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that the amplitude of the electric signals depends on the initial concentration of alloy
admixture (Ca 2C ,Mn 2C ,I and others) (Tyunyaev and Mineev 1973 ). Recently
Freund ( 2000 , 2002 ) have assumed that the shock polarization effect in different
kinds of rocks can be due to a short-term increase in mobility of positive hole charge
carriers, i.e., defect electrons/holes. The temperature increase at the shock front can
result in transition from an insulator state to a conduction one similar to that in
p-type semiconductors (Freund and Pilorz 2012 ).
It should be noticed that the charge of a moving edge dislocation can have a
different sign for the cases of fast and slow deformation. The value of this charge
depends on the different bonding energies of vacancies of negative and positive
ions within a dislocation (Klein and Gager 1966 ; Tyapunina and Belozerova 1988 ).
Taking into account this circumstance, we shall consider further both point defects
and dislocations for the theoretical analysis of the shock polarization phenomenon.
We start with the kinetics of point and linear lattice defects in the region of a
SW front (Sirotkin and Surkov 1986 ). This approach has an advantage because
it succeeds in accounting for the dependence of diffusion coefficients and the
multiplication velocity of lattice defects on parameters of the SW and on the
structure of the crystal lattice.
Let us consider 1D compression, along the x-axis, of a dielectric influenced
by a plane SW. We suppose that the SW front has a finite spatial width. At first
we consider the processes associated with electric charge transfer by point defects.
An intensive multiplication of point defects gives rise to the generation of the so-
called Frenkel defects, which represent the pairs composed of a vacancy and an
interionic/interstitial ion. Compression of the crystal lattice causes distortion of the
equilibrium configuration of ions in the vicinity of defects, which in turn can result
in the defects motion.
Let n i1 .x a=2;t/ and n i2 .x C a=2;t/ be the number density of defects in
the sections with coordinates .x a=2/ and .x C a=2/, where a denotes a lattice
constant and i is a number of the defect species. Let i be the frequencies of the
defect jumps from an equilibrium place to another one, i.e., of one interatomic dis-
tance, a. The superscripts ˙ refer to displacement of the defects along and opposite
to the direction of SW propagation (Malkovich 1982 ). The projection of particle
flux density, f ix ,onthex-axisisassumedtobef ix .x;t/ D i1 n i1 i2 n i2 a,
where i1 D i .x a=2;t/ and i2 D i .x C a=2;t/. We expand the right-hand
side of this expression in a power series of parameter a, and also take into account
that motion of the material that results in transfer of the defects coupled with it. This
can also be considered to be the transfer caused by an electric field. Thus, in the first
approximation, adding to the total flux these additional fluxes, we get
f ix D n i a h i i
2 @ x i C i i
a
a 2
2 i C i @ x n i C n i V x C
i E x
q i
:
(9.7)
 
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