1. Chapter 5 Defects in solids

2. Defects in solids All solid materials… Solidification process…
contain large # of defects.
Solidification process…
classification
above Tm
Defects…
imperfection in structures of solid materials
crystal structure due to irregular/disordered atomic
arrangement.
amorphous structure due to molecular chains error.
- classify in terms of geometry (dimension) & size.
normally, formed during solidification process.
zero dimension
one dimension
two dimension
three dimension
liquid
nuclei
Solidification process…
result of primary materials forming/working.
i.e: for metals, casting process.
2 steps:
1. Nuclei form – formation of stable nuclei.
2. Nuclei grow to form crystals – formation of grain
structure.
start with a molten (all liquid) material & grains (crystals) grow until they meet each other.
point defects
Linear/dislocation defects
area/planar/surface defects
volume defects (i.e: crack)
crystals growing
crystal growing
- Grains structure can be:
1. equiaxed grains (roughly same size in all directions).
2. columnar grains (elongated grains).
room temp.
grain structure
Columnar grains in area with less undercooling
Mold
Equiaxed grains
due to rapid cooling (greater T) near wall
Casting process

3. Defects in solids classification Point defects in ceramics
1. Vacancies
- vacancies exist in ceramics for both
cations and anions.
2. Interstitials
- exist for cations only.
- interstitials are not normally observed for
anions because anions are large relative
to the interstitial sites.
3. Frenkel defect
- a cation vacancy-cation interstitial pair.
4. Schottky defect
- a paired set of cation and anion vacancies.
Cation
Interstitial
Vacancy
Anion
Defects in solids
classification
zero dimension
point defects
Schottky
defect
Frenkel
metals
ceramics
polymers
Point defects in metals
2. Vacancies
1. Self-Interstitials
vacant atomic sites exist in a structure.
form due to a missing atom.
form (one in 10,000 atoms) during
crystallization, mobility of atoms or
rapid cooling.
- "extra" atoms positioned between atomic
sites.
- cause structural distortion.
self-interstitial
distortion
of planes
Vacancy
distortion
of planes
interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurity
self-interstitial & vacancy (metals)
interstitial & substitutional (metal alloys)
Chain packing error
Point defects in polymers
Defects due in part to chain packing errors and
impurities such as chain ends and side chains.
i.e: thin platelets
10 nm
Adapted from Fig. 4.12, Callister & Rethwisch 3e.

4. Measuring Activation Energy…
Equilibrium concentration: Point defects
Measuring Activation Energy…
Defects in solids
• We can get Qv from an experiment.
classification
equilibrium # of point defects (vacancies) for
solids depends on & increase with temperature.
apply the formula:
• Measure this... N v
zero dimension
# of vacancy sites, Nv
Vacancy concentration =
total # of atomic sites, N
point defects
exponential æ  ö N Q
dependence! v = ç v
exp ç è ø N k T T
Defect vacancy) concentration
Nv = # of defects (vacancies site)
N = total # of atomic sites
• Replot it...
T = temperature 1/ T N v ln - Q /k
slope
metals
ceramics
polymers
Qv = activation energy
k = Boltzmann's constant
(1.38 x J/atom-K)
(8.62 x 10-5 eV/atom-K)
- each lattice/atom site is potential vacancy site.
Example:
Answer:
interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurity
8.62 x 10-5
eV/atom-K
0.9 eV/atom
1273 K ç ÷ N v =
exp - Q k T æ è ö ø
= 2.7 x 10-4
self-interstitial & vacancy (pure metals)
interstitial & substitutional (metals alloy)
Chain packing error
(a)
In 1 m3 of Cu at 1000C, calculate:
(a) vacancy concentration, Nv/N.
(b) equilibrium # of vacancies, Nv.
Given that, r
= 8.4 g /
cm3
(b)
 = N ACu
VCu NA Qv
= 0.9 eV/atom
ACu
= 63.5 g/mol
For 1 m3
, N = N A Cu r x
1 m3
= 8.0 x 1028 atom sites NA
= 6.02 x 1023
atoms/mol N v =
(2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 vacancies

5. Defects in solids classification General concept…
Impurities in ceramics
Defects in solids
Electroneutrality (charge balance) must be
maintained when impurities are present.
2. Substitutional anion impurity
classification O 2-
i.e: NaCl Na + Cl -
zero dimension
cation - -
point defects
1. Substitutional cation impurity Cl Cl
vacancy
without impurity O 2- Ca 2+
impurity + Na an
ion vacancy Na + Ca 2+
without impurity Ca 2+
impurity
with impurity
metals
ceramics
polymers
with impurity
Impurities in metals
Metal alloys are used in most
engineering applications.
Metal alloy is a mixture of two or
more metals and nonmetals.
Solid solution is a simple type of
metal alloy in which elements are
dispersed in a single phase.
General concept…
Two outcomes if impurity (B) added to host (A):
1. Small amount of B added to A
interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurity
self-interstitial & vacancy (metals)
interstitial & substitutional (metal alloys)
Chain packing error
Substitutional solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(e.g., C in Fe)
2. Large amount of B added to A plus particles of a
new phase
Second phase particle
- different composition.
- often different structure.

6. Electro-negativity difference
Impurities in metals
The solubility of solids is greater if:
r (atomic radius difference) < 15%.
Proximity in periodic table
-- i.e, similar electronegativities.
Same crystal structure for pure metals.
Valency
-- all else being equal, a metal will
have a greater tendency to dissolve
another metal of higher valency than
one of lower valency.
Conditions for solid solubility
- apply W. Hume – Rothery rule.
have 4 conditions which is applied for
substitutional solid solution.
Specification of composition
determine the composition for a 2
element in alloy system.
specify in weight percent, wt
atom percent, at %.
weight percent, wt%
atom percent, at%
C2 = 100 – C1
C’2 = 100 – C’1
C1 = m1 x 100
m1+ m2
C’1 = nm1 x 100
nm1+ nm2
m1 & m2 = mass of component 1 & 2
C1 & C2 = composition (in wt%) of component 1 & 2
nm1 = m1/A1
nm2 = m2/A2
nm1 & nm2 = number of moles of component 1 & 2
A1 & A2 = at. weight of component 1 & 2
C’1 & C’2 = composition (in at%) of component 1 & 2
Defects in solids
Element Atomic Crystal Electro- Valence Radius (nm) Structure negativity
Cu FCC C H O Ag FCC Al FCC Co HCP Cr BCC Fe BCC Ni FCC Pd FCC Zn HCP
Would you predict more Al or Ag to dissolve in Zn?
2. More Zn or Al in Cu?
Example 1:
classification
zero dimension
point defects
metals
ceramics
polymers
Example 2:
System
Atomic radius
difference
Electro-negativity difference
Solid
solubility
Cu-Zn
3.9%
0.3
38.3%
Cu-Pb
36.7%
0.2
0.17%
Cu-Ni
2.3%
0.1
100%
interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurity
self-interstitial & vacancy (metals)
interstitial & substitutional (metal alloys)
Chain packing error
Lower solid solubility (interstitial S.S)
Higher solid solubility (subs. S.S)
Example 3:
A hypothetical alloy consist of 120 g element A & 80 g element B. Determine the composition (in wt%) for each element?

7. Defects in solids classification Linear defects in materials
SEM micrograph shows dislocation as a dark lines
also known as dislocations.
defects around which atoms are misaligned
in a lattice distortions are centered
around a line.
slip between crystal planes result when disl.
moves.
formed during permanent
deformation.
classification
Dislocations in Zinc (HCP)
one dimension
linear defects
slip steps
Type of dislocations…
SEM micrograph
1. Edge dislocation:
- extra half-plane of atoms inserted in a
crystal structure.
- b perpendicular to dislocation line.
All materials
initial
after tensile elongation
2. Screw dislocation:
spiral planar ramp resulting from shear
deformation.
- b parallel to dislocation line.
edge dislocation
screw dislocation
mixed dislocation
3. Mixed dislocation:
- most crystal have components of both
edge and screw dislocation.
Edge dislocation
Edge
Screw
Mixed
Screw Dislocation
Burgers vector b
Dislocation
line
(a) b
(b)
Mixed dislocation
Screw dislocation

8. Dislocations & Crystal Structures
• Structure: close-packed
planes & directions
are preferred.
view onto two
close-packed
planes.
close-packed directions
close-packed plane (bottom)
close-packed plane (top)
• Comparison among crystal structures:
FCC: many close-packed planes/directions;
HCP: only one plane, 3 directions;
BCC: none
• Specimens that
were tensile
tested.
Mg (HCP)
tensile direction
Higher solid solubility (subs. S.S)
Al (FCC) 8

9. planar/surface defects
Planar defects in materials
Defects in solids
Defects due to formation of grains structure.
classification
1. Grain boundaries
- region between grains (crystallites).
- formed due to simultaneously growing
crystals meeting each other.
- slightly disordered.
- restrict plastic flow and prevent dislocation
movement (control crystal slip).
- low density in grain boundaries
-- high mobility.
-- high diffusivity.
-- high chemical reactivity.
two dimension
planar/surface defects
All materials
Grain boundaries
in 1018 steel
2. Twin boundaries
- essentially a reflection of atom positions
across the twin plane.
- a region in which mirror image of structure
exists across a boundary.
- formed during plastic deformation and
recrystallization.
- strengthens the metal.
grain boundaries
twin boundaries
stacking faults
3. Stacking faults
- piling up faults during recrystallization due to
collapsing.
- for FCC metals an error in ABCABC packing
sequence, i.e: ABCABABC.
Twin
Twin plane

10. Catalysts and Surface Defects
Catalyst is a substance in solid form.
A catalyst increases the rate of a chemical reaction without being consumed.
Reactant molecules in a liquid phase (CO, NOx & O2) are absorbed onto catalyst surface.
Reduce the emission of exhaust gas pollutants.
Adsorption/active sites on catalysts are normally surface defects.
Fig. 5.15, Callister & Rethwisch 3e.
Single crystals of (Ce0.5Zr0.5)O2 used in an automotive catalytic converter
Fig. 5.16, Callister & Rethwisch 3e. 10

11. Defects in solids microscopic examination Microscopic examination
Process flow…
1. mount
2. grind
3. polish
4. clean
5. etch
6. observe
7. analyze
0.75mm
Defects in solids
such microscope used to observe & analyze
defects of materials.
i.e: OM, IM, SEM, TEM, STM, AFM etc.
microscopic examination
Grain boundaries observation
used metallographic techniques.
the metal sample must be first mounted for easy
handling.
- then the sample should be ground and polished
-- with different grades of abrasive paper and
abrasive solution.
-- removes surface features (e.g., scratches).
the surface is then etched chemically.
-- tiny groves are produced at grain boundaries.
-- groves do not intensely reflect light.
-- may be revealed as dark lines.
- hence observed by optical microscope.
Fe-Cr alloy
grain boundary
surface groove
polished surface
Optical Microscope (OM)
Inverted Microscope (IM)
Scanning Electron Microscope (SEM)
Transmission Electron Microscope (TEM)
Scanning Tunneling Microscope (STM)
Atomic Force Microscope (AFM)
metallographic techniques
Effect of etching…
Unetched
Steel
200 X
Etched
Brass
observe grain structure & boundaries
analyze grain size
examine topographical map (surface features)
SEM micrograph
STM topographic

12. Defects in solids microscopic examination Size of grains…
- affects the mechanical properties of the material.
the smaller the grain size, more are the grain
boundaries.
more grain boundaries means higher resistance to
slip (plastic deformation occurs due to slip).
more grains means more uniform the mechanical
properties are.
Defects in solids
How to measure grain size?
use the formula:
N = 2n -1
microscopic examination
n = ASTM grain size number.
N = number of grains per square inch
of a polished & etched specimen
at 100x magnification.
ASTM grain size number ‘n’ is a
measure of grain size.
Measuring average grain diameter
Average grain diameter, d more directly
represents grain size.
Random line of known length is drawn on
photomicrograph.
- Number of grains intersected is counted.
Ratio of number of grains intersected to length of
line, nL is determined.
d = C/nL(M) C = 1.5 & M = magnification
n < 3 – Coarse grained
4 < n < 6 – Medium grained
7 < n < 9 – Fine grained
n > 10 – ultrafine grained
Optical Microscope (OM)
Inverted Microscope (IM)
Scanning Electron Microscope (SEM)
Transmission Electron Microscope (TEM)
Scanning Tunneling Microscope (STM)
Atomic Force Microscope (AFM)
- If ASTM grain size #, n increase,
-- size of grains decrease.
-- # of grains/in2, N increase.
metallographic techniques
3 inches 5 grains
1045 cold rolled steel, n=8
observe grain structure & boundaries
analyze grain size
examine topographical map (surface features)
Example:
1018 cold rolled steel, n=10
Determine the ASTM grain size number of a metal specimen if 45 grains per square inch are measured at a magnification of 100x.
log N = (n-1) log 2
n = log N
+ 1
log 2
n = log 45
+ 1
log 2
n = 6.5

13. 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.) 13