Ionic conductivity in solid solutions of PbF2 and YF3

Article abstract of DOI:10.1016/S0025-5408(01)00634-1

Ionic conductivity of a series of fluorite-type solid solutions Pb_1-xY_xF_2+x (0.007 ≤ x ≤ 0.222) has been measured in the frequency range 100 Hz - 3 MHz and in the temperature range 25-250°C under vacuum. The conductivity decreases and the activation energy increases gradually upon increasing the yttrium content up to ～ 4.5 mol% of Y³⁺ whereas, beyond that and up to 22 mol% of Y³⁺, the ionic conductivity increases and the activation energy decreases. Thus two distinct regions in the general composition Pb_1-xY_xF_2+x could be delineated, in one the polarizability factor predominates over the number of extra-interstitial F anions and vice-versa in the other region. These results indicate the competing effects between the disorder caused by interstitial F anions and the polarizability of the host and guest cations.

Full text of DOI:10.1016/S0025-5408(01)00634-1

Materials Research Bulletin 36 (2001) 1743–1749
Pergamon
Ionic conductivity in solid solutions of PbF2 and YF3
S.J. Patwea, P. Balayab, P.S. Goyalb, A.K. Tyagia,*
aApplied Chemistry Division, Bhabha Atomic Research Centre Mumbai – 400 085, India
bInter University Consortium for DAE Facilities, Mumbai Centre, Bhabha Atomic Research Centre
Mumbai – 400 085, India
(Refereed)
Received 26 January 2001; accepted 11 March 2001
Abstract
Ionic conductivity of a series of fluorite-type solid solutions Pb1-xYxF2ϩx (0.007 Յ x Յ 0.222) has
been measured in the frequency range 100 Hz – 3 MHz and in the temperature range 25–250oC under
vacuum. The conductivity decreases and the activation energy increases gradually upon increasing the
yttrium content up to ϳ 4.5 mol % of Y3ϩ whereas, beyond that and up to 22 mol % of Y3ϩ, the ionic
conductivity increases and the activation energy decreases. Thus two distinct regions in the general
composition Pb1-xYxF2ϩx could be delineated, in one the polarizability factor predominates over the
number of extra-interstitial F anions and vice-versa in the other region. These results indicate the
competing effects between the disorder caused by interstitial F anions and the polarizability of the host
and guest cations. © 2001 Elsevier Science Ltd. All rights reserved.
Keywords: A. Fluorides; C. X-ray diffraction; D. Phase equilibria, D. Ionic conductivity
1. Introduction
PbF2 on heating undergoes an irreversible phase transition from orthorhombic (␣) to
cubic (␤) form at about 315oC. The ␤-form can also be stabilized at room temperature
on cooling. It was found that ␤-PbF2 was more stable at room temperature and ambient
pressure. However, a partial conversion of ␤-PbF2 to ␣-PbF2 was effected by pressing
the material at above 30,000 PSI [1]. Obserschmidt et al. [2] investigated a systematic
effect of hydrostatic pressure on the ionic conductivity and the phase transition in PbF2.
* Corresponding author. Fax: ϩ91-22-5505151.
E-mail address: aktyagi@magnum.barc.ernet.in (A.K. Tyagi).
0025-5408/01/$ – see front matter © 2001 Elsevier Science Ltd. All rights reserved.
PII: S0025-5408(01)00634-1

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It was found that the transition temperature increases linearly with increasing pressure
at higher temperature.
A comparison of the electrical properties of ␤-PbF2 with other fluoride ion conductors
such as CaF2, BaF2 shows that ␤-PbF2 is a better ionic conductor, due to the high
polarizability of the Pb2ϩ ions compared to that of Ca2ϩ and Ba2ϩ ions. The rare-earth
trifluorides (e.g. Y3ϩ, La3ϩ etc.,) have reasonably high solubility in ␤-PbF2. Hence,
several studies have been made with an aim to enhance the conductivity by replacing a
part of Pb2ϩ with other cations, while retaining the basic fluorite structure [3]. The
substitution of Pb2ϩ with Y3ϩ increases the concentration of interstitial fluoride ions and
thus resulting in an enhanced ionic conductivity [3-7]. Therefore, the aliovalently doped
␤-PbF2 based solid solutions are perspective solid electrolyte with a fast fluoride ion
conductivity at low and moderate temperatures as one can significantly alter the anionic
sub-lattice. In view of this, Reau et. al., [3] investigated the ionic conductivity in the
fluorite type solid solutions Pb1-xYxF2ϩx (0.02 Յ x Յ 0.30) which were prepared by
quenching from 820oC. We have investigated the ionic conductivity of the solid solu-
tions Pb1-xYxF2ϩx (0.007 Յ x Յ 0.222) prepared by short annealing (3 hours) at low
temperature (ϳ 700oC) and slow cooling (@ 2oC/min.) to room temperature. This paper
reports the correlation between composition, ranging from very low doping (0.7 mol %)
to the maximum solubility (22 mol %) limit of Y3ϩ ion in ␤-PbF2 and the activation
energy and in-turn ionic conductivity.
2. Experimental
PbF2 used was of spectroscopic grade. YF3 was synthesized by the reaction between Y2O3
and NH4HF2 (in excess) at 3500C followed by drying at 2500C for 5 hours in an argon
atmosphere. The solid solution of YF3 and PbF2 were synthesized by solid state reaction [8].
The required amounts of the constituents were mixed and pressed into 8 mm pellets. This
pellet was wrapped in platinum foil and kept in a quartz tube that was evacuated (10Ϫ5 mbar)
and sealed online. The sealed quartz tube along with the pellet was then heated at 700oC for
three hours to facilitate the formation of solid solution. The samples were then slow cooled
at a rate of 2oC/min. The products obtained were characterized by powder XRD using
Ni-filtered Cu-K␣ radiation.
Impedance measurements on the pressed pellets were carried out using Impedance/
Gain phase analyzer (HP 4194A) over the frequency range 100 Hz – 3 MHz, in
the temperature range 25–250oC with the help of a high temperature-measuring cell
[9] under vacuum of 10Ϫ5 mbar. The samples in the form of pellets were painted with
graphite paste for better electrical contact. The silver paint was not suitable as it diffused
into the sample during measurement. The samples were spring loaded between thick
silver electrodes for impedance measurement. The studies were done during heat-
ing cycle with a rate of 1oC/min. The dc conductivity was derived from the impedance
plot.

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Table 1
Lattice parameter of various compositions
x
Composition
a (Å)
(Pb1Ϫx YxF2ϩx
)
x ϭ 0.000
x ϭ 0.007
x ϭ 0.029
x ϭ 0.044
x ϭ 0.100
x ϭ 0.154
x ϭ 0.222
PbF2
5.940 (1)
5.936 (1)
5.926 (1)
5.919 (1)
5.904 (1)
5.871 (1)
5.842 (1)
Pb0.993 Y0.007F2.007
Pb0.971 Y0.029F2.029
Pb0.956 Y0.044F2.044
Pb0.900 Y0.100F2.100
Pb0.846 Y0.154F2.154
Pb0.778 Y0.222F2.222
3. Results and discussion
Recently, the low temperature phase equilibria in PbF2-YF3 system was reported by Patwe
et al., [9]. The composition with 22 mol % of YF3 in PbF2 was found to be the solubility limit
for the solid solutions while retaining the fluorite structure. A number of ordered phases were
also observed during the course of this work. The samples with the stoichiometric formula
Pb1-xYxF2ϩx (0.0 Յ x Յ 0.222) studied in the present investigation forms disordered
fluorite-type solid solutions. The unit cell parameters for these samples are given in Table I.
The fluorite unit cell parameters at the saturated solid solution (x ϭ 0.222) is found to be
5.842(2) Å as against 5.940(1) Å for pure ␤-PbF2. This is attributed to the difference in the
ionic radii of the two ions (rPb2ϩϭ1.29 Å and rY3ϩϭ1.02 Å) in eight-fold coordination.†
In a conventional DC measurement on ␤-PbF2 with silver as blocking electrodes, F anions
encounter the problem of space charge polarization due to blocking at the sample and
electrode interface. Thus the total measured resistance has the contributions from both the
sample and the electrode. To extract the true resistance of the sample, one usually performs
the measurements as a function of frequency. In such a case, the plot of ԽZЈԽ vs ԽZЉԽ
(impedance plot) exhibits a semicircle due to the sample and a low frequency spike due to
the electrode polarization. The resistance of the sample corresponds to the intercept of the
semicircle with the spike. The dc conductivity (␴dc) of the solid solutions Pb1-xYxF2ϩx
(0.0 Յ x Յ 0.222) is thus calculated from their true resistance extracted from the impedance
plot. Fig. 1 presents the impedance plots for the solid solutions at 25oC. Fig. 2 shows the dc
conductivity as a function of temperature, in the form of log␴dcT vs 1000/T. It may be
noticed from the Fig. 2 that at lower temperature, the ionic conductivity decreases consid-
erably at low concentration of the Y3ϩ ions and increases gradually beyond ϳ 4.5 mol % of
Y3ϩ content. As we increase the temperature the difference in conductivity with yttrium
content decreases. The conductivity data for all the samples are fitted to the Arrhenius
equation:
␴
ϭ ͑␴o/T͒*exp͑ϪE /kT͒
␴
dc
† VCH Periodic Table of Elements, Compiled by Fluck and Hermann.

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Fig. 1. Impedance plots at 25oC for the solid solutions Pb1-xYxF2ϩx. Arrow indicates true resistance.
where, E is the activation energy for the dc conduction. The values of E for the above
␴
␴
samples as a function of composition are plotted in Fig. 3. The activation energy for the solid
solution Pb0.993Y0.007 2.007 is comparable to a value of 0.50 eV [1] reported for ␤-PbF2. The
F
ionic transport in all the above samples is mostly due to the extrinsic anion vacancies and
interstitials.
The polarizability of Y3ϩ and Pb2ϩ are 1.5 Å3 and (3.7 to 5) Å3, respectively [10]. It is
known that higher polarizability of the cation enhances the ionic conduction of anions,
resulting in lower activation energy. It is seen clearly from Fig. 3 that with increasing yttrium
content, the activation energy for dc conduction first increases and subsequently it decreases
gradually. Thus there are two distinct regions in Fig. 3. In the first region, where the
activation energy increases on increasing Y3ϩ content, the polarizability factor predominates
over the number of extra-interstitial F anions which are rather insignificant. It is noted that
the activation energy starts decreasing as a function of Y3ϩ content, after attaining a peak at
the composition Pb0.956Y0.044 2.044
F
. This unusual observation can be attributed to the
number of interstitial F-anions which predominates over the polarizability factor in this
region. Thus the Pb0.778Y0.222 2.222 shows the lowest activation energy in this system. Reau
F
et al. [3], could not observe this peak in their plot of activation energy versus Y3ϩ content
in Pb1-xYxF2ϩx solid solutions. They performed the ionic conductivity measurements on the

S.J. Patwe et al / Materials Research Bulletin 36 (2001) 1743–1749
1747
Fig. 2. dc conductivity as a function of temperature.
high temperature quenched samples as against low temperature-short annealed and slow
cooled samples in the present investigation. The quenched samples are likely to have high
disorder and slightly higher cell volume also, which might cause the compensation of
polarizability factor. The slow cooled samples result in a better control over anionic
sub-lattice and microstructure which must have facilitated an unequivocal delineation of two
distinct regions, observed in the present investigations. It may be mentioned that the
variations in ␴ and E in Pb1-xYxF2ϩx system in our case are not as large as that in solid
dc
␴
solutions Pb1-xMxF2ϩx, where M is Bi, In and Sb [11,12] reported earlier. Probably, in these
systems the polarizability factor did not play a crucial role.
4. Conclusions
The substitution of Y3ϩ in ␤-PbF2 leads to a highly disordered cubic phase, resulting in
an extra-interstitial F-anions. This should result in a gradual increase in conductivity and a

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Fig. 3. Activation energy as a function of composition for the solid solutions Pb1-xYxF2ϩx
.
decrease in activation energy with yttrium content. Contrary to this, in the present study it
is found that at low concentrations of Y3ϩ the conductivity decreases and the activation
energy increases. But beyond 4.5 mol % of Y3ϩ conductivity increases gradually and the
activation energy decreases. These two distinct regions in the activation energy versus
composition curve are explained based on the polarization factor and the extra-interstitial F
anions. At higher content of Y3ϩ (Ͼ 10 mol %) these two competing effects result in only
a marginal variation in both conductivity and activation energy for Pb1-xYxF2ϩx solid
solutions, compared to other PbF2-MF3 (M ϭ Bi, In and Sb) systems in which the extra-
interstitial F-anions play a major role in enhancing the ionic conductivity.
Acknowledgement
Dr. N.M. Gupta is thanked for his encouragement during the course of this work and Mr.
S.N. Achary for useful discussions.

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REFERENCES
[1] J.H. Kennedy, R. Miles, J. Hunter, J. Electrochem. Soc. 120 (1973) 1441.
[2] J. Oberschmidt, D. Lazarus, Phys Rev. B. 21 (1980) 2952.
[3] J.M. Reau, P.P. Fedorov, L. Rabardel, S.F. Matar, P. Hagenmuller, Mat. Res. Bull. 18 (1983) 1235.
[4] P.P. Fedarov, V. Trnocova, G.I. Kocherba, B.P. Soboloev, Cryst. Reports 40 (1995) 716.
[5] P.P. Fedorov, I.P. Zibrov, E.V. Trnocova, Zh. Neorg. Khimii 33 (1988) 3222.
[6] J.E. Ten, W. Gunsser, S.V. Chernov, A.V. Glumov, I.V. Murien, Solid State Ionics 55/56 (1992) 843.
[7] V. Trnovcova, P.P. Fedorov, B.P. Sobolov, J. Electr. Eng. 46 (1995) 104.
[8] S.J. Patwe, S.N. Achary, A.K. Tyagi, Mater. Res. Bull., in press.
[9] P. Balaya, Proc. of Solid State Phys. Symp. 42 (1999) 260.
[10] C.K. Jorgensen, Topics in Current Chemistry, 56 (1975) 38.
[11] Ph. Darbon, J.M. Reau, P. Hagenmuller, Mater. Res. Bull., 16 (1981) 273.
[12] Ph. Darbon, J.M. Reau, P. Hagenmuller, C. Depierrefixe, J.P. Laval, F. Frit, Mater. Res. Bull. 16 (1981) 273.