Chapter 5 Defects in solids. Defects in solids Solidification process… classification zero...
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Transcript of Chapter 5 Defects in solids. Defects in solids Solidification process… classification zero...
Chapter 5Defects in solids
Defects in solids
Solidification process…
classification
zero
dim
en
sio
n
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.
on
e d
ime
nsi
on
two
dim
en
sio
n
thre
e d
ime
nsi
on
po
int
de
fect
s
Lin
ea
r/d
islo
catio
n d
efe
cts
are
a/p
lan
ar/
surf
ace
d
efe
cts
volu
me
de
fect
s (i.
e:
cra
ck)
- 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.
nucleiliquid
grain structure
All solid materials… - contain large # of defects.
Solidification process…
crystal growing
- 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
above Tm
room temp.
Mold
crystals growing
Casting process
Defects in solids
classification
zero dimension
point defects
me
tals
self-
inte
rstit
ial &
va
can
cy (
me
tals
)
cera
mic
s
inte
rstit
ial &
su
bst
itutio
na
l (m
eta
l allo
ys)
inte
rstit
ial,
vaca
ncy
, F
ren
kel &
Sch
ott
ky,
sub
stitu
tion
al a
nio
n &
ca
tion
imp
urit
y
po
lym
ers
Ch
ain
pa
ckin
g e
rro
r
Cation Interstitial
Cation Vacancy
Anion Vacancy
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.
Schottky defect
Frenkel defect
Point defects in metals
1. Self-Interstitials- "extra" atoms positioned between atomic sites.- cause structural distortion.
self-interstitial
distortion of planes
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.
Vacancy
distortion of planes
Point defects in polymers
10 nm
Adapted from Fig. 4.12, Callister & Rethwisch 3e.
- Defects due in part to chain packing errors and
impurities such as chain ends and side chains. i.e: thin platelets
Defects in solids
classification
zero dimension
point defects
me
tals
self-
inte
rstit
ial &
va
can
cy (
pu
re m
eta
ls)
cera
mic
s
inte
rstit
ial &
su
bst
itutio
na
l (m
eta
ls a
lloy)
po
lym
ers
Ch
ain
pa
ckin
g e
rro
r
inte
rstit
ial,
vaca
ncy
, F
ren
kel &
Sch
ott
ky,
sub
stitu
tion
al a
nio
n &
ca
tion
imp
urit
y
Equilibrium concentration: Point defects
k = Boltzmann's constant
(1.38 x 10-23 J/atom-K)(8.62 x 10-5 eV/atom-K)
Nv = # of defects (vacancies site)
Qv = activation energyT = temperature
- each lattice/atom site is potential vacancy site.
- equilibrium # of point defects (vacancies) for solids depends on & increase with temperature. - apply the formula:
çN v
N= exp
- Q v
k T
æ
è ç
ö
ø
N = total # of atomic sites
• We can get Qv from an experiment.• Measure this...
N v
N
T
exponential dependence!
Defect (@ vacancy) concentration
• Replot it...
1/ T
N
N vln
-Q v /k
slope
Measuring Activation Energy…
Example:
In 1 m3 of Cu at 1000-C, calculate:(a) vacancy concentration, Nv/N.(b) equilibrium # of vacancies, Nv.Given that,
ACu = 63.5 g/mol
r = 8.4 g/cm3
Qv = 0.9 eV/atom
NA = 6.02 x 1023atoms/mol
8.62 x 10-5 eV/atom-K
0.9 eV/atom
1273 K
ç ÷ NvN
= exp- QvkT
æ
è ç
ö
ø÷ = 2.7 x 10-4
Answer:
(a)
(b) - = N ACu
VCu NA
For 1 m3 , N =N
A
ACu
r x 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
Vacancy concentration
# of vacancy sites, Nv
total # of atomic sites, N=
Defects in solids
classification
zero dimension
point defects
me
tals
self-
inte
rstit
ial &
va
can
cy (
me
tals
)
cera
mic
s
inte
rstit
ial &
su
bst
itutio
na
l (m
eta
l allo
ys)
inte
rstit
ial,
vaca
ncy
, F
ren
kel &
Sch
ott
ky,
sub
stitu
tion
al a
nio
n &
ca
tion
imp
urit
y
po
lym
ers
Ch
ain
pa
ckin
g e
rro
r
Impurities in ceramics- Electroneutrality (charge balance) must be maintained when impurities are present.
i.e: NaCl Na+ Cl -
1. Substitutional cation impurity
without impurity Ca2+ impurity with impurity
Ca2+
Na+
Na+Ca2+
cation vacancy
2. Substitutional anion impurity
without impurity O2- impurity
O2-
Cl-
anion vacancy
Cl-
with impurity
Impurities in metals
Two outcomes if impurity (B) added to host (A):
1. Small amount of B added to A
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.
- 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…
Defects in solids
classification
zero dimension
point defects
me
tals
self-
inte
rstit
ial &
va
can
cy (
me
tals
)
cera
mic
s
inte
rstit
ial &
su
bst
itutio
na
l (m
eta
l allo
ys)
inte
rstit
ial,
vaca
ncy
, F
ren
kel &
Sch
ott
ky,
sub
stitu
tion
al a
nio
n &
ca
tion
imp
urit
y
po
lym
ers
Ch
ain
pa
ckin
g e
rro
r
SystemAtomic radius
difference
Electro-negativity difference
Solidsolubility
Cu-Zn 3.9% 0.3 38.3%
Cu-Pb 36.7% 0.2 0.17%
Cu-Ni 2.3% 0.1 100%
Example 2:
Element Atomic Crystal Electro-Valence Radius (nm) Structure negativity
Cu 0.1278 FCC 1.9 +2 C 0.071 H 0.046 O 0.060 Ag 0.1445 FCC 1.9 +1 Al 0.1431 FCC 1.5 +3 Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 Fe 0.1241 BCC 1.8 +2 Ni 0.1246 FCC 1.8 +2 Pd 0.1376 FCC 2.2 +2 Zn 0.1332 HCP 1.6 +2
1. Would you predict more Al or Ag to dissolve in Zn?
2. More Zn or Al in Cu?
Example 1:
Example 3:
A hypothetical alloy consist of 120 g element A & 80 g element B. Determine the composition (in wt%) for each element?
Impurities in metals
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.
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 & 2C1 & C2 = composition (in wt%) of component 1 & 2
nm1 = m1/A1 nm2 = m2/A2
nm1 & nm2 = number of moles of component 1 & 2A1 & A2 = at. weight of component 1 & 2C’1 & C’2 = composition (in at%) of component 1 & 2
Higher solid solubility (subs. S.S)
Lower solid solubility (interstitial S.S)
Defects in solids
classification
one dimension
linear defects
All materials
ed
ge
dis
loca
tion
Linear defects in materials- also known as dislocations.- defects around which atoms are
misaligned in a line @ lattice distortions are centered around a line. - slip between crystal planes result when
disl. moves.- formed during solidification @ permanent deformation.
scre
w d
islo
catio
n
mix
ed
dis
loca
tion
1. Edge dislocation: - extra half-plane of atoms inserted in a crystal structure. - b perpendicular to dislocation line.
2. Screw dislocation:- spiral planar ramp resulting from shear
deformation.- b parallel to dislocation line.
Screw Dislocation
Burgers vector b
Dislocationline
(a)
b(b)
Edge
Screw
Mixed
3. Mixed dislocation: - most crystal have components of both edge and screw dislocation.
SEM micrograph shows dislocation as a dark lines
Screw dislocation
Edge dislocation
Mixed dislocation
Type of dislocations… SEM micrograph
slip steps
after tensile elongation
initial
Dislocations in Zinc (HCP)
Dislocations & Crystal Structures• Structure: close-packed planes & directions are preferred.
view onto twoclose-packedplanes.
close-packed plane (bottom) close-packed plane (top)
close-packed directions
• 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)
Al (FCC)tensile direction
Higher solid solubility (subs. S.S)
Defects in solids
classification
two dimension
planar/surface defects
All materials
gra
in b
ou
nd
arie
s
Planar defects in materials- Defects due to formation of grains structure.
sta
ckin
g f
au
lts
twin
bo
un
da
ries
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.
Grain boundariesin 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.
Twin
Twin plane
3. Stacking faults - piling up faults during recrystallization due to collapsing. - for FCC metals an error in ABCABC packing sequence, i.e: ABCABABC.
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 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.
Fig. 5.15, Callister & Rethwisch 3e.
Fig. 5.16, Callister & Rethwisch 3e.
Single crystals of (Ce0.5Zr0.5)O2 used in an automotive catalytic converter
Defects in solids
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.
0.75mm
Fe-Cr alloy
grain boundary
surface groove
polished surface
Unetched Steel200 X
Etched Steel200 X
Unetched Brass200 X
Etched Brass200 X
Effect of etching…
Microscopic examination- such microscope used to observe &
analyze structures @ defects of materials. i.e: OM, IM, SEM, TEM, STM, AFM etc.
Opt
ical
Mic
rosc
ope
(OM
)
Sca
nnin
g E
lect
ron
Mic
rosc
ope
(SE
M)
Inve
rted
Mic
rosc
ope
(IM
)
Sca
nnin
g T
unne
ling
Mic
rosc
ope
(ST
M)
Ato
mic
For
ce M
icro
scop
e (A
FM
)
Tra
nsm
issi
on E
lect
ron
Mic
rosc
ope
(TE
M)
ob
serv
e g
rain
str
uct
ure
&
bo
un
da
ries
an
aly
ze g
rain
siz
e
Process flow…
1. mount
2. grind
3. polish
4. clean
5. etch
6. observe
7. analyze
exa
min
e t
op
og
rap
hic
al
ma
p (
surf
ace
fe
atu
res)
metallographic techniques
SEM micrograph
STM topographic
Measuring average grain diameter
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
microscopic examination
Opt
ical
Mic
rosc
ope
(OM
)
Sca
nnin
g E
lect
ron
Mic
rosc
ope
(SE
M)
Inve
rted
Mic
rosc
ope
(IM
)
Sca
nnin
g T
unne
ling
Mic
rosc
ope
(ST
M)
Ato
mic
For
ce M
icro
scop
e (A
FM
)
Tra
nsm
issi
on E
lect
ron
Mic
rosc
ope
(TE
M)
ob
serv
e g
rain
str
uct
ure
&
bo
un
da
ries
an
aly
ze g
rain
siz
e
exa
min
e t
op
og
rap
hic
al
ma
p (
surf
ace
fe
atu
res)
metallographic techniques
n < 3 – Coarse grained4 < n < 6 – Medium grained7 < n < 9 – Fine grainedn > 10 – ultrafine grained
N = number of grains per square inch of a polished & etched specimen at 100x magnification.
n = ASTM grain size number.
1018 cold rolled steel, n=10
1045 cold rolled steel, n=8
How to measure grain size?
- ASTM grain size number ‘n’ is a
measure of grain size.
- use the formula:
N = 2n -1
- If ASTM grain size #, n increase,
-- size of grains decrease.
-- # of grains/in2, N increase.
- 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
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.
log N = (n-1) log 2n = log N
log 2+ 1
n = log 45 log 2
+ 1
n = 6.5
• 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.)
Summary