Download Dislocations

MME 2001
MATERIALS SCIENCE 1
3.11.2015
vacancies
vacant atomic site/missing atom
Vacancy
distortion
of planes
All crystalline solids contain vacancies.
vacancies increase the entropy (the randomness) of
the crystal: thermodynamically favorable!
the number of vacancies increases exponentially
with T!
Observing equilibrium vacancy conc.
● Low energy electron microscope view of a (110)
surface of NiAl.
● Increasing T causes surface island of atoms to grow.
● Why? equil. vacancy conc. increases via atom
motion to the surface, where they join the island.
island grows/shrinks to maintain
I vancancy conc. in the bulk.
equil.
impurities in solids
● A pure metal consisting of only one type of
atom (extremely high purity!) is just not
possible!
● impurity or foreign atoms will always be
present!
● it is difficult to refine metals to 99.9999%.
● Even at purity level, 1022 to 1023 impurity
atoms will be present in 1m3 of material.
Solid solutions
Solid solution
● A solid solution forms when, the crystal structure
is maintained and no new structures are formed
upon the addition of the solute atoms.
● A solid solution is compositionally homogeneous;
the impurity atoms are randomly and uniformly
dispersed within the solid.
Second phase
● A second phase is formed when the impurity
atoms cannot be accommodated in solid solution
(solid solubility limit!)
Second phase particles
• Solid solution of B in A plus particles of a new
phase (usually for a larger amount of B)
Second phase particle
different composition
often different structure
Solid solution
Substitutional vs interstitial
Solid solutions
Two types of solid solutions:
Solid solution of B in A (i.e., random dist. of
point defects)
OR
Substitutional solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(e.g., C in Fe)
Substutional solid solutions
● solute atoms replace the host atoms.
● Several features of the solute and solvent atoms
determine the degree to which the former
dissolves in the latter:
● Atomic size factor:
● Appreciable quantities of a
solute may be accommodated
only when the difference
in atomic radii between
the two atom types
is  %15.
Substitutional solid solutions
Crystal structure
● crystal structures for metals of both atom types
must be the same.
Electronegativity
● Electropositive/electronegative pair of atoms
will form an intermetallic compound instead of a
substitutional solid solution.
Valences
● Other factors being equal, a metal will have
more tendency to dissolve another metal of
higher valency than one of a lower valency.
substitutional solid solutions
● Cu-Ni substitutional solid solution
● the atomic radii for copper and nickel are 0.128
and 0.125 nm,
● both have the FCC crystal structure,
● their electronegativities are 1.9 and 1.8
● finally, the most common valences are 1 for
copper and 2 for nickel.
● These two elements are completely soluble in
one another at all proportions.
substitutional solid solutions
Cu-Ni
substitutional
solid solution
substitutional solid solutions
Two metals
completely
soluble in
the liquid
state but
only partly
soluble in
the solid
state
substitutional solid solutions
Conditions for substitutional solid solution (S.S.)
 W. Hume – Rothery rule
 1. r (atomic radius) < 15%
 2. Proximity in periodic table
 i.e., similar electronegativities
 3. Same crystal structure for pure metals
 4. Valency
 All else being equal, a metal will have a
greater tendency to dissolve a metal of higher
valency than one of lower valency
substitutional solid solutions
Application of Hume–Rothery rules – Solid Solutions
Would you predict
more Al or Ag
to dissolve in Zn ?
More Al because
● size is closer and
● val. is higher (but
not too much)
● FCC in HCP
Element
Cu
C
H
O
Ag
Al
Co
Cr
Fe
Ni
Pd
Zn
Atomic Crystal
Radius Structure
(nm)
0.1278
0.071
0.046
0.060
0.1445
0.1431
0.1253
0.1249
0.1241
0.1246
0.1376
0.1332
Electronegativity
Valence
FCC
1.9
+2
FCC
FCC
HCP
BCC
BCC
FCC
FCC
HCP
1.9
1.5
1.8
1.6
1.8
1.8
2.2
1.6
+1
+3
+2
+3
+2
+2
+2
+2
substitutional solid solutions
More Zn or Al in Cu ?
Surely Zn since size is
closer thus causing
lower distortion
(4% vs 12%)
Element
Cu
Al
Zn
Atomic Crystal
Radius Structure
(nm)
0.1278
0.1431
0.1332
FCC
FCC
HCP
Electronegativity
Valence
1.9
1.5
1.6
+2
+3
+2
Specification of composition
to express the composition (or concentration) of an
alloy in terms of its constituent elements.
Weight percent
the weight of a particular element relative to the
total alloy weight. For an alloy that contains two
hypothetical atoms denoted by 1 and 2, the
concentration of 1 in wt%, C1, is defined as
m1 and m2 represent the weight (or mass) of
elements 1 and 2, respectively.
Specification of composition
atomic percent
number of moles of an element in relation to the
total moles of the elements in the alloy.
number of moles in some specified mass of an
element, nm:
n = m/A
m and A denote the mass (in grams) and atomic
weight.
Concentration in terms of atom percent of element
1 in an alloy containing element 1 and element 2
atoms, C1’
m
atom to weight % conversions
Pay attention to
the subscripts!
atom to weight % conversions
Determine the composition, in weight percent, of
an alloy that consists of 98.7 at% Al and 1.3 at% Cu.
CAl =
CCu =
98.7 x 26.98
98.7x26.98 + 1.3x63.55
1.3 x 63.55
98.7x26.98 + 1.3x63.55
x 100 = 97
x 100 = 3
interstitial solid solutions
● impurity atoms fill the voids or interstices among
the host atoms that are relatively small (APF)
● the atomic diameter of an interstitial impurity
must be substantially smaller than that of the
host atoms
● maximum allowable
concentration of interstitial
impurity atoms is less
than 10%
● they introduce some
lattice strains on the
adjacent host atoms.
interstitial solid solutions
● Carbon forms an interstitial solid solution when
added to iron;
● the maximum concentration of carbon is about
2%.
● The atomic radius of the carbon atom is much
less than that for iron: 0.071 nm vs 0.124 nm.
● Solid solutions are also
possible for ceramic
materials.
Carbon
Learning check
Name the point
defects in the sketch!
1: vacancy
2: self interstitial
3: interstitial
4: substitutional
5: substitutional
Line Defects
Dislocations:
● are line defects around which atoms are
misaligned
● introduced during solidification or when the
materials is deformed
TEM micrograph of
dislocations in Ti3Al
dislocations
 Edge dislocation:
 extra half-plane of atoms inserted in a crystal
structure
 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
Burgers vector
Johannes Martinus BURGERS
Burger’s vector
Burgers vector
Burgers vector
● The magnitude and direction of the lattice
distortion associated with a dislocation is
expressed in terms of a Burgers vector, b.
● For an edge dislocation, b is perpendicular
● for a screw, b is parallel to the dislocation line
● Virtually all crystalline materials contain
dislocations introduced during solidification,
during plastic deformation and due to thermal
stresses that result from rapid cooling.
edge dislocation – burgers vector
● In a perfect crystal make a right handed circuit
● Do the same in the dislocated crystal.
● The ‘missing link’ is the Burgers vector.
RHFS: Right Hand Finish to
Start convention
Burger’s vector
A Burgers circuit closes in a {100} plane of a cubic
crystal but fails to close by the Burgers vector, b,
when the same circuit encloses an edge
dislocation!
dislocations
Dislocations are visible in electron micrographs
A transmission electron
micrograph of a
titanium alloy in which
the dark lines are
dislocations. 51,000X
Edge dislocations
an extra portion of a
plane of atoms, or halfplane, the edge of which
terminates within the
crystal
atoms above the dislocation
line are squeezed together,
and those below are pulled apart
Stress field of an
edge dislocation
compression
tension
Motion of Edge Dislocation
● slip occurs when dislocations move
● Dislocation motion requires the successive
bumping of a half plane of atoms.
● Bonds across the slipping planes are
broken and remade in succession.
● deformation of crystalline materials occurs
by the motion of dislocations.
Glide of an edge dislocation
crss
crss: critical
crss
resolved shear
stress on the
slip plane in the
direction of b
Glide of an edge dislocation
crss
crss
Glide of an edge dislocation
crss
crss
Glide of an edge
dislocation

crss
crss
Glide of an edge dislocation
crss
Surface step,
not a
dislocation
crss
slip
slip
Schematic of plastically deformed Zinc (HCP):
before
deformation
after tensile
elongation
slip steps
Screw dislocation
often formed by a shear stress
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, line AB.
Screw Dislocation

Dislocation
Burgers
line
vector b
b
(b)
Screw
Dislocation
b || t
Slip plane
t
unslipped
slipped
b
Burgers
vector is
parallel to
the
dislocation
line!
Screw dislocation
● Named for the spiral stacking of crystal planes
around the dislocation line; results from shear
deformation
● b parallel () to dislocation line
screw dislocation
Motion of a screw dislocation leading to a step of b
b
dislocations
edge dislocation

screw dislocation
Mixed Dislocations
Most dislocations are neither pure edge nor pure screw,
but exhibit components of both types.
the lattice distortion away from the two faces is mixed,
having varying degrees of screw and edge character.
Mixed
Edge
Screw
Cross-slip
Slip plane 1
b
1
Cross slip is the process
by which a screw
dislocation moves from
one slip plane to another
2
3
Cross slip
dislocation loop
The line vector
t is always
tangent to the
dislocation line
t
b

b t
t
slip

No slip
The Burgers vector b is
constant along a dislocation line
t
b
b
Jog & kink
kink
jog
there is no such
thing as a
straight
dislocation.
Real
dislocations
contain kinks
and jogs
deviations from
a straight line
on atomic
dimensions.
Jog & kink
● a step equal in direction and magnitude to the
intersecting dislocation’s burgers vector!
● May have different character and slip plane than
the original dislocation
Jogs and kinks
Such steps in dislocation lines are generated via
thermal activation at high temperatures or by
intersection of dislocations.
Dislocation climb
● dislocation climb couples point defects and
dislocations in a very direct way.
● This has the immediate consequence that climb
processes will depend on temperature, because
● The types and concentration of equilibrium
point defects are temperature dependent.
● The supersaturation, which is the driving force
for point defect reactions including climb, is
temperature dependent.
● The mobility of point defects, i.e. their
diffusion coefficient, is temperature dependent.
Dislocation climb
Dislocation trapped
at a coarse
precipitate
Climb by
emission of
interstitials
Dislocation
free again!
Dislocation climb
interaction of vacancies
with an edge dislocation.
The edge dislocation moves
from one slip plane to
another.
Dislocation motion / slip
Metals
Dislocation motion easy!
Non-directional bonding
CP directions for slip
Electron
cloud
Ceramics-covalent
Dislocation mobility is low!
Covalent-directional
bonding
Ceramics-ionic
Motion difficult!
Need to maintain charge
balance
Dislocations
 The strength of a material with no
dislocations (perfect crystal!) 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.
Dislocations & Crystal Structures
Structure: close-packed planes & directions
are preferred.
view onto two
close-packed
planes.
close-packed
close-packed
plane (bottom)
directions
close-packed
plane (top)
Dislocations & Crystal Structures
Comparison among crystal structures:
FCC: many close-packed planes/directions;
HCP: only one plane, 3 directions;
BCC: none
Specimens that were tensile tested.
tensile direction
Mg (HCP)
Al (FCC)
Learning check
interfacial-planar-defects
Interfacial defects are boundaries that have two
dimensions and normally separate regions of the
materials that have different crystal structures
and/or crystallographic orientations.
grain boundaries
twin boundaries
stacking faults
phase boundaries
external surfaces
solidification
Start with a molten material – all liquid
 Nuclei form
 Nuclei grow to form crystals – grain structure
nuclei
liquid
crystals growing
grain structure
Crystals grow until they meet each other
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
low angle grain boundary
High angle grain
boundary
Grain boundaries
● atoms are bonded less regularly along a grain boundary
● there is an interfacial or grain boundary energy similar to
the surface energy just described. The magnitude of this
energy depends on the degree of misorientation, being
larger for high-angle boundaries.
● impurity atoms often preferentially segregate along these
boundaries because of their higher energy state.
● The total interfacial energy is lower in large or coarsegrained materials than in fine-grained ones, because
there is less total boundary area in the former. Grains
grow at elevated temperatures to reduce the total
boundary energy,
Grain boundaries
When the orientation mismatch is 
(a few degrees): small- (or low-)
angle grain boundary
These boundaries can be described
in terms of dislocation arrays.
An array of edge dislocations:
tilt boundary; with an angle of
misorientation, .
When the angle of misorientation is
parallel to the boundary,
an array of screw dislocations: a
twist boundary.
Grain boundaries
High-resolution
Transmission Electron
Microscope image of a tilt
grain boundary in
aluminum,
Sandia National Lab.
Twinning
Applied stress to a perfect crystal may cause a
displacement of the atoms, causing the formation
of a twin. Note that the crystal has deformed as a
result of twinning.
twin boundaries
a special type of boundary across which there is
a specific mirror lattice symmetry.
material between these boundaries is a twin.
Twins result from atomic displacements that are
produced from applied
mechanical shear
forces (mechanical
twins), and also
during annealing
following
deformation
(annealing twins).
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 slip)
● Small amount of deformation when compared
with slip.
Stacking fault
A stacking fault is a one or two layer interruption
in the stacking sequence of the crystal structure.
These interruptions carry a
certain stacking-fault energy.
For FCC metals an error in
ABCABC packing sequence:
ABC/AB/ABC
Solidification
Grains can be - equiaxed (same size in all directions)
columnar (elongated grains)
~ 8 cm
Heat flow
Columnar in
area with less
undercooling
Grain Refiner:
smaller, more uniform, equiaxed grains.
Shell of
equiaxed
grains due
to rapid
cooling
(greater
T) near
wall
External surfaces
●crystal structure terminates along external
surfaces.
●Surface atoms are not bonded to the maximum
number of nearest neighbors, and are therefore in a
higher energy state than the atoms at interior
positions.
●These partially loose surface atoms give rise to a
surface energy, expressed in units of energy per unit
area (J/m2 or erg/cm2).
●To reduce this energy, materials tend to minimize
the total surface area.
●For example, liquids assume a shape having a
minimum area—the droplets become spherical.
External surfaces
the atoms in the free surface are
bonded on only one side. The
structure of a real interface is
further complicated by bonding
interactions across the interface
and by chemical changes in the
interfacial plane. The dangling bonds at the interface provide favorable
sites for the adsorption of atoms that do not fit well into the bulk
lattice. The interface is often enriched in solute species (O, S, P).
Bulk-volume defects
Other defects exist in all solid materials that
are much larger than those discussed.
These include
pores,
cracks,
foreign inclusions, and
other phases.
They are normally introduced during
processing and fabrication steps.
Bulk-volume defects
200µm
200µm
Atomic vibrations
● Every atom in a solid material is vibrating very
rapidly about its lattice position within the
crystal. atomic vibrations may be thought of as
imperfections or defects.
● At a given temperature there will exist a
distribution of energies for the constituent atoms
about an average energy.
● With rising T, this average energy increases. At
room temperature, a typical vibrational
frequency is on the order of 1013 vibrations per
second, whereas the amplitude is a few
thousandths of a nanometer.
Microscopic Examination
 Crystallites (grains) and grain boundaries.
Vary considerably in size. Can be quite large
 ex: Large single crystal of quartz or
diamond or Si
 ex: Aluminum light post or garbage can see the individual grains
 Crystallites (grains) can be quite small (mm
or less) – necessary to observe with a
microscope.
Microscopic examination
Cross section of a cylindrical
copper ingot.
Cast aluminium samples
Microstructural examination
Optical microscopy
● For materials that are opaque to visible light (all
metals and many ceramics and polymers), only
the surface is subject to observation.
● The light microscope is used in the reflecting
mode.
● Image contrasts result from differences in
reflectivity of the various regions of the
microstructure. Investigations of this type are
often termed metallographic, because metals
were first examined using this technique.
Optical microscopy
Optical microscopy
● The specimen surface must first be ground and
polished to a smooth and mirrorlike finish by
using successively finer abrasive papers and
powders.
● The microstructure is revealed by a surface
treatment using an appropriate chemical reagent
in a procedure termed etching.
● The chemical reactivity of the grains of some
single-phase materials depends on
crystallographic orientation. Consequently, in a
polycrystalline specimen, etching characteristics
vary from grain to grain.
Optical Microscopy
● Useful up to 2000X magnification.
● Polishing removes surface features (e.g.,
scratches)
● Etching changes reflectance = f (crystal
orientation)
● Grain size estimations:
ASTM grain size number
N=2
n-1
number of grains/in2 at 100X
Optical microscopy
Grain boundaries
• are imperfections
• are more susceptible to etching
• may be revealed as dark lines
• change in crystal orientation
across boundary
Optical microscopy
Micrograph of brass (a Cu-Zn alloy)
grain size measurement
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 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.
Electron microscopy
● some structural elements are too fine or small to
permit observation using optical microscopy.
Under such circumstances the electron
microscope, which is capable of much higher
magnifications, may be employed.
● The image seen with a transmission electron
microscope (TEM) is formed by an electron beam
that passes through the specimen. Contrasts in
the image are produced by differences in beam
scattering or diffraction produced between
various elements of the microstructure or defect.
Electron microscopy
● Because solid materials are highly absorptive to
electron beams, a specimen to be examined
must be prepared in the form of a very thin foil;
● this ensures transmission through the specimen
of an appreciable fraction of the incident beam.
The transmitted beam is projected onto a
fluorescent screen or a photographic film so that
the image may be viewed.
● Magnifications approaching 1,000,000 are
possible with transmission electron microscopy,
which is frequently used to study dislocations.
TEM
electron microscopy
Scanning electron microscopy
● The surface of a specimen to be examined is scanned with
an electron beam, and the reflected (or back-scattered)
beam of electrons is collected, then displayed at the same
scanning rate on a cathode ray tube.
● The image on the screen represents the surface features
of the specimen.
● The surface may or may not be polished and etched, but
it must be electrically conductive; a very thin metallic
surface coating must be applied to nonconductive
materials. Magnifications ranging from 10 to in excess of
50,000 times are possible, as are also great depths of field.
● Accessory equipment permits qualitative and
semiquantitative analysis of the elemental composition
of very localized surface areas.
microscopy
Scanning probe microscopy
The scanning probe microscope (SPM) differs from
optical and electron microscopes in that neither
light nor electrons are used to form an image.
Rather, the microscope generates a topographical
map, on an atomic scale, that is a representation
of surface features and characteristics of the
specimen being examined.
Probe Techniques
Atomic Force Microscopy
Scanning Tunneling Microscopy (STM)
Near-Field Scanning Optical Microscopy (NSOM
Scanning Tunneling Microscopy (STM)
STM is an instrument for imaging surfaces at the
atomic level. Its development in 1981 earned its
inventors, Gerd Binnig and Heinrich Rohrer (at IBM
Zürich), the Nobel Prize in Physics in 1986.
Carbon monoxide
molecules
arranged on a
platinum (111)
surface.
Iron atoms
arranged on a
copper (111)
surface.
Scanning Tunneling Microscopy (STM)
STM is based on the concept of
quantum tunneling. When a
conducting tip is brought very near
to the surface to be examined, a
voltage difference applied between
the two can allow electrons to
tunnel through the vacuum between
them. The resulting tunneling
current is monitored as the tip's
position scans across the surface,
and is usually displayed in image
form.
A large scanning tunneling microscope, in
the labs of the London Centre for
Nanotechnology
Summary
• Point, Line, and Area defects exist in solids.
• The number and type of defects can be varied
and controlled (e.g., T controls vacancy conc.)
• 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.)
Microstructural examination
Structures of solids
disorder
see you next week!