled along
each side of the loop (shown here by the
numbers in the boxes):
In a perfect lattice, trace out the same
path, moving the same number of lattice
vectors along each direction as before.
This loop will not be complete, and the
closure failure is the Burgers vector:
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DISLOCATIONS AND PLASTICITY
The concept of the dislocation was invented independently by Orowan, Taylor
and Polanyi in 1934 as a way of explaining two key observations about the
plastic deformation of crystalline material:
o The stress required to plastically deform a crystal is much less than the
stress one calculates from considering a defect-free crystal structure
o Materials work-harden: when a material has
been plastically deformed it
subsequently requires a greater stress to
deform further.
The existence of dislocations experimentally
was verified in 1947
A transmission electron
micrograph of a titanium alloy
in which the dark lines are
dislocations
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DISLOCATIONS IN 2D
A 'raft' of equally sized bubbles floating on the surface of a liquid is a good
large-scale model of a single plane of atoms in a crystal structure. The forces
between the bubbles mimic the forces between atoms in a crystal. The bubbles
pack to form a close-packed plane. If the raft is made carefully, it is possible
to see a variety of structural features in the raft that also occur in real crystal
structures, such as grain boundaries, vacancies, dislocations and solute
'atoms'.
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DISLOCATIONS AND PLASTIC DEFORMATION
Plastic deformation corresponds to the motion of large numbers of dislocations.
When a shear stress is
applied to the dislocation,
the atoms are displaced,
causing the dislocation to
move one Burgers vector in
the slip direction
Continued movement
of the dislocation
eventually creates a
step
The crystal is
deformed
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PLASTIC DEFORMATION
From an atomic perspective,
plastic deformation
corresponds to the breaking of bonds with
original atom neighbors and then reforming
bonds with new neighbors as large numbers
of atoms or molecules move relative to one
another
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DISLOCATIONS AND PLASTIC FLOW
The edge dislocation is made by cutting, slipping, and rejoining
bonds across a slip plane
The dislocation line separates the part of the plane that has
slipped from the part that has not
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
EDGE DISLOCATIONS
The formation of a step on the surface of a crystal
by the motion of an edge dislocation
Dislocation line moves in the direction of the
applied shear stress
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When a dislocation moves it makes the material
above the slip plane slide relative to that below
(a): Initially perfect crystal
(b) – (d): the passage of the
dislocation across the slip
plane shears the upper part
of the crystal over the lower part
by the slip vector b; when it
leaves the crystal has suffered
a shear strain γ
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
WHY DOES A SHEAR STRESS MAKE
DISLOCATION MOVE?
Representation of the analogy between caterpillar and dislocation motion
In the different loading conditions, dislocations tend to move mainly
along different sets of directions.
Dislocation motion along a crystallographic direction is called glide or slip.
The direction along which dislocations generally move is that with the
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highest resolved shear stress - the component of an applied stress that
acts along a slip direction in a slip plane.
SCREW DISLOCATIONS
The upper front region of the crystal is shifted
one atomic distance to the right relative to the
bottom portion
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SCREW DISLOCATIONS
The formation of a step on the surface of a crystal
by the motion of a screw dislocation.
The dislocation line motion is perpendicular to
the stress direction
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DISLOCATION MOVEMENT
For a dislocation to move, only bonds along the
line it moves must be broken – this is significantly
easier than braking all of the bonds in the plane
In crystals there are preferred planes and
directions for which dislocation movement is easier
– these are called the slip planes and slip directions
Slip displacements are tiny – however, if a large
number of dislocations traverse a crystal, moving on
many planes, the material deforms at a macroscopic
level
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DISLOCATION SLIP
• Slip - The process by which a dislocation moves
and deforms a material.
Dislocations do not move with the same degree
of ease on all crystallographic planes of atoms
and in all crystallographic directions.
• Slip direction - The direction in which a
dislocation moves.
• Slip plane - The plane of preferred dislocation
movement.
• Slip systems - The combination of the slip
direction and slip plane makes up the slip system
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SLIP PLANES
The crystallographic plane along which the dislocation line moves
is the slip plane
The slip system depends on the crystal structure
For a particular crystal structure, the slip plane is that plane having the
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most dense atomic packing, that is, has the greatest planar density.
SLIP SYSTEMS IN FCC
How many slip systems are
there in FCC cell?
There are 12 slip systems: four unique
{111} planes and, within each plane,
three independent <110> directions.
Metals with FCC or BCC crystal
structures have a relatively large
number of slip systems (at least 12)
Three slip directions
These metals are quite ductile
because extensive plastic
deformation is normally possible
along the various systems.
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HCP metals, having few active slip
systems, are normally quite brittle.
Crystals resist the motion of dislocations with a friction-like
resistance f per unit length
Dislocations move from an applied shear stress τ – as they move
the upper half of the crystal shifts relative to the lower half by
a distance b
Dislocations move if
τ exceeds f/b
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
INTERACTION OF DISLOCATIONS
When metals are plastically deformed, some fraction of the deformation
energy (~ 5%) is retained internally; the remainder is dissipated as heat.
The major portion of this stored energy is as strain energy associated with
dislocations.
There are regions in which compressive,
tensile, and shear lattice strains are
imposed on the neighboring atoms
The strains extend into the
surrounding atoms, and their
magnitudes decrease with radial
distance from the dislocation.
The atoms near core of dislocation are displaced
from their proper places -> higher potential
energy -> to keep the energy as low as possible,
the dislocations should be as short as possible
Lattice strains. Slight displacements of atoms
relative to their normal lattice positions, normally
imposed by crystalline defects such as dislocations,
and interstitial and impurity atoms.
Line tension:
T≈½
Eb2
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DISLOCATIONS INTERACTIONS: REPULSION
The strain fields surrounding dislocations in close proximity to one another
may interact such that forces are imposed on each dislocation by the
combined interactions of all its neighboring dislocations.
Two edge dislocations of the same sign and lying on the
same slip plane exert a repulsive force on each other
Explain – why?
C and T denote compression
and tensile regions, respectively.
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DISLOCATIONS INTERACTIONS:
ANNIHILATION
Edge dislocations of opposite sign and lying on
the same slip plane exert an attractive force on
each other.
Upon meeting, they annihilate each other and
leave a region of perfect crystal.
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DEFORMATION BY TWINNING
In addition to slip, plastic deformation in some metallic materials can occur
by the formation of mechanical twins, or twinning
A shear force can produce atomic displacements such that on one side of a
plane (the twin boundary), atoms are located in mirror image positions of
atoms on the other side
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Open circles represent atoms that did not change position; dashed and
solid circles represent original and final atom positions, respectively
TWINNING
twinning occurs on a definite crystallographic
plane and in a specific direction that depend on
crystal structure
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MECHANISMS OF DEFORMATION
For a single crystal subjected to a shear stress,
(a) deformation by slip; (b) deformation by twinning.
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WHY MOST OF CERAMICS ARE BRITTLE
(NOT PLASTIC)?
ceramics
Plastic deformation occurs by
the motion of dislocations.
So, what is the problem?
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When the shear stress acts on an aggregate
of crystals, some crystals will have their
slip planes oriented favorably with respect
to the shear stress
In samples that have many grains, the tensile
stress required to cause yielding is
approximately three times the shear
strength of a single crystal
GRAIN BOUNDARIES
Grain boundaries form
when
differently oriented
crystals meet –
the individual crystals
are called grains, the
meeting
surfaces are grain
boundaries
POLYCRYSTALLINE STRUCTURE
The grain boundaries is a
narrow zone where the atoms
are not properly spaced
Grain boundaries may be 41
also considered as defects!
GRAIN BOUNDARIES
Boundaries can be described in terms of
dislocation arrays
The atoms are bonded less regularly
along a grain boundary, there is an
interfacial or grain boundary energy
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SLIP LINES ON THE
SURFACE OF A POLYCRYSTALLINE SPECIMEN
Slip lines on the surface of a
polycrystalline specimen
of copper that was polished and
subsequently deformed
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NANOSTRUCTURED SOLIDS
Relative to microstructural features of micro-grained metals and alloys,
the nano-structured materials contain a higher fraction of grain
boundary volume (for example, for a grain size of 10 nm, between 14
and 27% of all atoms reside in a region within 0.5–1.0 nm of a grain
boundary); therefore,
grain boundaries play a significant role in the materials
properties.
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GRAIN BOUNDARIES IN NANOMETALS
Crystals contain internal interfacial defects, know as
grain boundaries, where the lattice orientation changes
The misfit between adjacent crystallites in the
grain boundaries changes the atomic structure
(e.g. the average atomic density, the nearestneighbor coordination, etc.) of materials.
At high defect densities the volume fraction
of defects becomes comparable with the
volume fraction of the crystalline regions.
In fact, this is the case if the crystal
diameter becomes comparable with the thickness
of the interfaces.
Non – equilibrium materials
DEFECTS !!!
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WHY
NANOSTRUCTURED POLYCRYSTALLINE
MATERIALS ARE UNSTABLE?
Disclinations and grain boundary
dislocations form elastically distorted Grain growth occurs in
layers (zones) near grain boundaries.
High density of defects
-> High energy
Nature -> seeks to
lower energy
materials to reduce the
overall energy of the
system by reducing the
total grain boundary
energy.
Therefore, grain growth in
NC materials is primarily
driven by the excess
energy stored in the grain
or interphase boundaries.
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PLASTIC FLOW IN POLYMERS
the interactions between lamellar and
intervening amorphous regions in
response to an applied tensile load.
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MATERIAL SURFACE
Surface is also a defect!!
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