Ionic conductivity properties and 19F NMR investigation of Pb1−xCrxF2+x solid solutions with fluorite-type structure

Ionic conductivity properties and 19F NMR investigation of Pb1−xCrxF2+x solid solutions with fluorite-type structure

Solid State Ionics 116 (1999) 229–239 Ionic conductivity properties and 19 F NMR investigation of Pb 12x Cr x F 21x solid solutions with fluorite-typ...

430KB Sizes 0 Downloads 24 Views

Solid State Ionics 116 (1999) 229–239

Ionic conductivity properties and 19 F NMR investigation of Pb 12x Cr x F 21x solid solutions with fluorite-type structure ´ ´ b , Jean-Maurice Reau ´ b ,* Mohamed El Omari a , Jean Senegas a

b

Department of Chemistry, Faculty of Science, Moulay Ismail University, Meknes, Morocco ` Condensee ´ de Bordeaux, 87 Av. Dr. A. Schweitzer, 33608 Pessac Cedex, France Institut de Chimie de la Matiere Received 17 August 1998; accepted 1 September 1998

Abstract The F 2 ion transport and diffusion properties inside the solid solution Pb 12x Cr x F 21x (0 # x # 0.12) with fluorite-type structure have been determined by impedance spectroscopy and 19 F NMR investigation. The various electrical parameters of Pb 12x Cr x F 21x are compared with those of Pb 12x Alx F 21x (0 # x # 0.12) whose structure derives also from the fluorite-type. The Cr 31 substitutional cation is of a slightly larger size than the Al 31 cation but both cations offer the same usual 19 coordination (CN 5 6) in ternary fluorides. Comparison of F NMR spectra of some compositions Pb 12x M x9 F 21x (M9 5 Al, Cr) at different temperatures has been realized in order to discover whether the clustering process proposed in Pb 12x Alx F 21x can be extended to Pb 12x Cr x F 21x .  1999 Published by Elsevier Science B.V. All rights reserved.

1. Introduction The anion-excess solid solutions Pb 12x M x9 21 a F 21 a x (a 5 1,2), the structure of which is derived from the fluorite-type, are very fast F 2 ion conductors. As a matter of fact, these materials offer characteristic features, in agreement with optimization criteria required for high F 2 mobility: vacancies in the anionic sublattice resulting from nonstoichiometry, cationic high polarizability, size and charge difference between host and substitutional cations... [1,2]. These criteria are also responsible for the establishment of a short range order in these long range disordered phases. As a consequence, the clustering, which expands with increasing x, has an *Corresponding author. Tel.: 133-55684-6332; fax: 13355684-2761; e-mail: [email protected]

essential influence on the transport properties. A clustering process model was set up relating, in a continuous manner, the composition dependence of electrical properties and the progressive extension of clustering when x increases [3]. The solid solutions Pb 12x Bi x F 21x , Pb 12x In x F 21x and Pb 12x Zr x F 212x have been proved as characterized by the presence of column clusters involving, along the , 001 . direction, single-file vacancies (n 1 1:2n:1:0 in Pb 12x Bi x F 21x ) or two-file vacancies (2n 1 2:3n:2:0 in Pb 12x In x F 21x and 2n 1 2:4n:2:0 in Pb 12x Zr x F 212x ) as x increases [4,5]. Such clusters, labelled n 1 :n 2 :n 3 :n 4 , are electrically neutral and based on the association of n i vacancies in the normal anionic positions (1 / 4, 1 / 4, 1 / 4) of the fluorite-type network, n 2 F9 (1 / 2, u, u:0.35 # u # | 0.41) and n 4 F-(v2 , v2 , 0.40), n 3 F0(v1 , v1 , v1 :v1 5 v2 :0.28 # v2 # 0.33) interstitial fluoride ions, close to

0167-2738 / 99 / $ – see front matter  1999 Published by Elsevier Science B.V. All rights reserved. PII: S0167-2738( 98 )00347-6

230

M. El Omari et al. / Solid State Ionics 116 (1999) 229 – 239

n substitutional cations [2]. Inside each of three solid solutions, a conductivity maximum is observed for the composition corresponding to the presence of clusters of (n 5 2) size; that composition is characterized, in agreement with the clustering process model, by a maximum number of (Fi ) m ions responsible for long range motions. Correlations between short range order and F 2 ion conductivity have been recently established inside the Pb 12x Al x F 21x solid solution which offers a trivalent cation of very small size. A new clustering process has been proposed on the basis of the classical coordination number (CN 5 6) for the Al 31 cations in most aluminium ternary fluorides and of the results issued for 19 F 2 and 27 Al NMR investigations; it allows us to explain the composition dependence of conductivity; it consists of a peculiar column cluster, more and more extended as x increases, in which the AlF 6 octahedra constitute edge-sharing chains along the , 110 . direction. Two different types of aluminium ions, (Al) in and (AI) ex , have been identified and are located respectively inside and at both ends of the chain. Four types of fluoride ions have been distinguished, the F i and F n fluoride ions located in the surroundings of Pb 21 cations are the classical interstitial and normal fluoride ions, the F rd and F ra ions located around Al 31 cations are anions relaxed respectively along diagonals of elementary cubes of the fluorite structure and along edges common to AlF 6 octahedra. The cluster proposed, formulated 6n 1 2:3n:2n 1 4:2n 2 2, means that the numbers of vacancies in normal sites and the numbers of fluoride ions F i , F rd and F ra are respectively proportional to 6n 1 2, 3n, 2n 1 4 and 2n 2 2 [6,7]. Examination of different clusters inside the Pb 12x M x9 F 21x (M9 5 Al, In, Bi) solid solutions shows that each substitutional cation is characterized, according to its size, by its own classical coordination number, 6 for Al 31 , 7 for In 31 , 9, 10 for Bi 31 ion [2,7]. Other solid solutions Pb 12x M x9 F 21x , where 31 31 31 31 the substitutional cation M9(M9 5 Ti , V , Cr , Fe 31 , Ga 31 ) is of size intermediate between those of Al 31 and In 31 cations and offers, as the Al 31 cation, generally the (CN 5 6) coordination number, have been isolated [8]. It results from these considerations that the solid solutions Pb 12x M x9 F 21x (M9 31 5 Ti 31 , V 31 , Cr 31 , Fe 31 , Ga 31 ) are, possibly, characterized

by a clustering process close to that shown in Pb 12x Al x F 21x . Selecting the Cr 31 ion as substitutional cation, we have consequently undertaken, in order to confirm such an hypothesis, a 19 F NMR investigation of the Pb 12x Cr x F 21x (0 # x # 0.12) solid solution. The transport properties of Pb 12x Cr x F 21x have been first determined by impedance spectroscopy in order to compare them with those of Pb 12x Al x F 21x .

2. Experiments Quantities of PbF 2 (Merck) and CrF 3 (expected purity . 99.9%), corresponding precisely to the required value of x in the formula Pb 12x Cr x F 21x were mixed and ground in a dry box. After degassing under vacuum at 425 K for 2 h to eliminate the risk of hydrolysis at higher temperatures, each mixture was heated under dry nitrogen in a sealed gold tube at 825 K for 15 h and quenched from that temperature. The nature of products thereby obtained in microcrystalline form, single-phase or not, was determined by X-ray diffraction analysis. The impedance spectroscopy measurements were | 8 mm diameter and performed on ceramic discs of 5 about 1 mm thickness, prepared by sintering of pressed microcrystalline powders under dry nitrogen in sealed gold tubes at 825 K for 15 h and then quenched from that temperature. Compactness of pellets thereby sintered is about 90%. These pellets are inspected by X-ray diffraction analysis. Gold electrodes were deposited on both disc faces of each sample by cathodic sputtering. Each metallic pellet is then introduced into the measurement cell which is degassed at 473 K for 2 h to eliminate the risk of hydrolysis and filled up with dry argon. The electrical properties were determined by the complex impedance method using a frequency response analyser (Solartron 1260). The frequency range was 10 22 –10 16 Hz and measurements were carried out, under dry argon, between 150 and 600 K for several temperature cycles. 19 F NMR experiments were performed on a Bruker MSL-200 spectrometer (B0 5 4.7 T) equipped with a standard variable temperature unit in the temperature range 125 to 460 K. For each temperature measurement, the powder samples are kept for 1

M. El Omari et al. / Solid State Ionics 116 (1999) 229 – 239

h at that temperature, in order to reach a good thermal stability. Storage after 5 h of a large number of acquisitions allowed high resolution signals to be registered. The «Onepulse» acquisition program was used in the following operating conditions gathered in Table 1. This program was selected because it delivers a spectral irradiation large enough to cover the different spectral widths of each type of F 2 anions [9]. Signals obtained were processed by Fourier transformation, using the «WlNNMR 1 D» program [10].

3. Results

3.1. Room temperature structural properties Analysis of the X-ray diffractograms of compositions obtained after quenching from 825 K has allowed the showing of a small range of solid solution of formulation Pb 12x Cr x F 21x (0 # x # 0.12), the structure of which is derived from the fluoritetype. The unit cell parameter decreases linearly from ˚ for x 5 0 to a c 5 5.870 A ˚ for the upper a c 5 5.940 A limit x L 5 0.12. No surstructure line appears in the X-ray diffractograms, proving that Pb 12x Cr x F 21x is, as Pb 12x Al x F 21x for instance, disordered at long range, in spite of the large size difference between the host and substitutional cations.

3.2. Electrical properties The (x 5 0.03, 0.06, 0.09 and 0.12) Pb 12x Cr x F 21x samples have been studied by impedance spectroscopy. Some complex impedance diagrams (Z0 v.s. Z9) registered at various temperatures are given in Fig. 1: a first curve characteristic of volume properties is observed for the high frequencies whereas Table 1 Experimental conditions of the Pb 12x Cr x F 21x Spectrometer frequency Pulse width Dead time delay Recycle delay time Spectral width Filter width

19

F NMR investigation of 188.283 MHz 0.7 ms 6 ms 10 s 1 MHz 2 MHz

231

the experimental points corresponding to lower frequencies are located on an inclined straight line which is specific to electrode polarization phenomena [11]. The bulk ohmic resistance relative to each experimental temperature is the intercept on the real axis of the zero phase angle extrapolation of the highest frequency curve. Temperature dependence of conductivity between 165 and 500 K is represented in Fig. 2a by (log s T v.s. 1000 /T ): a behavior of Arrhenius-type, s T 5 s0 exp (2DEs /kT ), is shown, with a fit R 5 0.98. Using the complex modulus formalism M* 5 1 / ] ´ * 5 j(v C0 )Z*, where j 5Œ 2 1, v (v 52pf ) is the angular frequency and C0 the vacuum capacitance of the empty measuring cell, an analysis of ac impedance data of Pb 12x Cr x F 21x compositions was carried out in order to determine the conductivity relaxation parameters. Frequency dependence of the 99 ) at normalized imaginary part of M*(M0 /M max. different temperatures is given in Fig. 3 for the Pb 12x Cr x F 21x compositions studied: the modulus peak maximum shifts to higher frequencies as temperature increases but the shape and full-width at half-height (FWHH) of M0 /M 99 max do not change in the temperature range considered. The temperature dependence of fP , the relaxation frequency relative to 99 , given in Fig. 2b, can be compared with the M max. temperature dependence of the conductivity (Fig. 2a): for each Pb 12x Cr x F 21x composition, both lines observed are typical of an Arrhenius behavior and are quasi-parallel; the activation energy DEf issued from the modulus spectra is very close to the activation energy DEs issued from the impedance spectra (Table 2). These results suggest that the F 2 ion transport in Pb 12x Cr x F 21x is probably due to a hopping mechanism [12]. On the other hand, the 99 curves are not symmetric, implyobtained M0 /M max. ing a non-exponential behavior of the conductivity relaxation which can be described by a Kohlrausch function f (t)5exp[2(t /ts ) b ], where ts (ts 5l / 2pfP ) and b parameters are respectively the conductivity relaxation time and the Kohlrausch exponent [13,14]. The smaller the value of b, the larger is the deviation of the relaxation with respect to a Debye-type 99 relaxation ( b 51). The (FWHH) of the M0 /M max. spectra is wider than the breath of a Debye peak (1.14 decade) and it results in a b value ( b 51.14 / FWHH) equal to 0.6160.01 (Fig. 3). The b parame-

232 M. El Omari et al. / Solid State Ionics 116 (1999) 229 – 239

Fig. 1. Complex impedance diagrams of Z0 vs Z9 for Pb 12x Cr x F 21x at different temperatures (x50.03, 0.06, 0.09, 0.12).

M. El Omari et al. / Solid State Ionics 116 (1999) 229 – 239

233

Fig. 2. Inverse temperature dependence of (a) log s T and (b) log fP where fP is the peak frequency of M 99max. for Pb 12x Cr x F 21x .

ter does not depend on temperature in the considered temperature range. Its value, that is also independent of x, is close to the value obtained for Pb 12x Al x F 21x ( b 50.6060.01) [15]. The b parameter can be interpreted as representative of a distribution of relaxation times [16]. That distribution could then implicate the presence of different types of F 2 ions in Pb 12x Cr x F 21x as in Pb 12x Al x F 21x [6,7]. Composition dependence of log s at 333 and 500 K, DEs and log s0 determined for both solid solutions Pb 12x Al x F 21x and Pb 12x Cr x F 21x can be compared in Fig. 4 a,b,c from the (x50.03) compositions to (x50.12). Each solid solution offers a conductivity increase with increasing x associated with a DEs decrease. The diagram (log s v.s. DEs ) represented in Fig. 4d for T5333 and 500 K shows, as a matter of fact, a quasi-linear increase of log s when DEs decreases for each solid solution. The fact that the slope of pseudo-lines is steeper with M95Cr

than with M95Al points out a more important influence of DEs on conductivity in Pb 12x Cr x F 21x than in Pb 12x Al x F 21x . The variation of log s0 with x depends, on the other hand, on the nature of substitutional cation, appreciable decreasing with increasing x for M95Al with no notable variation for M95Cr (Fig. 4c). Inside each solid solution, the limit compositions, Pb 0.88 Al 0.12 F 2.12 and Pb 0.88 Cr 0.12 F 2.12 are characterized by very close values of each electrical parameter. On the contrary, considering the (x50.03) compositions, the aluminium–lead fluoride offers at the same time a higher activation energy and a clearly larger value of preexponential factor than the chromium–lead fluoride. As these characteristics have an opposite influence on conductivity, the electrical performance of Pb 0.97 Al 0.03 F 2.03 are slightly higher only than those of P0.97 Cr 0.03 F 2.03 . The higher value of log s0 determined for

234 M. El Omari et al. / Solid State Ionics 116 (1999) 229 – 239

Fig. 3. Plots of normalized modulus M0 /M 99max against log f for Pb 12x Cr x F 21x at various temperatures (x50.03, 0.06, 0.09, 0.12).

M. El Omari et al. / Solid State Ionics 116 (1999) 229 – 239

235

and leads to a maximum. The increase of conductivity with x inside Pb 12x Cr x F 21x is much more regular and it can be shown from that comparative study of electrical properties that Pb 12x Cr x F 21x could be characterized by a clustering process different from that shown in Pb 12x Al x F 21x .

3.3. F NMR results The 19 F NMR spectra at various temperatures are given in Fig. 5 for the compositions Pb 12x Cr x F 21x relative to x50.03, 0.06 and 0.12. The origin of the frequency scale corresponds to the nominal irradia-

Fig. 4. Composition dependence of (a) log s at 333 and 500 K, (b) DEs (c) log s0 and (d) variation of log s at 333 and 500 K as a function of DEs for Pb 12x M 9x F 21x (M95Al, Cr).

Pb 0.97 Al 0.03 F 2.03 is probably due to a larger disorder entropy term resulting from the larger size difference between the Al 31 and Pb 21 cations. The log s0 decrease from (x50.03) to (x50.12) inside Pb 12x Al x F 21x results from the progressive establishment of a short-range order on the form of clusters 6n12:3n:2n14:2n22 more and more extended when x increases [6,7]. Consequently, inside Pb 12x Al x F 21x , a fast increase of conductivity is observed for the small values of x, up to x50.06; above that value, the conductivity increase is weaker Table 2 Electrical characteristics of the Pb 12x Cr x F 21x compositions x

log s (333 K) (V.cm)21 (60.02)

log s0 (V.cm)21 (60.1)

DEs (eV) (60.01)

DEf (eV) (60.01)

0.03 0.06 0.09 0.12

25.18 24.43 23.78 23.27

4.9 4.5 4.8 5.0

0.50 0.42 0.40 0.38

0.48 0.41 0.39 0.37

Fig. 5. Thermal variation of the Pb 12x Cr x F 21x (x50.03, 0.06, 0.12).

19

F NMR spectra for

236

M. El Omari et al. / Solid State Ionics 116 (1999) 229 – 239

tion frequency (188.283 MHz). Whatever x, the spectrum appears as formed by a single peak at low temperatures and this peak becomes narrower when temperature increases. Centered at low temperatures at n 5 25, 210 and 215 kHz for x50.03, 0.06 and 0.12 respectively, the peak is shifted slightly towards higher frequencies at increasing temperature and this shift is all the larger as x increases. Furthermore, a second peak of very weak intensity can be detected for each composition at n 5 215 kHz for temperatures higher than 370 K. The 19 F NMR spectra of compositions Pb 12x Cr x F 21x studied can be compared with those obtained at the same temperature for the composi-

tions Pb 12x Al x F 21x (x50.03, 0.06, 0.09, 0.12) [6]. The experimental temperatures selected are 175 K, which is in fact a rigid lattice temperature for all these materials, and 400 K, temperature above which all F 2 ions in Pb 12x Al x F 21x can be considered as mobile in the NMR time scale [6]. These spectra are shown in Fig. 6a,b. Several remarks result from the examination of these spectra: Whatever the temperature, the spectrum of chromium material is clearly broader than that of aluminium material corresponding to the same temperature and the same x value. The existence of broad spectra for the Pb 12x Cr x F 21x compositions is due to the presence of very strong dipolar interac-

Fig. 6. Composition dependence of the 19 F NMR spectra at (a) T5175 K, (b) T5400 K, of Dn ]12 at (c) T5175 K, (d) T5400 K, and of npeak at e) T5400 K for Pb 12x M 9x F 21x (M95Al, Cr).

M. El Omari et al. / Solid State Ionics 116 (1999) 229 – 239

tions between the F 2 nuclei and the paramagnetic Cr 31 ions (Ar.4s 0 3d 3 ) which have three un-paired electrons. Composition dependence of the linewidth (Dn ]12 ) at T5175 and 400 K, given in Fig. 6c,d for both solid solutions confirms such a result: at 175 K, the Dn ]21 increase with x is small for Pb 12x Al x F 21x but very important for Pb 12x Cr x F 21x ; at 400 K, Dn ]12 does not depend any more on x inside Pb 12x Al x F 21x , but the Dn ]21 increase in Pb 12x Cr x F 21x is still quite significant. The low-temperature spectra (T5175 K) of chromium compositions differ clearly from those of aluminium (Fig. 6a): two separate peaks are observed on the spectra of aluminium materials, they have been assigned respectively as the lower frequency peak to fluoride ions located in the closest surroundings of Al 31 cations, the higher frequency peak to fluoride ions bound to Pb 21 cations [6]; the appearance of a single peak on the spectra of chromium compositions reveals no information on the distribution of F 2 ions in Pb 12x Cr x F 21x . The spectra of aluminium compositions are characterized at increasing temperature by the existence of a new peak of lorentzian type which has been assigned to F 2 ions mobile on the NMR time scale; growing with temperature, it subsists only at T .400 K (Fig. 6b); no peak of that kind is detected even at high temperature on the spectra of chromium compositions. Composition dependence of the frequency peak observed at T5400 K for both solid solutions is given in Fig. 6e: whatever x, the frequency of peak is higher for the chromium compositions than for those of aluminium and a peak shift with increasing x towards higher frequencies is observed for Pb 12x Cr x F 21x whereas a shift towards lower frequencies characterizes Pb 12x Al x F 21x . Such a result is due probably to a different type of chemical bonds inside both solid solutions. This investigation proves that the F 2 ion diffusion properties in Pb 12x Cr x F 21x differ from those shown in Pb 12x Al x F 21x . The Pb 12x Cr x F 21x solid solution is probably characterized by a clustering process distinguishable from that proposed in the Pb 12x Al x F 21x solid solution. Temperature dependence of Dn ]12 is given for the Pb 12x Cr x F 21x compositions in Fig. 7a. The experimental points relative to a given x value are

237

Fig. 7. Variation of (a) Dn ]21 and (b) ns as a function of temperature and of (c) DEs and DENMR as a function of x for Pb 12x Cr x F 21x .

located on a curve which can be simulated by a Boltzman function: DnR 2 Dnr Dn ]12 (T ) 5 Dnr 1 ]]]]]] 1 1 exp[(T 2 T 0 ) /DT ] where 2 Dn ]12 (T ) is the line width at temperature T; Dnr is a residual half-width due to the field inhomogeneity at T max . 5460 K; 2DnR is the halfwidth of the rigid lattice determined at low temperature (T5200 K); 2T 0 is the center of the Boltzman function; 2DT5o|(T j 2T i ) /n is the average temperature difference between two successive experimental temperatures T i and T j , with (n11) the number of measurement temperatures. The calculated parameters for the simulation function are gathered for three Pb 12x Cr x F 21x compositions in Table 3. Above T5200 K, Dn ]21 decreases progressively at increasing temperature. This narrowing is due to

M. El Omari et al. / Solid State Ionics 116 (1999) 229 – 239

238

Table 3 Simulation function parameters for Pb 12x Cr x F 21x x

DnR (kHz)

Dnr (kHz)

T0 (K)

DT (K)

0.03 0.06 0.12

31.5 43.0 53.4

5.2 6.7 9.6

343 323 293

19.4 32.5 36.2

the NMR time scale are short range. Composition dependence of DENMR and DEs , in Fig. 7c, shows that DENMR , as DEs , decreases with increasing x, proving that the F 2 ion motions at long range in Pb 12x Cr x F 21x are, of course, somewhat correlated to short range motions.

4. Conclusions mobile F 2 ions motions that average out the F–F dipolar interactions. At T #200 K, the experimental values of Dn ]21 are higher than calculated values and the differences between experimental and calculated values increase, whatever x, when temperature decreases. These differences are due probably to strong interactions between the F nuclei and the un-paired electrons of Cr 31 cations. These interactions are, of course, all the stronger as x increases, it results that DnR and Dnr increase with increasing x, which is experimentally observed (Fig. 7a). In contrast the T 0 parameter decreases when x increases (Table 3); that T 0 variation can be correlated to a larger mobility of F 2 ions on the NMR time scale, result in agreement with the increase with x of electrical properties at long range determined by impedance spectroscopy. The activation energy of F 2 ions mobile on the NMR time scale has been calculated for each Pb 12x Cr x F 21x composition from the thermal variation of the jump frequency ns . Linenarrowing 2 occurs when the F ion jump frequency ns is of the same order as the rigid lattice linewidth. The thermal variation of ns can be deduced from that of Dn ]21 by the expression [17]:

ns 5 a uDn ]12 2

2 Dnr u / tan[(p / 2)u(Dn ]21 2 Dnr ) /(DnR 2 Dnr )u ] Dnr and DnR have been defined above, the a parameter is a constant function of line shape. The gaussian line shape at low temperature led to a choice of unity for the value of a. The inverse temperature dependence of ns over the range 200,T ,350 K in Fig. 7b, shows ns follows, whatever x, an Arrhenius-type relation, with ns 5 n0 exp(2DENMR /kT ). For each x value, the activation energy DENMR is clearly lower than the activation energy DEs determined by impedance spectroscopy (Fig. 7c). This result means that F 2 ion motions on

The study by impedance spectroscopy of electrical properties at long range in Pb 12x Cr x F 21x shows, as in Pb 12x Al x F 21x , a conductivity increase when x rises and the electrical performance of both limit compositions, Pb 0.88 Cr 0.12 F 2.12 and Pb 0.88 Al 0.12 F 2.12 are very close. In contrast, the conductivity variation with x in Pb 12x Cr x F 21x differs from that observed in Pb 12x Al x F 21x . Pb 12x Al x F 21x is characterized for the small x values (x50.03) by a high value of disorder entropy term due to the large size difference between the Pb 21 and Al 31 cations; the entropy term decrease for the higher x values is due to the establishment of a short range order in Pb 12x Al x F 21x , more and more developed with increasing x. It results in a fast increase of conductivity for x#0.06 then a slower increase and a tendency towards a maximum for x$0.06. The increase in conductivity with x in Pb 12x Cr x F 21x is much more regular. It is probable that the short range order in Pb 12x Cr x F 21x , whatever it may be, expands with x much less quickly than in Pb 12x Al x F 21x . 19 The F NMR investigation of Pb 12x Cr x F 21x has shown that the F 2 ion diffusion properties in the chromium solid solution differ from those shown in the aluminium solid solution. The presence of very strong dipolar interactions between the F 2 nuclei and the paramagnetic Cr 31 cations has not allowed to obtain high resolution signals, the 19 F 2 NMR spectra of Pb 12x Cr x F 21x are broad and no information on the distribution of F 2 ions in Pb 12x Cr x F 21x could be revealed. An investigation by neutron diffraction of Pb 12x Cr x F 21x will be undertaken in order to determine the nature of the short-range order inside that solid solution. The activation energy DENMR of F 2 ions mobile on the NMR time scale has been determined from temperature dependence of the jump frequency in Pb 12x Cr x F 21x Whatever x, DENMR is smaller than

M. El Omari et al. / Solid State Ionics 116 (1999) 229 – 239

DEs , the F 2 ion motions on the NMR time scale are short range and they are all the faster as x increases.

References ´ [1] J.M. Reau, P. Hagenmuller, Appl. Phys. A49 (1989) 3. ´ [2] J.M. Reau, P. Hagenmuller, Bull. Electrochem. 11 (1995) 34. ´ ´ ´ [3] J.M. Reau, M. Wahbi, J. Senegas, P. Hagenmuller, Phys. Stat. Sol. b169 (1992) 331. ´ [4] C. Lucat, J. Portier, J.M. Reau, P. Hagenmuller, J.L. Soubeyroux, J. Solid State Chem. 32 (1980) 279. ´ ´ ´ [5] J.M. Reau, M. El Omari, J. Senegas, P. Hagenmuller, Solid State Ionics 38 (1990) 123. ´ ´ ´ [6] M. El Omari, J. Senegas, J.M. Reau, Solid State Ionics 100 (1997) 233. ´ ´ ´ [7] M. El Omari, J. Senegas, J.M. Reau, Solid State Ionics 100 (1997) 241.

239

¨ [8] J. Ravez, M. Darriet, R. Von der Muhll, P. Hagenmuller, J. Solid State Chem. 3 (1971) 234. [9] Onepulse program, Bruker Spectrospin S.A., Wissenbourg, France. «Products for Spectrometer Type MSL-200» [10] WlN NMR 1 D program, Bruker Spectrospin S.A., Wissembourg, France. «1 D NMR data processing, version 95 0901 1 No. SPP-501. [11] J.F. Bauerle, J. Phys. Chem. Solids 30 (1969) 2657. [12] B.V.R. Chowdari, R. Gopalakrishnan, Solid State Ionics 23 (1987) 225. [13] K.L. Ngai, S.W. Martin, Phys. Rev. B 40 (1989) 10550. [14] K.L. Ngai, Phys. Rev. B 40 (1993) 13481. [15] M. El Omari, Thesis, Meknes, Morocco, 1997. [16] F.S. Howell, R.A. Bose, P.B. Macedo, C.T. Moynihan, J. Phys. Chem. 78 (1974) 639. [17] N. Bloembergen, E.M. Purcell, R.V. Pound, Phys. Rev. 73 (1948) 679.