CHAPTER 5:
IMPERFECTIONS IN SOLIDS
ISSUES TO ADDRESS
ADDRESS...
• What are the solidification mechanisms?
• What types
yp of defects arise in solids?
• Can the number and type of defects be varied
and controlled?
• How do defects affect material properties?
• Are defects undesirable?
Imperfections in Solids
• Solidification- result of casting of molten material
– 2 steps
p
• 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. 5.19 (b), Callister & Rethwisch 3e.
• Crystals grow until they meet each other
2
Polycrystalline Materials
Grain Boundaries
• regions between crystals
• transition from lattice of
one region
i tto th
thatt off the
th
other
• slightly disordered
• low density in grain
boundaries
– high mobility
– high diffusivity
– high chemical reactivity
Adapted from Fig
Fig. 5
5.12,
12
Callister & Rethwisch 3e.
3
Solidification
Grains can be - equiaxed (roughly same size in all directions)
- columnar (elongated grains)
~ 8 cm
heat
flow
Columnar in
area with less
undercooling
Adapted from Fig. 5.17,
Callister & Rethwisch 3e.
Shell of
equiaxed grains
due to rapid
cooling (greater
ΔT) near wallll
Grain Refiner - added to make smaller
smaller, more uniform
uniform, equiaxed grains
grains.
4
Imperfections in Solids
There is no such thing as a perfect crystal.
• What are these imperfections?
y are they
y important?
p
• Why
Many of the important properties of
materials are due to the presence of
imperfections.
5
Types of Imperfections
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
Point defects
• Dislocations
Line defects
• Grain Boundaries
Area defects
6
Point Defects in Metals
• Vacancies:
-vacant
vacant atomic sites in a structure
structure.
Vacancy
distortion
of planes
• Self-Interstitials:
-"extra" atoms positioned between atomic sites.
selflf
interstitial
distortion
of planes
7
Equilibrium Concentration:
Point Defects
• Equilibrium concentration varies with temperature!
No. of defects
No. of potential
defect sites
Activation energy
⎛ Q
Nv
= exp ⎜⎜ − v
⎝ kT
N
⎞
÷
÷
⎠
Temperature
Boltzmann's constant
-23
23
(1.38 x 10 J/atom-K)
-5
(8.62 x 10 eV/atom-K)
Each lattice site
is a potential
vacancy site
8
Measuring Activation Energy
• We can get Qv from
an experiment.
⎛ −Q
Nv
v
= exp ⎜⎜
⎝ kT
N
• Measure this...
• Replot it...
Nv
ln
N
Nv
N
⎞
÷
÷
⎠
slope
-Qv /k
exponential
dependence!
T
1/T
defect concentration
9
Estimating Vacancy Concentration
• Find the equil. # of vacancies in 1 m3 of Cu at 1000°C.
• Given:
ρ = 8.4 g /cm 3
A Cu = 63.5 g/mol
Qv = 0.9 eV/atom NA = 6.02 x 1023 atoms/mol
0 9 eV/atom
0.9
⎛
⎞
−Q v ÷
Nv =
⎜
-4
÷
exp
p⎜
⎝ kT ⎠ = 2.7 x 10
N
For 1
m3 ,
N= ρ x
NA
A Cu
1273 K
8 62 x 10-5 eV/atom
8.62
eV/atom-K
K
x 1 m3 = 8.0 x 1028 sites
• Answer:
Nv = (2.7
(2 7 x 10-44)(8.0
)(8 0 x 1028) sites
it = 2.2
2 2 x 1025 vacancies
i
10
Observing Equilibrium Vacancy Conc
Conc.
• Low energy electron
microscope
i
view
i
off
a (110) surface of NiAl.
• Increasing temperature
causes surface island of
g
atoms to grow.
• Why? The equil. vacancy
conc. increases via atom
motion from the crystal
to the surface, where
they join the island.
island
Island grows/shrinks to maintain
q
vancancy
y conc. in the bulk.
equil.
Reprinted with permission from Nature (K.F. McCarty,
J A Nobel,
J.A.
Nobel and N.C.
N C Bartelt,
Bartelt "Vacancies
Vacancies in
Solids and the Stability of Surface Morphology",
Nature, Vol. 412, pp. 622-625 (2001). Image is
5.75 μm by 5.75 μm.) Copyright (2001) Macmillan
Publishers Ltd
Publishers,
Ltd.
11
Point Defects in Ceramics (i)
• Vacancies
-- vacancies
acancies e
exist
ist in ceramics for both cations and anions
• Interstitials
-- interstitials exist for cations
-- interstitials are not normally observed for anions because anions
are large relative to the interstitial sites
Cation
Interstitial
Cation
Vacancy
Anion
Vacancy
Adapted from Fig. 5.2, Callister &
R th i h 3
Rethwisch
3e. (Fig.
(Fi 5
5.2
2 iis ffrom
W.G. Moffatt, G.W. Pearsall, and
J. Wulff, The Structure and
Properties of Materials, Vol. 1,
Structure John Wiley and Sons
Structure,
Sons,
Inc., p. 78.)
12
Point Defects in Ceramics (ii)
• Frenkel Defect
-- a cation vacancy-cation interstitial pair.
• Shottky Defect
-- a paired set of cation and anion vacancies.
Shottky
Defect:
Adapted from Fig. 5.3, Callister &
Rethwisch 3e. (Fig. 5.3 is from
W.G. Moffatt, G.W. Pearsall, and
J Wulff,
J.
W lff The
Th Structure
St t
and
d
Properties of Materials, Vol. 1,
Structure, John Wiley and Sons,
Inc., p. 78.)
Frenkel
Defect
• Equilibrium concentration of defects
∝ e −QD /kT
13
Imperfections in Metals (i)
Two outcomes if impurity (B) added to host (A):
• Solid
S lid solution
l ti off B in
i A (i.e.,
(i
random
d
di
dist.
t off point
i td
defects)
f t )
OR
Substitutional solid soln.
(
(e.g.,
C in
Cu
i Ni)
Interstitial solid soln.
(
(e.g.,
C in
i Fe)
F )
• Solid solution of B in A plus particles of a new
phase
h
((usually
ll ffor a llarger amountt off B)
Second phase particle
-- different composition
-- often different structure.
14
Imperfections in Metals (ii)
Conditions
C
diti
ffor substitutional
b tit ti
l solid
lid solution
l ti (S
(S.S.)
S)
• W. Hume – Rothery
y rule
– 1. Δr (atomic radius) < 15%
– 2.
2 Proximity in periodic table
• i.e., similar electronegativities
–3
3. Same crystal structure for pure metals
– 4. Valency
• All else being equal, a metal will have a greater tendency
to dissolve a metal of higher valency than one of lower
valency
15
Imperfections in Metals (iii)
Application of Hume–Rothery
Hume Rothery rules – Solid
Solutions
Element
Atomic Crystal
ElectroRadius Structure
S
(nm)
1. Would
ou d you p
predict
ed ct
more Al or Ag
to dissolve in Zn?
2. More Zn or Al
in Cu?
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
Valence
negativity
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
Table on p. 159, Callister & Rethwisch 3e.
16
Imperfections in Ceramics
• Electroneutrality (charge balance) must be maintained
when
h iimpurities
iti are presentt
Cl • Ex: NaCl Na +
• Substitutional cation impurity
cation
vacancy
Ca 2+
Na +
Na +
without impurity
Ca 2+ impurity
• Substitutional anion impurity
Ca 2+
with impurity
anion vacancy
O2-
without impurity
Cl Cl O2- impurity
with impurity
17
Point Defects in Polymers
•
Defects due in part to chain packing errors and impurities such
as chain
h i ends
d and
d side
id chains
h i
Adapted
p
from Fig.
g 5.7,,
Callister & Rethwisch 3e.
Adapted from Fig. 5.7,
Callister & Rethwisch 3e.
18
Impurities in Solids
• Specification
S
ifi ti off composition
iti
– weight percent
C1 =
m1
x 100
m1 + m2
m1 = mass of component 1
– atom percent
C1' =
n m1
x 100
n m1 + n m 2
nm1 = number of moles of component 1
19