CHE 333 CLASS 20

DIFFUSION

DIFFUSIONDiffusion – 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.

MECHANISMS1. 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.

RATES OF DIFFUSIONSteady 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 5x10-12 2x10-9

Carbon FCC iron 5x10-15 3x10-11

Iron BCC iron 10-20 3x10-14

Nickel FCC iron 10-23 2x10-16

Silver Silver Xtal 10-17

Silver Silver Grain Bound 10-11 Distance

Conc

Gradient is constant with time

dC/dx

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 5x10-12 2x10-9

Iron BCC iron Subst 10-20 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 LawNon Steady State – Concentration changes at position x as a function of time, eg Cu Ni

c/t=D(2C/x2) 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

Distance

100%

50%

0%

t=0

t=equilib

t=0.5 equilib

ExampleTime 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)

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

Diffusion and TemperatureDiffusion 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

Decarburizing.

HypereutectoidSteel – 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 surfaceFor the carbon to diffuse out and leave a ferrite layer either side of the crack.

Other ApplicationsBonding – 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 theSurface for wear resistance.

Removal of hydrogen after electroplating – heat up to 350F for 24 hours to reducehydrogen 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 flowcompared to tablets which have a high initial amount then quickly low.

MaterialsDifferent Materials and Diffusion RatesMetals 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, moisturepick up in composites.

Useful Surface treatments of metals, for example carburizing, nitridingPorous materials, lubricant impregnated bearings.

Permeation – like diffusion but use volume defects.Concrete – moisture, salt, leads to steel corrosion – Fick’s second law.