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POINT DEFECTS, INTERACTION.DEFECT
ASSOCIATION IN SrCl2 DOPED WITH Na+, K+,
Rb+ OR Gd3+
A. Gervais, M. Jacquet, M. Bathier
To cite this version:
POINT DEFEC TS, IN TERA
C
T/ON=
DEFECT ASSOCIATION
IN
SrCI,
DOPED
WITH
Na+.
K + ,
Rb*
OR
Gd3+
A. GERVAIS, M. JACQUET and M. BATHIER
Universitt de Clermont, U. E. R. des Sciences, Groupe de Physique des Matkriaux, B. P. 45, 63170 Aubikre, France
R6sum6. - La conductivite extrinsbque des cristaux de SrC12 dope avec Naf, K+ ou Rb* est interpretbe par la theorie de Lidiard-Debye-Huckel en tenant compte de la presence d'ions mono- valent~ en position interstitielle. Dans le cas de SrCl2 : Na+, nous calculons l'knergie libre de Gibbs de solubilite. De 1'6tude des cristaux de SrC12 : Gd3+, nous d6duisons l'enthalpie de mobilite du chlore interstitiel.
Abstract. - The extrinsic conductivity of SrC12 crystals doped with Na+, K+ or Rbf is interpreted by the Lidiard-Debye-Huckel theory, taking into consideration the presence of monovalent ions in interstitial positions. For SrCl, : Na+ we calculate the Gibbs free energy of solubility. The study of SrC12 : Gd3f crystals gives the value of the mobility enthalpy of the interstitial chlorine.
1. Introduction.
-
Strontium chloride, SrCl,, has the fluorite, CaF,, arrangement. Intrinsic defects, in the SrCI, lattice, are anion Frenkel defects : one C1- ion leaves its normal site and occupies one of the four neighbouring interstitial sites at the unoccupied corners of the surrounding cube. The addition of a trivalent ion, e. g. Gd3+, necessarily adds one extra interstitial C1- ion for every substitutional cation and the electrical neutrality is maintained. On the other hand, when monovalent cations, e. g. N a f , are incorporated substitutionally, C1- vacancies are added. Barsis and Taylor [I], Hood and Mor- rison [2], Jacquet et al. [3] deduce from conductivitymeasurements that all the monovalent ions intro- duced into the crystal occupy the sites of Sr2+ ions and cause the formation of C1- vacancies. Pailloux
et al. [4] show, from dielectric absorption measure-
ments, the existence of impurity (Na' or Kf)-vacancy pairs in nearest-neighbour sites, which is in agreement with Wachtman's [5] hypothesis whereas Lefrant
et al. [6] identify a F centre perturbed by an interstitial
alkali metal ion in second-neighbour position. Using certain results of [3] together with new measurements and Lidiard's [7] theory where the Debye-Hiickel approximation describes the long range Coulomb interactions, we demonstrate that the M+ ions intro- duced do not all give rise to anion vacancies. Dielec- tric absorption measurements confirm these results. 2. Theory.
-
The substitutional M + ions createanion vacancies which can be either isolated or bound with impurities, thus forming neutral complexes. For this equilibrium we can write the following equation :
where k is Boltzmann's constant, T the absolute temperature, p the degree of association, Z a geome- tric entropy term which is 8 for nearest neighbours [4],
C the concentration of substitutional monovalent
ions (M:) in molar fractions, Sa the entropy and
ha the enthalpy of association of the complex, respec-
tively ; the Debye-Hiickel energy is given by
where R is the distance of closest approach under which we can assume that the Mf ion and the vacancy are paired. We may take
where a = 6.963
A
is the cell edge.The screening parameter IC, which depends on the
concentration of the free vacancies and the static dielectric constant E, = 7.1 [4], is given by
In this theory the mobility of vacancies is corrected by a factor which represents the hindrance to ion motion by the Debye-Hiickel cloud ; this factor is
The jump distance of the vacancy being a/2, if the thermal disorder is neglected, we can write the expression of the conductivity in the extrinsic region :
C7-282 A. GERVAIS, M. JACQUET AND M. BATHIER
where S, is the entropy and h, the enthalpy of mobility of the vacancy, and Wo Debye frequency. We take Wo = 5.22 x 1012 s-I according to Hisano et al. [8].
At low concentrations, C equals the dosed concen- tration ; at higher concentrations, C is the con- centration of foreign M: ions because some M' ions may occupy interstitial positions according to following reaction for the partition :
where M' is the interstitial monovalent ion, ~r:' the Sr2+ vacancy and M; the free substitutional mono- valent ion. Lidiard [9] proposes an analogous reaction for CaF,. The equilibrium equation corresponding to eq. (3) is :
Assuming that [Cl;] w [M:] and using the equi- librium equation of Schottky defects, we obtain from eq. (4) :
[M:] = [M:]~ exp -2 ,
K T )
the entropy factors being neglected. In eq. (5), h,
is the partition enthalpy.
In SrCI, : Na+ crystals, the nature of the preci- pitate is not known, which makes it difficult to determine the number of cation vacancies. For the dissolution process in the SrC1, lattice, we write the reaction
precipitate
+
Na:+
Cl;-
G , (6)where Naff is the free sodium ion dissolved in the lattice and G, = h, - TS, the Gibbs free energy of dissolution of the precipitate. The equilibrium equation corresponding to eq. (6) can be written :
[Na:] [Cl;] = exp -
-
2)
Expressing the concentration of free dissolved sodium by
and using eq. (5), we obtain
Eqs. (1) and (5) give the following expression of the total concentration C , of dissolved sodium in terms
+
4[~a:]~ exp(
-
-2)
exp (ha;?)
.
3. Experimental techniques.
-
The single crys- tals on which the measurements have been carried out were prepared in our laboratory by the Stock- barger-Bridgman technique of growth, either in a graphite crucible under an atmosphere of pure argon in the presence of PbCI, to scavenge the oxide, orin a silica envelope coated with a carbon film and sealed off under an atmosphere of chlorine and argon. The salt we used is the Hopkins-Williams SrCI,,
6 H,O reagent for atomic absorption spectropho-
tometry. The six molecules of hydration are driven
off by heating the salt slowly in a vacuum oven. The dopant (i. e. NaCI, KCl, RbCl or GdCl,) is added to the anhydrous powder. Alkali impurities are dosed by the atomic absorption method, either in the samples themselves or in neighbouring lamellae ;
the precision is about 10 per cent for concentrations higher than 50 ppm ; lower concentrations are esti- mated from ITC measurements and we conclude that all nominally pure crystals contain a residual concentration C % 10 ppm of Na'.
The conductivity and dielectric absorption measu- rements are carried out in a purified helium atmos- phere [lo]. Good electrical contact between the sample and the electrodes of the apparatus is ensured by a graphite layer. The ac measurements of the conductivity are made with a Wayne Kerr bridge Model 224 in the frequency range 1 to 15 kHz in order to avoid polarization effects. Readings are taken either in steps of 15 K after the thermal equi- librium of the crystal has been attained or in steps of 5 K while the temperature is being increased at the rate of 30 K/h. The dispersion of the results is never greater than x 3
%
for increasing or decreasing temperatures, except in the dissolution zone. The dielectric absorption is measured with a General Radio 1620 assembly.4. Results and discussion. - 4.1 EXTRINSIC CON- DUCTIVITY OF SrCl, : Gd3+.
-
aT us T-' curves fortwo SrC1, crystals doped with Gd3+ ions (130 ppm and 400 ppm, respectively) are shown in figure 1. Good reproducibility could be obtained only after the crystals had been annealed at temperature 773 K. EPR measurements on annealed or quenched crystals show that the symmetry of most Gd3+ ions is cubic ;
this property has been established by Abraham
et al. [ll]. Association phenomena are therefore
DEFECT ASSOCIATION IN SrC12 DOPED WITH Na+, K+, Rb+ OR Gd3+ 0 - 2 8 3
centration of ~ r ? + can be neglected. A least squares
method leads to a mobility enthalpy of interstitial
CI- ions of h,, = 1.0 eV that we may neglect in the study of SrC1, : M + crystals.
FIG. 1.
-
Temperature dependence of the conductivity of SrC12 : Gd3+ crystals :v
C = 130 ppm, C = 400 ppm and SrC12 : K+ crystals :A
C = 53 ppm, 0 C = 96 ppm,4- C = 300 ppm, C = 354 ppm, x C = 730 ppm.
4.2 EXTRINSIC CONDUCTIVITY AND DIELECTRIC ABSORPTION OF SrCl, : NaC.
-
The conductivity curves of SrCl, containing NaCl are shown in figure 2. For concentrations higher than 195 ppm, the con- ductivity does not depend on the concentration at temperature T = 630 K. We have determined the parameters of eq. (2) ; the discrepancy between measured values and values calculated from eq. (2) reaches 7 per cent ; it is not possible to obtain a correct fit without changing noticeably the parameters of eq. (2) and the values of dosed concentrations. That is the reason why we think that for the greatest concentrations (C 2 195 ppm) and measures corres- ponding to temperatures T < 500 K for the 103 pprn crystal, the concentration of ~ a : depends on the temperature. The values of parameters h,, S,, haand S,, determined from the measurements on the 10 ppm, 20 pprn and 103 pprn crystals at tempe- ratures T > 500 K, lead to a correct fit between eq. (2) and the extrinsic conductivity curves. These parameters remain unchanged in the study of other concentrations. In order to fit eq. (2) to experimental values, we used eqs. (1) and (5) simultaneously to determine the concentration of free vacancies. In table I, where the values of the parameters are given, it will be noticed that the difference between dosed
FIG. 2.
-
Temperature dependence of the conductivity of SrC12 : Na+ crystals : C = 10 ppm, 0 C = 20 ppm,-a-
C = 103 ppm,V
C = 195 ppm,+
C = 500 ppm, C = 2 000 ppm, x C = 3 720 ppm.Parameters found from thejit of the conductivity curves for SrCI, : NaC crystals
and computed concentrations is never greater than
10 per cent.
C7-284 A. GERVAIS, M. JACQUET AND M. BATHIER
FIG. 5.
-
Dielectric loss factor E" as a function of frequencyat T = 203 K for SrC12 : Na+ crystals quenchedfrom T = 863 K :
+
C = 1 360 ppm, C = 2 000 ppm,A
C = 2 830 ppm,x C = 3 720 ppm.
FIG. 4.
-
Temperature dependence of the Na+ solubility in method which has been described for SrC1, : Naf.SrC12.
FIG. 3.
-
Temperature dependence of the conductivity in thedissolution zone for SrC12 : Na+ crystals :
+
C = 1 360 ppm, interactions. A correction can be made with the ColeC = 2000 PPm,
A
c
= 2 830 PPmj X C = 3 720 PP* and Cole distribution law of relaxation times. Letus assume that quenching retains the same number of ~ a ' ions as at 863 K and let us express the ratios
with eq. (7) and the values of ha7 S a and hp given by Parameters found from thefit of the conductivity curves table I, we fit the obtained values to the model des- for SrCI, : K f crystals
cribed by eq. (8). The dissolution enthalpy and entropy
have been determined to be h, = 1.80 eV and Cdosed C c o r n ~ u t e d
respectively. The curve in figure 4 is derived from these values of the parameters.
Pailloux [4] established that vacancies and ~ a : ions paired, in agreement with Wachtman's model. To confirm the presence of ~ a : ions we measured the dielectric loss factor E" at different frequencies
for the four crystals whose dopant concentration exceeds 1 360 pprn ; these crystals were quenched from the temperature of 863 K. The results are shown in figure 5. The curves are wider than the Debye
curve ; the widening is caused mainly by dipole-dipole
of the concentration of ~ a ions in the 2 z 000 ppm, 2 830 pprn and 3 720 pprn crystals, respectively, to
the concentration of ~ a : in the 1 360 ppm crystal,
on the one hand from results in figure 5, on the other hand from data in table I. The latter values never exceed the former by more than 10
%
.
4 . 3 EXTRINSIC CONDUCTIVITY OF SrC1, : Kf
.
-Figure 1 shows the extrinsic conductivity curves of
SrCl, : K f . A previous study having shown that in
the 730 ppm, 354 pprn and 300 pprn crystals a certain
number of K + ions were in interstitial positions, we determine the parameters h,, S,, ha and Sa of eq. (2)
with the 96 pprn and 53 pprn crystals. The presence
4 -
3 -
2-
b
7 Yu"
1
-
Table II shows the results. The values of h, given in
tables I and I1 agree with the results obtained by
Pailloux [4], i. e. h,,, = 0.34 eV, and Jacquet [to be
0-7i25
qb
i35
PI*~)
of residual Na+ ions is taken into account in our calculations. For the fit of other crystals, we use theDEFECT ASSOCIATION IN SrClz DOPED WITH Na+, K+, Rb+ OR Gd3+ C7-285
published], i. e.
EN,+
= 0.33 eV and EK+ = 0.305 eV (from ITC measurements).5. Conclusion.
-
From a few conductivity mea- surements made on SrCl, : Rb', we could infer that some Rb+ ions are in interstitial positions too when the dopant concentration exceeds 200 ppm. Our results agree with the conclusions of Lefrant who found perturbed F centres with the same dopants. The development of a shell model to describe theSrCl, lattice behaviour would be necessary for computing theoretical values of the Schottky and partition enthalpies.
Acknowledgments. - The authors are grateful to Professor Chapelle who supplied a pure SrCl, crystal. They would also like to thank M. and Mme Vasson for carrying out the EPR measurements, Mme Philibert for dosing the samples and M. Roudil for technical assistance.
References
[I] BARSIS, E. and TAYLOR, A., J. Chem. Phys. 45 (1966) 1154.
[2] HOOD, G. M. and MORRISON, J. A., J. Appl. Phys. 38
(1967) 4797.
[3] JACQUET, M., GERVAIS, A. and BATHIER, M., C. R. Hebd.
SPan. Acad. Sci. 278B (1974) 709.
[4] PAILLOUX, M., GERVAIS, A., JACQUET, M. and BATHIER,
M., C. R. Hebd. SPan. Acad. Sci. 274B (1972) 991. [5] WACHTMAN, J. B., Jr., Phys. Rev. 131 (1963) 517.
[6] LEFRANT, S., HARKER, A. H. and TAUREL, L., J. Phys. C 8
(1975) 1119.
[7] LIDIARD, A. B., Handbuch der Physik, ed. S. Hiigge (Sprin- ger, Berlin) 1962, vol. 20,246.
[8] HISANO, K., OHAMA, N. and MATUMURA, O., J. Phys. Soc. Japan 20 (1965) 2294.
[9] LIDIARD, A. B., Crystals with the Fluorite Structure, ed. W. Hayes (Clarendon Press, Oxford) 1974, 101. [lo] GERVAIS, A., These docteur-ingknieur, Clermont-Fd,
1969.
[ l l ] ABRAHAM, M. M., BOATNER, L. A. and LEE, E. J., Phys.
Lett. 25A (1967) 230.
DISCUSSION
B. V. R. CHOWDARI. - Can you elaborate on the EPR measurements of Gd3+ doped SrCl, ?
