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CHE 333 CLASS 12. DIFFUSION. EXAM Wednesday. Martensite Heat treatment of steels Age Hardening Defects. DIFFUSION. Diffusion – is the movement of matter driven by chemical and thermal processes such as concentration gradients and heating. Both are

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CHE 333 CLASS 12

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CHE 333 CLASS 12


EXAM Wednesday

  • Martensite

  • Heat treatment of steels

  • Age Hardening

  • Defects


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.


  • 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.


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.

SoluteSolventD at 500 C D at1000 C

CarbonBCC iron5x10-12 2x10-9

CarbonFCC iron5x10-15 3x10-11

IronBCC iron10-20 3x10-14

NickelFCC iron10-23 2x10-16

Silver Silver Xtal10-17

SilverSilver Grain Bound10-11




Gradient is constant with time

Substitutional and Interstitial

  • From the data, interstitial diffusion is much faster then substitutional diffusion, by several orders of magnitude.

    SoluteSolventTypeD at 500 C D at 1000 C

    CarbonBCC ironInter5x10-12 2x10-9

    IronBCC ironSubst10-20 3x10-14

  • 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.

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





t=0.5 equilib




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 0.5 = erf(x/2((Dt)-1/2))

0.5 = erf(0.5205)



Dt = x2



t= 25x10-8/5x10-12


=13.8 hours

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 – 1.987 cal/mole.K

y= c +mx

Slope = Q/R if ln D plotted against 1/T

Practical Example



Steel – Carpenter #11

Decarburized layer - ferrite

1600F for 10 minutes then air cool – etch 5% Nital mag X20.

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.

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.


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.


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.

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