Abstract. â Audio frequency dielectric relaxation measurements are reported over a temperature range 150-250 K for various samples of calcium fluoride doped ...
JOURNAL DE PHYSIQUE
Colloque C 6 , supplément
au rfi 7, Tome 4 1 , Juillet 1980, page C6-458
Electrical relaxation in double doped calcium fluoride and activation volume for the RI relaxation J. J. Fontanella, R. J. Kimble, Jr. and M. C. Wintersgill Physics Department, U.S. Naval Academy, Annapolis, Md. 21402, U.S.A. C. Andeen and M. K. Smith Physics Department, Case Western Reserve University, Cleveland, Ohio 44106, U.S.A.
Résumé. — On rend compte des mesures de la constante diélectrique aux fréquences auditives dans un intervalle de température 150-250 K. On a utilisé des échantillons de fluorure de calcium dopés par deux terres rares différentes. Par conséquent on a étudié la région de la relaxation RI. On a constaté que cette région RI dans les échantillons doublement dopés se compose des contributions des relaxations des échantillons séparément dopés. Ce résultat Tépond à l'opinion courante que cette relaxation est attribuable aux terres rares substituantes isolées accompagnées par des ions fluors interstitiels proches voisins (emplacements tétragonaux). Déplus, on a mesuré la constante diélectrique complexe sous haute pression à 0,4 GPa à la température de 195 K pour les échantillons de fluorure de calcium dopés à l'erbium ou au terbium. Le volume d'activation pour déplacement est évalué à 2,9 ± 0,2 cm 3 /mol en comparaison de la valeur théorique de 2,4 cm 3 /mol calculée par le modèle de diffusion dynamique de Flynn. De plus, les résultats sont comparés au volume d'activation des dipôles Type II en fluorure de strontium, et des dipôles impureté-lacune en fluorure de calcium, récemment déterminés.
Abstract. — Audio frequency dielectric relaxation measurements are reported over a temperature range 150-250 K for various samples of calcium fluoride doped with two different rare-earths. Consequently, the RI relaxation region has been studied. It is found that the RI relaxation region in the double-doped samples is composed only of the RI relaxations found in the singly-doped materials. This is consistent with the usual association of the RI relaxation with a simple point defect consisting of a substitutional rare-earth and a nearest neighbor interstitial fluorine ion (tetragonal site). In addition, the complex dielectric constant for calcium fluoride doped with either erbium or terbium has been measured at pressures up to 0.4 GPa at 195 K. The activation volume for the motion is found to be 2.9 ± 0.2 cm3/mol. For comparison, a theoretical value of 2.4 cm3/mol is calculated using Flynn's dynamical diffusion model. In addition, the results are compared with recent activation volume data for Type II dipoles in strontium fluoride and impurity-vacancy dipoles in calcium fluoride.
1. Introduction. — Following the recent analysis [1] of the RIV relaxation in double-doped calcium fluoride samples, further examination of the results of these studies allows the characterization of the RI relaxation. In particular the effects of using two different rareearth dopants are compared with the results for the individual impurities. The scope of the investigation was further extended by analyzing results of a study of the effects of pressure on the RI region in singly-doped calcium fluoride samples. These results are compared with recent pressure data for sodium-doped calcium fluoride [2] and for strontium fluoride doped with erbium [3]. 2. Experimental procedure. — Samples of calcium fluoride doped with 0.05 mol-% each of the rareearths (a) Nd and Tb, (b) Nd and Dy and (c) Er and Sm are the same samples as were studied previously [1].
The experimental and data reduction techniques used to determine the complex dielectric constant : (1) are the same as described in that paper. The samples used for the high pressure studies, calcium fluoride doped with 0.1 mol-% of either erbium or terbium were the same as those studied previously [4]. The procedures used to arrive at values of the complex dielectric constant at pressures up to 0.4 GPa are the same as described in reference [3]. In the present work, measurements were made at 195 K by using a dry-ice Freon-11 temperature bath. 3. Results and discussion. — 3.1 ZERO-PRESSURE,
— The imaginary part of the dielectric constant for the sample of Nd and Tb doped calcium fluoride over the temperature range DOUBLE-DOPED STUDIES.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19806119
ELECTRICAL RELAXATION IN DOUBLE DOPED CALCIUM FLUORIDE AND ACTIVATION VOLUME C6-459
Table I. - Dipole strength for constituents of the RI relaxatioiz region in double-doped calcium ,fluoride. Impurity '42 (K) A, (K) -
1
Nd Nd Er
2 Tb DY Sm
-
-
8.30 8.97 7.23
5.35 4.70 6.66
Fig. 1. - E" vs. temperature for calcium fluoride doped with 0.05 mob% each of neodymium and terbium. The curves from left to right are for loZ, lo2.', lo3, lo3.' and 104 Hz, respectively.
region in the double-doped samples is composed solely of contributions expected from the singly-doped samples. This is consistent with the usual identification of the RI relaxation with the reorientation of a nearest neighbor fluorine interstitial about a single substitutional rare-earth i.e. a simple point defect.
160-260 K is plotted in figure 1. It is apparent that for each frequency only a single relaxation region is observed. Analysis of the data indicated that the peak was broader than a Debye peak indicating a distribution of relaxation times. An excellent fit to this broadened peak was obtained by simply combining two Debye peaks characteristic of the singly-doped samples. Specifically, it was assumed that :
3 . 2 HIGHPRESSURE, SINGLY-DOPED STUDIES. - For the singly-doped samples, it is found that' the RI relaxation shifts to a higher temperature at a fixed frequency or a lower frequency at fixed temperature with the application of pressure. In order to determine the peak position and hence relaxation time in the present work, the data for E" VS. frequency was fitted by a broadened Debye peak using the Cole-Cole expression [5] :
T CKJ
8''
=
A1 wT1
1+
02T:
A2 +
I
+
or2 m2 r:
(2)
and ri = ( ~ ~exp(Eiikr> 1, .
(3)
The values of the activation energy, Ei, and reciprocal frequency factor, ( T , ) ~ , were taken from a previous paper [4]. The best fits of equation (2) to the data, with the dipole strengths, A,, being the only adjustable parameters, are also shown in figure 1. In figure 2
(EL - &;j)COS (~17~12) E~.p,o=
2 { cosh [(I - or) x]
+ sin (~71.12))
(4)
where X = In ( w ~ and ) in this case .r represents the most probable relaxation time. a is the Cole-Cole parameter and EL and are the low and high frequency limits of the dielectric constant where low and high mean relative to the effects of the relaxation only. Also, it is assumed that
where A is known as the dipole strength and is proportional to the product of the concentration and the square of the dipole moment. Some data for terbium doped calcium fluoride are shown in figure 3 along with the best fits of equation (4).
Fig. 2. - E" vs. temperature for calcium fluoride at 1 000 Hz, doped with 0.05 mol-% each of neodymium and terbium. Also shown are the constituent curves.
the l 000 Hz data and best fit curve are shown with the constituent peaks. The values of A, for the various double doped samples are given in table I. It is clear that the fit is quite good implying that the RI relaxation
Fig. 3. - 8'' vs. frequency at two pressures and 195.1 K for calcium fluoride doped w ~ t h0.1 mol-% of terbium.
C6-460
J. J. FONTANELLA, R. J . KIMBLE Jr., M . C WINTERSGILL, C. ANDEEN AND M. K. SMITH
The variation of the most probable relaxation time with pressure for both samples is shown in figure 4. I N C W S I N G PRESSURE L!
I
Flg. 4. - Ln (7) vs. pressure at 195.1 K for samples of calcium fluoride doped with 0.1 mol-% of erbium and terbium.
The pressure data allow a determination of the activation volume, Vm,which is defined by :
since the relaxation time can be written :
where v, is the frequency with which the interstitial i6n approaches the barrier. Consequently, Vmcan be calculated from :
where
is the approach mode Gruneisen parameter. This quantity is not known exactly. However the approach mode should be similar to the long wavelength transverse optic mode where the lattice of positive ions vibrates in antiphase with the lattice of negative ions. A similar situation has been noted for impurityvacancy dipoles in alkali halides [6]. Consequently, it is concluded that v, = vTo or y, = yTo. The existing experimental values for yT0 are 1.8 [7] and 3.2 [8] and consequently there is considerable uncertainty in the experimental value. However, it has been shown that [9] under the assumption that the Szigetj effective charge, e*, is volume independent, yTo = 2.65. If the usual interpretation of e" as a measure of distortion is correct, the actual value of yTo should be only slightly less than 2.65. This is consistent with a shell model calculation of yTo for calcium fluoride where a value of 2.29 is obtained [lo]. In lieu of a reliable experimental value, it will be assumed that y, = y,, = 2.6. The value of I/,
calculated on the basis of equation (8) for both samples was found to be 2.9 $- 0.2 cm3/mol. This value is approximately the same as found for Type I dipoles in lanthanum doped strontium fluoride, 3.26 cm3/mol [ll]. It is noted that both values are significantly smaller than the activation volume for Type I1 dipoles in erbium doped strontium fluoride. As pointed out elsewhere [ll], the data for Type I1 dipoles should not be interpreted as a general result since the data are for a crystal in which the Type I1 dipole exists alone, SrF, : Er. In particular, the activation parameters indicate [12] that for the case where Type I and Type I1 dipoles coexist, as in gadolinium doped strontium fluoride, the relaxation mechanism may be different from the case where Type 11 dipoles exist alone. In any event, one possible explanation for the difference between the activation volumes for Type I1 dipoles in erbium doped strontium fluoride and Type I dipoles is that the relaxation mechanism is different. Specifically, the relatively low value for Type 1 dipoles may imply that the reorientation proceeds by a concerted or interstitialcy mechanism where the interstitial migrates by replacing a lattice fluorine, etc. [13] while the reorientation for Type I1 dipoles in erbium doped strontium fluoride proceeds by a direct interstitial jump. It might be expected that the former would have a smaller activation volume than the latter since the lattice should be less perturbed by the saddle point configuration. Further theoretical investigation of this point is required, however. The value of 2.9 cm3/mol is, however, larger than the value of 1.7 cm3/mol found for the reorientation of impurity-vacancy complexes in alkali metal doped calcium fluoride [3]. Finally, it is of interest to compare the results with the dynamical diffusion model of Flynn [I41 from which it has been shown that a theoretical expression for the activation volume can be written [2, 31 :
Using the experimental values mentioned above and the value of va(vTo)due to Denham et al. [15], Vm is calculated to be 2.4 crn3/mol which is in reasonable agreement with the experimental value. ' 4. Summary. - In summary, it is found that the RI relaxation region in samples of calcium fluoride doped with two rare-earths is composed only of the RI relaxations found in the singly-doped materials. This is consistent with the usual association of the RI relaxation with a simple point defect composed of a substitutional rare-earth and a nearest neighbor interstitial fluorine ion. In addition, an activation volume for the reorientation process has been determined to be 2.9 $- 0.2 cm3/mol. This value is smaller than the
ELECTRICAL RELAXATION IN DOUBLE DOPED CALCIUM FLUORIDE AND ACTIVATION VOLUME C6-461
activation volume for Type 11 dipoles in strontium fluoride but larger than that for impurity-vacancy dipoles in calcium fluoride. Finally, reasonable agreement is found with a theoretical value calculated using Flynn's dynamical diffusion model.
Acknowledgments. - The authors would like to thank Donald Schuele of Case Western Reserve
University and C. G. Homan of Watervliet Arsenal for their encouragement and help throughout the duration of the work. In addition, they would like to thank Fred Wasem of USNA for his efficient administrative and technical assistance. One of the authors (R.J.K.) was supported by the Naval Academy Research Council. The remainder of the work was supported by the U.S. Army Research Office.
DISCUSSION
Comment. - P. V ~ O T S O S .
this prediction. Another point I would like to point out : the measurements of Prof. Fontanella showed
1 believe that the results of Prof. Fontaneila and his co-workers are very important. The experimental fact that the thermal expansion coefficient and the compressibility of the migration volume vm are quite different than the bulk ones is the important point we have proposed. We have proposed this point two years earlier (J. ~ h ~ s i ~ u e - ~38e t(1977) t. L-455 ; Phys. Rev. 18 (1978) 2683, Phys. Status Solidi 1978) and it is very nice to see measurements to confirm
that -
is not negligible
it is
to vm. This has been predicted by us (Phys. Rev. B 18 (1978) 2683) and it will be useful in the future to give as
separately the contribution - T s l ,
and
gl . T
These experimental results show acc&rding to- ky opinion, that a static calculation technique cannot give a correct value of vm at T > 0.
References [l] ANDEEN,C., MATTHEWS, G. E. Jr., SMITH,M. K. and FONTANELLA, J., Phys. Rev. B 19 (1979) 5293. [2] FONTANELLA, J., WINIERSGILL, M. C. and ANDEEN,C., Phys. Status Solidi, to be published. [3] ANDEEN, C., HAYDEN, L. M. and FONTANELLA, J., Phys. Rev., B 21 (1980) 794. [4] ANDEEN, C., LINK,D. and FONTANELLA, J., Phys. Rev. B 16 (1977) 3762. [5] SMYTH,C. P., Dielectric Behavior and Structure (McGraw-Hill, New York) 1955, p. 69. R. G., J. Phys. C : Solid State [6] DRYDEN,J. S. and HEYDON, Phys. 11 (1978) 393. [7] FERRARO, J. R., HORAN,H. and QUATTROCHI, A., J. Ckem. Phys. 55 (1971) 664.
R. P., J. Phys. C : Sold State Phys. 4 (1971) 3083. [8] LOWNDES, [9] ANDEEN,C., SCHUELE, D. and FONTANELLA, J., Phys. Rev. B 6 (1972) 591. [lo] RUPPIN,R., J. Phys. Chem. Solids 33 (1972) 83. [ l l ] ANDEEN,C., WINTERSGILL, M. C. and FONTANELLA, J., J. Phys. C :Solid State Phys., to be published. [12] FONTANELLA, J., JONES,D. L. and ANDEEN,C., Phys. Rev. B 18 (1978) 4454. [I 31 CATLOW, C. R. A., J. Phys. C : Solid State Phys. 9 (1976) 1845. [14] FLYNN,C. P., Point Defects and Dzffusion (Clarendon Press, Oxford) 1972. [15] DENHAM,P., FIELD,G. R., MORSE,P. L. R. and WILKINSON, G. R.,PTOC.Roy. Soc. Lond. A 317 (1970) 55.
