IN IMPERFECTIONS SOLIDS
(DEFECTS)
Chapter 4 - 1
Types of Imperfections
Vacancy atoms
Interstitial atoms
Substitutional atoms
Point defects
Dislocations
Line defects
Grain Boundaries
Area defects
Cracks, voids etc
Bulk defects
Chapter 4 - 2
POINT DEFECTS
Chapter 4 - 3
Chapter 4 - 4
Vacancies:
Point Defects
-vacant atomic sites in a structure.
Vacancy
distortion
of planes
Self-Interstitials:
-"extra" atoms positioned between atomic sites.
distortion
of planes
selfinterstitial
Chapter 4 - 5
VACANCY CONCENTRATION
Equilibrium concentration varies with temperature!
No. of defects
No. of potential
defect sites.
Activation energy
Q
Nv
v
= exp
kT
N
Boltzmann's constant
Temperature
Chapter 4 - 6
Diffusion
Mass transport by atomic motion
Chapter 4 - 7
Diffusion
Interdiffusion: In an alloy, atoms tend to migrate
from regions of high conc. to regions of low conc.
Initially
After some time
Adapted
from Figs.
5.1 and 5.2,
Callister 7e.
Chapter 4 - 8
Diffusion
Self-diffusion: In an elemental solid, atoms
also migrate.
Label some atoms
C
A
D
B
After some time
C
D
A
B
Chapter 4 - 9
Diffusion Mechanisms
Vacancy Diffusion:
atoms exchange with vacancies
applies to substitutional impurities atoms
rate depends on:
--number of vacancies
--activation energy to exchange.
increasing elapsed time
Chapter 4 - 10
Diffusion Mechanisms
Interstitial diffusion smaller atoms can
diffuse between atoms.
Adapted from Fig. 5.3 (b), Callister
7e .
More rapid than vacancy diffusion
Chapter 4 - 11
Processing Using Diffusion
Case Hardening:
--Diffuse carbon atoms
into the host iron atoms
at the surface.
--Example of interstitial
diffusion is a case
hardened gear.
Adapted from
chapter-opening
photograph,
Chapter 5,
Callister 7e.
(Courtesy of
Surface Division,
Midland-Ross.)
Result: The presence of C
atoms makes iron (steel) harder.
Chapter 4 - 12
Processing Using Diffusion
Doping silicon with phosphorus for n-type semiconductors:
0.5 mm
Process:
1. Deposit P rich
layers on surface.
magnified image of a computer chip
silicon
2. Heat it.
3. Result: Doped
semiconductor
regions.
silicon
light regions: Si atoms
light regions: Al atoms
Adapted from chapter-opening
photograph, Chapter 18, Callister 7e.
Chapter 4 - 13
Chapter 4 - 14
SOLID SOLUTIONS of Alloys
Two outcomes if impurity (B) added to host (A):
Solid solution of B in A
OR
Substitutional solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(e.g., C in Fe)
Chapter 4 - 15
LINE DEFECTS
Chapter 4 - 16
DISLOCATIONS
Dislocations
Are one-dimensional defects around which atoms are
misaligned
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
Burgers vector, b: measure of lattice distortion
Chapter 4 - 17
Imperfections in Solids
Edge Dislocation
Fig. 4.3, Callister 7e.
Chapter 4 - 18
Chapter 4 - 19
Imperfections in Solids
Screw Dislocation
Dislocation
line
Burgers vector b
b
(b)
(a)
Adapted from Fig. 4.4, Callister 7e.
Chapter 4 - 20
Edge, Screw, and Mixed Dislocations
Mixed
Edge
Adapted from Fig. 4.5, Callister 7e.
Screw
Chapter 4 - 21
ENORMOUS NUMBERS OF DISLOCATIONS ARE FOUND IN MATERIALS.
DISLOCATION DENSITY
FOR SOFTEST METALS
HEAVILY DEFORMED
MATERIALS
TOTAL LENGTH OF DISLOCATIONS
PER UNIT VOLUME
DISL. DENSITY 106 cm/cm3
(TYPICAL)
DISL. DENSITY 1012 cm/cm3
Chapter 4 - 22
Dislocations are visible in electron micrographs
Adapted from Fig. 4.6, Callister 7e.
Chapter 4 - 23
Dislocation Motion
Dislocations & plastic deformation
Cubic & hexagonal metals - plastic deformation by plastic
shear or slip where one plane of atoms slides over adjacent
plane by defect motion (dislocations).
If dislocations don't move,
deformation doesn't occur!
Adapted from Fig. 7.1,
Callister 7e.
Chapter 4 - 24
Dislocation Motion
Dislocation moves along plane slip in slip direction
perpendicular to dislocation line
Slip direction same direction as Burgers vector
Edge dislocation
Adapted from Fig. 7.2,
Callister 7e.
Screw dislocation
Chapter 4 - 25
Chapter 4 - 26
Chapter 4 - 27
Single Crystal Slip
Adapted from Fig.
7.9, Callister 7e.
Adapted from Fig. 7.8, Callister 7e.
Chapter 4 - 28
PLASTIC DEFORMATION
Dislocations:
are line defects,
slip between crystal planes result when dislocations move,
produce permanent (plastic) deformation.
Schematic of Zinc (HCP):
before deformation
after tensile elongation
slip steps
Adapted from Fig. 7.8, Callister 7e.
Chapter 4 - 29
Deformation Mechanisms
Slip System
Slip plane - plane allowing easiest
slippage
highest planar densities
Slip direction - direction of
movement - Highest linear densities
Chapter 4 - 30
CRYSTALLOGRAPHIC PLANES
(001) Plane referenced
to the origin at point 0
z
0
z
y
0
Other equivalent
(001) planes
x
z
y
x
Other equivalent
(110) planes
(111) Plane referenced
to the origin at point 0
0
x
(110) Plane referenced
to the origin at point 0
y
Other equivalent
(111) planes
Chapter 4 - 31
Chapter 4 - 32
Chapter 4 - 33
Chapter 4 - 34
Chapter 4 - 35
Chapter 4 - 36
Chapter 4 - 37
Interfacial Defects
GRAIN BOUNDARIES
Chapter 4 - 38
Polycrystalline Materials
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
Adapted from Fig. 4.7, Callister 7e.
Chapter 4 - 39
Imperfections in Solids
Solidification- result of casting of molten material
2 steps
Nuclei form
Nuclei grow to form crystals grain structure
Start with a molten material all liquid
nuclei
liquid
crystals growing
grain structure
Adapted from Fig.4.14 (b), Callister 7e.
Crystals grow until they meet each other
Chapter 4 - 40
GRAINS
GRAIN
BOUNDARIES
Chapter 4 - 41
Solidification
Grains can be - equiaxed (roughly same size in all directions)
- columnar (elongated grains)
~ 8 cm
heat
flow
Columnar in
area with less
undercooling
Shell of
equiaxed grains
due to rapid
cooling (greater
T) near wall
Adapted from Fig. 4.12, Callister 7e.
Grain Refiner - added to make smaller, more uniform, equiaxed grains.
Chapter 4 - 42
Optical Microscopy
Useful up to 2000X magnification.
Polishing removes surface features (e.g., scratches)
Etching changes reflectance, depending on crystal
orientation.
crystallographic planes
Adapted from Fig. 4.13(b) and (c), Callister
7e. (Fig. 4.13(c) is courtesy
of J.E. Burke, General Electric Co.
Micrograph of
brass (a Cu-Zn alloy)
0.75mm
Chapter 4 - 43
4 Strategies for Strengthening:
Solid Solutions
Impurity atoms distort the lattice & generate stress.
Stress can produce a barrier to dislocation motion.
Smaller substitutional
impurity
Larger substitutional
impurity
A
C
B
Impurity generates local stress at A
and B that opposes dislocation
motion to the right.
D
Impurity generates local stress at C
and D that opposes dislocation
motion to the right.
Chapter 4 - 44
SOLID SOLUTION
STRENGTHENING
Be
Sn
Be
Yield Strength [ MPa ]
250
Zn
200
Si
Sn
150
Al
Ni
Zn
100
50
0
10
20
30
Percent Alloying Element
FIG : Shows the effect of several alloying
elements on the yield strength of copper
EFFECT OF S.S. STRENGTHENING
ON PROPERTIES :
Y , T and H : [ INCREASE ]
DUCTILITY :
[ DECREASES ]
ELEC. COND : [ DECREASES ]
Chapter 4 - 45
4 Strategies for Strengthening:
Reduce Grain Size
Grain boundaries are
barriers to slip.
Barrier "strength"
increases with
Increasing angle of
misorientation.
Smaller grain size:
more barriers to slip.
Hall-Petch Equation:
Adapted from Fig. 7.14, Callister 7e.
(Fig. 7.14 is from A Textbook of Materials
Technology, by Van Vlack, Pearson
Education, Inc., Upper Saddle River, NJ.)
yield = o + k y d 1 / 2
Chapter 4 - 46
Chapter 4 - 47
Chapter 4 - 48
Chapter 4 - 49