Environmental Engineering Reference
In-Depth Information
Figure 3.2 Resistivity of pure metals tends to
zero at zero temperature, limited by impurities.
The ratio of resistivity at 300 K to that at 4 K,
called the
residual resistance ratio,
can be as
large as amillion in an extremely pure crystalline
metal. The linear region of resistivity with
temperature is a well-known effect of the
thermal vibrations of the atoms, characterized
by
D
, the Debye temperature. (Figure 11.5 from
Electrons and Phonons
by J.M. Ziman, Oxford
University Press,1960).
would show up if we slowly increase a weak scattering interaction between it and an
array of atoms.
3.3
Energy Bands and Gaps
As we learned in connection with Figure 2.2, the Davisson
-
Germer experiment
implies that a free electron of momentum
p ¼h
/
l
is described by a wave
y¼
e
ikx
¼
e
(
i
2
px
)/
l
. Suppose this wave, moving to the right, weakly scatters from atoms at
spacing
a
, as sketched in Figure 3.3.
Here,
k ¼
2
p
/
l
is the de
nition of
wave number
, the number of radians advance in
phase permeter, corresponding to 2
p
per wavelength,
l
. l.We see that the condition for
strong coherent backreflection (
Bragg scattering
)is
