Environmental Engineering Reference
In-Depth Information
or
N
e
a
0
1. This means that the greater the
electron number density, the more the properties of a degenerate electron gas de-
termine the properties of a quantum plasma. In contrast, the role of the Coulomb
interaction between charged particles of the plasma decreases with increase of the
electron number density.
We can apply the model of a degenerate electron gas to describe the behavior
of electrons in metals. Table 1.7 lists parameters of real metallic plasmas at room
temperature. It can be seen that
1, that (1.95) is equivalent to
is small at room temperature, meaning that the
metallic plasma has the character of a quantum plasma. But the Coulomb inter-
action involving electrons and ions of metals is comparable to the exchange inter-
action potential of electrons, determined by the Pauli principle. Thus, a metallic
plasma is a quantum plasma in which the potential of the Coulomb interaction
of charged particles and the exchange interaction potential of the electrons have
the same order of magnitude. As is seen, in all the cases of a metallic plasma
according to the data in Table 1.7 the Coulomb interaction between the nearest
electrons exceeds the exchange interaction between electrons, but these values are
comparable.
Positive ions of real metals form a crystalline lattice at low temperatures. An
important role in these crystals is played by the non-Coulomb interaction of free
electrons with ions and bound electrons. Consider a simplified problemwhere elec-
trons and ions of the metal participate only in the Coulomb interactions between
them. The ions of this system form a crystalline lattice, and the energy per coupled
pair of charged particles (one electron and ion) is
η
3
p
F
10
m
e
e
2
N
1/3
ε
D
,
(1.96)
e
where the first term is the mean electron kinetic energy, the second term is the
mean energy of the Coulomb interaction between charged particles, and
depends
on the lattice type. Here we take into account the redistribution of charged particles
resulting from their interaction that leads to the attractive character of the mean
interaction energy.
Accounting for
p
F
N
1/
e
and optimizing (1.96) for the specific plasma energy,
we find that the optimal parameters for the plasma are
4/3
5
π
a
0
N
1/3
2
,
D
D
0.174
,
ε
D
ε
(1.97)
e
min
0
3
5/3
Ta b l e 1 . 7
Parameters of metallic plasmas at room temperature.
Metal
Li
Na Mg
Al
K
Cu
Ag
Cs
Au
Hg
N
e
,10
22
cm
3
4.6
2.5
8.6
18
1.3
8.4
5.9
0.85
5.9
8.5
,10
3
η
5.5
8.2
3.6
2.2
13
3.7
4.6
17
4.6
3.6
1.8
2.2
1.4
1.1
2.7
1.4
1.6
3.1
1.6
1.4
