1. TOPIC 2: Diffusion in Solids
ISSUES TO ADDRESS...
• How does diffusion occur?
• Why is it an important part of processing?
• How can the rate of diffusion be predicted for
some simple cases?
• How does diffusion depend on structure
and temperature?

2. Diffusion
Diffusion - Mass transport by atomic motion in materials (solids, liquids or gases)
Mechanisms
Gases & Liquids – random (Brownian) motion
Solids – vacancy diffusion or interstitial diffusion
Diffusion mechanism depends on material

3. Why diffusion is important?
Heat treatment (phase transformation from solid to solid)
Solidification (liquid to solid)
Surface hardening of steel (carburising, nitriding, etc…)
Coatings
sintering of ceramics

4. Diffusion in solid materials
Temperature should be high enough to overcome energy barriers to atomic motion
Heat : causes atoms to vibrate
Vibration amplitude : increases with temperature
Melting occurs when vibrations are sufficient to rupture bonds

5. Two types of diffusion in crystalline solids:
impurity diffusion or interdiffusion
Occurs in a solid material with more than one type of element (such as an alloy)
(2) Self-diffusion
Occurs in chemically pure materials (only one type of atoms)

6. Diffusion • Interdiffusion: In an alloy, atoms tend to migrate
from regions of high conc. to regions of low conc.
Initially
After some time
Adapted from Figs. 5.1 and 5.2, Callister 7e.

7. Diffusion • Self-diffusion: In an elemental solid, atoms C C A D A D B
also migrate.
Label some atoms
After some time A B C D A B C D

8. Diffusion Simulation • Simulation of interdiffusion
across an interface:
• Rate of substitutional
diffusion depends on:
--vacancy concentration
--frequency of jumping.
(Courtesy P.M. Anderson)

9. Diffusion mechanism Atoms are constantly in motion and vibrating
Change of atomic position requires:
Vacant site
Energy to break atomic bonds
Two types of diffusion mechanism:
Vacancy diffusion or substitutional diffusion
Interstitial diffusion

10. Diffusion Mechanisms Vacancy Diffusion:
• atoms exchange with vacancies
• applies to substitutional impurities atoms
Both self diffusion and interdiffusion occur by this mechanism
• rate depends on:
--number of vacancies
--activation energy to exchange.

11. Diffusion Mechanisms
Interstitial diffusion – smaller atoms can diffuse between atoms.
this is essentially mechanism in amorphous materials such as polymer membranes
Adapted from Fig. 5.3 (b), Callister 7e.
More rapid than vacancy diffusion because the interstitial atoms are smaller, thus more mobile. Also, there are more empty interstitial positions than vacancies.

12. INTERSTITIAL SIMULATION
• Applies to interstitial
impurities.
• More rapid than
vacancy diffusion.
• Simulation:
--shows the jumping of a
smaller atom (gray) from
one interstitial site to
another in a BCC
structure. The
interstitial sites
considered here are
at midpoints along the
unit cell edges.
(Courtesy P.M. Anderson)

13. Processing Using Diffusion
• Case Hardening:
--Diffuse carbon atoms
into the host iron atoms
at the surface.
--Example of interstitial
diffusion is a case
hardened gear.
Adapted from chapter-opening photograph, Chapter 5, Callister 7e. (Courtesy of
Surface Division, Midland-Ross.)
• Result: The presence of C atoms makes iron (steel) harder.

14. Steady-State Diffusion
Rate of diffusion independent of time (no change in concentration of solute atoms with time)
Flux proportional to concentration gradient = C1 C2 x x1 x2
Fick’s first law of diffusion
D  diffusion coefficient

15. 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:
C1 = 0.44 g/cm3
C2 = 0.02 g/cm3

16. Example (cont). Solution – assuming linear conc. gradient Data: glove
paint
remover
skin
D = 110 x 10-8 cm2/s
C2 = 0.02 g/cm3
C1 = 0.44 g/cm3
x2 – x1 = 0.04 cm
Data: C2 x1 x2

17. Diffusion and Temperature
• Diffusion coefficient increases with increasing T. Arrhenius equation: D = Do
exp æ è ç ö ø ÷ - Qd R T
= pre-exponential [m2/s]
= diffusion coefficient [m2/s]
= activation energy [J/mol or eV/atom]
= gas constant [8.314 J/mol-K]
= absolute temperature [K]

18. Diffusion and Temperature
D has exponential dependence on T
1000 K/T
D (m2/s)
C in a-Fe
C in g-Fe
Al in Al
Fe in a-Fe
Fe in g-Fe
0.5
1.0
1.5
10-20
10-14
10-8
T(C)
1500
1000
600
300 D
interstitial
>> D
substitutional
C in a-Fe
C in g-Fe
Al in Al
Fe in a-Fe
Fe in g-Fe
Adapted from Fig. 5.7, Callister 7e. (Date for Fig. 5.7 taken from E.A. Brandes and G.B. Brook (Ed.) Smithells Metals Reference Book, 7th ed., Butterworth-Heinemann, Oxford, 1992.)

19. What is the diffusion coefficient at 350ºC?
Example: At 300ºC the diffusion coefficient and activation energy for Cu in Si are
D(300ºC) = 7.8 x m2/s
Qd = 41.5 kJ/mol
What is the diffusion coefficient at 350ºC?
transform data D
Temp = T
ln D
1/T

20. Example (cont.) T1 = 273 + 300 = 573 K T2 = 273 + 350 = 623 K
D2 = 15.7 x m2/s

21. Non-steady State Diffusion
The concentration of diffusing species is a function of both time and position C = C(x,t).
In most cases non-steady state diffusion is occurs, where the concentration of solute atoms at any point in the materials changes with time.
e.g. If carbon is being diffused in the surface of a steel camshaft to harden its surface, the concentration of carbon under the surface at any point will change with time as the diffusion process progresses.
In this case Fick’s Second Law is used
In the non-steady state the concentration profile develops with time.
Fick’s Second Law

22. Summary Diffusion FASTER for... Diffusion SLOWER for...
• open crystal structures
• smaller diffusing atoms
• lower density materials
Diffusion SLOWER for...
• close-packed structures
• larger diffusing atoms
• higher density materials