Transcript lecture 13 powerpoint

Defects in Solids
• 0-D or point defects
– vacancies, interstitials, etc.
– control mass diffusion
concentrations 
• 1-D or linear defects
– dislocations
– control deformation processes
• 2-D or planar defects
– grain boundaries, surfaces, interfaces
• 3-D or volume defects
– voids, secondary components (phases)
Diffusional Processes
diffusion
coefficient
Pd
flux
H2
J  D
concentration gradient
c
x
c
0
x
J 0
response  driving force
cH
+ CO
+ CO2
H
Fick’s first law (similar to Ohm’s law)
phenomenological
Applies under steady state conditions
c(x)  f(t)
x
hydrogen separation membrane
Diffusional Processes
Steady-state: c(x)  f(t)
A
B
J  D
Non steady-state: c(x) = f(t)
Continuity requirements
t=0
CA
CB
  c 
c
J
 D 

x  x 
t
x
Fick’s second law
t>0
CA
CB
c   c 
 D 
t x  x 
if D  f(x)
c
 2c
D 2
t
x
c
x
Defects in Solids
• 0-D or point defects
– vacancies, interstitials, etc.
– control mass diffusion
concentrations 
• 1-D or linear defects
– dislocations
– control deformation processes
• 2-D or planar defects
– grain boundaries, surfaces, interfaces
• 3-D or volume defects
– voids, secondary components (phases)
Linear (line) defects
Dislocations intimately tied to mechanical properties
s = F/A stress
small stress
 elastic deformation
recoverable
large stress
 plastic deformation
permanent
??
huge energy penalty, yet
happens easily in metals
answer: slip, dislocation glide
Dislocation Motion = Deformation
dislocation
slip plane
Dislocations
Edge
b  dislocation line
Burger’s vector
vector between finish and start
Dislocations
Screw
b || dislocation line
Dislocations: Mixed
Burger’s vector is constant
Dislocation Loops
Dislocation Loops
Dislocation Loops
Dislocation Loops
in projection
“missing” half-plane
(top part of crystal)
“extra” half-plane
(top part of crystal)
“jog” in crystal planes
Dislocation Loops
Dislocation Loops
Dislocation lines cannot simply terminate. They either
form complete loops or terminate at crystal edge