The polarization of a crystal is an electrical current of density icon

The polarization of a crystal is an electrical current of density



НазваниеThe polarization of a crystal is an electrical current of density
Дата конвертации28.08.2012
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The polarization of a crystal is an electrical current of density

(92)

which allocates, and with negative friction absorbs quantity of heat dQ under by action of a Lorenz - Wise field with intensity El

(93)

Polarization under action of an external electrical field is connected by absorption of heat

(94)

(95)

Where - difference of potentials, enclosed on the condenser, of potentials, d- distance between it surfices.

(96)

The electrocaloric effect is maximal near to phase transition, where a dielectric susceptibility changes maximum quickly, that is conditions of excitation of autooscilla-

tions of polarization.

The power, taked away from a ferroelectric sample , shunted by the loading with resistance R, by the auto oscillations of polarization P (t) or by its compelled oscillations, which are the oscillations of an electromagnetic field in the condenser formed by surfaces of a sample, with capacity C, is allocated on resistance of loading R. These oscillations in a circuit of sample and of loading create the electromoving force E, which is equal to the sum of voltages on loading and on the internal resistance of the sample Ri, and the current which is equal to the polarization current

E = j R + j Ri (97)

and electrical current by force, equal to force of a current of polarization

j = dP/dt

current through that internal resistance E = Ri dP/dt

(98)

which transfers through a surface of a sample a charge dq = C dU = C (Ed h). It is determined by a voltage on surfaces of the specified condenser, distance between which is equal h, or by intensity of a depolarizing field in a sample Ed = Edo - En. This intensity develops of intensity in absence of shunting loading Edo and the opposite intensity created by the voltage Un on the loading En. = Un/h = j R/h

On the other hand



gif" name="object11" align=absmiddle width=301 height=38> (99)

To the moment of supervision t the intensity of a field in a sample is equal



With R = 0, Ed = 0. A crystal shortly close and the depolarizing field in it is absent. With in a free crystal the depolarizing field is maximum.

The decreasing of Ed by the shunting load increases the phase transition temperature Tt, and increasing - decreases it. The cooling of the sample increases the polarization, and with it reduces Tt after reduction of temperature Т, that supports conditions of occurrence of auto oscllations. The selection of loading stabilizes these conditions with lowered temperature. Change of temperature is inverse proportion to heat capacity [1]. The selection of a loading resistance provides average shift of temperature from tempera-

ture of transition < Tt -T > such, that in a significant part of a period of oscillations the heat capacity appears rather small that the electrocaloric effect was significant.




Co


C

P Ed Eн


R

Ri


Fig. 2. The installation for detection of dynamic electrocaloric effect.

(100)

The selection of resistance of loading provides average shift of temperature from temperature of transition < Tt -T > such, that a significant part of a period of oscillations the heat capacity appears rather small, that the electrocaloric effect was significant.

With temperature Т, which is close to temperature of transition Tt, parameter of absorption of the electromagnetic energy of a compelling variable field becomes negative. This aspiration is visible from curves of dispersion , fig. ,and from the experienced data for barium titanat [1,2,3]. The unsufficient resolution on temperature in these experiences was not allowed to find out negative absorption.


CONCLUSION

1. The ferroelectric phase transition is relaxation process of the elasticity of soft sublattice and polarization of crystal from the unstable initial phase to the equilibrum final phase.

  1. The properties of ferroelectrics essentially depend on their sizes and their form through influence of depolarizing field on phase transition temperature.

3. The depolarizing field with intensity which proportional to the polarization reduсes the phase transition temperature, but the decay of polarization causes its growth. There are autooscillations of polarization

4. The law of polarization relaxation due to a positive feedback of polarization and Lorentz -Wise field with small polarization determines force of negative friction, and with polarizations which exceed the spontaneous polarization determines a force of positive friction in the equation of a movement.

5. The solution of this equation shows existence of avtooscillations of polarization with temperatures close to temperature of phase transition.

6. The shunting of a ferroelectric sample by the loading resistance results to dynamic electrocaloric effect, which is stabilized due to decrease of temperature of phase transition by increase of intensity of depolarizing field.

  1. The selection of resistance of loading provides an average shift of temperature from temperature of transition < Tt -T > such, that in a significant part of a period of oscillations the heat capacity appears rather small that the electrocaloric effect is significant.

LITERATURE

1. M.E. Lines, A.M. Gluss. Ferroelectrics and related materials.М. Science, 1985, 736 с.

2. Acoustic crystals. Ed. M. P.Shаsкkolskaja, М., Science, 1982.

3. B.A. Strukov, A.P. Levanukk. Physical bases of the ferroelectrics phenomena in crystals. М., Science, 1983.

4. L.D. Landau, E. M. Livshitz. Electrodynamics of continuous environments. M. Sience, 1980.

5. V.G. Vaks. Introduction to the micriscopic theory of ferroelectrics. M. Sience,1973.

6. G.A. Smolenski, V.A. Bockov, at all. Ferroelectrics and aniferroelectrics. L. Sience, 1985.

7. A.S. Davidov. The theory of a solid. М., Science, 1976.

8. V.G. levich. Curses of theoretical physics. Т. 2, 1965.

9. A.F.Aleksandrov, A.S. Bogdankevich, A.A. Rukhadze. Foundations of plasma electrodynamics . М., Science, 1978.

10. A.Z. Patashinski, V.L.Pokrovski. Fluctuatig theory of phase transitions. М., Science, 1975.

11. M.N. Galijarova, S.U. Gorin, L.H. Vologirova, A.V. Shilnikov, L.V. Shuvalov. About some features of ferroelectric phase transition in cezium digidrophosfat crystals in connection with their background. Izvestija AN USSR, s. Phys. v. 54, N4, 1990.

12. A.A. Mokejev, An.A.Mokejev. Procedinds of IV international conference: «Cristalls: growth, form, applications ». Aleksandrov, VNIISIMS, 1999.

13. A.A. Mokejev, An.A. Mokejev. Procedinds of V international conference: «Cristalls:

growth, form, applications». Aleksandrov, VNIISIMS, 2001.

14. A.A. Mokejev, An.A. Mokejev. Procedinds of VI international conference: «Cristalls:

growth, form, applications». Aleksandrov, VNIISIMS, 2003.

15. M.L. Rjazanov. Electrodynamics of the condenced substance. M. Science, 1984.

16. J.G. Punnovko. Introduction in the theory of mechanical oscillations. М., Science, 1991.

17. S. De-Groot, G. Masur. Nonequilibrium thermodynamics. M., Mir, 1964.

18. D.N. Zubarjev, V.G. Morozov, G. Repke. Statistical mechanics of Nonequilibrium processions. M. PhysMathLitt. 2002.

19. Ju. A. Brichkov, O. I. Marichev. A.P. Proodnikov. The tables of nondefined integrals. M., Science, 1986.

20. V.P. Djakonov. The directory on MathCad 6 Pro. SK-PRESS, 1997.

21.A.A. Mokejev. www.avtoferelrheo.narod.ru




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