Under action of garmonic electrical field with intensity icon

Under action of garmonic electrical field with intensity



НазваниеUnder action of garmonic electrical field with intensity
Дата конвертации28.08.2012
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Under action of garmonic electrical field with intensity

E(t) = Eo exp(i  t)

which are weaker than a depolarized field Eds created by the spontaneous polarization

Ps = -o d Eds the transition temperature Tt (Ed (X)), approximately does not depend on displacement Х in (69) . The movement equation has a constant factors

(79)

Its solution is represented by decomposition in a Fourie series on plane waves



The neglect of spatial dispersion for enough low frequencies and substitution of this decomposition in the equation of a movement give



for each established harmonic oscillation

(80)

The polarization in moment t arising under action of a molecular field which delay from the moment t '



gives the contribution in the complete polarization



Multiplication on (dt/tr) exp(i  t), where tr is a time of relaxation of elasticity of polarization, and the integration on dt



gives Fourie component of polarization



and of susseptibility

(82)

In quasistatic stationary processes the susceptibility does not depend on time t, and depends only on delay t-t ' and the integral on dt is brought in the integral on dt ' [15]. The time t can be anyone, in particular t = 0

(83)

Far from phase transition the own frequency s() oscillations of soft sublattice is in infra-red area, and close to frequency of stabilization. It has the order of return time of relaxation of the module of stabilization elasticity. At low frequencies, when forces of inertia smaller than elastic forces, which are relaxed with delay = t-t' , polarization is determined by a retarded susceptibility

gif" name="object11" align=absmiddle width=322 height=22> (84) Where tr =1/ - scale multiplier ensuring performance of a boundary condition which is coincidence of a susceptibility with zero frequency with a static susceptibility. It gives for a Fourie-making susceptibility the expression

(85)

With T < Tt , b = 0,  - f << a,





(86)

(87)

with a low frequansis





dispersion is absent, and the absorption grows with growth of frequency

with high frequencies



susceptibility decreases with growth of frequency



and the absorption remains constant with growth of frequency

With Tc < T< Tt , b = 0,  (To-T)+ - f = (T-Tc)





(88)

with low frequencies





dispersion is absent, and the absorption grows with growth of frequency

with high frequencies



reaches a minimum about T = Tt



with growth of temperature the susceptibility reaches a minimum near the temperature of phase transition, and the absorption decreases with growth of frequency

With T> Tt a = 0,  - f = 0 in own ferroelectrics Tc < Tt << To the phase transition does not mention stabilization

(89)

with low frequencies

,

dispersion is absent, and the absorption grows with growth of frequency

with high frequencies

,

the susceptibility is decreased and the absorption is increased with growth of frequency about reached a maximum and decreases with much frequency.

The velocity of relaxation of polarization smaller than the high frequence and the maximum of a susceptibility with growth of frequencys is reduced to minimum with heating to temperature of phase transition Tt with high frequencies.

Then it increases to a maximum and decreases under the Curie-Wisse law. A maximum of absorption with growth of frequency raises, as with T = Tt all frequencies high that is coordinated with the experienced data [1,2] for Pb3 Mg Nb2 O3..

The association of all special cases by one interpolation dependence with the help of the

generalized Hevisid function gives

,



(90)



With temperatures which are in the interval T = (0-200 K) and



(91)

(a)

Fig. 4. Dispersion of dielectric susseptibility (a) dependence on temperature.




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