ON SOME POSSIBILITIES OF DETERMINING THE VOLUME OF KÄNZIG REGIONS IN FERROELECTRICS

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ON SOME POSSIBILITIES OF DETERMINING THE VOLUME OF KÄNZIG REGIONS IN

FERROELECTRICS

Dr. Rolov

To cite this version:

Dr. Rolov. ON SOME POSSIBILITIES OF DETERMINING THE VOLUME OF KÄNZIG RE- GIONS IN FERROELECTRICS. Journal de Physique Colloques, 1972, 33 (C2), pp.C2-257-C2-258.

�10.1051/jphyscol:1972289�. �jpa-00215025�

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JOURNAL DE PHYSIQUE

Colloque C2, supplkment au no 4, Tome 33, Avril 1972, page C2-257

ON SOME PO S SIBILITIE S OF DETERMINING

THE VOLUME OF KANZIG REGIONS IN FERROELECTRICS

Dr. B. N. ROLOV

Chair of Theoretical Physics Latvian State University, 19, Rainis blv., Riga, U. S. S. R.

R6sumB.

- Nous avons considkrk plusieurs mkthodes pour dkterminer le volume des rkgions de Kiinzig dans les ferroklectriques

B

partir de differentes donnkes exp6rimentales (thermiques, Blec- triques, dynamique des cristaux). Nous discutons les aspects thkoriques des diffkrents phenomknes.

Abstract. - Several methods for determining the volume of Kanzig Regions in ferroelectrics from different experimental data (thermal, electrical, dynamic of crystal, etc.) are considered.

Theoretical aspects of different cooperative phenomena are discussed.

Diffuse ferroelectric phase transitions (D. F. P. T.) are regarded at present as a rather common pheno- menon. Since there is no general molecular theory of the phase transitions so far, their nature has to be explained on the basis of some phenomenological model. The most elaborated in this respect is the Model of Kanzig Regions (M. K. R.) [I], [2] according to which a ferroelectric near its phase transition point is assumed to be comprised of a number of so called Kanzig Regions (K. R.). Such regions have been first observed experimentally by W. Kanzig 131, and to the present time there is a number of considerations suggesting that the K. R. behave like equilibrated thermodynamical systems. A direct confirmation to these conclusions recently has been provided by G. Shirane and collaborators [4] having observed quasi- elastic scattering of slow neutrons on polarization seeds which the authors [4] refer to as critical fluctuations.

The volume of the K. R. is one of the parameters determining the degree and the nature of D. F. P. T.

For this reason the estimation of the volume of K. R.

is of doubtless interest. The linear dimensions of the K. R. first were determined from X-ray data by Kanzig and appeared to be 1 0 - ~ - 1 0 - ~ cm [3]. All of the existing methods for estimating the volume of the K. R. at present are based essentially on a number of principles which can be conditionally classified into several groups as follows hereafter.

lo

Different models according to which the calcu- lated or measured experimentally quantities depend on the volume v, of an individual K. R. as a physical parameter. In this case experimentally measured values of the corresponding physical quantities may be used to determine the volume v,. The anomalous heat capacity C,(T) is considered as a particular example of this kind. According to the M. K. R. three methods may be offered to determine the vk [5], [6], 171. The first exists in calculating the v, from maximum value of the ano- malous capacity Ca ,,,

:

where k is the Boltzman factor Tk-the Curie tempera-

ture, Qo-transition heat. The other method is related to the half-width

⁷

of the curve Ca(T)

:

The third method of estimating the v, is based on finding the switching function n/N(T) from the anoma- lous heat capacity. It gives

:

where AT

=

T, - T. This method, in distinction to the first two, enables to obtain the

v,

as a function of temperature v,

=

vk(T).

The calculations of vk by means of formulae (I), (2) and (3) on the basis of experimental data for BaTiO, and solid solution (Ba,-,, Sr,)TiO, are presented in tables I and I1 correspondingly.

In a similar way the value of

v,

can be estimated

Experimental data v, x 1019 ccm according

source expression

-

(1)

-

(2)

-

(3)

Blattner, Merz 181 1.9 1.5 1.7

Volger [9] 14.6 17.3 6.4

Shirane, Takeda [lo] 3.1 2.7 1.7 Kanzig, Maikoff [ l l ] 1.9 1.8 2.0 Borman, Strukov,

Taraskin, Fritzberg [12] 13.3 11.5 16.5

Concentration x in

v,

x 1019 ccm according

solid solution expression

(Ba, -,, Sr,)TiO, [12]

-

(1)

- (2)

A

(3)

A

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972289

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C2-258 DR. B. N. ROLOV from experimental data on some other physical

characteristics of ferroelectrics. The basic results are given in table 111.

As it is seen from the calculations most of experimental data yield the value of vk

=

10-19-10-18 ccm.

Physical phenomena - X-Ray scattering [3]

Polarization [13], [14], [15], [16], [171, 1181

Dielectric permeability [13], [14], [151,[191

Heat capacity [51,[61,

PI,

[151,

P O I ,

[211

Thermal expansion [5], [20], [22], 1231

Thermal conductivity [24], [25]

Polarization switching and hyste- resis [26]

Vk x loL9 ccm - 10-lo4 2-10 1-90 0,9-17

2-10 1-10 1,9-19 20 If the

K. R.

is considered as a seed of a new phase, the theory of heterophase fluctuations can be applied. In this case the volume of

K.

R., as a rule, is determined by relation between the bulk and surface energies of the seed. The accuracy of calculations of vk by these methods is determined by the accuracy of the surface and bulk energies of the particular ferroelectric material. As a rule, the major difficulties arising

here are related to the surface energy which can be found in an indirect way only and has a rather wide dispersion of values. If -the conventional values of energy are used, the volume of the seeds

(K. R.)

is find to be of the order 10-19-10-18 ccm [20], [21], [27].

30 The estimation of the size of

K. R.

can be made on the basis of some considerations of the dynamic theory of crystal lattice,

e.

g. from amplitudes of ion oscillations and areas of coherent rearrangement 1281,

[29], 1301, [31]. This approach yields uk w 10-19-10-17 ccm

.

A farther progress in these methods is likely to be expected with some ideas of

W.

Cochran,

R.

Cowley,

N.

Bogolubov and others.

These experimental observations thus suggest that in the case of ferroelectric phase transition of a funda- mental importance are the

K.

R. the origin of which is likely to be related to the display of cooperative phenomena. From this point of view the different appea- rances of these phenomena and the names found in different sources (fluctuations, critical fluctuations, heterophase fluctuations,

K.

R., areas of coherent rearrangement, correlation radius, etc.) can be assumed to have essentially a common basis.

It should be noticed that a more detail study of the part played by cooperative phenomena in ferroelectric phase transitions requires proper experiments to be performed. Especially it concerns the effects of different conditions (pressure, composition, etc.).

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Nauk. S . S. S . R., ser. fiz., 1964, 28, 649 ; 1965, 29, 1019.

R o ~ o v (B. N.), Proceedings of the International Meeting on Ferroelectricity, 1, Prague, 1966, 154.

KANZIG (W.), Helv. Phys. Acta, 1951, 24, 175.

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R o ~ o v (B. N.). Izv. Akad. Nauk. S. S. S. R., ser. fiz., , - .

1969, 33,227.

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tekh.

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[20] HOTSCHENKOV (A. G.), Thesis, Ped. Institute Kalinin, 1969.

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