Figure 15. Some practical cases in which nonuniform strain generates electric polarization of ice. The
arrows indicate the direction of motion of charge carriers.
r t r r r r
Ω = ∫ j1 - j2 - j3 + j4 dt.
amount of work against this pressure
Eai(P) = Eai(0) + Pγai
The quantities ηi are given by
where γai is the so-called activation volume.* For the
ηi = 1,1,1,1
for i = 1,2,3,4
defects that increase volume, γai is positive, and their
formation energy is raised proportionally to the applied
pressure. This results in an exponentially decreasing
concentration of such defects with increasing pressure.
Since the formation energy of defects Eai depends on
the applied pressure P according to eq 20, in tr e pres-
where roo = 2.76 is the oxygenoxygen distance in
ence of a pressure gradient, there is a force Fi acting
ice (Jaccard 1964). To find the electrical field strength
caused by the pressure gradient ∇P, we should solve
upon the defects
the system of eq 2223 under particular initial and
Fi = -grad(Eai ) = -γ ai grad(P) .
boundary conditions. Thus, in the case of one dominat-
ing carrier type and static ∇P
To find a resulting flux of the defects ji , we have to
add this force to the transport equation
ei + ∞ 0 ⋅ Φ
ji = ei E - ηiΦΩ ni i - Di grad ni
while for two types of charge carriers, for example
where ei =
electric charge of the defects
H3O+ ions and L-defects, and static pressure gradient
electric field strength
the electrical field is
r (γ - γ a1)∇P
E = a4
defect diffusion coefficient
(see Evtushenko et al.  and Evtushenko and Pe-
Normally, in solids pressure is not hydrostatic, i.e., σ11 ≠ σ22 ≠ σ33.
stable and growing cracks was calculated in another
Then, instead of eq 20 we should use
publication (Petrenko 1993a). Electromagnetic emis-
Eai(σij) = Eai(0) + γai(σ11 + σ 2 + σ 3) = Eai(0) + γaiσjj
sion generated by such cracks will be described in the
Eai(εij) = Eai(0) + αaiεjj
Equations 2627 show how the defect's activation
volumes can be determined from measurements of the
where αai is a deformation-potential constant of ith type charge carrier.