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Frequency response of polycrystalline samples of α−Zr(HPO4)2·H2O at different relative humidities
Solid State Ionics 17 (1985) 287-293 North-Holland, Amsterdam
FREQUENCY RESPONSE OF POLYCRYSTALLINE SAMPLES OF
a-Zr(HP04)Z~Hz0 AT DIFFERENT RELATIVE HUMIDITIES * M. CASCIOLA and D. BIANCHI Dipartimento di Chimica, Universitd di Peru&, Vii Elce di Sotto 10.06100 Peru&, Italy Received 4 June 1985 Accepted 11 July 1985
Polycrystalline samples of a-Zr(HP04)aHz0, conditioned at various relative humidities, were investigated in the temperature range -20 to 20°C by admittance measurements. The frequency response was fitted by complex non-linear regression to an equivalent circuit consisting of a parallel combination of a resistance, a geometrical capacitance and a constant phase angle element. As a consequence of increasing surface hydration, the dc conductivity increases by about two orders of magnitude as the relative humidity goes from 5 to 90%. The parameterization of the dc conductivity shows that these increments are essentially due to a change in activation energy from 12 to 6 kcal/mol. A quantitative correlation between the dc conductivity and the parameters of the constant phase angle element is observed and discussed on the basis of different models.
1. Introduction
The electrical conductivity of monohydrated alayered zirconium phosphate (o-Zr(HPO4)2H,O) is due for the most part to diffusion of protons along the hydrated surface of the microcrystals: it depends on the number of the surface ionogenic groups [l] and the particle dimensions [2]. In a previous paper [3] it was shown that the frequency response of polycrystalline samples is also influenced appreciably by changes in relative density, causing a modification of the interparticle contacts; nevertheless, for relative densities ranging from 75 to 90%, the complex admittance is accurately modelled by the same equivalent circuit, consisting essentially of a parallel combination of a resistance, a geometrical capacitance and a constant phase angle element. In addition, the results of this investigation indicate that the same dc conducting phase (i.e. surfaces and intergranular contacts) is also responsible for ac conduction; therefore a study of the electrical properties of (YZr(HP04)2H20 under different experimental conditions should allow some quantitative correlation to be .* This work was supported by Progetto Finalizzato Energetica CNR-ENEA, Sottoprogetto Energla Elettrica.
0 167-2738/85/$ 03.30 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
observed between the parameters regulating ac and dc conduction. On the other hand it has recently been found [4] that the dc conductivity of o-Zr(HPO4)2H2O equilibrated over water vapour is about one order of magnitude higher than that measured at 40% relative humidity. Although no quantitative information is available about a water adsorption on o-zirconium phosphate surface, the conductivity change must be ascribed to a different surface hydration, the content of the bulk crystallization water being constant in a wide range of relative humidity (from P4010 up to 100%). These findings indicate that the equilibration of polycrystalline samples at different relative humidities allows the surface transport properties to be modified without altering the bulk chemical composition. In order to completely characterize the dependence on surface hydration of the conductivity and, more generally, of the frequency response, the admittance of polycrystalline o-Zr(HPO4)2H,O was determined as a function of temperature at different relative humidities and fitted to a suitable equivalent circuit by using a complex non-linear least squares procedure.
288
M. Casciola,D. Bianchi / Polycrystallinesamples of arZr(HPO4)2-Hz0
2. Experimental a-Zr(HP04)~H~0 was prepared by the direct precipitation method in the presence of hydrofluoric acid [5]. After washing with distilled water up topH 3.54, the microcrystals were stored over P,O,, . Compact discs, 10 mm in diameter and 2-2.5 mm thick with bulk densities of about 88-90% of the theoretical density, were prepared by pressing microcrystalline cr-Zr(HP0,)2H20 at 60 kN/cm2. The two opposite sides of the discs were coated with a thin film of a silver conductive paint, Admittance measurements were made by a sealedoff cell connected to a Hewlett Packard 4192 A impedance analyzer in the frequency range 10 Hz to 5 MHz, at a signal voltage lower than 1 V. Before measurements the discs were equilibrated at 20°C for a week at a known relative humidity. Relative humidities between 5 and 90% were obtained by using saturated solutions or sulphuric acid water mixtures [6]. In order to prevent any change in the water content of the microcrystal surfaces, the discs were located in the measuring cell operating within a box at controlled relative humidity. All measurements taken went from the highest to the lowest relative humidity and, for each relative humidity, from the highest to the lowest temperature.
3. Results and discussion 3.1. Equivalent circuit Admittance measurements were carried out on polycrystalline samples of ~Y-Z~(HFQ~)~H~O over a wide range of relative humidities (from 5 to 90%) at temperatures between 20 and -5O’C. Since each sample had previously been equilibrated at 20°C at a controlled relative humidity, no measurements were made above this temperature in order to avoid any water loss from the surface of the microcrystals. The variation of relative humidity modifies- the impedance appreciably, but does not affect the shape of the X-R plot, which in any case consists of a semicircular arc with a low frequency tail (fig. 1). In a previous paper [3] it was shown that this trend is consistent with the equivalent circuit of fig. 1: here K and Q are two constant phase angle elements, the
0.5
I
/
I
05
I
1.0 R(B)
x 10-’
Fig. 1. Impedance plot obtained at 20°C for polycrystalline a-Zr(HPO&H20 equilibrated at 90% relative humidity. The equivalent circuit, to which the frequency response was fitted, is also shown. The solid line was calculated using the parameters listed in table 2.
second representing the impedance of the electrodeelectrolyte interface. R is a resistance accounting, together with K, for the impedance of the polycrystalline sample, while Cg is a geometrical capacitance arising from the high frequency dielectric constant of the electrolyte and the parasitic capacitance of the measuring cell. The admittance of K (Yi) and the impedance of Q (2;) are: Yi = k(io)” ,
26 = q(h)-P
(1) ,
(2)
where k, n, q and p are frequency-independent parameters. The total admittance for the circuit of fig. 2 is Y* = ioC, + {[l/R t k(io)“]-l
+ q(iw)-P}-l
.
(3)
The six parameters of this equation were calculated using a fitting procedure based on a non-linear leastsquares analysis of the complex admittance, as described in ref. [3]. The conductivity (u) at 2O”C, calculated from R and disc dimensions, is plotted in fig. 2 as a function of relative humidity (rh) together with the specific values of k at the same temperature. Although the conductivities reported here (from 3.4 X 10v6 to 2.3 X lo-* S cm-l) are considerably lower than those of ref. [4], probably due to a different surface area, their decrease from 90 to 40% rh is proportionately comparable with that of [4]. Like R and k, the parametern is appreciably influenced by changes in relative humidity, but not in temperature: in the range 20/
289
M. Casciola,D. Bianchi f Polycrystallinesamples of cr-Zr(HPOJ~~H~O
60%r.h
-6.5
L 2
I
I
20
I
I
I
1
1
60
40
I
I
60
’ log f(Hz)
4
6
Fig. 3. Conductance as a function of frequency for polycrystalline o-Zr(HPO&HzO at 20°C and different relative humidities. Solid lines were calculated using the parameters listed in table 2.
%r.h.
Fig. 2. IJ and k values at 20°C as a function of relative humidity for polycrystalhne or-Zr(HPO&HaO.
-20°C, n is constant within the error limits of the non-linear least squares procedure. Average n values (3) for each relative humidity are listed in table 1. Some computer simulations of the real and imaginary parts of the admittance are shown in figs. 3 and 4; the solid line too, which interpolates the points of the impedance plot (fig. l), was calculated on the basis of the proposed equivalent circuit. Although the variation of relative humidity modifies the frequency response appreciably, the standard deviation of the fit,
calculated according to [ 171, lies in any case within the range 0.05-0.005, with an average value of 0.02. These results, together with those obtained for poly crystalline samples with different densities, indicate that the proposed equivalent circuit is able to give a
90%
r.h.
Table I Average n values (E) and associated standard deviations (un) in the temperature range 20 to -20°C at different relative humidities. rh
n
on
90 75 60 SO 2.5 5
0.65 0.63 0.61 0.59 0.57 0.55
0.007 0.009 0.006 0.003 0.005 0.007
I
1
I
I
2
I
4
I
I
6
log f(Hz) Fig. 4. Susceptanceas a function of frequency for polycrystalline (r-Zr(HPO&HaO at 20°C and different relative humidities. Solid lines were calculated using the parameters listed in table 2.
M. Casciola,D. Bianchi / Polycrystallinesamples of cu-Zr(HPO4)2*H20
290
Table 2 Parameters used to fit to the equivalent circuit the experimental data of figs. 1, 2 and 3. SDF is the standard deviation of the overall admittance fit. The parameters here reported refer to measurements made at 20°C on the same disc of polycrystalline OLZr(HP04)aHaO. R X lo-’ (a)
rh
90 60 25
0.833 4.93 28.4
k x 1O’O (S sn)
n
8.04 5.34 4.23
0.632 0.618 0.573
fairly accurate model of the frequency response of (YZr(HF’04),H20 independently of relative humidity (from 90 to 5%) and relative density (from 90 to 75%). 3.2. Activation energy Typical Arrhenius plots are shown in fig. 5 : log(oT) is a linear function of l/T in the temperature range 20 to -20°C while a considerable variation in the slope is found at lower temperatures. This trend, which is probably due to some change in the transport mechanism, has been observed for all relative humidities as well as for ~-Ti(HF’04)22H20 [7] and some intercalation compounds of ~-ZI@IF’O~)~H~O[8]. Since conductivity measurements themselves cannot
4 x 10-7 (52 s-n)
P
0.854 1.38 3.03
0.151 0.76 0.83
SDF
53
(pF) 6.64 6.7 6.82
0.019 0.023 0.033
account for this phenomenon, only the data obtained between 20 and -20°C will be discussed in the present paper. From fig. 2 it is seen that the conductivity of polycrystalline cu-Zr(HP04)2H20 increases by about two orders of magnitude for relative humidities going from 5 to 90%; we therefore thought it of interest to investigate to what extent the variation of (I arose from a change in activation energy (E,) by parameterizing the conductivity data on the basis of the equation: UT = u. exp(-E,/RT)
.
-4 _ z
Y
‘i
E
:: i= 5
-
s -s_
z
F
7
4
E
::
3I
1
-6 _
d
-B
I
I
1
I
20
40
%rh I” I.,..
60
80
4 25
3 7s 10?T(K)
Fig. 5. Arrhenius plots for polycrystalJine a-Zr(HPO4)aHsO conditioned at 90 and 40% relative humidity.
Fig. 6. Activation energy (E,)and pre-exponential factor (co) for polycrystalline a-Zr(HPO&HaO equilibrated at different relative humidities. E, and o. were calculated by parameterizing the conductivity using eq. (4).
291
hi. Caseiola,D. Bianchi/ Polycrystalline samplesof eZr(HPO4)2*H20
According to the hopping model, the pre-exponential factor is temperature independent and proportional to the activation entropy, to the effective carrier concentration and its hopping attempt frequency [9]. The values of u. and E, are plotted in fig. 6 as a function of relative humidity. With rh decreasing from 90 to 5% the activation energy doubles, while the pre-exponential factor remains constant down to 25% rh and then begins to increase sharply between 25 and 5% rh. These results show that the variation of u between 90 and 25% rh is explained for the most part by the change in activation energy. The dependence of E, on the surface hydration can be understood by considering recent experimental evidence [lo] indicating that the proton is not able to diffuse along the anhydrous surface of o-zirconium phosphate, due to the distance (5.3 A) between the barycentres of neighbouring ionogenic groups. Consequently, surface proton diffusion needs the presence of water molecules forming bridges between the $POH groups: the number and arrangement of these molecules determine the diffusion characteristics. About the water arrangement, it may be observed that the structure of a-zirconium phosphate [ 1 l] is such as to create two kinds of semi-cavities on the surface where water molecules can be lodged (fig. 7); in addition the possible adsorption of more water, with the formation of one or more monolayers, should be taken into account.
0.. .o.. ,_-\ ,..~y&g ,.,... , ..(J (J.,,,.. ~ ..0..
Since the presence of water is indispensable for proton surface diffusion, it seems to be improbable that the high value of u. at 5% rh arises from an increase in the effective carrier concentration. On the contrary, a variation of the hopping attempt frequency and/or activation entropy, probably also associated with some change in the transport mechanism, may reasonably be suggested. 3.3. k/o correlation The results obtained in the present and the previous paper [ 31 by parameterizing the frequency response of polycrystalline o-Zr(HP0,)2H20 indicate that the factors regulating the dc conductivity also appreciably influence the parameters (n and k) of the constant phase angle element, so that some quantitative correlation between k, n and u may be expected. In relation to this it was found that at the lowest relative humidities (i.e. from 40 to 5%), plots of log k as a function of (1 - ii) log u can be fairly accurately interpolated by straight lines with unit slope (fig. 8). At the highest relative humidities (from 60 to 90%) a considerable scatter in the log k values is observed, due to the error associated with k; nevertheless, taking the error into account, it is seen that the experimental points cluster about straight lines with unit slope in these cases too. Thus the following empirical relation can be written: k = Aul--n 9
.,,.,.,..
‘,
r.... .
% ‘i
6
-3.6 -9.8
(5)
T
1
JY
I _ .
$-IS
_
YF60%
2 8:
B
-10.2 _
...
I
5%
on the surface of o-zirconium phosphate. Dashed circles indicate the sites available for water adsorption. Dotted lines represent the projection into the hydroxyl plane of the bonds (P-0-Zr) bridging the surface phosphates to the underlying plane of Zr atoms; each Zr is located at the intersection of three lines.
40%
25%
p,:ii I
I
-3.5
Fig. 7. Schematicrepresentationof the hydroxyl arrangement
90%
75%
1
I
-3.0 (1-E).loga(S
I
I
-2.5
I
I
-2.0
cm-‘)
Fig. 8. Log k as a function of (1 - ii) log (I, in the range -20 to 20°C, for polycrystalhne aZr(HP04)2H20 conditioned at different relative humidities. Vertical bars represent the average error associated with log k for each relative humidity. All straight lines have unit slope.
M. Casciola,D. Bianchi / Polyqwtalline samples of wZr(HPOJ z*HzO
292
where A is a temperature-independent parameter. Since u is entirely due to surface transport, eq. (5) indicates that no significant contribution from the crystal bulk response is present in the element k, thus confirming quantitatively the suggestions made in previous papers [3,12]. We may discuss eq. (5) on the basis of two different models. On analyzing the frequency dispersion of the electrode polarization capacitance, Scheider [ 131 has shown that eq. (5) holds for constant phase angle admittances composed of capacitive and dispersive elements, such that the first are invariant with u and the second directly proportional to it. It can be pointed out that this condition can be satisfied in a microcrystalline powder: specifically, if the temperature changes do not alter the composition of the interpartitle phase, then the geometrical capacitance of each intergranular contact should be independent of temperature and hence of electrolyte conductivity. In the present case, the conductivity measurements have been carried out so that the amount of adsorbed water was kept constant with changing temperature; thus, for each relative humidity the conditions leading to eq. (5) seem to be satisfied. A substantialIy different model concerning with the k/a correlation has recently been proposed by Almond and West [ 14,151. According to this model, based on the Jonscher universal dielectric response function, the activation energy fork (Ek) is given by &=Ef+(l-n)&,
(6)
Ef
and Ed being the activation energies for defect formation and carrier diffusion, respectively. This model is of interest because, once E,, Ek and n are known, Ef and Ed can be determined, since E, is equal to Ef + Ed. Eq. (5) implies the following relation between Ek and E, : Ek = -R
a
ln(kT)/a(l/T)
= (1 - n)E, + nRT.
(7)
Since nRT is not greater than 0.5 kcal/mol, Ek is about (1 - n)E, and Ef 2: 0 independent of relative humidity. In our opinion this is quite surprising. Although the mechanism of the’proton transport along the surface of o-zirconium phosphate is not yet known, it is reasonable to suppose that the first step consists in the dissociation of the ?POH groups: ,1POH+H20+PO-
+H,O+.
(8)
It is not easy to estimate the enthalpy of this process. According to Albertsson [ 161, the bonding of each phosphate to three Zr(IV) atoms should enhance the acidity of the monohydrogen group compared with that of HPOi- in water solution. On the other hand it is known that the acid strength is also influenced by the solvation of the dissociation products. From this point of view the acidity of a phosphate group belonging to the surface should not be greater than in water and should depend on the number of water molecules coordinating sPO_ and H, O+ : the more hydrated they are, the more stable the dissociated state should be. Hence the dissociation enthalpy is expected to show some dependence on surface hydration and, consequently, on relative humidity. We think that a more reliable test concerning the possibility of applying eq. (6) to microcrystalline zirconium phosphate can be performed by investigating the frequency response of anhydrous o-zirconium phosphate: experimental evidence [ 10,18,19] indicates that protonic transport occurs in the interlayer space and, in the absence of water, the phosphate dissociation should involve neighbouring ?POH groups belonging to adjacent layers: =_POH+ SmH =+SPO- + >PO@.
(9)
In this case, the interaction of ?PO- and $POHi groups with the hydroxyls of the interlayer region should not be stronger than that associated with the full hydration of H30+ and >PO- groups present on the surface, (eq. (8)). Thus the enthalpy of the process (9) is expected to be greater than that of the reaction (8) the gPOH group being less basic than H20.
4. Conclusion The study of polycrystalline cr-Zr(HP0,)2H20 carried out in the present and in a previous paper [3] has allowed the frequency response to be characterized as a function of temperature, relative humidity and density. It has been shown that both the dc and the ac conduction can be accounted for by the variation of the electrical characteristics of the microcrystal surfaces and intergranular contacts. On the basis of these results, some discrepancies which are found in comparing the results reported in previous papers can be ex-
M. Casciola,D. Bianchi / Polycrystalline
plained: for example, the fact that the activation energy resulting from isoconductivity measurements [l] is lower than that obtained for pressed powders [2] can be partially associated with different surface hydration. Finally the knowledge acquired of the electrical conduction and frequency response of (YZr(HPO,),H,O should turn out to be helpful for understanding protonic transport in new materials (such as hydrated pellicular zirconium phosphate) exhibiting chemical and structural characteristics similar to those of monohydrated zirconium phosphate.
Acknowledgement The authors whish to thank Prof. G. Alberti helpful and valuable suggestions.
for
References
[ 1] G. Alberti, M. Casclola, U. Costantino, G. Levi and G. Ricciardi, J. Inorg. Nucl. Chem. 40 (1978) 533.
[ 21 E. Krogh Andersen, LG. Krogh Andersen, C. Knakkergard Mdller, K.E. Simonsen and E. Skou, Solid State Ionics 7 (1982) 301.
samples of c+Zr(HPO4)2’H20
293
I31 D. Bianchi and M. Casciola, Solid State Ionics 17 (1985) 7. 141 S. Yde-Andersen, J.S. Lundsgaard, J. Mailing and J. Jensen, Solid State Ionics 13 (1984) 81. I51 G. Alberti, S. Alhdli, U. Costantino and M.A. Massucci, J. Inorg. Nucl. Chem. 37 (1975) 1779. 161 R.H. Stokes and R.A. Robinson, Ind. Eng. Chem. 41 (1949) 2013. [71 M. Bracardi, D. Chem. Thesis (Dept. of Chemistry, University of Per&a, Italy, 1980). ]81 M. Casciola, work in progress. ]91 R.A. Huggins, in: Diffusion in solids, eds. A.S. Nowick and J.J. Burton (Academic Press, New York, 1975) Chap. 9. 1101 G. Alberti, M. CascioIa, U. Costantino and M. Leonardi, Solid State Ionics 14 (1984) 289. 1111 A. Clearfield and G.D. Smith, Inorg. Chem. 8 (1969) 431. 1121 M. Casciola, U. Costantino, S. Fazzini and G. Tosoratti, Solid State Ionics 8 (1983) 27. 1131 W. Scheider, J. Phys. Chem. 79 (1975) 127. [141 D.P. Almond, A.R. West and R.J. Grant, Solid State Commun. 44 (1982) 1277. 1151 D.P. Almond and A.R. West, Solid State Ionics 9/10 (1983) 277. ]161 J. Albertsson, A. Oskarsson, R. Teligren and J.O. Thomas, J. Phys. Chem. 81 (1977) 1574. 1171 D.R. Franceschetti, J. Schoonman and J.R. Macdonald, Solid State Ionics 5 (1981) 617. [ 181 G. Alberti, M. Casciola, U. Costantino and R. Radi, Gazz. Chim. ItaI. 109 (1979) 421. [ 191 P. Jerus and A. Clearfield, Solid State Ionics 6 (1982) 79.
FREQUENCY RESPONSE OF POLYCRYSTALLINE SAMPLES OF
a-Zr(HP04)Z~Hz0 AT DIFFERENT RELATIVE HUMIDITIES * M. CASCIOLA and D. BIANCHI Dipartimento di Chimica, Universitd di Peru&, Vii Elce di Sotto 10.06100 Peru&, Italy Received 4 June 1985 Accepted 11 July 1985
Polycrystalline samples of a-Zr(HP04)aHz0, conditioned at various relative humidities, were investigated in the temperature range -20 to 20°C by admittance measurements. The frequency response was fitted by complex non-linear regression to an equivalent circuit consisting of a parallel combination of a resistance, a geometrical capacitance and a constant phase angle element. As a consequence of increasing surface hydration, the dc conductivity increases by about two orders of magnitude as the relative humidity goes from 5 to 90%. The parameterization of the dc conductivity shows that these increments are essentially due to a change in activation energy from 12 to 6 kcal/mol. A quantitative correlation between the dc conductivity and the parameters of the constant phase angle element is observed and discussed on the basis of different models.
1. Introduction
The electrical conductivity of monohydrated alayered zirconium phosphate (o-Zr(HPO4)2H,O) is due for the most part to diffusion of protons along the hydrated surface of the microcrystals: it depends on the number of the surface ionogenic groups [l] and the particle dimensions [2]. In a previous paper [3] it was shown that the frequency response of polycrystalline samples is also influenced appreciably by changes in relative density, causing a modification of the interparticle contacts; nevertheless, for relative densities ranging from 75 to 90%, the complex admittance is accurately modelled by the same equivalent circuit, consisting essentially of a parallel combination of a resistance, a geometrical capacitance and a constant phase angle element. In addition, the results of this investigation indicate that the same dc conducting phase (i.e. surfaces and intergranular contacts) is also responsible for ac conduction; therefore a study of the electrical properties of (YZr(HP04)2H20 under different experimental conditions should allow some quantitative correlation to be .* This work was supported by Progetto Finalizzato Energetica CNR-ENEA, Sottoprogetto Energla Elettrica.
0 167-2738/85/$ 03.30 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
observed between the parameters regulating ac and dc conduction. On the other hand it has recently been found [4] that the dc conductivity of o-Zr(HPO4)2H2O equilibrated over water vapour is about one order of magnitude higher than that measured at 40% relative humidity. Although no quantitative information is available about a water adsorption on o-zirconium phosphate surface, the conductivity change must be ascribed to a different surface hydration, the content of the bulk crystallization water being constant in a wide range of relative humidity (from P4010 up to 100%). These findings indicate that the equilibration of polycrystalline samples at different relative humidities allows the surface transport properties to be modified without altering the bulk chemical composition. In order to completely characterize the dependence on surface hydration of the conductivity and, more generally, of the frequency response, the admittance of polycrystalline o-Zr(HPO4)2H,O was determined as a function of temperature at different relative humidities and fitted to a suitable equivalent circuit by using a complex non-linear least squares procedure.
288
M. Casciola,D. Bianchi / Polycrystallinesamples of arZr(HPO4)2-Hz0
2. Experimental a-Zr(HP04)~H~0 was prepared by the direct precipitation method in the presence of hydrofluoric acid [5]. After washing with distilled water up topH 3.54, the microcrystals were stored over P,O,, . Compact discs, 10 mm in diameter and 2-2.5 mm thick with bulk densities of about 88-90% of the theoretical density, were prepared by pressing microcrystalline cr-Zr(HP0,)2H20 at 60 kN/cm2. The two opposite sides of the discs were coated with a thin film of a silver conductive paint, Admittance measurements were made by a sealedoff cell connected to a Hewlett Packard 4192 A impedance analyzer in the frequency range 10 Hz to 5 MHz, at a signal voltage lower than 1 V. Before measurements the discs were equilibrated at 20°C for a week at a known relative humidity. Relative humidities between 5 and 90% were obtained by using saturated solutions or sulphuric acid water mixtures [6]. In order to prevent any change in the water content of the microcrystal surfaces, the discs were located in the measuring cell operating within a box at controlled relative humidity. All measurements taken went from the highest to the lowest relative humidity and, for each relative humidity, from the highest to the lowest temperature.
3. Results and discussion 3.1. Equivalent circuit Admittance measurements were carried out on polycrystalline samples of ~Y-Z~(HFQ~)~H~O over a wide range of relative humidities (from 5 to 90%) at temperatures between 20 and -5O’C. Since each sample had previously been equilibrated at 20°C at a controlled relative humidity, no measurements were made above this temperature in order to avoid any water loss from the surface of the microcrystals. The variation of relative humidity modifies- the impedance appreciably, but does not affect the shape of the X-R plot, which in any case consists of a semicircular arc with a low frequency tail (fig. 1). In a previous paper [3] it was shown that this trend is consistent with the equivalent circuit of fig. 1: here K and Q are two constant phase angle elements, the
0.5
I
/
I
05
I
1.0 R(B)
x 10-’
Fig. 1. Impedance plot obtained at 20°C for polycrystalline a-Zr(HPO&H20 equilibrated at 90% relative humidity. The equivalent circuit, to which the frequency response was fitted, is also shown. The solid line was calculated using the parameters listed in table 2.
second representing the impedance of the electrodeelectrolyte interface. R is a resistance accounting, together with K, for the impedance of the polycrystalline sample, while Cg is a geometrical capacitance arising from the high frequency dielectric constant of the electrolyte and the parasitic capacitance of the measuring cell. The admittance of K (Yi) and the impedance of Q (2;) are: Yi = k(io)” ,
26 = q(h)-P
(1) ,
(2)
where k, n, q and p are frequency-independent parameters. The total admittance for the circuit of fig. 2 is Y* = ioC, + {[l/R t k(io)“]-l
+ q(iw)-P}-l
.
(3)
The six parameters of this equation were calculated using a fitting procedure based on a non-linear leastsquares analysis of the complex admittance, as described in ref. [3]. The conductivity (u) at 2O”C, calculated from R and disc dimensions, is plotted in fig. 2 as a function of relative humidity (rh) together with the specific values of k at the same temperature. Although the conductivities reported here (from 3.4 X 10v6 to 2.3 X lo-* S cm-l) are considerably lower than those of ref. [4], probably due to a different surface area, their decrease from 90 to 40% rh is proportionately comparable with that of [4]. Like R and k, the parametern is appreciably influenced by changes in relative humidity, but not in temperature: in the range 20/
289
M. Casciola,D. Bianchi f Polycrystallinesamples of cr-Zr(HPOJ~~H~O
60%r.h
-6.5
L 2
I
I
20
I
I
I
1
1
60
40
I
I
60
’ log f(Hz)
4
6
Fig. 3. Conductance as a function of frequency for polycrystalline o-Zr(HPO&HzO at 20°C and different relative humidities. Solid lines were calculated using the parameters listed in table 2.
%r.h.
Fig. 2. IJ and k values at 20°C as a function of relative humidity for polycrystalhne or-Zr(HPO&HaO.
-20°C, n is constant within the error limits of the non-linear least squares procedure. Average n values (3) for each relative humidity are listed in table 1. Some computer simulations of the real and imaginary parts of the admittance are shown in figs. 3 and 4; the solid line too, which interpolates the points of the impedance plot (fig. l), was calculated on the basis of the proposed equivalent circuit. Although the variation of relative humidity modifies the frequency response appreciably, the standard deviation of the fit,
calculated according to [ 171, lies in any case within the range 0.05-0.005, with an average value of 0.02. These results, together with those obtained for poly crystalline samples with different densities, indicate that the proposed equivalent circuit is able to give a
90%
r.h.
Table I Average n values (E) and associated standard deviations (un) in the temperature range 20 to -20°C at different relative humidities. rh
n
on
90 75 60 SO 2.5 5
0.65 0.63 0.61 0.59 0.57 0.55
0.007 0.009 0.006 0.003 0.005 0.007
I
1
I
I
2
I
4
I
I
6
log f(Hz) Fig. 4. Susceptanceas a function of frequency for polycrystalline (r-Zr(HPO&HaO at 20°C and different relative humidities. Solid lines were calculated using the parameters listed in table 2.
M. Casciola,D. Bianchi / Polycrystallinesamples of cu-Zr(HPO4)2*H20
290
Table 2 Parameters used to fit to the equivalent circuit the experimental data of figs. 1, 2 and 3. SDF is the standard deviation of the overall admittance fit. The parameters here reported refer to measurements made at 20°C on the same disc of polycrystalline OLZr(HP04)aHaO. R X lo-’ (a)
rh
90 60 25
0.833 4.93 28.4
k x 1O’O (S sn)
n
8.04 5.34 4.23
0.632 0.618 0.573
fairly accurate model of the frequency response of (YZr(HF’04),H20 independently of relative humidity (from 90 to 5%) and relative density (from 90 to 75%). 3.2. Activation energy Typical Arrhenius plots are shown in fig. 5 : log(oT) is a linear function of l/T in the temperature range 20 to -20°C while a considerable variation in the slope is found at lower temperatures. This trend, which is probably due to some change in the transport mechanism, has been observed for all relative humidities as well as for ~-Ti(HF’04)22H20 [7] and some intercalation compounds of ~-ZI@IF’O~)~H~O[8]. Since conductivity measurements themselves cannot
4 x 10-7 (52 s-n)
P
0.854 1.38 3.03
0.151 0.76 0.83
SDF
53
(pF) 6.64 6.7 6.82
0.019 0.023 0.033
account for this phenomenon, only the data obtained between 20 and -20°C will be discussed in the present paper. From fig. 2 it is seen that the conductivity of polycrystalline cu-Zr(HP04)2H20 increases by about two orders of magnitude for relative humidities going from 5 to 90%; we therefore thought it of interest to investigate to what extent the variation of (I arose from a change in activation energy (E,) by parameterizing the conductivity data on the basis of the equation: UT = u. exp(-E,/RT)
.
-4 _ z
Y
‘i
E
:: i= 5
-
s -s_
z
F
7
4
E
::
3I
1
-6 _
d
-B
I
I
1
I
20
40
%rh I” I.,..
60
80
4 25
3 7s 10?T(K)
Fig. 5. Arrhenius plots for polycrystalJine a-Zr(HPO4)aHsO conditioned at 90 and 40% relative humidity.
Fig. 6. Activation energy (E,)and pre-exponential factor (co) for polycrystalline a-Zr(HPO&HaO equilibrated at different relative humidities. E, and o. were calculated by parameterizing the conductivity using eq. (4).
291
hi. Caseiola,D. Bianchi/ Polycrystalline samplesof eZr(HPO4)2*H20
According to the hopping model, the pre-exponential factor is temperature independent and proportional to the activation entropy, to the effective carrier concentration and its hopping attempt frequency [9]. The values of u. and E, are plotted in fig. 6 as a function of relative humidity. With rh decreasing from 90 to 5% the activation energy doubles, while the pre-exponential factor remains constant down to 25% rh and then begins to increase sharply between 25 and 5% rh. These results show that the variation of u between 90 and 25% rh is explained for the most part by the change in activation energy. The dependence of E, on the surface hydration can be understood by considering recent experimental evidence [lo] indicating that the proton is not able to diffuse along the anhydrous surface of o-zirconium phosphate, due to the distance (5.3 A) between the barycentres of neighbouring ionogenic groups. Consequently, surface proton diffusion needs the presence of water molecules forming bridges between the $POH groups: the number and arrangement of these molecules determine the diffusion characteristics. About the water arrangement, it may be observed that the structure of a-zirconium phosphate [ 1 l] is such as to create two kinds of semi-cavities on the surface where water molecules can be lodged (fig. 7); in addition the possible adsorption of more water, with the formation of one or more monolayers, should be taken into account.
0.. .o.. ,_-\ ,..~y&g ,.,... , ..(J (J.,,,.. ~ ..0..
Since the presence of water is indispensable for proton surface diffusion, it seems to be improbable that the high value of u. at 5% rh arises from an increase in the effective carrier concentration. On the contrary, a variation of the hopping attempt frequency and/or activation entropy, probably also associated with some change in the transport mechanism, may reasonably be suggested. 3.3. k/o correlation The results obtained in the present and the previous paper [ 31 by parameterizing the frequency response of polycrystalline o-Zr(HP0,)2H20 indicate that the factors regulating the dc conductivity also appreciably influence the parameters (n and k) of the constant phase angle element, so that some quantitative correlation between k, n and u may be expected. In relation to this it was found that at the lowest relative humidities (i.e. from 40 to 5%), plots of log k as a function of (1 - ii) log u can be fairly accurately interpolated by straight lines with unit slope (fig. 8). At the highest relative humidities (from 60 to 90%) a considerable scatter in the log k values is observed, due to the error associated with k; nevertheless, taking the error into account, it is seen that the experimental points cluster about straight lines with unit slope in these cases too. Thus the following empirical relation can be written: k = Aul--n 9
.,,.,.,..
‘,
r.... .
% ‘i
6
-3.6 -9.8
(5)
T
1
JY
I _ .
$-IS
_
YF60%
2 8:
B
-10.2 _
...
I
5%
on the surface of o-zirconium phosphate. Dashed circles indicate the sites available for water adsorption. Dotted lines represent the projection into the hydroxyl plane of the bonds (P-0-Zr) bridging the surface phosphates to the underlying plane of Zr atoms; each Zr is located at the intersection of three lines.
40%
25%
p,:ii I
I
-3.5
Fig. 7. Schematicrepresentationof the hydroxyl arrangement
90%
75%
1
I
-3.0 (1-E).loga(S
I
I
-2.5
I
I
-2.0
cm-‘)
Fig. 8. Log k as a function of (1 - ii) log (I, in the range -20 to 20°C, for polycrystalhne aZr(HP04)2H20 conditioned at different relative humidities. Vertical bars represent the average error associated with log k for each relative humidity. All straight lines have unit slope.
M. Casciola,D. Bianchi / Polyqwtalline samples of wZr(HPOJ z*HzO
292
where A is a temperature-independent parameter. Since u is entirely due to surface transport, eq. (5) indicates that no significant contribution from the crystal bulk response is present in the element k, thus confirming quantitatively the suggestions made in previous papers [3,12]. We may discuss eq. (5) on the basis of two different models. On analyzing the frequency dispersion of the electrode polarization capacitance, Scheider [ 131 has shown that eq. (5) holds for constant phase angle admittances composed of capacitive and dispersive elements, such that the first are invariant with u and the second directly proportional to it. It can be pointed out that this condition can be satisfied in a microcrystalline powder: specifically, if the temperature changes do not alter the composition of the interpartitle phase, then the geometrical capacitance of each intergranular contact should be independent of temperature and hence of electrolyte conductivity. In the present case, the conductivity measurements have been carried out so that the amount of adsorbed water was kept constant with changing temperature; thus, for each relative humidity the conditions leading to eq. (5) seem to be satisfied. A substantialIy different model concerning with the k/a correlation has recently been proposed by Almond and West [ 14,151. According to this model, based on the Jonscher universal dielectric response function, the activation energy fork (Ek) is given by &=Ef+(l-n)&,
(6)
Ef
and Ed being the activation energies for defect formation and carrier diffusion, respectively. This model is of interest because, once E,, Ek and n are known, Ef and Ed can be determined, since E, is equal to Ef + Ed. Eq. (5) implies the following relation between Ek and E, : Ek = -R
a
ln(kT)/a(l/T)
= (1 - n)E, + nRT.
(7)
Since nRT is not greater than 0.5 kcal/mol, Ek is about (1 - n)E, and Ef 2: 0 independent of relative humidity. In our opinion this is quite surprising. Although the mechanism of the’proton transport along the surface of o-zirconium phosphate is not yet known, it is reasonable to suppose that the first step consists in the dissociation of the ?POH groups: ,1POH+H20+PO-
+H,O+.
(8)
It is not easy to estimate the enthalpy of this process. According to Albertsson [ 161, the bonding of each phosphate to three Zr(IV) atoms should enhance the acidity of the monohydrogen group compared with that of HPOi- in water solution. On the other hand it is known that the acid strength is also influenced by the solvation of the dissociation products. From this point of view the acidity of a phosphate group belonging to the surface should not be greater than in water and should depend on the number of water molecules coordinating sPO_ and H, O+ : the more hydrated they are, the more stable the dissociated state should be. Hence the dissociation enthalpy is expected to show some dependence on surface hydration and, consequently, on relative humidity. We think that a more reliable test concerning the possibility of applying eq. (6) to microcrystalline zirconium phosphate can be performed by investigating the frequency response of anhydrous o-zirconium phosphate: experimental evidence [ 10,18,19] indicates that protonic transport occurs in the interlayer space and, in the absence of water, the phosphate dissociation should involve neighbouring ?POH groups belonging to adjacent layers: =_POH+ SmH =+SPO- + >PO@.
(9)
In this case, the interaction of ?PO- and $POHi groups with the hydroxyls of the interlayer region should not be stronger than that associated with the full hydration of H30+ and >PO- groups present on the surface, (eq. (8)). Thus the enthalpy of the process (9) is expected to be greater than that of the reaction (8) the gPOH group being less basic than H20.
4. Conclusion The study of polycrystalline cr-Zr(HP0,)2H20 carried out in the present and in a previous paper [3] has allowed the frequency response to be characterized as a function of temperature, relative humidity and density. It has been shown that both the dc and the ac conduction can be accounted for by the variation of the electrical characteristics of the microcrystal surfaces and intergranular contacts. On the basis of these results, some discrepancies which are found in comparing the results reported in previous papers can be ex-
M. Casciola,D. Bianchi / Polycrystalline
plained: for example, the fact that the activation energy resulting from isoconductivity measurements [l] is lower than that obtained for pressed powders [2] can be partially associated with different surface hydration. Finally the knowledge acquired of the electrical conduction and frequency response of (YZr(HPO,),H,O should turn out to be helpful for understanding protonic transport in new materials (such as hydrated pellicular zirconium phosphate) exhibiting chemical and structural characteristics similar to those of monohydrated zirconium phosphate.
Acknowledgement The authors whish to thank Prof. G. Alberti helpful and valuable suggestions.
for
References
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[ 21 E. Krogh Andersen, LG. Krogh Andersen, C. Knakkergard Mdller, K.E. Simonsen and E. Skou, Solid State Ionics 7 (1982) 301.
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293
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