Page 177 - Materials Science and Engineering An Introduction

5.5 Factors that Influence Diffusion • 149

Solution
This is a diffusion problem in which Equation 5.6b may be employed. Because at both 500 C
and 600 C the composition remains the same at some position, say x 0 , Equation 5.6b may be
written as
2 2
x 0 x 0
=
D 500 t 500 D 600 t 600
with the result that 5

D 500 t 500 = D 600 t 600
or

2
(5.3 * 10 -13 m /s)(10 h)
D 600 t 600
t 500 = = -14 2 = 110.4 h
4.8 * 10 m /s
D 500
5.5 FACTORS THAT INFLUENCE DIFFUSION
Diffusing Species
The magnitude of the diffusion coefficient D is indicative of the rate at which atoms dif-
fuse. The diffusing species and the host material influence the diffusion coefficient. For
example, there is a significant difference in magnitude between self-diffusion and carbon
interdiffusion in a-iron at 500 C, the D value being greater for the carbon interdiffusion
2
(3.0 10 21 vs. 1.4 10 12 m /s). This comparison also provides a contrast between rates
of diffusion via vacancy and interstitial modes, as discussed earlier. Self-diffusion occurs
by a vacancy mechanism, whereas carbon diffusion in iron is interstitial.
Temperature
Temperature has a profound influence on the coefficients and diffusion rates. For exam-
ple, for the self-diffusion of Fe in a-Fe, the diffusion coefficient increases approximately
2
six orders of magnitude (from 3.0 10 21 to 1.8 10 15 m /s) in rising temperature from
500 C to 900 C. The temperature dependence of the diffusion coefficients is
Dependence of the
diffusion coefficient Q d (5.8)
on temperature D = D 0 exp a - RT b
where
2
D 0 a temperature-independent preexponential (m /s)
Q d the activation energy for diffusion (J/mol or eV/atom)
activation energy
#
#
5
R the gas constant, 8.31 J/mol K or 8.62 10 eV/atom K
T absolute temperature (K)
The activation energy may be thought of as that energy required to produce
the diffusive motion of one mole of atoms. A large activation energy results in a

5 For diffusion situations wherein time and temperature are variables and in which composition remains constant at
some value of x, Equation 5.6b takes the form
Dt = constant (5.7)