DIFFUSIONEngineering Materials Class

Copper Nickel

Diffusion Couple

Copper Nickel

Copper Nickel

Con

cent

ratio

n

Position0

100

Mechanisms of Diffusion

Self Diffusion

Vacancy

Vacancy Diffusion

Interstitial Diffusion

Activation Energy

Ener

gyVacancy Diffusion

Interstitial Diffusion

Diffusion Flux (J)

Concentration

Concentration Gradient

Diffusion Flux (J)

Mass or atoms diffused per unit area per time

20

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Unit area

J=M/At

Concentration Gradient

Con

cent

ratio

n

Position0

100

xA xB

CA

CB

=C/x

Ficks First Law

J=D (C/x) Kg/m2s

D= Diffusion Coefficient = Doexp(-Q/RT) m2/sQ= Activation Energy (given) J/molR= Gas constant (given) J/mol KT= Temperature KDo = Preexponential (given) m2/s

Ficks First law is applicable at steady state diffusion

Steady State = Constant Diffusion Flux

Con

cent

ratio

n

Position

Con

cent

ratio

n

Position

Steady State Non Steady State

Ficks Second Law

Co=initial ConcentrationCs=Final ConcentrationCx= Concentration at position xerf= Gaussian error function (given)t= time (sec)

Ficks Second law is applicable at non steady state diffusion (mostly used)

Non Steady State = Variable Diffusion Flux

Example

The surface of a 0.1% C steel gears is to be hardened by carburizing. In

gas carburizing, the steel gears are placed in an atmosphere that

provides 1.2% C at the surface of the steel at a high temperature

(Figure 5.1). Carbon then diffuses from the surface into the steel. For

optimum properties, the steel must contain 0.45% C at a depth of 0.2

cm below the surface. Design a carburizing heat treatment that will

produce these optimum properties. Assume that the temperature is

high enough (at least 900oC) so that the iron has the FCC structure.