Point defect parameters for strontium chloride from ionic conductivity studies

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Point defect parameters for strontium chloride from

ionic conductivity studies

A. Chadwick, F. Kirkwood, R. Saghafian

To cite this version:

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Point defect parameters for strontium chloride from ionic conductivity studies

A. V. Chadwick, F. G. Kirkwood and R. Saghafian

University Chemical Laboratory, University of Kent at Canterbury,

Canterbury, Kent CT2 7NH, England

Rbsumb - Nous avons mesur6 la conductivitt des cristaux de SrClz dopts avec les ions M + et M 3 + . Les donntes ont ete analysees a l'aide de techniques des moindres carrts non lintaires pour obtenir des valeurs numtriques des paramttres gouvernant la formation et la migration des dtfauts. Les paramktres montrent que les anions interstitiels sont les plus mobiles dkfauts aux hautes tempkratures.

Abstract. - We have measured the conductivity of SrClz crystals doped with M + and M 3 + ions. The data have been analysed using non-linear least squares techniques to yield numerical values of the parameters governing the formation and migration of defects. The parameters obtained predict that the interstitial anions are the more mobile defects at high temperature.

1 . Introduction. - Recently there has been a considerable interest in the defect properties of materials with the fluorite structure [I]. Although it has long been established that the predominant disorder in these materials is anion Frenkel defects there is a lack of precise experimental values of the defect energies and determinations of the diffusion mecha- nisms. As a result of the HADES calculations good progress has been made in terms of theoretically evaluating the defect properties of fluorites, particu- larly for the alkaline earth fluorides [2]. The speci- fic heat anomaly and the associated occurrence of high temperature fast-ion conductivity in the fluorites has excited the interest in these materials and the details of these phenomena are currently being stu- died by many workers 131. From an experimental viewpoint SrC12 has a number of advantages for investigations of the behaviour of fluorites. It has a relatively low melting point and is less reactive to O2 and H 2 0 than the alkaline earth fluorides. Inves- tigations of this compound have included conductivity studies [4-91, neutron scattering experiments 110-121, a HADES calculation of the defect energies [13] and a molecular dynamics simulation of the fast-ion conduction [14, 151. In this paper we report conductivity results which have been computer analysed in an attempt to provide the first com- prehensive set of defect parameters for SrC12.

2. Experimental.

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Single crystals of SrC1, were grown by the Stockbarger technique using graphite crucibles with a growth atmosphere of argon or HCl. Two types of nominally pure crystal were grown ; H W crystals (grown from Hopkins and Williams SrC126 H 2 0 material for atomic absorption

spectroscopy) and M crystals (grown from Merck

SrC12 Selectipur grade). Dominant impurities were Na+ and K + (HW crystals, 58 p.p.m. N a + , 13 p.p.m. K+ ; M crystals, 200 p.p.m. N a f , 50 p.p.m. K+). Gd3+ doped crystals were prepared by re-growing HW crystals with anhydrous GdCI3 (Koch-Light Limited). Neutron activation analysis showed the Gd3+ concentration to be 200 p.p.m.

The conductivity apparatus and measurement technique were similar to those employed in previous work [9, 16, 171. A.c. conductivities were measured at several frequencies up to 500 kHz and above 20 kHz the measurements were frequency- independent. It is these latter results that are report- ed here. The cell atmosphere was HCI gas (B.D.H. electronic grade) and the results were reproducible on thermal cycling.

3. Data analysis.

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The analysis used in this study followed very closely that described for CaF2 by Jacobs and Ong 1181 and the detailed equations can be found in their paper. Like these workers we assumed that for M + doped crystals the impurity was only present on substitutional sites with charge compensation occurring by the formation of C1- vacancies. Thus the conductivity, a, of these crystals can be expressed in terms of nine parameters [18] ;

the Frenkel formation enthalpy, h F , and corresponding entropy, s~ ; the vacancy migration enthalpy

Ah, and corresponding entropy, As, ; the interstitial migration enthalpy, Ahi, and corresponding entropy, Aq ; the Mf-Cl- vacancy association enthalpy, h a l , and the corresponding entropy, s a l ,

and the total M + concentration,

4.

In a similar manner a M3+ doped crystal can be described by

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POINT DEFECT PARAMETERS FOR STRONTIUM CHLORIDE C6-217 nine parameters [18] : hF : SF ; Ah, ; As, ; Ahi ; Asi ;

the M3+-C1- interstitial association enthalpy, ha, and corresponding entropy, sa2 ; and the total M3+

concentration,

4.

In our model we assumed that the interstitial C1- migrated by a non-collinear interstitialcy mechanism.

We employed a non-linear least squares pro- gramme, NLIN 2 [19], to fit the conductivity data to the above mentioned parameters. The long-range coulomb interactions between defects were taken into account by evaluating activity coefficients using the Debye-Hiickel-Lidiard theory [20] and correct- ing the mobility for the effect of the ion atmosphere with the Onsager-Pitts factor 1211. In the calculation of the conductivity the effect vibrational frequency,

v , was taken t o be the Debye frequency, 5.22 x 1012 s-1 [22]. Ideally both the temperature- dependence of the lattice parameter, a , and the per- mittivity, E , should be included in the calculation. A polynominal fit to the data of Dickens et a/. [lo] was

used to correct for the variation of a. The only data we could find for E was the value at 20 "C of 7.1 [23].

4. Results and discussion. - The conductivity plots that were obtained are shown in figure 1. Close exa- mination of the data showed that transition to the fast-ion conduction region begins above 909 K (lO3/T = 1.1) and all data points above this temperature were excluded from the analysis. The results of the analysis are given in table I along with the data from previous studies, Figures 2 and 3 show the diffe- rences between calculated and experimental conductivities for crystals M I and Gd2, respectively. The goodness of fit, as determined by the standard deviation, is comparable to that obtained for computer analyses of the alkali halides. The deviation plots show a reasonable approximation to random behaviour. It is difficult t o assess the errors on the parameters in this type of analysis, however, the enthalpies should be accurate to at least 4 0.1. eV.

Table 1.

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Defect parameters for strontium chloride.

The results form this work are derived from a computer analysis of the conductivity data.

L = number of data points and s.d. = standard deviation. An underlined parameter means that it was held constant during the fitting.

L 206 124 107 106

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c?fiob J 168 8 2,94 2 s

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s.d.xlo3

3.a

5.28 4.94 3.43

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sF/k 6,YI 9,27 4,53 3,zg

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Present Work r y s t a l MI @f+ @ed) rystal im-l (M+ doped) r y s t a l Gdl (cd3+ doped) r y s t a l Gd2 (Gd3+ doped) rvais e t a 1 (1976) Jacquet et a 1 (1974) F a + doped)

Hood and Morrison (1967)

Barsis and Taylor (19661

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Fig. 1. - Conductivity plots for SrC12 :

---

crystal M1 ; - crystal HWI ;

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crystal Gdl. The plots for crystals

Gdl and Gd2 were virtually identical.

Fig. 2.

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The difference between experimental (e), and calculated (c) values of log (07) for crystal M I .

Fig. 3. - The difference between experimental (e), and calculated (c) values for log (u7) for crystal Gd2.

The fitted values of c$ are in reasonable agreement with the values obtained from chemical analysis and the defect parameters change only slightly if

the fitting is performed with P, held constant at the latter values. The fitted values of

4 for the Gd3f

are much lower than expected. Allowing for compensation of Gd3+ by inherent M + impurities cO,

would have been expected to be

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100 p.p.m. However the low knee in the conductivity plots is consistent with a low level of effective dopant in these crystals. The anomaly in C; is probably due to

significant formation of Gd2O3 during crystal prepa- ration, in spite of the use of a HCl growth atmos- phere. Effective M3+ doping of SrC12 is clearly a problem and similar discrepancies between a and the expected c\ can be seen in previous studies 14, 51.

The present values of hF, 1.92-2.02 eV, are consistent with previous work [4, 71. Since the Gd3+ doped crystals had a longer range of intrinsic behaviour the values of SF obtained from their conductivities should

be the more reliable. Obviously the more reliable values of the defect migration parameters are obtained from crystals in which the dopant enhances the concentration of that defect. Our values of Ah,, As,, h, and sav are in very good agreement with those obtained by Gervais et al. [8] from a thorough analy- sis of the extrinsic a of Na+ doped SrCI,. Unlike these workers we found no evidence for Na+ on interstitial sites, however, it could be that our M+ concentrations were too low for this to be an important effect. There are no comparable detailed analyses of M3+ doped crystals with which we can compare our values of Ahi and Asi. The values of ha2 and s* are probably the least reliable of all our parameters as these are effective over a very short temperature region of our data. The vaIue of hF from the HADES calculation [13] is

consistent with our results, however, both the calculated Ah, and Ahi are much lower. For Ahj this is somewhat surprising since the HADES calculations for the alkaline earth fluorides give values in good agreement with experiment 12, 17, 181.

In figure 4 we have used the parameters from crystal MI to calculate the vacancy transport number in pure SrC12. The interesting feature is that the inter-

Fig. 4.

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The value of the transport number in pure SrCI, cal-

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POINT DEFECT PARAMETERS FOR STRONTIUM CHLORIDE C6-219

stitial is much the more mobile species at high tempe- Acknowledgments.

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We thank Mr. P. J. Bendall ratures. It has been suggested that vacancies are the providing a copy of his results prior to their publica- mobile species in the fast-ion region and this would tion and Professor M. Bathier for stimulating corres- require considerable changes in the relative defect pondence. We are grateful to Professor P. W. M.

mobilities in the transition from normal to fast-ion Jacobs for assistance with the computing and for

behaviour. numerous discussions.

DISCUSSION

Question.

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P. W. M. JACOBS.

I think we have some independent evidence for your defect parameters for SrC1, from ITC measurements. For M + doped crystals there is a low-temperature ITC peak with E

--

0.3 eV. For your Gd3+-doped crystal we could find no depolarization, which suggests a high activation energy

>

0.8 eV. The high-temperature peaks often seen in ITC of SrC1, are due to water in some form.

Reply.

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A. V. CHADWICK.

We are very pleased to hear the results of your experiments.

Question.

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L.

SLIFKIN and R. J. FRIAUF. Would any representative from HADES like to comment on the sizable discrepancy for the intersti-

tialcy migration enthalpy ? There also seems to be some discrepancy for the vacancy migration enthalpy.

Reply. - C . R. A. CATLOW.

First, I think we should remember that the values for the defect parameters in SrC1, seem to be far from certain. Perhaps we should wait before worrying too much about the theoretical values. However, I accept that the calculated interstitialcy migration energy is probably low. This probably reflects on inadequacies in the C1

...

Cl potential used in the calculations. I think they may be inferior to the F-

. . .

F- potential used in the alkaline earth fluorides work. The situa- tion will probably improve when we gain more expe- rience in modelling chlorides. As far as the vacancy energy is concerned, I think the agreement is quite satisfactory considering the uncertainties in the analyses of the experimental data.

References

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