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Submitted on 1 Jan 1972
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DIELECTRIC DISPERSION OF TGS
G. Luther
To cite this version:
G. Luther. DIELECTRIC DISPERSION OF TGS. Journal de Physique Colloques, 1972, 33 (C2),
pp.C2-221-C2-222. �10.1051/jphyscol:1972276�. �jpa-00215012�
JOURNAL DE PHYSIQUE Colloque C2, supplkment au no 4, Tome 33, Avril 1972, page C2-221
DIELECTRIC DISPERSION OF TGS
G. LUTHER
Institut fiir Experimentalphysik 11,
D-66 Saarbriicken, Universitatscampus 4, Germany
Rbsurnk.
-La dispersion ferroklectrique de TGS est du type Debye avec un simple temps de relaxation. Seulement dans une petite rkgion de temperature autour de To, nous avons trouve une ldgkre deviation qui peut &re due aux imperfections ou inhomogenkites. Le quotient des constantes de Curie dans la region des micro-ondes a ete trouvk kgal a 4,75, ce qui est un peu plus grand que la valeur theorique prkvue par la thkorie thermodynamique. L76nergie d'activation est 0,35 eV dans la rkgion ferroelectrique, tandis qu'elle n'est que 0,02 eV ou moins dans la rkgion paraklectrique, ce qui montre que TGS ne subit pas une transition du type ordre-dksordre.
Abstract. - The ferroelectric dispersion of TGS is of Debye type with a single relaxation time ; only in a small temperature region around To we found a slight deviation, which may be caused by imperfections or inhomogenities. The quotient of the Curie constants in the microwave region was measured to 4.75, which is somewhat larger than the theoretic value predicted by thermodyna- mic theory. The activation energy is in the ferroelectric region 0.35 eV, whereas in the paraelectric region it is 0.02 eV or less, thus indicating that TGS doesn't undergo an order-disorder transition.
In 1962 Hill and Ichiki [I] published their results on the ferroelectric dispersion of TGS. They measured a very large distribution of relaxation times in the whole temperature range. The real part of the dielectric constant,
E ' ,showed a maximum at the Curie point in the whole microwave region. Also the early dispersion measurements on RS [2] gave a broad distribution, but now new measurements [3], [4] proofed, that RS shows a dispersion of Debye-type. We studied the ferroelectric dispersion of TGS, but we could not confirm Hill and Ichiki's results [ 5 ] , [6].
For frequencies up to 10'' cps we used a coaxial system. Particular care was taken for temperature homogenity, therefore we constructed a special sample holder, where the shorting piston is made of two concentric rings. The outer ring is movable and can be set over the sample until to the inner conductor.
Thus a temperature difference between the two faces of the sample is compensated before measuring [6].
The admittance of the sample is received by a reflec- tometer set up.
Experimental results.
-1) Outside of a small region about the transition point the ferroelectric dispersion of TGS is well described by the Debye formalism with a single relaxation time : The E',
E"plots are circles with the center on the real axis. The frequency distribution on the circles is also conform with the Debye-type dispersion. If the relaxation frequency f, is eliminated from the Debye equations
and drawn against the measuring frequency v, it is confirmed that the so receivedf, depends not on v.
2) Approaching the transition point the type of dispersion gradually changes to a slight distribution.
In a very small temperature region from around
0.1 deg around T o this distribution becomes much more pronounced. The development of the distribution angle a is seen from figure 1. The sharp peak at To
55 57 59 61TC'CI
-
L
T G S 1/69 dzll5rnm
FIG. 1. - Development of the distribution angle a
=h - 90"
by approaching the transition point.
can be explained by the assumption of not homoge- neous surface layers. We calculated two models :
a) an equal weighted distribution of the thickness of the surface layer between two borders to and t,.
b) a linear increasing surface layer between to at the center of the cylindrical sample and the thick- ness t, at its edge.
The dispersion of the bulk is assumed to be of the Debye type. In both models there exists at To a dis- tribution of relaxation times, but the range where an evident distribution angle a exists, extends only to 0.1 or 0.2 deg, depending on the relation tilto. Therefore we can by these simple models explain only the sharp peak in figure 1, but not the slight deviation from Debye-formalism which occurs up to the Debye-type region. Perhaps some domains even in the paraelectric region cause additional dispersions, or crystal imper- fections and inhomogenities are the reason for the slight distribution. The largest static dielectric cons- tant, which we obtained at the transition, was some- what larger than lo5.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972276
C2-222 G . LUTHER
3) TGS obeys very well the thermodynamic theory for a transition of second order. It is in the paraelectric region not piezoelectric, therefore TGS shows no remarkable decrease of the dielectric constant up to the ferroelectric dispersion.
The critical slowing down is very accentuated, from 63 0C to To the relaxation frequency drops from 10" cps to lo7 cps. In the ferroelectric region the relaxation frequency grows steeper, because there the dielectric constant is at high frequencies adiabatic and clamped. The quotient of the para- and ferroelec- tric Curie-Constants for the high freque;icy
((static
))dielectric constants was measured to Cp/Cf = 4,75.
It is somewhat larger than the theoretic value obtained from thermodynamic theory, which gives 3.7-4, according to the election of elastic, electrostrictive and thermal constants found in various papers. We believe that the discrepancy shows that there are still some inaccuracies in the elastic, electrostrictive or thermal constants, because Cp/C, is relatively exact measurable. Also Hill and Ichiki [I] obtained with Cp/Cf = 4.5 a larger value than the theoretic one.
4) Just below To the ferroelectric dispersion is immediately followed by a further dispersion, which is in the frequency range of the
((domain wall
))dis- persion reported by Fousek [7] and by Lauginie [S], as shown in figure 2.
FIG. 2. - Cole-Cole plots of TGS in the range 0 . 2 until 2 000 x 1 0 6 cps in the ferroelectric region just below To.
5) The relaxation frequency of the dielectric modul P* = 1 /E* is calculated from
in a double minimum potential, an Arrhenius equation for fa is expected
where AU is the activation energy, k the Boltzmann factor and T the absolute temperature. In figure 3 In f,, calculated from eq. (2) with E, = 9 [9], is drawn against 1/T. In the region, where there is no deviation from Debye type (a = he900 = 0) the scatter of the points is sufficiently small, but around To (h # 0) the measurements are not exact enough, because in eq. (2) the parameter h is in the exponent and a little error in h causes a great error in f,. For the straight lines in figure 3 only the data from the region where the dispersion is of the Debye type are taken into account. Figure 3 shows that in the ferroelectric region
1 1
-3.20 -3.10 Slo3[~-? - -3.00
RG. 3. -Determination of activation energy in the ferro- and paraelectric region ( f a in 109 cps).
the activation energy is about 0.35 eV, whereas in the paraelectric region the activation energy is so small, that we are not sure, if there is anyone at all. In an order-disorder transition the molecular mechanism which causes the polarisation of an elementary dipole is the same in the ferro- and in the paraelectric region.
No abrupt change of the activation energy is then expected at the transition point. We therefore believe, that our experiments are not consistent with the order- disorder &ode1 for the ferroelectric phase transition (2) of TGS.
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