Transcript greater valency area

Chapter 5
Defects in solids
Defects in
solids
one dimension
two dimension
three dimension
Linear/dislocation defects
area/planar/surface defects
volume defects (i.e: crack)
point defects
zero dimension
classification
All solid materials…
Solidification process…
- contain large # of defects.
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.
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.
- Grains structure can be:
1. equiaxed grains (roughly same size in all directions).
2. columnar grains (elongated grains).
Columnar grains
in area with less
undercooling
Equiaxed grains
due to rapid cooling
(greater T) near wall
crystals
growing
room temp.
Mold
Casting
process
crystal growing
grain structure
Point defects in ceramics
1. Vacancies
- vacancies exist in ceramics for both
cations and anions.
Defects in
solids
2. Interstitials
- exist for cations only.
- interstitials are not normally observed for
anions because anions are large relative
to the interstitial sites.
classification
zero dimension
Cation
Vacancy
Anion
Vacancy
Schottky
defect
polymers
3. Frenkel defect
- a cation vacancy-cation interstitial pair.
Frenkel
defect
4. Schottky defect
- a paired set of cation and anion vacancies.
Point defects in metals
1. Self-Interstitials
- "extra" atoms positioned between atomic
sites.
- cause structural distortion.
distortion
of planes
Chain packing error
ceramics
interstitial, vacancy, Frenkel & Schottky,
substitutional anion & cation impurity
interstitial & substitutional (metal alloys)
metals
point defects
self-interstitial & vacancy (metals)
Cation
Interstitial
distortion
of planes
self-interstitial
Vacancy
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.
2. Vacancies
- 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.
Equilibrium concentration: Point defects
Defects in
solids
- equilibrium # of point defects (vacancies) for
solids depends on & increase with temperature.
- apply the formula:
# of vacancy sites, Nv
Vacancy
classification
concentration
N
total # of atomic sites, N
exponential
dependence!
polymers
Nv = # of defects (vacancies site)
N = total # of atomic sites
T = temperature
Qv = activation energy
k = Boltzmann's constant
(1.38 x 10-23 J/atom-K)
(8.62 x 10-5 eV/atom-K)
ln
T
Defect (@ vacancy) concentration
• Replot it...
slope
Nv
N
- Q v /k
- each lattice/atom site is potential vacancy site.
1/ T
Example:
Chain packing error
ceramics
interstitial, vacancy, Frenkel & Schottky,
substitutional anion & cation impurity
metals
point defects
interstitial & substitutional (metals alloy)
Nv
 

N
Q
v = exp 
v

 k T 
N
zero dimension
self-interstitial & vacancy (pure metals)
=
Measuring Activation Energy…
• We can get Qv from an experiment.
• Measure this...
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
Qv = 0.9 eV/atom
ACu = 63.5 g/mol
NA = 6.02 x 1023atoms/mol
Answer:
 Q
(a) N
v = exp 
v


N
kT
(b) r = N ACu
0.9 eV/atom

÷
÷ = 2.7 x 10-4

1273 K
8.62 x 10-5 eV/atom-K
VCu NA
For 1 m3 , N = r x
NA
A Cu
x 1 m3 = 8.0 x 1028 atom sites
Nv = (2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 vacancies
Impurities in ceramics
- Electroneutrality (charge balance) must be
maintained when impurities are present.
Defects in
solids
i.e: NaCl Na +
classification
without impurity
+
Na
polymers
Na+
without impurity
Ca2+ impurity
ClClO2- impurity
anion vacancy
Ca2+
with impurity
with impurity
Impurities in metals
Two outcomes if impurity (B) added to host (A):
General concept…
1. Small amount of B added to A
- Metal alloys are used in most
engineering applications.
- Metal alloy is a mixture of two or
more metals and nonmetals.
Chain packing error
ceramics
interstitial, vacancy, Frenkel & Schottky,
substitutional anion & cation impurity
metals
cation
vacancy
Ca2+
point defects
interstitial & substitutional (metal alloys)
O2-
Cl -
1. Substitutional cation impurity
zero dimension
self-interstitial & vacancy (metals)
2. Substitutional anion impurity
Substitutional solid soln. Interstitial solid soln.
(e.g., Cu in Ni)
(e.g., C in Fe)
- Solid solution is a simple type of
metal alloy in which elements are
dispersed in a single phase.
2. Large amount of B added to A plus particles of a
new phase
Second phase particle
- different composition.
- often different structure.
Impurities in metals
Defects in
solids
Conditions for solid solubility
- apply W. Hume – Rothery rule.
-have 4 conditions which is applied for
substitutional solid solution.
classification
zero dimension
polymers
Specification of composition
- determine the composition for a 2
element in alloy system.
- specify in weight percent, wt % @
atom percent, at %.
weight percent, wt%
Chain packing error
ceramics
interstitial, vacancy, Frenkel & Schottky,
substitutional anion & cation impurity
interstitial & substitutional (metal alloys)
self-interstitial & vacancy (metals)
metals
point defects
The solubility of solids is greater if:
1. r (atomic radius difference) < 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
another metal of higher valency than
one of lower valency.
C1 = m1 x 100
m1+ m2
C2 = 100 – C1
m1 & m2 = mass of component 1 & 2
C1 & C2 = composition (in wt%) of component 1 & 2
Example 1:
1. Would you predict more Al or Ag to dissolve in
Zn?
2. More Zn or Al in Cu?
Element Atomic
Crystal
Radius (nm) Structure
Cu
C
H
O
Ag
Al
Co
Cr
Fe
Ni
Pd
Zn
0.1278
0.071
0.046
0.060
0.1445
0.1431
0.1253
0.1249
0.1241
0.1246
0.1376
0.1332
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
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
Example 2:
Atomic
radius
difference
System
Electronegativity
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%
Lower solid solubility (interstitial S.S)
Higher solid solubility (subs. S.S)
atom percent, at%
C’1 = nm1 x 100 C’ = 100 – C’
2
1
nm1+ nm2
nm1 = m1/A1 nm2 = m2/A2
Electronegativity
Example 3:
A hypothetical alloy consist of 120 g element A
& 80 g element B. Determine the composition
(in wt%) for each element?
Defects in
solids
classification
one dimension
linear defects
mixed dislocation
screw dislocation
edge dislocation
All materials
Linear defects in materials
SEM micrograph
shows dislocation
- also known as dislocations.
as a dark lines
- defects around which atoms are misaligned
in a line @ lattice distortions are centered
Dislocations in Zinc
around a line.
(HCP)
- slip between crystal planes result when disl.
moves.
- formed during solidification @ permanent
slip steps
deformation.
Type of dislocations…
1. Edge dislocation:
- extra half-plane of atoms inserted in a
initial
crystal structure.
after tensile
- b perpendicular to dislocation line.
elongation
2. Screw dislocation:
- spiral planar ramp resulting from shear
deformation.
- b parallel to dislocation line.
3. Mixed dislocation:
- most crystal have components of both
edge and screw dislocation.
Mixed
Edge dislocation
Screw Dislocation
Dislocation
line Burgers
Edge
vector b
Screw
SEM micrograph
Mixed dislocation
b
(b)
(a)
Screw dislocation
Dislocations & Crystal Structures
• Structure: close-packed
planes & directions
are preferred.
view onto two
close-packed
planes.
close-packed plane (bottom)
close-packed directions
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)
Defects in
solids
classification
two dimension
planar/surface
defects
stacking faults
twin boundaries
grain boundaries
All materials
Planar defects in materials
- Defects due to formation of grains structure.
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.
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.
3. Stacking faults
- piling up faults during recrystallization due to
collapsing.
- for FCC metals an error in ABCABC packing
sequence, i.e: ABCABABC.
Grain boundaries
in 1018 steel
Twin plane
Twin
Catalysts and Surface Defects
• Catalyst is a substance in
solid form.
• A catalyst increases the rate
of a chemical reaction without
being consumed.
Fig. 5.15, Callister & Rethwisch 3e.
– Reactant molecules in a gas @
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.
Single crystals of (Ce0.5Zr0.5)O2
used in an automotive catalytic
converter
Fig. 5.16, Callister & Rethwisch 3e.
Microscopic examination
Defects in
solids
- such microscope used to observe & analyze
structures @ defects of materials.
i.e: OM, IM, SEM, TEM, STM, AFM etc.
Atomic Force Microscope (AFM)
Scanning Tunneling Microscope (STM)
Transmission Electron Microscope (TEM)
Scanning Electron Microscope (SEM)
Inverted Microscope (IM)
Optical Microscope (OM)
microscopic
examination
Process flow…
1. mount
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.
2. grind
3. polish
4. clean
5. etch
6. observe
7. analyze
0.75mm
polished surface
surface groove
grain boundary
Effect of etching…
examine topographical
map (surface features)
analyze grain size
observe grain structure
& boundaries
metallographic
techniques
SEM
micrograph
Fe-Cr alloy
Unetched
Steel
200 X
Etched
Steel
200 X
Unetched
Brass
200 X
Etched
Brass
200 X
STM
topographic
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
Atomic Force Microscope (AFM)
Scanning Tunneling Microscope (STM)
Transmission Electron Microscope (TEM)
Scanning Electron Microscope (SEM)
Inverted Microscope (IM)
Optical Microscope (OM)
microscopic
examination
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
How to measure grain size?
- use the formula:
N = 2n -1
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.
n < 3 – Coarse grained
4 < n < 6 – Medium grained
7 < n < 9 – Fine grained
n > 10 – ultrafine grained
- If ASTM grain size #, n increase,
-- size of grains decrease.
-- # of grains/in2, N increase.
1045 cold rolled steel, n=8
examine topographical
map (surface features)
analyze grain size
observe grain structure
& boundaries
metallographic
techniques
3 inches 5 grains
Example:
Determine the ASTM grain
size number of a metal
specimen if 45 grains per
square inch are measured
at a magnification of 100x.
1018 cold rolled steel, n=10
log N = (n-1) log 2
n = log N
+1
log 2
n = log 45
+1
log 2
n = 6.5
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.)