slip systems and twinning
DESCRIPTION
An introductionTRANSCRIPT
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MATERIALS SCIENCE AND
BITSPilaniPilani Campus
MATERIALS SCIENCE AND ENGINEERING
Dr. Subrata Bandhu Ghosh
Department of Mechanical Engg.
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Vacancy atoms
Interstitial atoms
Substitutional atomsPoint defects
1-2 atoms
Types of Imperfections
Dislocations Line defects
1-dimensional
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Dislocations
The strength of a material with no
dislocations is 20-100 times greater than
the strength of a material with a high
dislocation density.
So, materials with no dislocations may be
very strong, but they cannot be deformed.
The dislocations weaken a material, but
make plastic deformation possible.
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are line defects,
slip between crystal planes result when dislocations
move,
produce permanent (plastic) deformation.
Dislocations:
Schematic of Zinc (HCP): after tensile elongation
Line Defects
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before deformation after tensile elongation
slip steps
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Line Defects (Dislocations) Are one-dimensional defects around which atoms
are misaligned
Edge dislocation: extra half-plane of atoms inserted in a crystal
structure
b (the Bergers vector) is (perpendicular) to dislocation line
Screw dislocation: Screw dislocation: spiral planar ramp resulting from shear deformation
b is || (parallel) to dislocation line
Burgers vector, b: is a measure of lattice distortion
and is measured as a distance along the close
packed directions in the lattice
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Imperfections in Solids
Linear defects are associated primarily with mechanical deformation.
Types of dislocations: edge, screw
Edge dislocation:
extra half-plane of atoms inserted in a crystal structure; the edge
of the plane terminates within the crystal.
Around the dislocation line there is some localized distortion.
b perpendicular () to dislocation line b perpendicular () to dislocation line
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Bonds across the slipping planes are broken and
remade in succession.
The (plastic) permanent deformation of most
crystalline materials is by dislocation movement.
Most contain some dislocations that were introduced
Motion of Edge Dislocation
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during solidification, plastic deformations, and rapid
cooling (thermal stresses).
To deform plastically means to slide atomic planes
past each other.
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Imperfections in Solids
Screw dislocation:
Named for the spiral stacking of crystal planes around the
dislocation line; results from shear deformation
b parallel (||) to dislocation line
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Characteristics of Dislocations
During plastic deformation, the number of dislocations
increase dramatically to densities of 1010 mm-2.
Grain boundaries, internal defects and surface
irregularities serve as formation sites for dislocations
during deformation.
The number of dislocations in a material is expressed The number of dislocations in a material is expressed
as the dislocation density- the total dislocation
length per unit volume or the number of
dislocations intersecting a unit area. Dislocation
densities can vary from 105 cm-2 in carefully solodified
metal crystals to 1012 cm-2 in heavily deformed metals.
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Dislocations During Cold Working
Ti alloy after cold working.
Dislocations entangle with one
another during cold work.
Dislocation movement
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Dislocation movement
becomes more difficult.
Dislocations are visible in
electron micrographs
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Vacancy atoms
Interstitial atoms
Substitutional atomsPoint defects
1-2 atoms
Types of Imperfections
Dislocations Line defects1-dimensional
Grain Boundaries
twins, twists
Area/Planar defects
2-dimensional
The free or external surface of any material is the most
common type of planar defect!
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Polycrystalline Materials
Grain Boundaries regions between crystals
transition from lattice of one
region to another
(a) The atoms near the boundaries of
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(a) The atoms near the boundaries of
the 3 grains do not have an
equilibrium spacing or
arrangement; slightly disordered.
(b) Grains and grain boundaries in a
stainless steel sample. low density
in grain boundaries
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Planar Defects in Solids - Twinning
A shear force that causes atomic displacements such that the atoms on one side of a plane (twin boundary) mirror the atoms on the other side. A reflection of atom positions across the twin plane.
Displacement magnitude in the twin region is proportional to the atoms distance from the twin plane.
Takes place along defined planes and directions depending Takes place along defined planes and directions depending upon the system.
Ex: BCC twinning occurs on the (112)[111] system
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Slip Systems
Usually there are preferred slip planes and
directions in crystal systems.
The combination of both the slip plane and
direction form the slip system.
Slip plane is generally taken as the closest Slip plane is generally taken as the closest
packed plane in the system
Slip direction is taken as the direction on the
slip plane with the highest linear density.
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Slip Systems
FCC and BCC materials have large numbers of slip systems (at
least 12) and are considered ductile.
HCP systems have few slip systems and are quite brittle.
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Slip Systems
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Twinning
Applied stress to a perfect crystal (a) may cause a displacement of the atoms,
(b) causing the formation of a twin. Note that the crystal has deformed as a
result of twinning.
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Properties of Twinning
Of the three common crystal structures BCC, FCC and
HCP, the HCP structure is the most likely to twin.
FCC structures will not usually twin because slip is
more energetically favorable.
Twinning occurs at low temperatures and high rates of
shear loading (shock loading) conditions where there are
few present slip systems (restricting the possibility of few present slip systems (restricting the possibility of
slip)
Small amount of deformation when compared with slip.
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Comparison
Slip Twinning
orientation of atomsremains the same
reorientation of atomicdirection across twin planeremains the same direction across twin plane
displacements take placein exact atomic spacings
atomic displacement is lessthan interatomic spacing
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Microscopic Examination
Applications
To Examine the structural elements and defects that
influence the properties of materials.
Ensure that the associations between the properties and
structure (and defects) are properly understood.structure (and defects) are properly understood.
Predict the properties of materials once these
relationships have been established.
Structural elements exist in macroscopic and
microscopic dimensions
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Microscopic Examination
Metallography sample preparation is necessary to examine the surface of materials (metals, ceramics, polymers).
A smooth mirror-like finish is obtained by grinding and polishing using successively finer abrasive papers and powder mixed with water.abrasive papers and powder mixed with water.
The microstructure (grain size, shape, orientation) is revealed using a chemical reagent (etching solution) on a polycrystalline sample.
Etching characteristics vary from grain to grain.
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Microscopy
Optical (light) resolution (0.1 m = 100 nm = 10-7 m)
For higher resolution need higher frequency
X-Rays are difficult to focus.
Electrons
wavelengths are roughly 3 pm (0.003 nm) wavelengths are roughly 3 pm (0.003 nm)
(Magnification - 1,000,000X)
Atomic resolution possible
Electron beam focused by magnetic lenses.
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Useful up to 2000X magnification.
Polishing removes surface features (e.g., scratches)
Etching changes reflectance, depending on crystal
orientation.
Optical Microscopy
Micrograph of
brass (a Cu-Zn alloy)
0.75mm
crystallographic planes
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Grain boundaries...
are imperfections,
are more susceptible
Optical Microscopy
grain boundary
surface groove
polished surface
are more susceptible
to etching
may be revealed as
dark lines
change in crystal
orientation across
boundary.
grain boundary(a)
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Polycrystalline Deformation
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The grain size is often determined when the properties of
a polycrystalline material are under consideration. The
grain size has a significant impact of strength and
response to further processing
Linear Intercept method
Straight lines are drawn through several
photomicrographs that show the grain
Grain Size Determination
photomicrographs that show the grain
structure.
The grains intersected by each line segment are
counted
The line length is then divided by an average
number of grains intersected.
The average grain diameter is found by dividing this
result by the linear magnification of the
photomicrographs.
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ASTM (American Society for Testing and Materials)
VISUAL CHARTS (@100x) each with a number
Quick and easy used for steel
ASTM has prepared several standard comparison charts, all having different
average grain sizes. To each is assigned a number from 1 to 10, which is
termed the grain size number; the larger this number, the smaller the grains.
Quick and easy used for steel
N = 2 n-1No. of grains/square inch
Grain size no.
NOTE: The ASTM grain size is related a grain area
AT 100x MAGNIFICATION
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Determining Grain Size, using a Micrograph
taken at 300x
We count 14 grains
in a 1 in2 area on the
image
To report ASTM
2
12100
M is mag. of image
N is measured grain count at M
now solve for n:
n
M
M
MN
=
To report ASTM
grain size we need N
at 100x not 300x
We need a
conversion method!
( ) ( )( ) ( ) ( )
( ) ( )( )
( ) ( )
now solve for n:
log( ) 2 log log 100 1 log 2
log 2log 41
log 2
log 14 2log 300 41 7.98 8
0.301
M
m
N M n
N Mn
n
+ =
+ = +
+ = + =
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For this same material, how many Grains
would I expect /in2 at 100x?
1 8 1 22 2 128 grains/in
Now, how many grain would I expect at 50x?
nN
= =
2 2
8 1
2 2
100 100N 2 128*
50
N 128*2 512 grains/in
M
M
M
= =
= =
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300
400
500
600
N
u
m
b
e
r
o
f
G
r
a
i
n
s
/
i
n
2
At 100x
0
100
200
0 2 4 6 8 10 12
Grain Size number (n)
N
u
m
b
e
r
o
f
G
r
a
i
n
s
/
i
n
2
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Electron Microscopes
beam of electrons of
shorter wave-length
(0.003nm) (when
accelerated across large
voltage drop)
Image formed with
Magnetic lenses
High resolutions and
magnification (up to
50,000x SEM); (TEM up
to 1,000,000x)
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Uses a moveable Probe of very small diameter
to move over a surface
Atoms can be arranged and imaged!
Photos produced from
the work of C.P. Lutz,
Zeppenfeld, and D.M.
Eigler.
Scanning Tunneling Microscopy (STM)
Carbon monoxide
molecules arranged on
a platinum (111)
surface.
Eigler.
Iron atoms arranged
on a copper (111)
surface. These Kanji
characters represent
the word atom.
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Summary
Point, Line, and Area defects exist in solids.
The number and type of defects can be varied and controlled
T controls vacancy conc.
amount of plastic deformation controls # of dislocations
Weight of charge materials determine concentration of Weight of charge materials determine concentration of substitutional or interstitial point defects
Defects affect material properties (e.g., grain boundaries control crystal slip).
Defects may be desirable or undesirable
e.g., dislocations may be good or bad, depending on whether plastic deformation is desirable or not.
Inclusions can be intention for alloy development