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TRANSPORT IN FLUORITE
STRUCTURESSelf-diffusion and ionic conductivity in SrCl2
M. Bénière, M. Chemla, F. Bénière
To cite this version:
M. Bénière, M. Chemla, F. Bénière. TRANSPORT IN FLUORITE STRUCTURESSelf-diffusion and ionic conductivity in SrCl2. Journal de Physique Colloques, 1980, 41 (C6), pp.C6-213-C6-215.
�10.1051/jphyscol:1980654�. �jpa-00220092�
JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 7, Tome 41, Juillet 1980, page (26-213
TRANSPORT IN FLUORITE STRUCTURES.
Self-diffusion and ionic conductivity in SrCI,
M. BCni&re, M. Chemla
Laboratoire d'Electrochimie, UniversitC Paris VI
and F. Bknibre
Dkpartement de Physique Cristalline, Universitb de Rennes, 35000 Rennes-Beaulieu, France
~&sumk. - Les coefficients d'autodiffusion dans des monocristaux de SrC12 pur ont 6tC mesurks it l'aide des radioisotopes CI-36 et Sr-88 par la methode du sectionnement au microtome. La conductivitk ionique a ttt mesurk simultankment pendant les expkriences de diffusion. Le facteur de corrklation a ktk determine par la relation de Nernst-Einstein. Le rapport de Haven du coefficient de diffusion de C1- au coefficient.de diffusion deduit de la conductivitt est trouvk tgal $0,85 0,03 avec une influence a peine perceptible de la tempkrature dans le domaine intrindque (440-630 OC). Les diffkrents mecanismes de transport possibles sont discutts.
Abstract. - The self-diffusion coefficients in pure SrC12 single crystals have been measured using the radiotracers C1-36 and Sr-88 and the microtome sectioning technique. The ionic conductivity was simultaneously measured during the diffusion runs. The correlation factor was determined through the Nernst-Einstein relation. The Haven ratio of the anion tracer diffusion coefficient to the diffusion coefficient derived from the conductivity measure- ment is found to t%e equal to 0.85 f 0.03 with a hardly significant temperature dependence in the intrinsic range (440-630 OC). The different possible transport mechanisms are discussed.
1 . Introduction. - The last thirty years have seen the development of the investigations of transport properties in the alkali halides to the degree of refi- nement reached nowadays. The logical continuation is now to study the fluorite structures which follow the alkali halides in the scale of complexity. Some early studies have already been achieved in the alka- line earth halides and reviewed by Lidiard [I]. More and more thorough investigations have been publish- ed [2-41 but the very first question of the nature of predominating defect responsible for transport remains open. This basic problem could be solved by two ways : (i) by determining the correlation factor; (ii) by analyzing the basic data of the ionic conductivity or self-diffusion coefficient and deriving the thermodyna- mic parameters of formation and motion of the lattice defects. This is the method to be described for SrC12 in the next paper by Chadwick et al. 151. On the other hand, we have chosen the first method of the correla- tion factor.
2. Theoretical haven ratio. - The major disorder in the fluorite structures is of Frenkel type in the anion sub-lattice [I]. Migration of the anion can be due to any of the three possible mechanisms :
- free vacancy, - direct interstitial,
- indirect non-collinear interstitialcy
.
The corresponding correlation factors have been calculated by Compaan and Haven [6] who found
f
= 0.653, f = 1 and f = 0.985 respectively. Thecorrelation factor can be determined by comparing the tracer diffusion coefficient D* to the conductivity- diffusion coefficient D, defined from the ionic conduc- tivity o through the Nernst-Einstein relation :
where N is the number of ions per unit volume, k, T and e the Boltzmann constant, absolute tempera- ture and electronic charge. Strictly, D* should be taken as the sum of the cation and anion diffusion coefficients. However, the present results confirm those of Hood and Morrison [7] and allow to neglect the contribution of the cation. D* is therefore just equal to the diffusion coefficient of C1-. In fact, the haven ratio defined as D*/D, is not in all cases iden- tical to the correlation factor, in particular for the interstitialcy mechanisms. The theoretical values of this ratio have been reported [8] for the three mecha- nisms :
- 0.653 for the free vacancy, - 1 for the interstitial,
- 0.739 for the indirect non-collinear interstitialcy.
3. Experimental techniques and difficulties. - For an improved accuracy, both quantities D*(CI-) and o are measured simultaneously in a same run in the conductivity cell. D* is obtained by sputtering a layer of SrC12 marked with the radioisotope C1-36 onto both main surfaces of two single crystals. The samples are then coated with platinum deposited by
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980654
C6-214 M . BENIBRE, M. CHEMLA AND F. B ~ N I E R E
evaporation under vacuum. The samples are heated at constant temperature and the conductivity is measured and recorded during all the time of the diffusion anneal. The marked advantage of this pro- cedure is to cancel out the uncertainty on the tempe- rature, which would strongly affect the results because of the high activation energy.
Any trace of water must also be absolutely excluded.
At the beginning of the diffusion anneal, the unavoi- dable water traces present on the crystal are removed by a liquid nitrogen trap. This works efficiently as the crystal is hot and under vacuum. In addition, an atmosphere of HC1 gas is then introduced in the cell to prevent any formation of oxides, hydrates or oxichlorides.
The diffusion coefficient is then measured by the microtome sectioning method. However, the section- ing has to be done quickly after the silica cell is open.
Otherwise, the crystal becomes breakable at the surface under the microtome blade, probably because of the formation of dislocations due to a new unavoi- dable absorption of traces of water.
4. Results and discussion. - As the experimental values of D"(C1-) and o are reported elsewhere [8], we focus on the resulting Haven ratio. The average of the measurements taken at nine different temperatures in the range 440-630 O C is :
The influence of temperature is small : the ratio only increases by a few
%
with temperature in this range. It coincides therefore with none of the values corresponding to the pure possible elementary mecha- nisms (Fig. 1). This is a common situation where two or more mechanisms have to be considered simul- taneously. From the results obtained by doping the crystals [2, 51 as well as theoretical calculations [4], one might have expected the vacancy to play the major role, for which the value of 0.65 should have been found for the Haven ratio. The different possible complementary mechanisms are illustrated in figure 1 :- Contribution of the cation to the conductivity : Excluded because of the relatively very low cation self-diffusion coefficient (measured with Sr-88).
- Contribution of vacancy pairs to diffusion of C1- : Excluded also because of the negligible mobility of the cation.
- Contribution of impurity-vacancy pairs : Excluded in this intrinsic range of highly pure crystals.
- Contribution of the cyclic exchange mechanism as suggested by Catlow et al. [4]. This is a possible mechanism in the anion sub-lattice of the fluorite structure provided the cycle includes both lattice sites and interstitial sites [8].
- Contribution of interstitial-vacancy pairs : This would also increase the Haven ratio to a value higher
Fig. 1. - Haven ratio resulting from combination of the different possible migration mechanisms in the anion sub-lattice in the fluorite structure.
than 0.65. In fact, the easiest way for the pair to move is by exchange of sites of the ion between the inter- stitial and the vacant sites. In other words, the motion would imply a permanent process of formation and recombination of the pair. Finally, this is equivalent to the preceding hypothesis of the cyclic exchange mechanism [8].
- Last, but probably not least, one may. consider that the interstitials - which are in same number as the vacancies in the intrinsic range - also take place in the anion motion. This is in fact the conclusion of the next paper to be presented by Chadwick et al. [5].
In their data analysis, they obtain almost equivalent transport numbers for the vacancies and the inter- stitial~, though they assume that the interstitial moves by the interstitialcy mechanism. If one would rather consider equivalent transport numbers but the direct interstitial mechanism, one would obtain :
a value consistent with the present results.
5. Conclusion. - There seems to be at the present stage two possible interpretations : (i) A vacancy contribution of 80
%
with a contribution of an exchange mechanism of 20%,
or (ii) Almost equal contributions of the vacancies and the interstitials assuming a direct mechanism. In this later caseSELF-DIFFUSION AND IONIC CONDUCTIVITY IN SrCl2 C6-215
however, the higher migration enthalpy (about 1 eV) (i) dominant vacancy : H{ = 2.98 eV [8] in agree- than for the vacancy (about 0.33 eV) has to be com- ment with the specific heat data of Schroter and pensated by a corresponding extremely high migra- Nolting [9];
tion entropy. (ii) comparable vacancy and interstitial : The resulting value for the Frenkel defect formation H{ = 2 eV [5] as found by Chadwick et al. in agree- energy also depends on the model: ment with the calculation of Bendall [10].
DISCUSSION
Question. — L. HEYNE. Question. — M. J. GIIXAN.
Did you find an influence of the H O pressure that You find a value of about 3 eV for the Frenkel was applied ? In order to define the solid's deviation formation energy in SrCl2. In general, throughout the from stoichiometry in a thermodynamically exact way series of fluorite crystals, there is a constant ratio one should fix the Cl2 partial pressure (or the partial between the Frenkel energy and the superionic tran- pressures of a H2/HC1 mixture). The validity of the sition temperature. Your value would not fit in with assumption of ideal stoichiometry could be checked this. Do you have any comment ?
by showing that the results do not depend on the gas atmosphere.
Reply. — F. BENIERE.
Results obtained in three different laboratories Reply. — F. BENIERE.
(Clermont-Ferrand, Canterbury and Paris) and under H( = 3 eV is obtained when one assumes a domi- different atmospheres closely agree in the present nant vacancy mechanism and 2 eV with an equivalent temperature range. They therefore do not seem to contribution of the interstitials. Further experimental depend on the gas atmosphere. evidences.
References
[1] LIDIARD, A. B., in Crystals with the Fluorite Structure, edited [6] COMPAAN, K. and HAVEN, Y., Trans. Faraday Soc. 54 (1958) by Hayes, W., p. 101, Clarendon Press, New York (1974). " 1498.
[2] GERVAIS, A., JAQUET, M. and BATHIER, M., J. Physique Colloq. [7] HOOD, G. M. and MORRISON, J. A., J. Appl. Phys. 38 (1967) 37 (1976) C7-281. 4796.
[3] CARR, V. M., CHADWICK, A. V. and SAGHAFIAN, R., J. Phys. [8] BENIERE, M., CHEMLA, M. and BENIERE, F., J. Phyt. Chem.
C. Solid State Phys. 11 (1978) L-637. Solids 40 (1979) 729.
[4] CATLOW, C. R. A., NOKGETT, M. J. and Ros"s, T. A., J. Phys. [9] SCHROTER, W. and NOLTING, J., / . Physique Colloq. 41 (1980) C. Solid State Phys. 10 (1977) 1627. C6-20.
[5] CHADWICK, A. V., KERWOOD, F. G. and SAGHAFIAN, R., t1 0l BENDALL, P. J., / . Physique Colloq. 41 (1980) C6-61.
/ . Physique Colloq. 41 (1980) C6-216.
