Geoscience Reference
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explain the observations. However, the free electrons in metals can be considered
as a possible candidate for explanation of this effect (e.g., Gurevich
1957
; Alekseev
et al.
1984
). The strains caused by the acoustic wave can modulate distributions
of electron and ion number densities in metals in such a way that they exceed the
equilibrium density level in those regions which are compressed by the acoustic
wave. Due to their high mobility the electrons diffuse from the compressed regions
towards the depression areas thereby producing the potential difference between
these regions. The diffusion flux of electrons is partly compensated by electric
current flowing in the inverse direction.
The state of thermodynamics equilibrium of the electron subsystem of metal is
characterized by the equality
e'
D
const;
(9.1)
where denotes chemical potential which is approximately equal to the Fermi
energy, "
F
, of electrons in the metal under zero temperature. The strength of the
extrinsic forces,
E
e
, can thus be described by
E
e
Dr
=e. Rearranging this
equation in the following way we obtain
d
dn
e
r
n
e
Š
"
F
en
e
r
n
e
D
"
F
e
r
;
E
e
D
(9.2)
where is a dimensionless coefficient of the order of unity, n
e
is the electron number
density, e is the elementary charge, and is the density of medium. Assuming that
the magnetic field in metals can be neglected, then the total current is equal to zero;
that is,
.
E
C
E
e
/
C
"
0
@
t
E
D
0:
(9.3)
In the acoustic frequency range the displacement current density "
0
@
t
E
is much
smaller than the conduction one due to high conductivity of the metals. In the first
approximation we suppose that goes into infinity. Considering that the sum of
conduction and extrinsic current densities; that is
j
D
.
E
C
E
e
/, has to be finite we
conclude that the electric field in the metal
E
E
e
. We now estimate the last term
in Eq. (
9.3
)
j
d
"
0
@
t
E
e
which is related to the charge density through Maxwell's
equations. Substituting Eq. (
9.2
)for
E
e
into this equation and taking into account
that the density variations are small, we get
@
t
r
"
0
"
F
e
"
0
"
F
e
r
.@
t
/:
j
d
D
(9.4)
Now let us apply the continuity equation in the form
@
t
Dr
.
V
/;
(9.5)
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