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Objectives

1. Explain the mechanisms of diffusion and

the effect of grain boundaries, free

surfaces, and dislocations on the diffusion

process.

2. Use Ficke’s first and second laws topredict diffusional behavior.

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 Team Task 

 Think of three reasons that aluminum might be

used as a layer in the packaging material for a

juice bag.

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Mechanism?

How do these atoms interpenetrate?

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Mechanism?

How do these atoms interpenetrate?

 Three possibilities Zener ring mechanism

Direct switch

 Vacancy Drift

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Mechanisms

Direct Switch

Zener Ring

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Diffusion

 A. Zener Ring 

B. Direct Switch

C.  Vacancy Drift A

B

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Experimental Investigation

Embedded wires in diffusion couple as

boundary markers

Couple heated for extended period

Position of wires measured

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Kuykendall Experiment

The Wires Move!

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Question

 Which of the three mechanisms will produce

movement by the wires in the Kuykendall

experiment?

a. Direct switch

b. Zener ring c. Vacancy diffusion

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 Vacancy Diffusion

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Differing Diffusion in Couples

 Two elements will not necessarily have the same

diffusion rates in each other.

Imbalance in flow will result in voids on one

side (shrinkage) and overpacking on the other

(expansion)

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Copper/Nickel Diffusion Couple

Diffusion of copper into Nickel is greater than Nickel into

Copper!

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Diffusion

1.  Two major mechanisms

-Vacancy (substitutional)

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Diffusion

1. Two major mechanisms

-Vacancy (substitutional)

-Interstitial (between atoms)

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Diffusion

2. Diffusion Easier at Surfaces,

Grain Boundaries, Dislocations

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Diffusion

3. Can we demonstrate Self-

Diffusion?

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Ficke’s 1st Law 

Steady State DiffusionConcentration is Constant in Time

= -DC = -DC

X  X 

D - Diffusivity 

C - Concentration

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1st Law Diffusion

Callister, Materials Science & Engineering 

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 Application: Metal Membrane for

Hydrogen Purification

 Wah Chang  – Outlook 2nd Qtr 2000

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Diffusivity Temperature Dependence

D = DO exp  – (QD

/ RT)

DO, QD, R – Tables

T – Kelvin

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Diffusivity Assumption

 We are going to assume that Diffusivity does

not vary with species concentration.

 According to the next slide, is this reasonable?

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Effect of Concentration

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Ficke’s 2nd Law

Time Dependent Concentration

CX - CO = 1 – erf ( x / 2 Dt )

CS - CO 

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Ficke’s 2nd Law

CX - CO = 1 – erf (x / 2 Dt)

CS - CO 

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Which of Ficke’s Laws should you use? 

1. A pipeline is carrying hydrogen gas which

diffuses through the wall into the

atmosphere.2. A tooth absorbs flouride from a gel during

flouridation treatment at the dentist’s office. 

3. Carbon diffuses through iron walls of acharcoal furnace.

4. A drive shaft is packed in graphite and heated

to increase its surface hardness.

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Process Modification

D – Diffusivity 

t – time

X - Depth

.

2

Const  Dt 

 X