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Difusão em engenharia de materiais
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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
03 B
rook
s/C
ole,
a d
ivis
ion
of T
hom
son
Lear
ning
, Inc
. Th
omso
n Le
arni
ng
is a
trad
emar
k us
ed h
erei
n un
der l
icen
se.
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.