Electronic conductivity and chemical diffusion coefficient of cadmium-doped cuprous iodide

Solid State Ionics 46 ( 1991 ) 211-216 North-Holland

Electronic conductivity and chemical diffusion coefficient of cadmium-doped cuprous iodide R . A . M o n t a n i i a n d J.C. Baz~in 2 Departamento de Quimica e Ing. Qulmica, Universidad Nacional del Sur, 8000 Bahia Blanca, Argentina

Received 4 December 1989; accepted for publication 26 March 1991

The electronic (hole) conductivity and chemical diffusion coefficient for pure and cadmium-doped Cul were measured both as a function of temperature and cadmium content. The conductivity results are interpreted taking into account the explicit temperature dependence of the hole mobility, which was obtained from earlier measurements of Vine and Maurer. The chemical diffusion coefficient (/~) data are explained by the assumption of a trapping process of the electronic defects by cadmium ions occupying normal copper sites.

I. Introduction

The study o f the transport properties o f solid electrolytes should involve, besides the characterization o f the pure c o m p o u n d s , the d e t e r m i n a t i o n o f the influence o f the gas a t m o s p h e r e and or o f dopants, due to the possible considerable effect they m a y exert on these properties. Solid cuprous i o d i d e is p r e d o m i n a n t l y ionic conductor, which has been subject o f several studies as a m o d e l solid electrolyte. It exhibits, besides its ionic conductivity, a small but noticeable electronic (hole) conductivity when equilibrated with metalic copper; pertinent d a t a have been reported by Wagner and Wagner [ 1 ] and Jow a n d Wagner [ 2 ]. The latter authors p r o v i d e d also values o f the chemical diffusion coefficient. As for the influence o f d o p a n t s Matsui and Wagner [3] have r e p o r t e d on the influence o f doping with c a d m i u n i o d i d e on the ionic conductivity o f cuprous iodide in equilibrium with copper and interpreted their results on the basis o f the following i n c o r p o r a t i o n reaction: CdI2 = Cdcu + V~u + 2 I ~ ,

(1)

To whom all correspondence should be addressed. Research Fellow of Comision the Investigaciones Cientificas de la Provincia de Buenos Aires (C.I.C), Argentina. Elsevier Science Publishers B.V. (North-Holland)

where, according to the K r 6 g e r - V i n k notation Cdcu represents a c a d m i u m ion in a n o r m a l copper site in the lattice, Vbu a negatively charged cation vacancy and I~ a n o r m a l iodide ion in the lattice. In the present paper, we report on the influence o f CdI2 doping on the electronic conductivity, and on the chemical diffusion coefficient in copper iodide at several temperatures. It is found that the c a d m i u m iodide diminishes considerably the electronic transport properties as o p p o s e d to the e n h a n c e m e n t it causes on the ionic conductivity. The results are explained taking into account the effect o f reaction ( 1 ) on the defect equilibrium, and the explicit function o f t e m p e r a t u r e for each o f the involved factors.

2. Experimental aspects 2.1. Theoretical considerations

The electronic conductivity was determined by the H e b b - W a g n e r polarization method, using a cell f o r m e d by sandwiching a pellet o f the solid electrolyte between a copper cathode and a graphite anode, the later acting as the blocking electrode: ( - ) C u / C u I ( d o p e d or u n d o p e d ) / C ( + ) .

212

R.A. Montani, J. C. Bazc~n / Cadmium-doped cuprous iodide

For a mixed electronic-ionic conducting electrolyte in which the electronic carriers are holes, the expression relating the hole current (lh) and the applied potential (E) in the Hebb-Wagner method [4] is the following: lOglh~IOg(a°ART/LF)+EF/2.303RT,

(2)

where a ° is the electronic conductivity of the electrolyte in equilibrium with its parent metal; L and A the geometrical length and area o f the sample, respectively; T the absolute temperature; R and F the gas and Faraday constant, respectively. Eq. (2) is valid when ( E F / R T ) >> 1. The chemical diffusion coefficient was determined by the potential technique introduced by Weiss [5], which uses the same cell as the polarization method. The method is based on the interruption of the applied potential in the polarization cell, after the stationary state is reached. As the system tends to re-equilibrate the deviation of the stoichiometry as introduced by the applied potential, an open circuit potential-time transient is measured, which in the case of a hole conductor follows the expression

[2]: /)t =

4 _ 2 In - 7c-

{~2exp[V(t)F/RT]-I} 4exp(EF/RT)-I

LYP potentiostat and a Linseis LY 1800 X - t recorder with a voltage follower at the signal input. A chromel-alumel thermocouple very near the specimen recorded the temperature which was controlled through an o n - o f f temperature controller unit. The applied potential was varied between 0.1 and 0.350 V, well under the decomposition potential of Cul.

3. Results

Fig. 1 shows some experimental plots of Iog(lh) versus E for pure and doped Cul at different temperatures. From these graphs the corresponding values of the hole conductivity a ° were obtained, according to eq. (2). In fig. 2 a plot o f l o g ( a ° ) versus 1 / T is shown. The pure CuI data agree with those published by Jow and Wagner [2]. The experimental values obtained with the potential relaxation method are shown in fig. 3, plotted as ln{exp [ V ( t ) F / RT] - 1 } against t. Finally, from fig. 4 it is observed that the obtained values of the chemical diffusion coefficient fit into an Arrhenius-type plot. Again, the values obtained for pure CuI are in agreement with

(3)

'

w h e r e / 5 is the chemical diffusion coefficient, t the time and V(t) the open circuit potential. 2.2. Sample preparation

The cuprous iodide was synthesized from cupric sulfate and sodium iodide both of pro-analysis quality. The cadmium iodide, which is soluble in all proportions in CuI [3] was dried by heating for 24 h under nitrogen atmosphere before use. The samples were prepared by weighing the adequate amounts of CuI and CdI2 to obtain 0.5, 3.2, 5, and 20 mole% of dopant in the mixture; heating in evacuated pyrex tubes at 400°C for 24 h; ground and pressed at 3500 Kg c m - 2 into pellets of 1 cm diameter and lengths varying between 0.15 and 0.55 cm. The cell was mounted inside a pyrex glass furnace and maintained under a pure nitrogen atmosphere during the measurements, which covered the temperature range between 240 and 517 ° C. The electrical and measuring circuit comprised a

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0.1

0.2

0.3

0.4

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Fig. 1. Plot of log electronic (hole) current versus applied potential. Full lines correspond to the theoretical slope according to the Wagner equation: (o) pure Cul, T=295°C; (11) 5% Cd]2, T=312°C; (sample length in both cases: 0.32 cm.) (A) 20% Cdl2, T= 319 °C. Sample length: 0.35 cm.

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1.3

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of the Wagner model. At higher potentials some deviation is to be seen. This phenomenon has already been dealt with by the present authors [6,7 ]. As for the measurements made with doped CuI, it is to be noted that Wagner's method is valid, provided that the sample is in thermodynamic equilibrium. In this case this conduction is not met, for the cadmium activity is not fixed. However, in the literature there are several examples of this type of measurements conducted in systems lacking complete thermodynamical equilibrium conditions in which the observation of slopes of the theoretical value is considered to be a sufficient criterion of validity [8]. In the present study this condition was assured for the CdI2 doped CuI by working at applied potentials not higher than 0.28 V.

[s]

Fig. 3. Potential relaxation data plotted according to eq. ( 3 ) (see text): ( A ) pure CuI, T: 512°C, ( o ) pure CuI, T: 355°C; (sample length in both cases 0.41 cm. ) ( • ) 3% Cdl2, T= 319 ° C, sample length 0.35 cm; ( • ) 3% Cdl2, T= 517 °C, sample length 0.34

4. Discussion

4.1. The electronic (hole) conductivity

cm.

those reported by Jow and Wagner [2]. It is observed that both the hole conductivity and the chemical coefficient values decrease with increasing amount of dopant. Considering now fig. 1, it is seen that the slopes for undoped CuI show the theoretical value of F/2.303 RT, predicted by eq. (2), at potentials under 0.32 V. This is normally taken as a proof of the applicability

The equilibrium between the solid and its gas phase is expressed by: ½I(g) =Inx +V~u +h"

(4)

with an equilibrium constant K,: K i = [h'] [V~u]/P~/2 ,

(5)

where h" stands for a positive charged hole. In the intrinsic case (undoped CuI) the electroneutrality

214

R.A. Montani, J.C. Bazdn / Cadmium-doped cuprous iodide

condition is given by the Frenkel equilibrium: [V~u] ~ K 1/2 ,

(6)

Table 1 Calculated values for the incorporation entbalphy, for a- and ~CuI.

where KF is the corresponding equilibrium constant. Introducing eq. (6) into eq. (5) yields, K~ = K~/2 [ h" ]/PJ/2 2 .

(7)

On the other hand from the data reported by Vine and Maurer [9], the following relationship is found between the hole mobility (#h) and the temperature for CuI: / t h = l . 2 × 1 0 1 1 T -3"~ ( c m 2 " V - l ' s - l ) .

a-phase 7-phase

Taking into account the temperature dependence of the iodine partial pressure, resulting from the CuI formation reaction at the copper-electrolyte interphase, (9)

(10)

,

where q is the charge o f the electronic defect, the following expression is obtained: a° T 3 8 = c o n s t . exp[ ( A H f + A H v / 2 -

AH~)/RT] ,

(ll) where AHf, AHv and AH~ stand for the enthalpy changes o f CuI formation, Frenkel equilibrium and equilibration reaction o f eq. (4), respectively. Fig. 5 shows the plot l o g ( a ° T s8) versus 1 / T . Two slopes are observed from which, using the values o f AHv given by Matsui and Wagner [ 3 ] and of AHf calculated from the tables presented by H a m e r et al.

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CdI2 (mole%)

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[ 10 ], the values of AH~ for the a and 7-CuI phases were calculated. The results are presented in table 1. For the case of Cd-doped CuI, the amount of extrinsic cation vacancies, being equal to the dissolved quantity of dopant [ 2 ], can be made higher than that provided by the Frenkel equilibrium. This situation is found for temperatures under 370°C, as shown by the data gathered in table 2. The electroneutrality condition is then given by: [CdI2] ~ [Cdcu] ~ [V~u] ~--KF/[Cul-]

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(13)

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(12)

instead of eq. (6). Introducing eq. (12) into eqs. (5) and (10), it results, assuming that the dopant exerts no influence upon the mobility, const. exp[(AHf-AHi)/RT [CdI2]

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(8)

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L

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Fig. 5. Plot of log(tr0hT 3.8) versus 1/ T for pure Cul.

Fig. 6 shows the plot of log(tr°T 3s) versus 1 / T . From the slope, and by using again the abovementioned value of AHf, an average value o f AH~ = - 16 ~ 4 K J . m o l - 1 is obtained for the extrinsic range. It should be pointed out, that at high concentration of dopant one can expect the existence of an interaction of the type ( C d c u - V~u)×. In this case: [CdI2] ~ [V~u] ..... isled + [V~,]~ee,

(14)

R.A. Montani, J.C. Bazdn / Cadmium-doped cuprous iodide

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which could indeed modify the assumed mobility dependence. However, the data at 20 mole% fit into the general pattern. This fact does not imply the validity of the assumed independence of the mobility upon dopant concentration, it would rather indicate that this dependence is of a lower order on T and/ or it is included in the preexponential term. In the former case it would be masked by the experimental error and in the second one it should be merely included in the preexponential term, this should lead to a relative displacement of the Arrhenius type plots, which in fact exhibit approximately the same slope at all dopant concentrations as seen in fig. 6.

where tj represents the ionic transport number and Dh the electronic defects diffusion coefficient, holes in this case. That is, the temperature dependence of the chemical diffusion coefficient should be the same as that of the hole mobility. For pure CuI, an explanation was given on the assumption of a low degree of ionization for the reaction of metal incorporation into the electrolyte. On this basis, an expression was found in which the chemical diffusion coefficient was expressed as the hole diffusion coefficient times an equilibrium constant whose exponential temperature dependence sufficed to explain the observed behavior. In the present case, however, the same reasoning cannot be followed for it is not possible to rule out the occurrence of extra defect interactions brought about by the dopant. On the other hand, an inverse dependence of the chemical diffusion coefficient upon the dopant concentration was found, as seen on fig. 7. A possible explanation for both effects may be postulated, following Heyne [ 12 ], by assuming the existence of a process in which the electronic defects are trapped by the extrinsic defects introduced by the dopant. In this way the chemical diffusion coefficient would be given by: ( 16 )

/~ = Delectronic/co ,

where co is the equilibrium constant between trapped and free electronic defects. In turn, co should be proportional to the dopant concentration, thus explaining the observed dependence of /3 upon [CdI2]. Moreover, this expression includes also a factor which, being an equilibrium constant, should be exponentially dependent on temperature.

-3 \ ,

E

4.2. The chemical diffusion coefficient

-4

As in the previously reported case of pure CuI, [11 ] the observed exponential dependence of the chemical diffusion coefficient upon temperature is not to be expected, when considering the accepted theoretical relationship, [ 12 ]:

D=tjOh ,

215

(15)

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LOG [CdI Fig. 7. Plot of log £3 versus log of calculated dopant concentration (in atoms/cm3): (11) 315°C, ( [ ] ) 327°C, ( o ) 360°C.

216

R.A. Montani, J. C. Bazdn / Cadmium-doped cuprous iodide

Acknowledgement T h i s w o r k was p a r t i a l l y f u n d e d b y g r a n t s f r o m C I C a n d C O N I C E T o f A r g e n t i n a . R . A . M . t h a n k s C I C for a fellowship.

References [ 1 ] C. Wagner and J.B. Wagner Jr., J. Chem. Phys. 26 (1957) 1597. [2 ] T. Jow and J.B. Wagner Jr., J. Electrochem. Soc. 125 ( 1978 ) 613. [3] T. Matsui and J.B. Wagner Jr., J. Electrochem. Soc. 124 (1977) 300.

[4] C. Wagner, Proc. 7th Meeting, Int. Com. Electrochem. Thermodyn. Kinetics, Lindau, 1955. [5] K. Weiss, Z. Phys. Chem. (NF) 59 (1968) 242. [ 6 ] R.A. Montani and J.C. Bazfin, Solid State Ionics 27 ( 1988 ) 227. [7] R.A. Montani and J.C. Bazfin, J. Phys. Chem. Solids 50 (1989) 1207. [8] T. Matsui and J.B. Wagner Jr., J. Electrochem. Soc. 124 (1977) 941. [9] B.H. Vine and R. Maurer, Z. Physik Chem. 198 ( 1951 ) 147. [ 10 ] W. Hamer, M. Malmberg and B. Rubin, J. Electrochem. Soc. 112 (1965) 750. [ 11 ] R.A. Montani and J.C. Bazfin, Solid State lonics 36 (1989) 65. [12] L. Heyne, in: Solid Electrolytes, ed. S. Geller (Springer, Berlin, 1977) p. 169.