Complex admittance study of β-PbF2 single crystals

Solid State Communications, Vol. 18, pp. 1005—1007, 1976.

Pergamon Press.

Printed in Great Britain

COMPLEX ADMITTANCE STUDY OF ~3-PbF2SINGLE CRYSTALS R.W. Bonne and J. Schoonman Solid State Department, Physical Laboratory, University of Utrecht, Utrecht, The Netherlands (Received 8 November 1975 by A.R. Miedema) The complex admittance of j3-PbF2 single crystals between two inert blocking electrodes was studied from R.T. to 730 K. A strong frequency dependence was observed over the frequency range 0.1 Hz—100 kHz. The bulk conductances were obtained from the frequency independent conductances. With increasing temperature the electrode discharge processes are dominated by a diffusional impedance. 1. INTRODUCTION THE SOLID ELECTROLYTE properties of lead fluoride have been the subject of recent investigations.17 Liang 4 showed that fluoride ion vacancies V and Joshi 1~are the mobile species in f3-PbF.~doped with KF, and that interstitial fluoride ions F are mobile in nominally pure 13-PbF2 and in (3-PbF2 doped 2with andYF3. Liang and Joshi4 Derrington and O’Keeffe recorded alternating current conductivities of polycrystalline samples over the frequency range 1—10 kHz. In this range frequency independent conductances were observed. Kennedy et aL3 found a strong frequency dependence for the measured conductances (Gm). For pressed pellets plots of Gm ( 1 IRm) vs frequency gave in the region 298—473 K straight lines whose zero frequency intercepts equalled the bulk conductance GB. Above 473 K straight lines were obtained when the measured resistances Rm were plotted vs the reciprocal of the square root of the angular frequency. The bulk resistance RB was obtained from extrapolation to infinite frequencies. l’his square root 3 dependence stems from concentration polarisation.

7 reported in the More recently, Schoonman et al. region 300—400 K frequency independent conductances for polycrystalline j3-PbF 2 over the frequency range 0.1—50 kHz. For temperatures above 400K a semicircle at lower frequencies appeared, when the data were plotted in the complex admittance plane. The extrapolation of the low frequencies did frequency not pass through end of the this origin semicircle as one at would lower expect for an equivalent circuit with the bulk resistance RB and interfacial capacitance Cdi in parallel with the geometric or high frequency capacitance CB This behaviour can also not be due to an electronic contribution to the conductance because of the low transference number for electronic species in j3-PbF 2 ~5,6 The observed behaviour has been ascribed to a grain boundary effect. For all temperatures, however, bulk properties of the pellets were derived from frequency independent conductances in the high frequency regime, contrary to the results reporte4 by Kennedy et al. who used for T < 473 K zero frequency intercepts of Gm vs f plots. In the present investigation the frequency dependence 13-PbFof the electrical conductivity of nominally pure 2 single crystals was studied in more detail in order ,~

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Fig. 1. A.c. voltage dependence of the admittance parameters. 1005

1006

COMPLEX ADMITTANCE STUDY OF (3-PbF2 SINGLE CRYSTALS

Vol. 18, No. 8

Table 1. Frequency independent conductances (G) as a

(a)

function ofsample 2) 0.389 dimensions 0.096 O(cm d/O(cm’) 0.517 8.89 G(~2’) 2.15 x iO~ 1.1 x l0-~

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o

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log aT

p-PbF 2 (Leitplatun) vacuum ON 2

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~ > 2

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0

0

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Air

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0.75

.0

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2.0 3 T1 (K1) 15

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Fig. 3. Temperature dependence of the1Ospecific bulk

IC

(c)

conductance of~3-PbF 2,plotted aslog aTvs T~’.

(%1

2

I

with platinum paint electrodes. The admittance para-

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10

5

102 y’

Fig. 2. Complex admittance plots of a nominally pure $3-PbF 2 crystal. Electrodes Leitplatin. (a) T = 403 K, 0.2 Hz—2O kHz. (b) T = 552 K, 0.7 Hz—50 kHz. (c) T = 721 K, 2Hz— 10 kHz. + +, low frequency bridge.~.., impedance bridge G.R. 1608 A. to separate the influence of interfacial polarisation phenomena from the bulk parameters.

meters ofwith the theand range fier-null-detector 50 (1608 Hz—SO A) kHzsamples external using (1232 a were General oscillator A). recordedin ForRadio frequencies (1210C) impedance smaller anbridge amplithan 8 in combination R~—C~ 50 Hz admittances combination were with measured an a.c. bridge in terms of a parallel with a Wavetek H.F. sweep generator (model 144) and a Tektronix storage scope (type 564 B). In Fig. 1 admittance parameters, G~(Y’)and wC~(Y”)are plotted as a function of the a.c. amplitude (peak to peak). The measured (~,,and G~values were independent of a.c. amplitudes in the region where conductances were independent of frequency. In practice admittance parameters were recorded in the voltage independent region. 3. RESULTS AND DISCUSSION

2. EXPERIMENTAL Figure 2 represents complex admittance plots The $3-PbF2 single crystals were kindly made availrecorded at different temperatures. Measurements were able by Dr. E.E. Schneider of the University of Newcastle performed in nitrogen or vacuum as ambient without upon Tyne. differences in results (compare Fig. 3). The~p~hed surfaces of the san~pl.eswere provided Frequency independent conductances are proportional

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COMPLEX ADMITTANCE STUDY OF $3-PbF2 SINGLE CRYSTALS

to the ratio between surface area and thickness of the samples in the region 300—720K indicating true bulk properties. Table 1 ifiustrates this dependence. In Fig. 3.the bulk conductance of several crystals as measured in different ambients is plotted as log aT vs T’.theUpconduction to about 580 K a straight line is andeV for activation enthalpy theobtained value 0.66 was calculated. This value is well in line with reported data.1’3’7 At temperatures about 580 K an increase in slope to about 1 eV is observed. This has been observed before.”6 Schoonman et aL1 reported for single crystals a conduction activation enthalpy of 1.05 eV in the region 500—680 K. Our present knowledge of the defect chemistry of j3-PbF 4 indicates that the value 0.66 eV represents the 2 enthalpy of interstitial fluoride ions ~ migration For the migration enthalpy of fluoride ion vacancies L~.Hv~’ Liang and Joshi obtained the value 0.18 eV. The high temperature conduction activation enthalpy is, therefore, likely to be an intrinsic conduction activation enthalpy; ~ + MIF’~).We then obtain for the formation enthalpy L~.Hffor anion Frenkel defects the value 0.78 eV. This has been confirmed by results obtained on a $3-PbF 9 crystal doped with silver. At 2high temperatures [Fig. 2(c)] the complex admittance behaviour reflects the presence of a diffusional impedance in series with the bulk resistance, l’his behaviour agrees with the frequency dependence of the conductance 3 as was observed for pressed pellets by Kennedy et al. It should be noted that in the entire temperature region our results obtained on pressed pellets of $3-Pb F2 exhibit the 9 same admittance behaviour as the single crystals.

1007

At intermediate temperatures [Fig. 2(b)] an additional complex impedance in series with the bulk resistance and the diffusional impedance can give rise to the semicircle-shape characteristics at higher frequencies. This behaviour has also reported for pressed 7 and ascribed tobeen internal polarisation at grain pellets boundaries. This complex impedance has been modelled as a parallel R—C combination. The grain boundary effect seems, however, unlikely in single crystals. The observed admittance plots at intermediate ternperatures reflect a behaviour as expected for the usual Randles circuit, frequently observed in aqueous solutions.1° However, as has been pointed out by Macdonald,’1 this equivalent circuit is inappropriate for an unsupported binary solid electrolyte. The present results could indicate that the charge transfer processes occurring at the two electrodes are different, whereby the role of oxide formation may be of influence. The observed admittances can also be discussed using a model where interstitial fluoride ions and fluoride ion vacancies contribute to the conductance, while their degree of blocking at the electrodes is different. A detailed analysis of the temperature dependences of the admittance parameters, and their relation with the defect chemistry of $3-PbF 9 wifi beresults published elsewhere. The 2present together with literature data reveal that for single crystals as well as pressed pellets of j3-PbF 2 frequency independent conductances represent true bulk activation enthalpy for the formationproperties. of Frenkel The disorder in 13-PbF 2 has a value of 0.78 eV. Acknowledgement The authors to Prof. Dr. G. Blasse for critically readingare the indebted manuscript. —

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SCHOONMAN J., DIRKSEN G.J. & BLASSE G.,J. Solid State Chem. 7,245 (1973).

2.

DERRINGTON C.E. & O’KEEFFE M.,Nature, Phys. Sci. 246, 44(1973).

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LIANG C.C. & JOSH! A.V.,J. Electrochem. Soc. 122,466(1975). SCHOONMAN J., KORTEWEG G.A. & BONNE R.W., Solid State Commun. 16,9(1975).

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BENZ R., Z. Phys. Chem. Neue Folge 95, 25 (1975).

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SCHOONMAN J., EBERT L.B., HSIEH C.H. & HUGGINS R.A.,J. Appi. Phys. 46, 2873 (1975).

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BRUININK J., Thesis, Utrecht (1973). BONNE R.W. (to be published).

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RANDLES J.E.B., Discuss. Faraday Soc. 1,11(1947).

11.

MACDONALD J.R., J. Electroanal. Chem. 47, 182 (1973).