Towards a self-consistent set of defect parameters for KCl

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Towards a self-consistent set of defect parameters for

KCl

L. Acuña, P. Jacobs

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 7, Tome 41, Juillet 1980, page C6-72

Towards a self-consistent set of defect parameters for KCl

L. A. Acufia (*) and P. W. M. Jacobs (*)

Departments of Physics and Chemistry, University of Western Ontario, London, Ontario N6A 5B7, Canada

RBsumC. - On a analyse des nouvelles donnkes experimentales sur la conductivite ionique du KC1 pur et du KC1 dopk par des ions Sr2+ ou SO:- en employant quatre modkles de defauts. 11s sont : (1) le modkle conventionnel des dkfauts de Schottky avec residus d'impuretks M Z f dans les cristaux purs et dopes par SO:- ; (2) une modification du modkle (1) dans laquelle on admet que dans les cristaux purs il y a des irnpuretts qui sont aussi bien des anions bivalents que des cations bivalents ; ( 3 ) une modification du modkle (1) dans laquelle on adrnet que les enthalpies et les entropies des defauts peuvent dependre de la temperature ; (4) un modkle qui admet que dans le KC1 il y a des dkfauts de Frenkel dans les sous-rkseaux aussi bien des cations que des anions outre les dkfauts de Schottky qui predominent. On a tirk avantage des rksultats des derniers calculs theoriques sur les Bnergies des defauts dans l'analyse avec I'ordinateur des donnees experimentales. Seulement le modkle (4) conduit a une analyse qui s'accorde avec les donnkes expkrimentales sur la conductivite.

Abstract.

-

New experimental data for the ionic conductivity of pure KC1 and for KC1 doped with SrZ+ or SO:- ions have been analysed on the basis of four defect models. These are : (1) the conventional Schottky defect model with residual M Z + impurity in the pure and SO:- doped crystals ; (2) a variant of model (1) in which pure crystals are supposed to contain both divalent-anion and divalent-cation impurities ; (3) a variant of model (1) in which the defect enthalpies and entropies are allowed to be temperature-dependent ; (4) a model which supposes that in KC1 there are Frenkel defects on both the cation and anion sublattices in addition to the predominant Schottky disorder. Full advantage has b-een taken of the results of recent theoretical calculations of defect energies in the computer analysis of the experimental data. Only model (4) leads to a consistent analysis of the experimental conductivity data.

1. Introduction. - Although there have been exten- sive measurements of the transport properties of KC1 [I-81 no generally accepted solution has been given to a problem that concerns the magnitude of the anion defect parameters. When the traditional Schott- ky defect model is used [4] to analyse conductivity data which cover the whole temperature range, the resulting values for the anion transport parameters are inconsistent with those derived from measure- ments of chloride ion diffusion coefficients [2]. Although BkniGre, Chemla and BkniGre [6] success- fully used this same Schottky defect model (including the association of M2+ impurity ions with nearest- neighbour cation vacancies and the formation of anion vacancy-cation vacancy pairs) in their combined fitting of ionic conductivity and diffusion data for KC1 in the intrinsic region, it should be emphasized that the discrepancies between the values of the anion transport parameters, as determined from diffusion and separately from conductivity, show up only when the whole conductivity curve is analysed, including both intrinsic and extrinsic regions. This is explicable because the extrinsic region is always characterized by the cation parameters, because of the

(*) Associated with the Centre for Interdisciplinary Studies in Chemical Physics, University of Western Ontario.

low solubility of anion dopants and the unavoidable presence of cation impurities. Inclusion of the extrinsic region in the analysis of the conductivity will fix the cation parameters and leave the anion parameters free to assume values that best fit the high-temperature conductivity. Any weakness in the model used will then show up in the values assumed by the anion parameters. Correspondingly, including only intrinsic conductivity data will compromise the values for the cation parameters which are best determined from the extrinsic region of the conductivity curve.

The inadequacies of simple defect models have led to the proposal of several new models for the interpretation of ionic transport. Among these are : (i) addi- tional transport processes involving trivacancies [9] ; (ii) Frenkel defects in the cation or both sub-lattices of alkali halides [lo], [5], [Ill ; (iii) ionic transport along dislocations [l 11 ; (iv) ihe temperature-dependence of the defect parameters [12-151. This paper summarizes the results of an analysis of new conduo tivity data for the systems : pure KCI, KC1 : Sr2+, KC1 : SO:-, using several models.

2. Experimental results. - Figures 1, 2 and 3 show

conductivity curves that are typical of the data ana- lysed. The results in figure 3 were obtained by the

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DEFECT PARAMETERS FOR KC1 C6-73

Fig. 1. - Ionic conductlvity of three crystals of nominally pure KCl. D . *

-

m - , . h lW ' . ' E Bo ~ -hl hi- Z ' - 2 . m - IL) L"

Flg. 2. - Ionic conduct~vity of two crystals of KC1 containing 0.043 0 and 0.081 5 mole % of SrC12, respectively.

K C 1 pure

d Run 23, lop crystal

3 Run 23, bottom crystol 5 Run 4

: :

%,"*"$d."$d.$..o ,

-

9

=--.

Fig. 3. - Ionic conductivity of a crystal of KC1 containing 0.003 64 mole % of KzSO,.

measurement of o and o, for a doped and pure KC1 crystal at the same temperature in a double cell. The slight scatter in the data is due to temperature fluctuations of the order of 0.1 K. Below 954 K the conductivity of the SO:- doped crystal decreases due to precipitation.

3. Analysis of data. - Defect parameters were

determined by fitting the theoretical conductivity, predicted using a particular model, to the experimental data using well-tried non-linear least-squares methods [l, 5,1 I]. In analysing the data for a particular system; only the parameters for those defects which are the main carriers in that system, were allowed to vary; all other parameters were held fixed at that stage. The set of parameters so obtained was cycled from system to system until a self-consistent set of parameters was obtained. The objective was to find a single and unique set of defect parameters which would fit the data for all three systems equally well. Four models were used in this analysis : (i) the Schottky defect model, including the association of M2+ impurity ions with nearest-neighbour (nn) cation vacancies and, in A2--doped KC], the association of A2- ions with nn anion vacancies; (ii) the same as (i), but assuming that nominally pure KC1 contains some divalent anion impurity A2- as well as M2+ ; (iii) the Schottky model (i) but with temperature-dependent defect parameters; (iv) Schottky defects, plus Frenkel defects in both sub-lattices. For model (i) a self-consistent set of defect parameters could not be obtained without unacceptably large deviations (> 5

%)

between calculated and experimental values of

oT.

Model (ii) provided an improvement over model (i) only if unrealistically large concentrations of A2- impurity were postulated. Although model (iii) did result in some improvement in the quality of the fittings, it did not lead to a self- consistent set of parameters and in fact behaved similarly to model (i). Model (iv), Schottky defects plus Frenkel defects, was the most promising model, the standard deviation of the fittings being a factor of 10 to 50 times better than for the traditional Schottky model. Moreover, (iv) was the only model tried that led to a set of defect parameters that came close to the idealized single self-consistent set. This set, which is given in table I, is not unique in the sense

Table I. - Defect parameters for KC1 : enthalpies

are given in eV and entropies in units of k . A

* indicates

that the value used was calculated theoretically.

S = Schottky ; F = Frenkel ; c = cation ; a = anion; v = vacancy ; i = interstitial ; 1 = nn complex ; A means a migration parameter.

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C6-74 L. A. ACURA A N D P. W. M. JACOBS

that some parameters are characterized by a range rather than by single values. This means that the fitting of the data was not noticeably changed if the particular parameter was varied within the range quoted. The values of the parameters for the anion interstitials reveal that their concentration is very small, compared to the concentration of anion vacancies. However, these interstitials are highly mobile, with the result that they can account for as much as 15

%

of the total ion transport at temperatures near the melting point of KCl. Perhaps the most direct and convincing evidence for the existence and importance of anion interstitials lies in the ability of the present model (iv) to explain the anomalous increase in the anion diffusion coefficient that has

been observed in KC1 crystals that have been heavily doped with Sr2+ ions [2, 161.

It should be stressed that the existence of ranges for the defect parameters in table I is due to the high correlation existing between parameters rather than to any inconsistency in the model used. We hope to reduce these ranges by further analysis of conductivity and diffusion data.

Acknowledgments. - This research was supported by the Natural Sciences and Engineering Research Council of Canada. L. A. gratefully acknowledges financial support provided by the Government of Venezuela through the Consejo Nacional de Investi- gaciones Cientificas y tecnologicas.

DISCUSSION

Question. - R. J. FRIAUF.. Question. - L. SLIFKIN.

A sensitive way of demonstrating the occurrence of interstitialcy motion is to observe low values of the diffusion ratio by means of careful tracer diffusion measurements. This might be a difficult undertaking in KCl, because of contributions of both cations and anions to ionic conductivity, and also because of contributions from vacancy pairs to diffusion of both kinds of ions. But until some demonstration of this kind is available, I feel that the presence of Frenkel defects of either kind is somewhat speculative.

Reply.

-

P. W. M. JACOBS.

Does not this analysis assume that all of the enthalpies and entropies are independent of temperature ?

Reply.

-

P. W. M. JACOBS.

Yes it does. We tried to include the effect of temperature dependent enthalpies, as calculated using the HADES program ; although this leads to some improvement in the fitting, it is necessary to introduce Frenkel defects to get a satisfactory analysis. Once one does this -it is not necessary to introduce temperature dependence at present levels of the accuracy with which transport data may be determined. It would, of course, be highly desirable to have

correlation-factor measurements-for anion diffusion _~ _~_-_{J. R ~ L F ~ .}_~ _~ _~ _i _~ _~ _. in M2+-doped KCI, but it would be difficult to do

a ) What values were used for the activation this with the required accuracy to provide an unam-

energies of migration of interstitial anions and biguous interpretation of the results since both non-

collinear and direct jumps contribute along with the cations ?

collinear interstitialcy jumps. But the dependence of b) Would You expect in other alkali halides that the

D,

on Sr2+ seems to be a direct confir- formation energies of anion and cation Frenkel mation of the presence of anion interstitials. vacancies would be so similar ?

Question. - Reply. - P. W . M. JACOBS.

-

It is surprising that you find such a high proportion a) The values used for the activation energies of of those SO:- ions which are dissolved, to be asso- interstitials were the calculated 0.38 eV for cations ciated with anion vacancies at these high temperatures. and 0.28 eV for anions.

b) Unfortunately there is no method of checking the

Reply. - P. W. M. JACOBS. _{accuracy of these numbers at present. The analysis}

This is because of the high association energy of the of the cbnductivity data tells u s that these values-are SO:--anion vacancy complex. At the precipitation roughly correct but differences of 0.2 eV or so would temperature the degree of association is about 0.6. probably give an equally good analysis.

References

[I] BEAUMONT, J. H. and JACOBS, P. W. M., J. Chem. Phys. 45 [3] FULLER, R. G., REILLY, M. H., MARQUARDT, C. L. and (1966) 1946. WELLS, J. C., Phys. Rev. Lett. 20 (1968) 662.

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DEFECT PARAMETERS FOR KC1 C6-75

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Solid 37 (1976) 525.

[7] ALLNATT, A. R. and JACOBS, P. W. M., Trans. Faraday Soc.

58 (1962) 116.

[8] FULLER, R. G., REILLY, M. H., MARQUARDT, C. L. and WELLS, J. C., Phys. Rev. 176 (1968) 1036.

[9] FULLER, R. G. and REILLY, A., J. Phys. Chem. Solids 39 (1959) 457.

[lo] ALLNATT, A. R. and PANTELIS, P., Solid State Commun. 6 (1968)

309.

[Ill BROWN, N. and JACOBS, P. W. M., J. Physique Colloq. 34 (1973) C9-437.

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(1975) 263.

1131 VAROTSOS, P. and ALEXOPOULOS, K., J. Phys. Chem. Solids

38 (1977) 997.

[14] CATLOW, C. R. A,, CORISH, J., DILLER, K. M., JACOBS, P. W. M. and NORGETT, M. J., J. Physique Colloq. 37 (1976) C7-253. 1151 CATLOW, C. R. A., CORISH, J., DILLER, K. M., JACOBS, P. W. M.

and NORGETT, M. J., J. Phys. C 12 (1979) 451.

1161 FULLER, R. G., The Chlorine Ion Dzjiusion in Potassium