Materials Science
Defects
Defects in solids
1 mole Fe = 55.85g; V= 7.10 cm3 (D=7.87g/cm3); ～ 6 x 1023 atoms
It would be nearly impossible to arrange so many atoms in exact
3D periodicity. So, formation of defects is not unexpected!
ISSUES TO ADDRESS...
• What types of defects arise in solids?
• How do defects affect material properties?
• Are defects undesirable?
Defects in solids
There is no such thing as a
perfect crystal.
 What are these
imperfections?
 Why are they important?
Many of the important
properties of materials are
due to the presence of
imperfections.
Types of imperfections
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
Point defects (0D)
• Dislocations
Line defects (1D)
• Grain Boundaries
Area defects (2D)
• Precipitates / cracks /
porosity
Volume defects (3D)
Point defects (Intrinsic)
• Vacancies -vacant atomic sites in a structure.
Vacancy
distortion
of planes
• Self-Interstitials- "extra" atoms positioned between atomic sites.
selfinterstitial
distortion
of planes
Intrinsic point defect concentration
• Equilibrium concentration varies with temperature!
No. of defects
No. of potential
defect sites.
Activation energy
-Q
Nv
= exp 
 v
 kT
N

÷
÷

unitless; probability
Absolute
Boltzmann's constant Temperature
Each lattice site
is a potential
vacancy site
Point defects (Extrinsic)
Two outcomes if impurity (B) added to host (A) - alloys:
• Solid solution of B in A (i.e., random dist. of point defects)
Insterstitial
site can
be calculated
using
simple
geometry.
OR
Substitutional solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(e.g., C in Fe)
Point defects (Extrinsic) - alloys
• 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.
Point defects – summary

Important for diffusion and mechanical properties
Line defects in solids (1D)

1-D defect in
which atoms are
mispositioned.
Line defects in Solids
Linear Defects (Dislocations)


Edge dislocation:



Are one-dimensional defects around which atoms are
misaligned
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
Line defects in solids

Screw dislocation
Screw Dislocation
Dislocation
line
Burgers vector b
(a)
Dislocations are visible in
electron micrographs
Dislocation motion
• Incrementally breaking bonds
• If dislocations don't move, deformation doesn't
happen! (But it will fracture like a ceramic)
Dislocations in materials
• Metals: Disl. motion easier.
-non-directional bonding
-close-packed directions
for slip.
electron cloud
• Covalent Ceramics
(Si, diamond): Motion hard.
-directional (angular) bonding
• Ionic Ceramics (NaCl):
Motion hard.
-need to avoid ++ and -neighbors.
ion cores
Dislocation density








Dislocation density: total dislocation length per unit
volume of material …
… or, the number of dislocations that intersect a unit
area of a random section
The dislocation density typically determines the
strength of a material
Metals (carefully solidified): 103 mm-2
Metals (heavily deformed): 109-1010 mm-2
Metals (heat treated): 105-106 mm-2
Ceramics: 102-104 mm-2
Single crystal silicon for ICs: 0.1-1 mm-2
Area defects (2D)
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
Area defects (2D) – grains

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.
0.75mm
Fe-Cr alloy
Volume defects (3D)



Precipitates in Al alloys (deliberate)
Cracks and damage (affects brittle materials)
Porosity (in ceramics/ metals)
Mechanical Properties
ISSUES TO ADDRESS...
• Stress and strain: What are they and why are
they used instead of load and deformation?
• Elastic behavior: When loads are small, how much
deformation occurs? What materials deform least?
• Plastic behavior: At what point does permanent
deformation occur? What materials are most
resistant to permanent deformation?
• Toughness and ductility: What are they and how
do we measure them?
Stress-Strain curves
Necking starts
STRESS
σUTS
REGION I
σYIELD
l0 + le
REGION II
HARDENING OCCURS
DISLOCATION MOTION
AND GENERATION !
E
REGION III
σFAILURE or σFRACTURE
Region I : Elastic Deformation
Hooke’s Law
Region II: Uniform Plastic Deformation
Strain is uniform across material
Region III: Non-uniform Plastic Deformation
Deformation is limited to “neck” region
l0 + l e + lp
STRAIN
l0
εYIELD
εUTS
Yield Strength : Comparison
Metals/
Alloys
Graphite/
Ceramics/
Semicond
Polymers
Composites/
fibers
2000
300
200
Al (6061) ag
Steel (1020) hr
Ti (pure) a
Ta (pure)
Cu (71500) hr
100
70
60
50
40
Al (6061) a
30
20
10
Tin (pure)
¨
dry
PC
Nylon 6,6
PET
PVC humid
PP
HDPE
LDPE
in ceramic matrix and epoxy matrix composites, since
in tension, fracture usually occurs before yield.
700
600
500
400
Ti (5Al-2.5Sn) a
W (pure)
Cu (71500) cw
Mo (pure)
Steel (4140) a
Steel (1020) cd
Hard to measure,
1000
Hard to measure ,
since in tension, fracture usually occurs before yield.
Yield strength, sy (MPa)
Steel (4140) qt
Yield strength – summary




Yield strength sy, the point at which stress is no
longer proportional strain
Above this level of stress permanent
deformation occurs
sy is a measure of resistance to plastic
deformation (onset of dislocation motion in metals)
Can be difficult to measure experimentally, but
can use proportional limit (0.2% strain offset).
Tensile Strength, TS
• Maximum stress on engineering stress-strain curve.
TS
F = fracture or
ultimate
strength
engineering
stress
sy
Typical response of a metal
Neck – acts
as stress
concentrator
strain
engineering strain
• Metals: occurs when noticeable necking starts.
• Polymers: occurs when polymer backbone chains are
aligned and about to break.
Tensile Strength : Comparison
Metals/
Alloys
Tensile strength, TS (MPa)
5000
3000
2000
1000
300
200
100
40
30
Graphite/
Ceramics/
Semicond
Polymers
C fibers
Aramid fib
E-glass fib
Steel (4140) qt
AFRE(|| fiber)
GFRE(|| fiber)
CFRE(|| fiber)
Diamond
W (pure)
Ti (5Al-2.5Sn)aa
Steel (4140)cw
Si nitride
Cu (71500)
Cu (71500) hr
Al oxide
Steel (1020)
ag
Al (6061) a
Ti (pure)
Ta (pure)
Al (6061) a
Si crystal
<100>
Glass-soda
Concrete
Nylon 6,6
PC PET
PVC
PP
HDPE
20
Composites/
fibers
Graphite
wood(|| fiber)
GFRE( fiber)
CFRE( fiber)
AFRE( fiber)
LDPE
10
wood (
1
fiber)
Tensile strength – summary



Maximum stress that a structure can sustain
Accompanied by plastic deformation and
necking
Design is to avoid this dangerous regime
Ductility
• Plastic tensile strain at failure:
Lf - Lo
x 100
%EL =
Lo
smaller %EL
Engineering
tensile
stress, s
larger %EL
Lo
Engineering tensile strain, e
Examples:
• Al 40%
•Al2O3 <1%
Definition: Degree of plastic deformation
before failure.
Lf
Toughness
• Energy to break a unit volume of material (J.m-3)
• Resistance to crack propagation
• Approximated by the area under the stress-strain
curve.
Engineering
tensile
stress, s
small toughness (ceramics)
large toughness (metals)
very small toughness
(unreinforced polymers)
Engineering tensile strain,
Brittle fracture: elastic energy
Ductile fracture: elastic + plastic energy
e
Resilience - Elastic recovery

Capacity of a material to
absorb energy during
elastic deformation and
then on unloading to
recover the energy

Modulus of resilience U is
strain energy per unit
volume required to stress
a material to the yield
point

i.e. area under stressstrain curve
Resilience, Ur

Ability of a material to store energy

Energy stored best in elastic region
Ur = 
ey
0
sde
If we assume a linear
stress-strain curve this
simplifies to
1
Ur @ sy e y
2
Hardness



Resistance of materials to localised plastic
deformation (dents or scratches)
Related to sy and E
Quantitative analysis
 Small
indenter forced into the surface and depth of
indent is a measure of hardness
 E.g. Vickers hardness, small diamond indenter

Arbitrary!
Hardness
• Large hardness means:
--resistance to plastic deformation or cracking in
compression.
--better wear properties.
apply known force
measure size
of indent after
removing load
e.g.,
10 mm sphere
D
most
plastics
brasses
Al alloys
Smaller indents
mean larger
hardness.
d
easy to machine
steels
file hard
cutting
tools
increasing hardness
nitrided
steels
diamond
Hardness: Measurement
Summary
• Stress and strain: These are size-independent
measures of load and displacement, respectively.
• Elastic behavior: This reversible behavior often
shows a linear relation between stress and strain.
To minimize deformation, select a material with a
large elastic modulus (E).
• Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches sy.
• Toughness: The energy needed to break a unit
volume of material.
• Ductility: The plastic strain at failure.