Geoscience Reference
In-Depth Information
Fig. 9.6
Model calculation
of the radial component of
electric field at the surface of
the collapsing pore versus
pore radius (Surkov
1991
)
E
, V/m
10
8
10
6
10
4
10
2
b
, mm
10
0
10
-4
10
-2
10
0
The linear dependence n./, which we have used above, holds true as the defect
number density n is smaller than the density n
of atoms in the crystal lattice. For
example, taking r
D
b and the numerical values n
10
28
-10
29
m
3
and M
D
10
25
m
3
we obtain that Eqs. (
9.47
) and (
9.49
) are valid if b>b
c
where the critical
pore radius b
c
D
b
0
.M=n
/
1=3
0:1b
0
. In order to estimate the electric field for
smaller pore radii one should consider that n
D
n
. In the pore radius range of
b
b
b
0
the electric field at the pore surface .r
D
b/ can be approximated by
the following expression (Surkov
1991
)
E
r
.b;t/
D
3
15
C
p
3
Ǜ
0
.
2
1
/b
0
t
s
M
1=3
n
2=3
=
4b
2
:
(9.50)
The numerical value
2
1
D
1 s
1
, which is typical for ionic crystal under
normal condition, can serve as the smallest estimate of this parameter. Then taking
t
s
D
1 ms and substituting these values into Eq. (
9.50
) we obtain that the electric
field E
r
begins to exceed the level of electrical breakdown for ionic crystals, which
is approximately equal to 10
8
V/m, as the pore becomes smaller than b
0:5 m.
A model calculation of E
r
at the pore surface on the pore radius is displayed in
Fig.
9.6
, in which we need the above parameters and b
D
0:1 m. Notice that the
electric discharge processes along with the recombination of the defects of crystal
lattice can lead to the stabilization of electric field during pore collapse.
Light flashes and electron emissions during SW output from the sample into
vacuum have been observed by Lyamkin et al. (
1983
) during high-pressure shock
compression of powder materials. These findings are evidence in favor of the
presence of strong electric fields in shock-compressed porous medium as it was
predicted by the above theory.
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