- Email: [email protected]
Protonic conductivity of (NH4) 4Fe(CN)6·1.5H2O by complex admittance method
SOLID STATE
Solid State lonics 48 ( 1991 ) 271-275 North-Holland
IONIC$
Protonic conductivity of (NH4) 4Fe (CN) 6" 1.5H20 by complex admittance method D . R . B a l a s u b r a m a n y a n a n d S.V. B h a t Department of Physics, Indian Institute of Science, Bangalore 560 012, lndia
Received 22 May 1991; accepted for publication 18 June 1991
The protonic conductivity of ammonium ferrocyanide hydrate has been studied by the complex admittance method. The admittance plots show departures from ideal Debye behaviour. The values of ionic conductivity (a= 3.7 X 10-5 (~ cm)-~) and diffusion coefficient (D= 3,8 x 10-~o cm2/s) obtained at room temperature are consistent with the corresponding values estimated by an earlier NMR study.
1. Introduction The early wideline nuclear magnetic resonance ( N M R ) study o f a m m o n i u m ferrocyanide hydrate (AFC), ( N H 4 ) 4 F e ( C N ) 6 ' 1.5H20, by Whittingham et al. [1], showed that this material is a protonic conductor. The proton N M R signal was observed to be narrowed by translational diffusion even at room temperature. The diffusion coefficient was estimated to be 1 X 10- ~ocm2/s with an activation energy of 19 kJ/mole. Further, assuming the N H + ions to be the mobile species, the ionic conductivity was estimated to be 1 × 10 -5 (1"2 c m ) - j at 300 K. With a view to obtaining a better understanding o f the nature of ionic motion in this c o m p o u n d we undertook (a) high resolution N M R (b) high pressure wideline ~H N M R and (c) electrical conductivity studies of AFC. The high resolution N M R study [2] has shown the presence o f two chemically shifted signals attributed to N H + and H 2 0 protons. From the temperature dependence o f the line widths and the chemical shifts it was concluded that the protons o f both N H + and H 2 0 take part in diffusion. The high pressure N M R study [3,4] has given a conclusive evidence for a room-temperature pressure-induced phase transition at 0.45 GPa. Further, it has been inferred from this study that the mechanism o f charge transport in AFC is vacancy-assisted ionic hopping. Recently this c o m p o u n d has been studied by the isothermal tran-
sient ionic current ( I T I C ) method [5], which has shown that the electronic conductivity of the sample is negligibly small. The 2H spin-lattice relaxation times also have been measured [6]. In this paper we present the results of our electrical conductivity study o f AFC undertaken with the specific purpose of obtaining direct information on the true bulk conductivity of the material.
2. Experimental The conductivity o f AFC was measured by the complex admittance method, first reported by Bauerle [ 7]. The basic principle of the method involves applying a low ac signal to the sample and measuring the conductance G and the susceptance B o f the sample as a function of the frequency o f the applied signal. The true bulk conductance of the sample is estimated from an analysis o f the B - G (or the complex admittance) plot. The sample used in the present study was in the form of a pellet o f diameter 0.95 cm and thickness 0.59 cm, pressed at 1 kbar, Silver paint was applied to the fiat surfaces o f the pellet to give a good electrical contact. The sample-holder assembly consisted of two well polished spring loaded brass electrodes between which the sample was held tightly. A tubular wirewound furnace, with a temperature stability of + 1 °C,
0167-2738/91/$ 03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.
272
D.R. Balasubramanyan, S. C Bhat/Protonic conductivity of (NH4)4Fe(CN)6. 1.5H:O
surrounding the electrodes was used to heat the sample. The temperature was recorded with a calibrated copper-constantan thermocouple, one junction of which was kept close to the sample. The admittance measurements were made using a two phase lock-in amplifier (LIA) (PAR Model 5206), provided with a digital panel meter to display the output. The input signal to the sample was taken from the internal reference source of the LIA. The circuit adopted for the measurements is shown in fig. 1. The method of measurement of G and B is as follows: First, the key Kl (fig. 1 ) is kept open and K 2 is closed so that the circuit consists of the signal generator and the two resistors R and R' only. An ac signal of known voltage V,n, and frequency f i s applied to the resistors and the in-phase component V; and the out of phase component Vqt of the output across R are read out. In principle, the output across R should be in phase with the input signal and not contain any out of phase component, as R and R' are supposed to be pure resistors. However, in practice, an out-of-phase component is always present, mainly due to the fact that the LIA in its internal mode has an inherent phase shift and partly due to the small inductive components in the resistors a n d / o r stray capacitances in the circuit. The mismatch in phase is compensated for by varying the phase of the input signal till V'q becomes zero (minimised) and V', is maximised. Next, K2 is kept open and K~ is closed so that R' is excluded and the sample cell is included in the circuit, and I~; and Vq components of the output across R are read out. The Vq now observed must KI
Iop a.c
signal
sample cell
K2
T
RI
~
R (known)
Fig. 1. The circuit adopted for the measuremem of complex admittance.
have come from the reactive component in the solid cell system. The conductance (G) and the susceptance (B) of the solid electrolyte at any frequency can be evaluated from the measured values of V,, Vq and V,, using the relations [ 8 ], G=
[;( ~,,,- l'~) - V~ G~ (V, _ ~ , ) 2 + V q ,
( 1)
B=
t% ( I;,, - v, ) + v, G --7---,-~~ Gk ( 1 ,,,-- I~,) + ~ q
(2)
where G~ = R -i In the present study B and G of the sample were evaluated at various frequencies and the data were used to obtain the complex admittance plots.
3. Results and discussion Complex admittance plots obtained for AFC at four different temperatures, namely, RT (302 K), 313 K, 323 K and 333 K are shown in fig. 2. Measurements above 333 K were not carried out because the substance starts losing water of hydration around 323 K and the loss of water becomes significant above 333 K as shown by thermogravimetric analysis ( T G A ) . The observed admittance plots for solid electrolytes usually show semicircular arcs well separated from each other. The plots obtained in our study do not contbrm to this behaviour and show overlapping semicircles. Kleitz and Kennedy [9] have shown that such an overlapping of the semicircles in the admittance plots occurs when the time constants or the relaxation frequencies of the RC elements representing the two semicircles are not much different from each other, both contributing significantly to B at some frequencies, resulting in the overlapping. The ideal Debye circuit for a solid electrolyte and its frequency response is shown in fig. 3a. The presence of two distinct frequency-dispersion regions in our experimental admittance plots and the fact that the semicircle representing the lower frequency dispersion does not pass through the origin, show that our specimen does not conform to the ideal behav-
D.R. Balasubramanyan, S. V. Bhat/Protonicconductivity of (NH,!J4Fe(CN)6"l. 5H20 T
~
~o ~ 20]
"TC~
302 K
273
800 1 18
313R
2o
12
E m
0
/\
,
,i
, o,,,
hl
10 20 30 40 50 CONDUCTANCE(G)xl06 _Q-1
60
D
"7 5O
~o 40
3
o
323K
o
/ 15 i30 I
0
1
0
1
0
1
45 60 75 CONDUCTANCE(G) x106Z)--1
3t
90
3 ~ 333.
~
,~40
x
~30
I ,
~t/3
0
i
o,
q
, ~,4
,,
I
25 5O 75 100 125 CONDUCTANCE(G) xl06 _(1_-1
o tn
15 30 45 60 CONDUCTANCE(G)xl0 6-r)- ~
U3
75
Fig. 2. Complex admittance plots for AFC at different temperatures. The numbers indicate frequencies in units of (O) Hz and ( A ) kHz.
R
Cint
vcv,
I r--~_
B
[
O
~
G
I/R
(a)
R1
iour and its electrical response cannot be explained by the ideal Debye circuit. Therefore we have chosen a different equivalent circuit suggested by Bauerle [7], to explain the behaviour o f our specimen. The circuit and its frequency response are shown in fig. 3b. In this circuit RI and C1 correspond to the resistance and the capacitance respectively of the electrode-electrolyte interface, R2 and C2 correspond to the resistance and capacitance respectively of the bulk electrolyte, and R3 is the resistance due to the grain boundaries. R2+R3 is the overall bulk resistance of the specimen. These resistances can be obtained from the parameters of the admittance plot using the following relations [ 7 ] : 1
R2
Rl = Gl
1
G2'
1
R2 = G2
I
G3'
1
R 3 - G3.
(3)
Ci
0 GI
C2
G2
G3
(b) Fig. 3. (a) The ideal Debye circuit and its frequency response; (b) the circuit chosen for the present study and its admittance plot (after ref. [7] ).
As explained by Bauerle [7], the semicircle representing the lower frequency dispersion corresponds to electrode polarisation and that representing the higher frequency dispersion corresponds to polarisation in the bulk of the electrolyte. The overall bulk conductance of the electrolyte is identified by the point on the G axis corresponding to the value for which the two semicircles meet or intersect (i.e.,
D.R. Balasubramanyan, S. I~ Bhat/Protonic conductivity of (Nlt4)4Fe(CW)o.1.5HeO
274
G2= 1/(R2+R3) ). Such an estimate from the room t e m p e r a t u r e (302 K ) a d m i t t a n c e plot gave GbuLk = 45 X 10 - 6 g'~ I. This corresponds to a bulk resistance Rbulk = 22.2 kfL To check the validity of our conclusions a four-probe dc resistance m e a s u r e m e n t was made on the specimen, and it gave a value of R = 21.2 k£2. The bulk conductance at 313 K and 323 K were also estimated in a similar way. This gave G = 53.1X10-6~ -1 at 313 K a n d G = 5 9 X 1 0 6 ~ - ~ at 323 K. These values o f G were used to calculate the ionic conductivities ( a ) from the formula a : G t / A (f~ c m ) - t
(4)
where A is the area o f cross section of the specimen in cm 2 and t is its thickness in cm. The conductivities at the three t e m p e r a t u r e s are given in table 1. Though the measurements were also carried out at one more temperature, namely 333 K, the data at that t e m p e r a t u r e are not included in the table because o f reasons to be discussed later. The diffusion coefficients were estimated using the N e r n s t - E i n s t e i n relation, namely,
akT D= Nq-~,
(5)
where N is the concentration o f the charge carriers, q is the charge on the mobile carrier and k is the Boltzmann constant. As m e n t i o n e d earlier, our high pressure N M R investigations o f this c o m p o u n d have shown that the charge transport in A F C is vacancyassisted ionic hopping. Morosin [10], on the basis o f a structural study o f A F C has p r o p o s e d that ionic diffusion in this c o m p o u n d involves molecular groups rather than H + ions. Therefore, assuming the N H + ions to be the mobile charge carriers and taking the v o l u m e o f a formula unit o f A F C to be 250 ~3, following W h i t t i n g h a m et al. [ 1 ], N is found to be 16X 1027 per m 3. The values o f D calculated at
different temperatures using this value o f N are also presented in table 1. The Arrhenius plot l n ( a T ) versus I / T obtained with this experimental data is shown in fig. 4. An activation energy E , = 1 3 . 3 k J / m o l e was calculated from the slope o f the graph. The values of a and D at 302 K o b t a i n e d from this study are of the same order of magnitude as those reported in the N M R study o f W h i t t i n g h a m et al. [ 1 ]. The activation barrier Ea obtained here, is lower than the corresponding value reported in the wideline N M R study [ l ], though it is quite consistent with the value obtained ( E , = 11.58 k J / m o l e ) from the T~ study [6]. The motional parameters d e t e r m i n e d from a local technique like N M R and the bulk technique of conductivity measurement very often are not consistent with each other in the case of fast ionic conductors [ 11 ] due to the fact that grain b o u n d a r y effects and different types o f charge carriers, if present, in the sample, contribute only to the latter result. However, in the present case, we do not analyse this aspect in detail because of the limited temperature range over which the conductivity is measured. The electrical b e h a v i o u r of the sample becomes rather anomalous at 333 K. The bulk conductance estimated from the B-G plot at this t e m p e r a t u r e is 2 7 X 1 0 -6 ~ ] which gives a value o f ~ = 2 . 2 X 10 -~ ( f ~ c m ) ~ c o m p a r e d to 4.91X l0 -5 ( f ~ c m ) -L at 323 K. Thus there is a more than two-fold decrease in the conductivity on going from 323 K to
-4.0-
Io -425v
Table 1 Temperature dependence of conductivity a and diffusion coefficient D of a m m o n i u m ferrocyanide hydrate. Temp. (K)
o ( f l c m ) -1
D (cm2/s)
302 313 323
3.75X 10 -s 4.42X 10 -5 4.91X 10 -s
3.8 x l 0 -~° 4.6 X10 -1° 5.32X 10 -~°
E
-4.5
3
3.1
3.2
1000/T(K
3.3
3]I+
-1 )
Fig. 4. Plot ofln(~rT) versus 1000/ T for AFC.
D.R. Balasubramanyan, S. V. Bhat/Protonic conductivity
333 K. T h i s s u d d e n d r o p m a y b e a t t r i b u t e d to t h e loss o f w a t e r o f c r y s t a l l i s a t i o n w h i c h starts a b o v e 323 K.
Acknowledgement U s e f u l d i s c u s s i o n s w i t h A.K. R a y c h o u d h u r i a r e g r a t e f u l l y a c k n o w l e d g e d . F i n a n c i a l s u p p o r t for t h e p r o g r a m m e w a s p r o v i d e d b y t h e D e p a r t m e n t o f Science and Technology and the ISRO-IISc Space Techn o l o g y Cell.
References [ 1 ] M.S. Whittingham, P.S. Connel and R.A. Huggins, J. Solid State Chem. 5 (1972) 321.
of (NH4)4Fe(CN)6.1.5HeO
275
[2] D.R. Balasubramanyan and S.V. Bhat, Solid State lonics 23 (1987) 267. [3] D.R. Balasubramanyan, S.V. Bhat, M. Mohan and A.K. Singh, Solid State lonics 28-30 (1988) 664. [4] D.R. Balasubramanyan and S.V. Bhat, J. Phys., Condensed Matter 1 (1989) 1495. [5] M.M. AbdeI-Gawad and S.V. Bhat, Solid State Ionics 2830 (1988) 647. [6] G. Mangamma and S.V. Bhat, Solid State lonics 35 (1989) 123. [7] J.E. Bauerle, J. Phys. Chem. Solids 30 (1969) 2657. [ 8 ] D.R. Balasubramanyan, Ph.D. Thesis (Indian Institute of Science, 1988) p. 104. [ 9 ] M. Kleitz and J.H. Kennedy, in: Fast Ion Transport in Solids, eds. P. Vashishta, J.N. Mundy and G.K. Shenoy (North Holland, Amsterdam, 1979)p. 185. [ 10] B. Morosin, Acta Cryst. B 34 (1978) 3730. [ 11 ] J.B. Boyce and B.A. Huberman, Phys. Rep. 51 (1979) 189.
Solid State lonics 48 ( 1991 ) 271-275 North-Holland
IONIC$
Protonic conductivity of (NH4) 4Fe (CN) 6" 1.5H20 by complex admittance method D . R . B a l a s u b r a m a n y a n a n d S.V. B h a t Department of Physics, Indian Institute of Science, Bangalore 560 012, lndia
Received 22 May 1991; accepted for publication 18 June 1991
The protonic conductivity of ammonium ferrocyanide hydrate has been studied by the complex admittance method. The admittance plots show departures from ideal Debye behaviour. The values of ionic conductivity (a= 3.7 X 10-5 (~ cm)-~) and diffusion coefficient (D= 3,8 x 10-~o cm2/s) obtained at room temperature are consistent with the corresponding values estimated by an earlier NMR study.
1. Introduction The early wideline nuclear magnetic resonance ( N M R ) study o f a m m o n i u m ferrocyanide hydrate (AFC), ( N H 4 ) 4 F e ( C N ) 6 ' 1.5H20, by Whittingham et al. [1], showed that this material is a protonic conductor. The proton N M R signal was observed to be narrowed by translational diffusion even at room temperature. The diffusion coefficient was estimated to be 1 X 10- ~ocm2/s with an activation energy of 19 kJ/mole. Further, assuming the N H + ions to be the mobile species, the ionic conductivity was estimated to be 1 × 10 -5 (1"2 c m ) - j at 300 K. With a view to obtaining a better understanding o f the nature of ionic motion in this c o m p o u n d we undertook (a) high resolution N M R (b) high pressure wideline ~H N M R and (c) electrical conductivity studies of AFC. The high resolution N M R study [2] has shown the presence o f two chemically shifted signals attributed to N H + and H 2 0 protons. From the temperature dependence o f the line widths and the chemical shifts it was concluded that the protons o f both N H + and H 2 0 take part in diffusion. The high pressure N M R study [3,4] has given a conclusive evidence for a room-temperature pressure-induced phase transition at 0.45 GPa. Further, it has been inferred from this study that the mechanism o f charge transport in AFC is vacancy-assisted ionic hopping. Recently this c o m p o u n d has been studied by the isothermal tran-
sient ionic current ( I T I C ) method [5], which has shown that the electronic conductivity of the sample is negligibly small. The 2H spin-lattice relaxation times also have been measured [6]. In this paper we present the results of our electrical conductivity study o f AFC undertaken with the specific purpose of obtaining direct information on the true bulk conductivity of the material.
2. Experimental The conductivity o f AFC was measured by the complex admittance method, first reported by Bauerle [ 7]. The basic principle of the method involves applying a low ac signal to the sample and measuring the conductance G and the susceptance B o f the sample as a function of the frequency o f the applied signal. The true bulk conductance of the sample is estimated from an analysis o f the B - G (or the complex admittance) plot. The sample used in the present study was in the form of a pellet o f diameter 0.95 cm and thickness 0.59 cm, pressed at 1 kbar, Silver paint was applied to the fiat surfaces o f the pellet to give a good electrical contact. The sample-holder assembly consisted of two well polished spring loaded brass electrodes between which the sample was held tightly. A tubular wirewound furnace, with a temperature stability of + 1 °C,
0167-2738/91/$ 03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.
272
D.R. Balasubramanyan, S. C Bhat/Protonic conductivity of (NH4)4Fe(CN)6. 1.5H:O
surrounding the electrodes was used to heat the sample. The temperature was recorded with a calibrated copper-constantan thermocouple, one junction of which was kept close to the sample. The admittance measurements were made using a two phase lock-in amplifier (LIA) (PAR Model 5206), provided with a digital panel meter to display the output. The input signal to the sample was taken from the internal reference source of the LIA. The circuit adopted for the measurements is shown in fig. 1. The method of measurement of G and B is as follows: First, the key Kl (fig. 1 ) is kept open and K 2 is closed so that the circuit consists of the signal generator and the two resistors R and R' only. An ac signal of known voltage V,n, and frequency f i s applied to the resistors and the in-phase component V; and the out of phase component Vqt of the output across R are read out. In principle, the output across R should be in phase with the input signal and not contain any out of phase component, as R and R' are supposed to be pure resistors. However, in practice, an out-of-phase component is always present, mainly due to the fact that the LIA in its internal mode has an inherent phase shift and partly due to the small inductive components in the resistors a n d / o r stray capacitances in the circuit. The mismatch in phase is compensated for by varying the phase of the input signal till V'q becomes zero (minimised) and V', is maximised. Next, K2 is kept open and K~ is closed so that R' is excluded and the sample cell is included in the circuit, and I~; and Vq components of the output across R are read out. The Vq now observed must KI
Iop a.c
signal
sample cell
K2
T
RI
~
R (known)
Fig. 1. The circuit adopted for the measuremem of complex admittance.
have come from the reactive component in the solid cell system. The conductance (G) and the susceptance (B) of the solid electrolyte at any frequency can be evaluated from the measured values of V,, Vq and V,, using the relations [ 8 ], G=
[;( ~,,,- l'~) - V~ G~ (V, _ ~ , ) 2 + V q ,
( 1)
B=
t% ( I;,, - v, ) + v, G --7---,-~~ Gk ( 1 ,,,-- I~,) + ~ q
(2)
where G~ = R -i In the present study B and G of the sample were evaluated at various frequencies and the data were used to obtain the complex admittance plots.
3. Results and discussion Complex admittance plots obtained for AFC at four different temperatures, namely, RT (302 K), 313 K, 323 K and 333 K are shown in fig. 2. Measurements above 333 K were not carried out because the substance starts losing water of hydration around 323 K and the loss of water becomes significant above 333 K as shown by thermogravimetric analysis ( T G A ) . The observed admittance plots for solid electrolytes usually show semicircular arcs well separated from each other. The plots obtained in our study do not contbrm to this behaviour and show overlapping semicircles. Kleitz and Kennedy [9] have shown that such an overlapping of the semicircles in the admittance plots occurs when the time constants or the relaxation frequencies of the RC elements representing the two semicircles are not much different from each other, both contributing significantly to B at some frequencies, resulting in the overlapping. The ideal Debye circuit for a solid electrolyte and its frequency response is shown in fig. 3a. The presence of two distinct frequency-dispersion regions in our experimental admittance plots and the fact that the semicircle representing the lower frequency dispersion does not pass through the origin, show that our specimen does not conform to the ideal behav-
D.R. Balasubramanyan, S. V. Bhat/Protonicconductivity of (NH,!J4Fe(CN)6"l. 5H20 T
~
~o ~ 20]
"TC~
302 K
273
800 1 18
313R
2o
12
E m
0
/\
,
,i
, o,,,
hl
10 20 30 40 50 CONDUCTANCE(G)xl06 _Q-1
60
D
"7 5O
~o 40
3
o
323K
o
/ 15 i30 I
0
1
0
1
0
1
45 60 75 CONDUCTANCE(G) x106Z)--1
3t
90
3 ~ 333.
~
,~40
x
~30
I ,
~t/3
0
i
o,
q
, ~,4
,,
I
25 5O 75 100 125 CONDUCTANCE(G) xl06 _(1_-1
o tn
15 30 45 60 CONDUCTANCE(G)xl0 6-r)- ~
U3
75
Fig. 2. Complex admittance plots for AFC at different temperatures. The numbers indicate frequencies in units of (O) Hz and ( A ) kHz.
R
Cint
vcv,
I r--~_
B
[
O
~
G
I/R
(a)
R1
iour and its electrical response cannot be explained by the ideal Debye circuit. Therefore we have chosen a different equivalent circuit suggested by Bauerle [7], to explain the behaviour o f our specimen. The circuit and its frequency response are shown in fig. 3b. In this circuit RI and C1 correspond to the resistance and the capacitance respectively of the electrode-electrolyte interface, R2 and C2 correspond to the resistance and capacitance respectively of the bulk electrolyte, and R3 is the resistance due to the grain boundaries. R2+R3 is the overall bulk resistance of the specimen. These resistances can be obtained from the parameters of the admittance plot using the following relations [ 7 ] : 1
R2
Rl = Gl
1
G2'
1
R2 = G2
I
G3'
1
R 3 - G3.
(3)
Ci
0 GI
C2
G2
G3
(b) Fig. 3. (a) The ideal Debye circuit and its frequency response; (b) the circuit chosen for the present study and its admittance plot (after ref. [7] ).
As explained by Bauerle [7], the semicircle representing the lower frequency dispersion corresponds to electrode polarisation and that representing the higher frequency dispersion corresponds to polarisation in the bulk of the electrolyte. The overall bulk conductance of the electrolyte is identified by the point on the G axis corresponding to the value for which the two semicircles meet or intersect (i.e.,
D.R. Balasubramanyan, S. I~ Bhat/Protonic conductivity of (Nlt4)4Fe(CW)o.1.5HeO
274
G2= 1/(R2+R3) ). Such an estimate from the room t e m p e r a t u r e (302 K ) a d m i t t a n c e plot gave GbuLk = 45 X 10 - 6 g'~ I. This corresponds to a bulk resistance Rbulk = 22.2 kfL To check the validity of our conclusions a four-probe dc resistance m e a s u r e m e n t was made on the specimen, and it gave a value of R = 21.2 k£2. The bulk conductance at 313 K and 323 K were also estimated in a similar way. This gave G = 53.1X10-6~ -1 at 313 K a n d G = 5 9 X 1 0 6 ~ - ~ at 323 K. These values o f G were used to calculate the ionic conductivities ( a ) from the formula a : G t / A (f~ c m ) - t
(4)
where A is the area o f cross section of the specimen in cm 2 and t is its thickness in cm. The conductivities at the three t e m p e r a t u r e s are given in table 1. Though the measurements were also carried out at one more temperature, namely 333 K, the data at that t e m p e r a t u r e are not included in the table because o f reasons to be discussed later. The diffusion coefficients were estimated using the N e r n s t - E i n s t e i n relation, namely,
akT D= Nq-~,
(5)
where N is the concentration o f the charge carriers, q is the charge on the mobile carrier and k is the Boltzmann constant. As m e n t i o n e d earlier, our high pressure N M R investigations o f this c o m p o u n d have shown that the charge transport in A F C is vacancyassisted ionic hopping. Morosin [10], on the basis o f a structural study o f A F C has p r o p o s e d that ionic diffusion in this c o m p o u n d involves molecular groups rather than H + ions. Therefore, assuming the N H + ions to be the mobile charge carriers and taking the v o l u m e o f a formula unit o f A F C to be 250 ~3, following W h i t t i n g h a m et al. [ 1 ], N is found to be 16X 1027 per m 3. The values o f D calculated at
different temperatures using this value o f N are also presented in table 1. The Arrhenius plot l n ( a T ) versus I / T obtained with this experimental data is shown in fig. 4. An activation energy E , = 1 3 . 3 k J / m o l e was calculated from the slope o f the graph. The values of a and D at 302 K o b t a i n e d from this study are of the same order of magnitude as those reported in the N M R study o f W h i t t i n g h a m et al. [ 1 ]. The activation barrier Ea obtained here, is lower than the corresponding value reported in the wideline N M R study [ l ], though it is quite consistent with the value obtained ( E , = 11.58 k J / m o l e ) from the T~ study [6]. The motional parameters d e t e r m i n e d from a local technique like N M R and the bulk technique of conductivity measurement very often are not consistent with each other in the case of fast ionic conductors [ 11 ] due to the fact that grain b o u n d a r y effects and different types o f charge carriers, if present, in the sample, contribute only to the latter result. However, in the present case, we do not analyse this aspect in detail because of the limited temperature range over which the conductivity is measured. The electrical b e h a v i o u r of the sample becomes rather anomalous at 333 K. The bulk conductance estimated from the B-G plot at this t e m p e r a t u r e is 2 7 X 1 0 -6 ~ ] which gives a value o f ~ = 2 . 2 X 10 -~ ( f ~ c m ) ~ c o m p a r e d to 4.91X l0 -5 ( f ~ c m ) -L at 323 K. Thus there is a more than two-fold decrease in the conductivity on going from 323 K to
-4.0-
Io -425v
Table 1 Temperature dependence of conductivity a and diffusion coefficient D of a m m o n i u m ferrocyanide hydrate. Temp. (K)
o ( f l c m ) -1
D (cm2/s)
302 313 323
3.75X 10 -s 4.42X 10 -5 4.91X 10 -s
3.8 x l 0 -~° 4.6 X10 -1° 5.32X 10 -~°
E
-4.5
3
3.1
3.2
1000/T(K
3.3
3]I+
-1 )
Fig. 4. Plot ofln(~rT) versus 1000/ T for AFC.
D.R. Balasubramanyan, S. V. Bhat/Protonic conductivity
333 K. T h i s s u d d e n d r o p m a y b e a t t r i b u t e d to t h e loss o f w a t e r o f c r y s t a l l i s a t i o n w h i c h starts a b o v e 323 K.
Acknowledgement U s e f u l d i s c u s s i o n s w i t h A.K. R a y c h o u d h u r i a r e g r a t e f u l l y a c k n o w l e d g e d . F i n a n c i a l s u p p o r t for t h e p r o g r a m m e w a s p r o v i d e d b y t h e D e p a r t m e n t o f Science and Technology and the ISRO-IISc Space Techn o l o g y Cell.
References [ 1 ] M.S. Whittingham, P.S. Connel and R.A. Huggins, J. Solid State Chem. 5 (1972) 321.
of (NH4)4Fe(CN)6.1.5HeO
275
[2] D.R. Balasubramanyan and S.V. Bhat, Solid State lonics 23 (1987) 267. [3] D.R. Balasubramanyan, S.V. Bhat, M. Mohan and A.K. Singh, Solid State lonics 28-30 (1988) 664. [4] D.R. Balasubramanyan and S.V. Bhat, J. Phys., Condensed Matter 1 (1989) 1495. [5] M.M. AbdeI-Gawad and S.V. Bhat, Solid State Ionics 2830 (1988) 647. [6] G. Mangamma and S.V. Bhat, Solid State lonics 35 (1989) 123. [7] J.E. Bauerle, J. Phys. Chem. Solids 30 (1969) 2657. [ 8 ] D.R. Balasubramanyan, Ph.D. Thesis (Indian Institute of Science, 1988) p. 104. [ 9 ] M. Kleitz and J.H. Kennedy, in: Fast Ion Transport in Solids, eds. P. Vashishta, J.N. Mundy and G.K. Shenoy (North Holland, Amsterdam, 1979)p. 185. [ 10] B. Morosin, Acta Cryst. B 34 (1978) 3730. [ 11 ] J.B. Boyce and B.A. Huberman, Phys. Rep. 51 (1979) 189.