1200°C (5min) 680°C (5
sec)water quench
Fe- 0.84 wt% Ni-0.1wt% C
1
Diffusion
• Are solids inert?
That is, is it the case that once a solid forms its structure
is fixed forever?
ABSOLUTELY NOT
• One mechanism for altering a solid’s internal
structure is diffusion.
• movement of atoms within a solid (crystalline or amorphous)
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What Is Diffusion?
• Mass transport by atomic motion
• Can occur in all states of matter (solid, liquid,
gas)
• The process of one element’s atoms diffusing
within another is termed impurity diffusion
• Atoms transport from high to low
concentration regions
• Self-diffusion: diffusion of pure metals; all
atoms exchanging positions are of the same
type
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Copper-Nickel Diffusion Couple
Diffusion couple:
Formed by
joining bars of
two different
metals together,
creating contact
between the
two. The couple
is then heated
for extended
periods of time
at high
temperatures.
A Copper-Nickel
Diffusion couple before a
high-temperature heat
treatment
A Copper-Nickel Diffusion
couple after a hightemperature heat treatment
4
Diffusion Alters Microstructure
• CuAl2 precipitates in Al matrix.
– Heated at 320oC for 15 minutes.
5
Vacancy Diffusion
•
•
Remember, all crystals have vacancies.
(Xv  10-4 at T = TM)
Atoms easily hop into adjacent vacant lattice
positions
•
We can equally think of the vacancy jumping or
of an atom jumping.
•
Atomic motion occurs in the opposite direction
compared to that of vacancy motion.
•
An atomic jump is successful only if there is a
vacancy next to the atom and the atom jumps
into this vacancy.
•
Both Self-diffusion and substitutional impurity
diffusion occur by this mechanism
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Diffusion Mechanisms
• For an atom to
diffuse or migrate
from one lattice site
to another, two
conditions must be
met:
1. There must be an
empty adjacent
site (vacancy)
2. The atom must
have sufficient
energy
Vacancy diffusion
Interstitial diffusion
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Interstitial Diffusion
•
•
•
Interstitial atoms are small
Atoms migrate from an interstitial position to a
neighboring one that is empty
Occurs more rapidly than vacancy diffusion
because interstitial atoms are small and more
mobile plus most neighboring interstitial sites
are vacant
(Click to Play)
Courtesy P. M. Anderson
8
Atom Motion in Crystals
• An atom’s energy is
lowest when it’s in a
lattice position.
• Atoms squeeze
through gaps.
– Activation barriers
• This is a thermally
activated process.
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Concept Test
In a certain crystal lattice, there are no
vacancies in it. Would any diffusion be able to
occur? (Assuming the atom has sufficient
energy)
a) Yes, because there is still empty space
between the atoms
b) No, because there are no vacancies
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Diffusion Simulation
• Illustrates diffusion
across an interface.
• The rate of diffusion
depends on:
(Click to Play)
– Concentration of
vacancies
– Rate of jumping
Courtesy P. M. Anderson
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Demo: Structure & Diffusion
Pucks (diffusing “atoms”) hop through prongs (“vacancies”) randomly,
analogous to diffusion in solids
Diffusion FASTER for...
Diffusion SLOWER for...
• open crystal structures
• close-packed structures
• lower melting T materials
• higher melting T materials
• materials with secondary bonding
• materials with covalent bonding
• smaller diffusing atoms
• larger diffusing atoms
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Steady-State Diffusion
• Diffusion of gas
through a metal plate
Concentrations are
held constant on both
surfaces
• Linear relationship
between concentration
and thickness
# of atoms
M
J
At
Cross sectional
area
13
Fick’s Law of Diffusion
•
Describes diffusion down a concentration
gradient
(the gradient provides the driving force)
•
The flux is due to random jumps
– The only reason we see a net flux is because
there is a difference in concentration.
Direction of
diffusion is down
the concentration
gradient
Diffusion
coefficient
dC
J  D
dx
Units of D:
m2/s
14
Diffusion of Carbon in Steel
• classic experiment by Smith (1953)
• controlled the concentration of carbon on
the inside and outside of a cylinder
C
J  D
r
• measured the amount of carbon passing
through the cylinder wall ( q )
• We can then back calculate the flux (J):
q = Jr=b · 2πbl
• In the final step we substitute J into Fick’s
law and we solve for D.
• This is a steady-state diffusion problem.
– Once established, concentrations do
not change with time
15
Effect of Temperature on
Diffusion
 Q 
D  D0 exp  d 
 RT 
Qd = the activation energy
for diffusion
• plot log D vs 1/T
– slope is –Q/(2.3R)
• High values of Q
mean the system
is temperature
sensitive
Reading Log Plots
• Some students have difficulty reading and
interpolating log plots
• Consider this section of a log scale ranging
from 10-12 to 10-10
– To read the value at the dashed blue line
find x and y up from the 10-11 marker. The
value at this point is
10x / y 1011  100.4 1011  2.5 1011
y
x
If x = 0, the value would be 1.0 x 10-11
If x = y, the value would be 10 x 10-11 = 10-10
– On the other hand, in order to locate a
point, say 6x10-12, first calculate log 6 =
0.78
b
a
– This point is located at a point given by a/b
= 0.78 above the 10-12 marker, as shown by
the red dotted line
17
Effect of Crystal Structure on
Diffusion
• Most elements diffuse faster in -Fe than
in -Fe.
Offer an explanation based on what you know
about the different crystal structures.
Answer:


18
-Fe has a more open structure than -Fe.
(-Fe is close packed.)
The activation barrier for diffusion is lower.
Processing Using Diffusion - I
Case Hardening:
•
•
Diffuse carbon atoms into
the host iron atoms at the
surface of a part
Case hardened gears are an
example of interstitial case
hardening
Result:
•
•
19
The ”case" is hard to deform:
C atoms "lock" the atomic
planes from shearing
The “case” is hard to crack:
C atoms put the surface in
compression
8
Processing Using Diffusion - 2
Doping Silicon with Al to make p-type semiconductors
Process:
1. Deposit Al rich
layers on surface.
silicon
2. Heat it.
3. Result: Doped
semiconductor
regions.
.
silicon
20
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