1. CHE 333 CLASS 20
DIFFUSION

2. DIFFUSION Diffusion – is the movement of matter driven by
chemical and thermal processes such as
concentration gradients and heating. Both are
needed as it is an activation controlled
process. An energy barrier is present so
external energy must be provided, such as heat.
Atoms will diffuse down a concentration gradient
provided they have overcome the
activation energy needed for the process.
Copper atoms will diffuse into the
nickel until an equal concentration is
achieved. Remember that Cu-Ni system
is one of complete solid solubility.

3. MECHANISMS 2. Interstitial diffusion involves small
Substitutional diffusion is vacancy controlled – a vacancy or missing atom on its lattice site is needed for the atom to jump into. As one atom jumps into a vacancy it leaves a vacancy.
2. Interstitial diffusion involves small
atoms diffusing in a matrix of large
atoms. For metallic atoms, the
H, C, N, O, B atoms are the ones
small enough to fit in the spaces
between the large metallic atoms.

4. J= -D(dC/dx) Ficks First Law
RATES OF DIFFUSION
Steady State Diffusion – constant linear concentration gradient.
J – Diffusion Flux – atoms/m2.sec – number of atoms moving through one m2 in one sec.
This is the rate of unidirectional mass motion per unit area per second.
J= -D(dC/dx) Ficks First Law
D – diffusivity or diffusion coefficient – m2/s. Depends on temperature, diffusing element,
bond strength, packing factor and imperfections.
dC/dx – concentration gradient.
Solute Solvent D at 500 C D at1000 C
Carbon BCC iron 5x x10-9
Carbon FCC iron 5x x10-11
Iron BCC iron x10-14
Nickel FCC iron x10-16
Silver Silver Xtal
Silver Silver Grain Bound 10-11
Conc
dC/dx
Distance
Gradient is constant with time

5. Substitutional and Interstitial
From the data, interstitial diffusion is much faster then substitutional diffusion, by several orders of magnitude.
Solute Solvent Type D at 500 C D at 1000 C
Carbon BCC iron Inter 5x x10-9
Iron BCC iron Subst x10-14
Grain boundary diffusion is faster then transgranular diffusion due to the
higher number of defects at a grain boundary. This is important in second phase growth under equilibrium conditions, as second phases are then usually found on grain boundaries of the initial phase. For example pro-eutectoid phases in steels.

6. Non Steady State Ficks 2nd Law
Non Steady State – Concentration changes at position x as a function of time, eg Cu Ni
dc/dt=D(d2C/dx2) Ficks 2nd Law
Solution to this :-
(Cx-Co)/(Cs-Co)= 1- erf(x/2((Dt)-1/2))
Cx – concentration at depth x at time t, wt%
Co – concentration in average in bulk, wt %
Cs – concentration at surface, fixed with time t, wt%
Co- concentration in average in bulk, wt%
erf – error function – look up in tables.
x – distance below surface, m
D – diffusion coefficient, m2/s
t – time in seconds
Cu Conc’n
100%
t=0
t=equilib
50%
t=0.5 equilib 0%
Distance

7. Example
Time for the carbon concentration at 500C to reach half way between the steel
composition level and the external level at 0.5mm below the surface.
Using Fick’s second law Cx-Co/Cs-Co= 1- erf(x/2((Dt)-1/2))
The left hand side is 0.5.
0.5= 1- erf(x/2((Dt)-1/2))
Rearranging = erf(x/2((Dt)-1/2))
0.5 = erf(0.5205) So
0.5=(x/2((Dt)-1/2))
Dt = x2
t=x2/D
=(5x10-4)2/(5x10-12)
t= 25x10-8/5x10-12
=5x104sec
=13.8 hours

8. Diffusion and Temperature
Diffusion increased with temperature
It is activation controlled so follows:-
D=Do exp(-E/kT)
Where D = Diffusivity(m2/sec)
Do = Constant
E = activation energy
k = Boltzman’s Constant
T = temperature in oK
k= 13.8x10-24 J/atom.K
lnD=lnDo – Q/RT
Q – cal/mole
R – cal/mole.K
y= c +mx
Slope = Q/R if ln D plotted against 1/T

9. Practical Example Decarburizing. Hypereutectoid
Steel – Carpenter #11
Decarburized layer - ferrite
1600F for 10 minutes then air cool – etch 5% Nital mag X20.

10. Practical Example
Decarburization at 1200F after quench crack in material. The crack left enough open surface
For the carbon to diffuse out and leave a ferrite layer either side of the crack.

11. Other Applications
Bonding – by placing metals close together and heating them, as atoms from one go
into the other, a bond is formed.
Nitriding, carburizing, for surface hardening of steels – forms hard compounds on the
Surface for wear resistance.
Removal of hydrogen after electroplating – heat up to 350F for 24 hours to reduce
hydrogen and stop hydrogen embrittlement in high strength steels.
Semi conductor processing – dopants added by diffusion to silicon wafers.
Vacuum heat treating of titanium – oxygen embrittles titanium so use a vacuum
atmosphere or remove a surface layer calculated from Ficks second law.
Fuel Cells – Proton Exchange Membrane hydrogen ion diffuses through a polymer.
Pharmaceutical drug delivery – controlled release through polymers, creates steady flow
compared to tablets which have a high initial amount then quickly low.

12. Materials Different Materials and Diffusion Rates
Metals in metals slow, interstitials in metals much faster.
Polymers – Fick’s Laws observed, fast diffusion, for example moisture into polymers
1.5% weight gain into “free volume” as it is not a crystal structure.
Ceramics – very low near zero diffusion rates – ionic and covalent bonding.
Composites –orientation dependent, along fiber interfaces high.
Damaging – decarburization, oxygen in titanium alloys, hydrogen in steels,
oxygen and nitrogen along grain boundaries in metals at high temperature, moisture
pick up in composites.
Useful
Surface treatments of metals, for example carburizing, nitriding
Porous materials, lubricant impregnated bearings.
Permeation – like diffusion but use volume defects.
Concrete – moisture, salt, leads to steel corrosion – Fick’s second law.