1. Chapter 6:
Diffusion

2. Important Concepts Applications of Diffusion
Activation Energy for Diffusion
Mechanisms for Diffusion
Rate of Diffusion (Fick’s First Law)
Factors Affecting Diffusion
Composition Profile (Fick’s Second Law)

3. Diffusion How does diffusion occur?
Why is diffusion 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?

4. Applications of Diffusion

5. Furnace for heat treating steel using carburization.
Carburizing is the addition of carbon to the surface of low-carbon steels at temperatures ranging from 1560°F to 1740°F.
Hardening is achieved when a high carbon martensitic case with good wear and fatigue resistance is superimposed on a tough, low-carbon steel core.

6. Case Hardening
Case hardening or surface hardening is the process of hardening the surface of a metal, often a low carbon steel, by diffusing elements into the material's surface, forming a thin layer of a harder alloy.
Carbon atoms diffuse into the iron lattice atoms at the surface.
This is an example of interstitial diffusion.
The C atoms make iron (steel) harder.
“Carbide band saw blade can cut through case hardened materials.” 6 6

7. ©2003 Brooks/Cole, a division of Thomson Learning, Inc
©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
Schematic of the microstructure of the Co-Pt-Ta-Cr film after annealing.
Most of the chromium diffuses from the grains to the grain boundaries after the annealing process. This helps improve the magnetic properties of the hard disk.

8. Hot-dip galvanizing is a form of galvanization
Hot-dip galvanizing is a form of galvanization. It is the process of coating iron, steel, or aluminum with a thin zinc layer, by passing the metal through a molten bath of zinc at a temperature of around 860 °F (460 °C).
When exposed to the atmosphere, the pure zinc (Zn) reacts with oxygen (O2) to form zinc oxide (ZnO), which further reacts with carbon dioxide (CO2) to form zinc carbonate (ZnCO3), a dull grey, fairly strong material.
In many environments, the steel below the coating will be protected from further corrosion.
Galvanized steel is widely used in applications where rust resistance is needed.
A hot-dip galvanizing 'kettle' with fume hood
Galvanized steel and coils popular for applications in industrial goods, automobile components, precision tubes, consumer durable and many more.
Galvanized i-beams.

9. Thermal barrier coatings (TBC) with a ceramic topcoat are widely used for protecting highly loaded gas turbine components against overheating.
For example, on internally cooled turbine blades the ceramic topcoat maintains a high temperature difference between the outer surface and the underlying metallic substrate.

10. Doping by Diffusion
Integrated circuits (ICs), found in numerous electronic devices have been fabricated using doping techniques.
The base material for these ICs is silicon that has been “doped” with other materials.
More precisely, controlled concentrations of impurities have been diffused into specific regions of the device to change the properties (improve electrical conductivity).

11. Processing Using Diffusion
• Doping silicon with phosphorus for n-type semiconductors:
• Process:
magnified image of a computer chip
0.5 mm
light regions: Si atoms
light regions: Al atoms
1. Deposit P rich
layers on surface.
silicon
2. Heat.
3. Result: Doped
semiconductor
regions.
silicon 11 11

12. Diffusion
Diffusion - Mass transport by atomic motion. Diffusion is a consequence of the constant thermal motion of atoms, molecules and particles that results in material moving from areas of high to low concentration.
Mechanisms
Brownian motion is the seemingly random movement of particles suspended in a liquid or gas.
Solids – vacancy diffusion or interstitial diffusion.

13. c06f01

14. Interdiffusion
• Interdiffusion (impurity diffusion): In an alloy, atoms tend to migrate from regions of high concentration to regions of low concentration.
After some time
Initially

15. Self-Diffusion
• Self-diffusion: In an elemental solid, atoms also migrate.
specific atom movement
After some time A B C D A B C D

16. Diffusion Mechanisms
Atoms in solid materials are in constant motion, rapidly changing positions.
For an atom to move, 2 conditions must be met:
There must be an empty adjacent site, and
The atom must have sufficient (vibrational) energy to break bonds with its neighboring atoms and then cause lattice distortion during the displacement.
At a specific temperature, only a small fraction of the atoms is capable of motion by diffusion. This fraction increases with rising temperature.
There are 2 dominant models for metallic diffusion:
Vacancy Diffusion
Interstitial Diffusion

17. Vacancy Diffusion Vacancy Diffusion: • atoms exchange with vacancies
• applies to substitutional impurity atoms
• rate depends on:
-- number of vacancies
-- activation energy to exchange.
increasing elapsed time

18. Interstitial Diffusion
Interstitial diffusion – smaller atoms (H, C, O, N) can diffuse between atoms.
this is essentially mechanism in amorphous materials such as polymer membranes
More rapid than vacancy diffusion due to more mobile small atoms and more empty interstitial sites.

19. Diffusion How do we quantify the rate of diffusion?
M =
mass
diffused
time
Measured empirically
Make thin film (membrane) of known surface area
Impose concentration gradient
Measure how fast atoms or molecules diffuse through the membrane
J  slope

20. Steady-state diffusion across a thin plate
c06f04
Rate of diffusion is independent of time; the diffusion flux does not change with time.
The concentration profile shows the concentration (C) vs the position within the solid (x); the slope at a particular point is the concentration gradient.

21. Steady-State Diffusion
Flux proportional to concentration gradient = C1 C2 x x1 x2
Fick’s first law of diffusion
D  diffusion coefficient

22. Example 1: 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 are worn.
If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through a glove?
Data:
diffusion coefficient for butyl rubber: D = 110 x10-8 cm2/s
surface concentrations:
C1 = 0.44 g/cm3
C2 = 0.02 g/cm3

23. Example 1 (cont). Solution – assuming linear conc. gradient Data:
glove C1
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

24. Diffusion and Temperature
• Diffusion coefficient increases with increasing T. 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]
Activation energy - energy required to produce the movement of 1 mole of atoms by diffusion.

25. Factors that influence diffusion
The diffusing species, host material and temperature influence the diffusion coefficient.
For example, there is a significant difference in magnitude between self-diffusion and carbon interdiffusion in α iron at 500 °C.

26. What is the diffusion coefficient at 350ºC?
Example 2: At 300ºC the diffusion coefficient and activation energy for Cu in Si are:
D(300ºC) = 7.8 x m2/s
Qd = 41,500 J/mol
What is the diffusion coefficient at 350ºC?
transform data D
Temp = T
ln D
1/T D = Do
exp æ è ç ö ø ÷ - Qd R T

27. Example 2 (cont.) T1 = 273 + 300 = 573 K T2 = 273 + 350 = 623 K
D2 = 15.7 x m2/s

28. Nonsteady State Diffusion
The concentration of diffusing species is a function of both time and position C = C(x,t). More likely scenario than steady state.
In this case, Fick’s Second Law is used.
In the non-steady state the concentration profile develops with time.
Fick’s Second Law

29. c06f06

30. Processing – Ex 6.3 • Copper diffuses into a bar of aluminum.
pre-existing concentration Co of copper atoms
Surface concentration C
of Cu atoms
bar s
• 10 hours at 600˚C gives C(x).
• How many hours would it take to get the same C(x) if processed at 500˚C?
115.5 hrs
• Answer:

31. Non-steady State Diffusion
Example 3: An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere that gives a surface carbon concentration constant at 1.0 wt%. If after 49.5 h the concentration of carbon is 0.35 wt% at a position 4.0 mm below the surface, determine the temperature at which the treatment was carried out.
Solution: use Eqn. 6.5

32. Example 3 Solution (1): t = 49.5 h x = 4 x 10-3 m
Cx = 0.35 wt% Cs = 1.0 wt%
Co = 0.20 wt%
 erf(z) =

33. c06tf01

34. Example 3 Solution (2):
We must now determine from Table 6.1 the value of z for which the error function is An interpolation is necessary as follows z
erf(z) z
z = 0.93
Now solve for D

35. D = Do
exp æ è ç ö ø ÷ - Qd R T
Example 4 Solution (3):
To solve for the temperature at which D has the calculated value, we use a rearranged form of Equation (6.9a);
from Table 6.2, for diffusion of C in FCC Fe
Do = 2.3 x 10-5 m2/s Qd = 148,000 J/mol 
T = 1300 K = 1027°C