Dielectric properties of ionic conductors : Yttria stabilized zirconia and forsterite

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Dielectric properties of ionic conductors : Yttria stabilized zirconia and forsterite

B. Cales, P. Abelard

To cite this version:

B. Cales, P. Abelard. Dielectric properties of ionic conductors : Yttria stabilized zirconia and forsterite.

Journal de Physique Colloques, 1980, 41 (C6), pp.C6-462-C6-464. �10.1051/jphyscol:19806120�. �jpa- 00220028�

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Dielectric properties of ionic conductors : Yttria stabilized zirconia and forsterite

Abstract. — Two ionic conductors : yttria stabilized zirconia and nonstoichiometric forsterite were studied by an impedance complex method. For both materials, this technique allows us to separate, on each side of a caracteristic frequency w^c, two domains corresponding to different relaxation mechanisms. The frequency a>^c has been identified as the jump frequency of the charge carriers. The frequency dependence of the dielectric permittivity, below and above coc, has been discussed on the basis of a new model recently introduced by Jonscher.

1. Introduction. — The interpretation of electrical conductivity measurements of ionic conductors is often uneasy, due to polarisation or barrier pheno- mena at the electrode-material interfaces [1], grain boundaries or microstructure effects [2]. The complex impedance technique [3] makes apparent these different contributions to the electrical conductivity and permits at the same time the study of the dielectric properties of the material itself. Thus two ionic conductors yttria stabilized zirconia (0.85 Z r 0²- 0.15 Y²0³) and non-stoichiometric forsterite (0.99 Mg²SiO⁴-0.01 Si0²) have been studied this way.

The nature of the mobile species, oxygen vacancies in yttria stabilized zirconia and magnesium vacancies in forsterite, their concentrations (0.15 and 0.02 respecti- vely) and the structure of the compounds (cubic and orthorhombic) are quite different but their dielectric properties appear to be very similar and makes the comparaison interesting.

2. Experimental. — The yttria stabilized zirconia specimens used, were Czochralski grown single crys- tals. The forsterite ones are polycristalline and syn- thesized from very pure oxyde powders (Johnson- Matthey), by solid state reactions. They are diskshaped and coated with platinum paste. A variable frequency alternating field (0.5 Hz-100 kHz) is applied and both real and imaginary parts of the sample impedance are measured with a double lock-in amplifier. The

temperature ranges investigated here are 373 K- 573 K for yttria stabilized zirconia and 673 K-l 173 K in the case of forsterite.

3. Impedance results. — In figure 1, the experi- mental results obtained for yttria stabilized zirconia are displayed in the complex impedance plane. The points are distributed along circles, the centers of which are depressed below the real axis by an angle a, independent of temperature. In the case of forsterite,

Fig. 1. — Complex impedance plots lor yttria stabilized zirconia 0.85ZrO2-0.15 Y203.

the same features may be observed but the angle is slightly smaller, of the order of 9° instead of 14°.

This angle a, cannot be explained on the basis of the JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 7, Tome 4 1 , Juillet 1980, page C6-462

B. Cales

Centre de Recherches sur la Physique des Hautes Températures, CNRS, 45045 Orléans-Cedex, France P. Abelard

Laboratoire de Géochimie Minéralogie, Université d'Orléans, 45045 Orléans, France

Résumé. — Deux conducteurs ioniques ". une zircone stabilisée à Foxyde d'yttrium et une forstérite non stoechiométrique, ont été étudiés par la méthode d'impédance complexe. Pour les deux matériaux cette technique nous a permis de séparer, de part et d'autre d'une fréquence caractéristique ioc, deux domaines distincts corres- pondant à des mécanismes de relaxation différents. La fréquence a>c a été interprétée comme la fréquence de saut des porteurs de charges. Dans chaque domaine, la variation en fréquence de la permittivité diélectrique a été étudiée sur la base d'un nouveau modèle récemment introduit par Jonscher.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19806120

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DIELECTRIC PROPERTIES OF IONIC CONDUCTORS : YTTRIA STABILIZED ZIRCONIA AND FORSTERITE C6-463

simple theory of Debye with one relaxation time [4].

A very broad distribution of relaxation time may be involved 15, 61 but then we do not know what physical processes are involved. In the next paragraph a new model proposed by Jonscher [7] will be considered.

The intersection of the circles with the real axis gives the bulk resistance of the material. In the temperature ranges considered, the electrical conductivity follows for both materials an Arrhenius law :

In each case the value of the pre-exponential term a, and the activation energy hE are in good agreement with previous litterature data [8, 91.

4. Dielectric properties. - Considering the bulk properties of the materials, the complex permittivity

~ * ( w ) may be deduced from the admittance Y*(w) measurements [7] :

pounds and higher below w, ( n

-

0.86) than above (rz

-

0.63); this corresponds to an increase of the energy loss

[A.

As first noted by Jonscher [lo] the Kramers-Kronig relations implie that the real part ^6'obey to the same frequency law than ^E". Finally the dielectric function can be written as [7] :

where ^E, is the constant value of E' approached at hlgh frequency and A a constant.

At low frequency, below m,, it may be shown that

E, can be neglected and indeed the real and imaginary parts of &*(a) in logarithmic coordinates are well represented by two parallel straight lines. In this case, as predicted by Jonscher [7], the value of n may be correlated very easily to the angle a previously defined :

cr = (iz - 1) 900

The high frequency region and the critical frequency where R, is the bulk resistivity of the sample, C , its are not apparent on the complex impedance plot vacuum geometrical and the (Fig, 1) eventhough 8, is not negligeable in this pad The figure 2 presents the variations of the real ^E'and but the corresponding curve does not depart very much of a circle. Thus the complex impedance repre-

log w

Fig. 2. - Frequency dependence of the real E' and imaginary E"

parts of the dielectric permittiv~ty : a) non stoich~ometric forsterite, b) yttria stabilized zirconia.

sentation, although often used, does not seem the most suitable.

5. Interpretation of o,. - On figure 2 it may be observed that the critical frequency a, is a temperature dependent parameter. An Arrhenius plot of Log w, versus l / T shows that w, is thermally activated with the same activation energy as the electrical

imaginary r" parts of the complex permittivity as a

I I

viour. On the plot of the part ' " 9 distinct Fig, 3, - Critical frequency ( .) and conductivity (0) against

frequency regions may be clearly distinguished below temperature.

and above a critical frequency w,. In each region the data are well fitted by the relation :

function of frequency at different temperatures for

& l l = 1 O < i 2 < 1 ( 2 ) conductivity (Fig. 3) and this is verified for both

compounds. So we may assume that co, corresponds where B and n are constants. Furthermore it may to the jump frequency of the mobile species, that is be noticed that n is almost the same for both com- magnesium vacancies in forsterite, oxygen vacancies

I I I I

both materials. They show indeed very similar beha- 1.2 1.3 1.4 1.5 10~111~)

_I

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C6-464 B. CALES, P. ABELARD

in the case of yttria stabilized zirconia. From simple random walk theory [I 11, the electrical conductivity is given by the relation :

where N denotes the defect concentration, q the charge of the mobile species, ( 1' ) the mean square displa- cement, k , the Boltzman constant. In figure 4 the electrical conductivity calculated this way is compared

Flg. 4. - Electrical conductivity v e r ~ u ~ temperature for yttria stabilized zirconia : A experimental data, o calculated values.

to experimental values deduced from complex impedance measurements. The very good agreement in the case of yttria stabilized zirconia allows us to conclude that o, is effectively the jump frequency of charge carriers. The same conclusion can be drawn in the case of forsterite although it is not cubic and that two slightly different mean square displacements must be considered.

6. Conclusion. - The complex impedance technique permitted us the simultaneous study of the electrical conductivity at low temperature and of the dielectric properties of two ionic conductors. Above and below the jump frequency of the mobile species, the dielectric properties are different and two relaxation processes must be involved. Above w,, the electric field is alternating too fast and the charge carriers remain probably localized in the vicinity of a dope ion. On the opposite below o,, charge transport is possible on a large scale. Furthermore, we note that although very different, the two ionic conductors have in common a high concentration of defects and many body interactions may be impor- tant. Then the Debye theory is no longer applicable.

In the case of the two studied compounds the model of Jonscher [12] fits very well the data in the frequency region investigated here.

DISCUSSION

Comment. - N. BONANOS. the corresponding complex permittivity plot for You successfully used the complex impedance studying the frequency dependance of your dielectric technique to extract conductivity data. Why not use data ?

References

[I] SCHOULER, E. and KLEITZ, M., J. Electroanal. Chem. 64 (1975) 135.

[2] CHU, S. H. and SEITZ, M. A , , J. Solid State Cornmuti 2 1

(1978) 297.

[3] BAUERLE, J. E., J. Phys. Chem. Solids 30 (1969) 2657.

[4] DEBYE, P., Polar Molecules, The Chemical Catalogue Company (Dover Publications, New York) 1929.

[5] COLE, K. S. and COLE, R. H., J . Chem. Phys. 9 (1941) 341.

[6] Fuoss, R. M. and KIRWOOD, J. G., J. Am. Ceram. Soc. 24 (1941) 385.

[7] JONSCHER, A. K., Phys. Status Solidt (a) 32 (1975) 665.

[8] ETSELL, T. H. and FLENGAS, S. M., Chem. Rev. 70 (1970) 339.

[9] MORIN, F. J., OLIVER, J. R. and HONSLEY, R. M., Phys. Rev.

B 16 (1977) 4434.

[lo] JONSCHER, A. K., Nature 253 (1975) 717.

[ I l l TALLAN, N. M., Electrical Conductivity in Ceramics and Glass ( H . Dekker Inc., New York) 1974.

[12] NGAI, K. L., JONSCHER, A. K. and WHITE, C. T., Nature 277 (1979) 185.