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qa
2
""
0
V
c
.n
0
C
M/
E
x
(9.17)
which are valid for >
: Thesignof in Eq. (
9.16
) is positive because d=d >
0 so that the positive charge is situated at the front of the SW. The charges with
opposite sign are either situated in the volume of the sample behind the SW at the
relaxation length or they are located on the sides of sample.
To estimate the charge density and electric field in the SW for the case of above-
barrier defect motion, we use the numerical values: "
D
5:3,
D
0:1 m,
D
5
10
12
Hz, M
D
10
25
m
3
, n
0
D
10
22
m
3
and a
D
0:3 nm as well as the
empirical parameters of shock-compressed NaCl at 10 GPa (Baum et al.
1975
):
V
c
D
4:4 km/s, and the strain amplitude
m
D
0:22. Then we find that
3:6
10
2
C/m
3
and E
7:7
10
5
V/m.
For the case of dislocations, the charge, q
d
, per unit length can be different for
the thermofluctuational and the sliding stages. Taking the parameters of dislocations
q
d
1:7
10
11
C/m (Tyapunina and Belozerova
1988
) and M
10
17
m
2
,we
obtain
3:8
10
2
C/m
3
and E
8:2
10
5
V/m which is close to the above
estimates for the vacancies.
The strain threshold for dislocations is equal to
D
Y=K, where Y is yield
strength and K is the modulus of bulk compression. For instance, in case of NaCl
the strain threshold of dislocations
.3
6/
10
3
which is smaller by 2-3
orders of magnitude than the threshold of cations (Sirotkin and Surkov
1986
). This
means that the dislocation mechanism of shock polarization effect in ionic crystals
can prevail over cation one due to the smaller threshold.
The effective charge density, †, per unit area of the SW front surface can be
estimated through the magnitude E
m
of the SW-induced electric field as follows:
†
D
2""
0
E
m
. Taking E
m
from Eq. (
9.17
)gives
†
2qa
2
M
m
=V
c
:
(9.18)
Results of laboratory tests with shock-compressed NaCl samples are displayed
in Fig.
9.3
(Mineev and Ivanov
1976
). Figures a, b, and c correspond to the SW
propagation along different crystallographic directions. The surface charge density
on the SW is shown with circles while the theoretical dependences of † on the
strain amplitude given by Eq. (
9.18
) are shown with solid lines. It is evident that
the linear character of the plotted functions †.
m
/ follows the linear dependence of
the multiplication rate of dislocations or point defects on the plastic strain rate. The
numerical values of the parameter M are chosen in such a way to fit the experimental
data. The results are shown in the table.
Direction M
d
;10
17
m
2
M
p
;10
25
m
3
E
;10
6
V/m
Œ1;0;0
4.5
4.7
4.7
0.29
Œ1;1;0
8.4
8.5
9.5
0.32
Œ1;1;1
2.3
2.4
2.6
0.31
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