9.
You are given three aluminum samples of the same purity: single crystal, polycrystal with an
average grain size of 10 microns, and polycrystal with an average grain size of 1 micron.
Now
you are to measure the selfdiffusion coefficient (i.e., diffusion of aluminum atoms in aluminum)
for each of these three samples at the same temperature.
(a)
Rank the three diffusion coefficients.
Explain how you arrive at this conclusion.
(b)
If you repeat these measurements with another metal having higher sublimation
energy (e.g., copper), what will you find about the corresponding diffusion coefficients
(larger or smaller)?
Why?
Solution
(a) Diffusion is faster along grain boundaries than through the bulk of the crystal.
There are
more grain boundaries available for diffusion in an aluminum polycrystals with 1 micron grain
size than that with 10 micron grain size.
Therefore, one can conclude the following:
D
Al, grain size 1 micron
> D
Al, grain size 10 micron
> D
Al, single crystal
(b) As shown in problem 4, larger sublimation energy corresponds to larger selfdiffusion
activation energy.
Increasing the activation energy
Q
results in smaller diffusion coefficient
D
,
as given by eq. (2.5):
−
=
RT
Q
D
D
o
exp
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2.
A pure gallium arsenide (GaAs) single crystal (a IIIV semiconductor) is doped with 1
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 Spring '10
 MatSci
 conduction electron concentration

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