Transcript Chapter 4

CHAPTER 4:
IMPERFECTIONS IN SOLIDS
ISSUES TO ADDRESS...
• What types 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?
Chapter 4- 1
TYPES OF IMPERFECTIONS
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
Point defects
• Dislocations
Line defects
• Grain Boundaries
Area defects
Chapter 4- 2
• Vacancies:
POINT DEFECTS
-vacant atomic sites in a structure.
distortion
of planes
Vacancy
• Self-Interstitials:
-"extra" atoms positioned between atomic sites.
distortion
of planes
selfinterstitial
Chapter 4- 3
EQUIL. CONCENTRATION:
POINT DEFECTS
• Equilibrium concentration varies with temperature!
No. of defects
Activation energy
Q 
ND 
exp
 D 

 kT 
N
No. of potential
Temperature
defect sites.
Boltzmann's constant
(1.38 x 10-23 J/atom K)
(8.62 x 10 -5 eV/atom K)
Each lattice site
is a potential
vacancy site
Chapter 4- 4
MEASURING ACTIVATION ENERGY
• We can get Q from
an experiment.
• Measure this...
• Replot it...
ND
ln
N
1
slope
-QD/k
1/T
Chapter 4- 5
ESTIMATING VACANCY CONC.
• Find the equil. # of vacancies in 1m3 of Cu at 1000C.
• Given:
0.9eV/atom
Q 
ND
 exp
 D 
= 2.7 · 10-4
 kT 
N
For 1m3, N =
• Answer:
Note that  in g/m3:
= atom mass×N/1m3
(in g/atom)
atom mass = A(atomic #)/NA
1273K
8.62 x 10-5 eV/atom-K
NA
x 1m3 = 8.0 x 1028 sites
 x
ACu
Chapter 4- 6
OBSERVING EQUIL. VACANCY CONC.
• Low energy electron
microscope view of
a (110) surface of NiAl.
• Increasing T causes
surface island of
atoms to grow.
• Why? The equil. vacancy
conc. increases via atom
motion from the crystal
to the surface, where
they join the island.
Reprinted with permission from Nature (K.F.
McCarty, J.A. Nobel, and N.C. Bartelt, "Vacancies in
Solids and the Stability of Surface Morphology",
Nature, Vol. 412, pp. 622-625 (2001). Image is
5.75 mm by 5.75 mm.) Copyright (2001) Macmillan
Publishers, Ltd.
Chapter 4- 7
POINT DEFECTS IN ALLOYS
Two outcomes if impurity (B) added to host (A):
• Solid solution of B in A (i.e., random dist. of point defects)
OR
Substitutional alloy
(e.g., Cu in Ni)
Interstitial alloy
(e.g., C in Fe)
• Solid solution of B in A plus particles of a new
phase (usually for a larger amount of B)
Second phase particle
--different composition
--often different structure.
Chapter 4- 8
COMPOSITION
Definition: Amount of impurity (B) and host (A)
in the system.
Two descriptions:
• Weight %
• Atom %
• Conversion between wt % and at% in an A-B alloy:
CB =
C'BAB
C'AAA + C'BAB
x 100
• Basis for conversion:
Chapter 4- 10
COMPOSITION EXAMPLE
Calculate the composition, in atom percent, of an alloy
that contains 97 wt% aluminum and 3 wt% copper.
C Al  97, CCu  3
C Al ACu
C Al 
 100
C Al ACu  CCu AAl
(97)(63.55g / m ol)
 100
(97)(63.55g / m ol)  (3)(26.98g / m ol)
 98.7 at%
CCu AAl
 
CCu
100
C Al ACu  CCu AAl

(3)(26.98g / m ol)
 100
(97)(63.55g / m ol)  (3)(26.98g / m ol)
 1.3 at%

Chapter 4- 10