Diffusion report

Powerpoint Templates
Page 1
Diffusion
Material Science Presentation
by Group 5

Page 2
Topics Covered
 What is Diffusion?
•Interdiffusion
•Self-diffusion
 Diffusion Mechanisms
 Vacancy Diffusion
 Interstitial Diffusion
 Mathematics of Diffusion (Fick’s Laws)
• Steady-State Diffusion
• Non Steady-State Diffusion
 Factors affecting Diffusion
• Diffusing Species
• Host Solid
• Temperature
• Microstructure

Page 3
What is Diffusion?
o It is the motion of atoms, ions, or vacancies
through a material.
o Inhomogeneous materials can become
homogeneous by diffusion.

Interdiffusion and Self-diffusion
Interdiffusion (Impurity Diffusion) occurs
in response to a concentration gradient.
Concentration Gradient - concentration
that exists between a two different
materials.
Page 4

Interdiffusion and Self-diffusion
Self-diffusion is the diffusion of an atom to a
new site in a crystal when all atoms are
of the same type.
Page 5

Page 6
Diffusion Mechanisms
1) Vacancy Diffusion
 An atom from its normal lattice
position changes position with an
adjacent vacancy lattice site, so the
atoms and vacancies travel in opposite
directions.

Page 7
1) Vacancy Diffusion

Page 8
2) Interstitial Diffusion
 Atoms move from one interstitial site to
another vacant interstitial site.
 Interstitial diffusion is generally faster
than vacancy diffusion because bonding
of interstitials to the surrounding atoms
is normally weaker and there are many
more interstitial sites than vacancy sites
to jump to.
 Requires small impurity atoms (e.g. C,
H, O) to fit into interstices in host.

Page 9
2) Interstitial Diffusion

Page 10
Other mechanisms which are quite rare but nonetheless
important in semiconductors are:
1)Indirect interstitial mechanism for self-interstitials
> The simulation shows the elementary
step: A self-interstitial (shown in light
blue for easier identification) pushes a
lattice atom into the interstitial lattice.
The net effect is the migration of an self-interstitial
from one interstitial site to an
different one.
2)The "kick-out" mechanism for impurity atoms
> Interstitial impurity atoms move rather
fast by a direct interstitial mechanism,
until they eventually displace a lattice
atom. This is shown in the simulation. We
now have a self-interstitial (that may or
may not be very mobile) and a rather
immobile substitutional impurity atom,
which may now diffuse with one of the
other (slow) mechanisms.

3) Frank-Turnbull mechanisms (or dissociative mechanism).
5) “Extended interstitial" mechanism
Page 11
> This is the pendant to the kick-out mechanism.
Except that the diffusing impurity atom does not
dislodge a lattice atom, but gets trapped in a
vacancy, whereupon it is almost immobile. The
total effect may be quite similar to the kick-out
mechanism.
4) Various direct diffusion mechanisms
> Shown is a direct exchange of places between
two atoms. Variants are exchanges involving
more that 2 atoms (a whole "ring" that
"rotates").
Direct mechanisms are every now and then
suggested in the literature to account for some
new diffusion phenomena, but so far do not seem
to occur in crystals.
> This is a possibility not yet discussed or
observed. It is mentioned just to show that
there might be more atomic mechanisms
than have been discovered so far.

dC
Fick’s First Law of
Diffusion
dC
Page 12
Mathematics of Diffusion
Steady-State Diffusion - Rate of diffusion
independent of time. Flux proportional to
concentration gradient =
dx
dx
J  D
Where:
D = diffusion
coefficient

C C
C
dC


if linear 2 1
Page 13
Steady-State Diffusion
C1
C2
x
C1
C2
x1 x2
x x
2 1
x
dx





C1 = 0.44 g/cm3
Page 14
Example: Chemical Protective Clothing (CPC)
Methylene chloride is a common ingredient of paint
removers. Besides being an irritant, it also may be
absorbed through skin. When using this paint remover,
protective gloves should be worn.
If butyl rubber gloves (0.04 cm thick) are used, what is
the diffusive flux of methylene chloride through the
glove?
Data: diffusion coefficient in butyl rubber:
D = 110 x10-8 cm2/s
surface concentrations:
C2 = 0.02 g/cm3

2
C C
D
dC

- 2 1
C1 = 0.44 g/cm3
Data:
(0.02 g/cm 
0.44 g/cm )
C1
skin paint
remover
(110 x 10 cm /s) 2
x x
g
Page 15
Example: Chemical Protective Clothing (CPC)
Solution – Assuming linear conc. Gradient
D
tb
6

2 1
dx
J D

  
cm s
1.16 x 10
(0.04 cm)
-5
3 3
-8 2 
J  
C2
x1 x2
D = 110x10-8 cm2/s
C2 = 0.02 g/cm3
x2 – x1 = 0.04 cm

Page 16
Non Steady-State Diffusion - Concentration
profile and the concentration gradient are
changing with time. The solution of this
equation is concentration profile as
function of time, C(x,t)
Fick’s Second
Law of Diffusion
Where:
D = diffusion
coefficient
t = temperature
x = position
C =
concentration
profile

Non Steady-State Diffusion
Page 17
퐶푥 − 퐶표
퐶푠 − 퐶표
= 1 − erf
푥
2 퐷푡
Where:
x – is the distance into the solid
Cx – is the concentration of diffusing
species at distance x
Co – is the initial bulk concentration of the
diffusing species in the solid.
Cs- is the surface concentration
(constant)
D- is the Diffusivity
t – is time
erf – is the Gaussian Error Function.

Page 18
Fick’s second law relates the rate of change
of composition with time to the curvature
of the concentration profile:
Concentration increases with time in
those parts of the system where
concentration profile has a positive
curvature. And decreases where
curvature is negative.

Page 19
Example:

Page 20
Solution:

Page 21
Factors Affecting Diffusion
 Diffusion of interstitials is typically faster
as compared to the vacancy diffusion
mechanism.
 Smaller atoms cause less distortion of the
lattice during migration and diffuse more
readily than big atoms.
 Diffusion is faster in open lattices or in
open directions.

Page 22
 Temperature - diffusion rate increases very
rapidly with increasing temperature
 Diffusion mechanism – diffusion by
interstitial mechanism is usually faster than by
vacancy mechanism
 Diffusing and host species - Do, Qd are
different for every solute, solvent pair
 Microstructure - diffusion is faster in
polycrystalline materials compared to single
crystals because of the accelerated diffusion
along grain boundaries.

Page 23
Formula (Arrhenius dependence):
Where:

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