Laboratory Study of Rock Deformation and Fracture - Ultra and Extremely Low Frequency Electromagnetic Fields - page 337

Here n 0 and 0 denote the number density and frequency of defect jumps ahead
of the SW front, i.e., when !1 . In the zero-order approximation .Ǜ D 0/,the
variations of number density n n 0 arise only from the defect multiplication. In the
next approximation, the variations of the defect number density due to displacement
of defects with respect to the lattice with frequency are accounted for by adding
further terms of the power series of Ǜ.
Combining Eqs. ( 9.10 ) and ( 9.12 ) for the case of only one type of defect we find
the electric charge density e ./ and the x component of the electric field E x ./ in
the vicinity of the SW front

qa 2
V s

d
d ./Œn 0 C M./;

e D (9.13)

qa 2
"" 0 V s f 0 n 0 ./Œn 0 C M./ g ;

E x D (9.14)

If the point defects and dislocations move by means of a thermofluctuational
mechanism, the frequency of defect jumps numbered by subscript i can be written
in the form

i D i exp Πu i =.k B T/; (9.15)

where k B is Boltzmann constant and T is the temperature. Because the inharmonic-
ity of lattice oscillations is insignificant . 1/, then the linear dependence of the
activation energy u i on the strain can be applied, that is u i D u i0 LJ i , where u i0
and LJ i are constant values.
Let the subscripts c and v denote the cations and vacancies, respectively. The
estimates of the parameters entering these equation for a crystal lattice of NaCl have
shown that the behavior of cations and vacancies of Na C in the SW are essentially
different (Sirotkin and Surkov 1986 ). The rise of shock pressure and shear strain
results in the increase of u c and the decrease of u v due to the opposite signs of
the parameters LJ c and LJ v . This implies that the shock polarization effect in ionic
crystals is rather due to vacancies than the cations. On the other hand the estimate
of electric field amplitude based on the thermofluctuational mechanism of the defect
displacement is not in agreement with observation at least for the case of ionic
crystals.
Another scenario can be realized if the shear strain exceeds a threshold value of
D u c0 =LJ c followed by above-barrier movement of cations. Taking into account
that the activation energy is equal to zero while the frequency reaches the maximal
value we come to the following relationships:

qa 2 M
V c

d
d ;

e D (9.16)