Electrical properties of CuI and the phase boundary Cu ¦ CuI

SolidStateIonics 76 ( 1995)229-235 ELSEVIER

Electrical properties of CuI and the phase boundary Cu 1 CuI S. Villain, J. Cabank, D. Roux, L. Roussel, P. Knauth EDIFIS, hboratoire

de M&allurgie assock’ au C.N.R.S. ((IRA 443). Faculte’ des Sciences de St. Jt+cime, Case .?I 1, 13397 Marseille Cedex 20, France

Received 13 June 1994; accepted for publication 24 November 1994

Abstract

The electrical conductivity of copper (I) iodide was investigatedbetween 50 and 450°C by ac measurements at different frequencies and four-point dc experiments. The resistance and capacitance of the phase boundary copper/copper iodide depend exponentially on temperature. The interfacial resistance is practically negligible in the OL-and P-phases, whereas the interfacial capacitance is very high. The electrical conductivity is in good agreement with previous electrochemical experiments. The enthalpy of formation of Frenkel defects and enthalpies of migration of copper vacancies and interstitials in copper iodide are reported. Keywords: Cuprous iodide; Phaseboundary; Frenkei defects; Ionic conductivity-copper

1. Introduction

Copper (I) iodide is a solid electrolyte with fast Cu+ ion conduction in the high temperature (Y-and pphases. The ionic and electronic conductivity of this compound was investigated by several authors [ l-101. Copper diffusion in (Y-,l3- and y-0.11 was studied by a radioactive tracer technique, and the diffusion coefficients and activation energies for diffusion were reported [ 11,121. Quite surprisingly, ionic conductivities calculated from the measured tracer diffusion coefficients using the Nernst-Einstein equation were one order of magnitude higher than the values determined by electrochemical measurements. This disagreement was related by the authors to possible “complications in the electrochemical experiments, such as electrodeelectrolyte contact resistance and electrode-electrolyte interfacial polarization” [ 121, In order to clarify this apparent contradiction, we investigated the electrical conductivity of high-purity 0167-2738/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDIO167-2738(94)00285-I

copper iodide and the electrical properties of the phase boundary copper/copper iodide. Impedance measurements at different ac frequencies [ 131 are the best way to determine the interfacial resistance between copper electrodes and copper iodide, and to study the total conductivity. To confirm our conclusions, we did also four-point de experiments with copper electrodes [ 14161. This technique is well adapted for the measurement of small resistances. The theory of the four-point technique [ 141 was adapted to the Van-der-Pauw configuration by Riess [ 15,161, who pointed out that overpotentials can disturb four-point measurements on mixed ionicfelectronic conductors, because the partial currents of ionic and electronic carriers are not zero at the voltage probes. Overpotentials should vanish in phases with predominant conduction by one type of charge carrier, especially in fast-ion conductors like (Y-CuI. Consequently, the four-point experiments were performed in the o-phase at 420°C. Furthermore, the applied cur-

230

S. Villain et al. /Solid State Ionics 76 (1995) 229-235

rents and measured voltages were small (E < RTI F) . Under this condition, the composition of the phase stays approximately uniform, and a linear relation between current and voltage is expected.

the literature value (5.7 1 g/cm3 [ 181) . Observations of annealed pellets by optical microscopy after etching with a methanol solution of hydrochloric acid revealed numerous twin boundaries and some small cracks, probably related to the phase transitions in the material.

2. Experimental 2.2. Electrochemical set-up Two types of samples were investigated: (i) commercial CuI (minimum purity: > 99.999%, JohnsonMatthey) used without further purification and (ii) CuI prepared in our laboratory from the high-purity elements. 2. I. Sample preparation and characterization

For the synthesis from the pure elements (99.999%, Strem), iodine was first filled in a phial with a fragile capillary. This phial was sealed under vacuum, while the iodine was cooled in liquid air. It was then placed in a bigger ampoule with the copper powder, which was reduced in situ under hydrogen flow at 150°C. Then the ampoule was sealed under vacuum. The inner iodine phial was broken by shaking and the reaction annealing was performed at 200°C (24 h) and at 450°C ( 13 h) . The X-ray diffractogram of the product showed only lines of pure y-CuI [ 17,181. Sample pellets were prepared by compression. The density of the pellets (5.65-5.71 g/cm3), determined by measuring their dimensions and weighing, was near

The solid state electrochemical cell is presented in Fig. 1. A pellet of copper iodide ( 1) was placed between electrodes (2) of high purity copper (99.999%, Johnson-Matthey), which were previously polished mechanically and etched in diluted nitric acid. The contacts (3) and the leads (4) were of pure rhenium (99.99%, Goodfellow). To ensure a good contact, a slight pressure was applied through the alumina stamp (5)) and a stainless steel compression spring (6) maintained in the alumina tube (7) outside the hot zone by alumina plugs (8). The temperature of the sample was measured with a chromel-alumel thermocouple (9)) calibrated by the temperatures of phase transition of CuI. The inner alumina tube was placed inside a quartz tube (10) connected to the vacuum system through a metal join ( 11). The temperature of the Adame1 furnace ( 12) was stabilized to within &-1 K by an Eurotherm type 847 controller. After several pumping cycles, the experiments were performed in a static atmosphere of pure argon.

Fig. 1. Electrochemical set-up.

S. Villain et al. /Solid State lonics 76 (1995) 229-23.5

~

f-4

Ri

Rv

CV

(4 Rv= [ R/(l+dV)

(b) + RJ(l+dTi’)

Cv= 1/Rv2[ RT/( 1+dV)

](I+w~ZV*)

+ RiTi/( 1+O*Ti*) I( l+dTv*)

IkRC, TizzRiCi,Tv=RvCv Fig. 2. (a) Circuit of the ac bridgeand (b) equivalent

circuitof the

cellcu 1GUIIcu. 2.2.1. AC measurements The impedance of the cell Cu / GUI]Cu was measured between 50 and 1500 Hz with an ac bridge using an external frequency generator (IlT Metrix GX 240). The impedance was indicated as a parallel resistance (&)-capacitance (C)-element (Fig. 2a). The applied ac voltage was less than 200 mV. 2.22. DC m~~urement~ A constant current source (Keithley 220) was used and the voltage measured with a high impedance electrometer (Keithley 617). Four point dc measurements with the cylindrical Van-der-Pauw configuration were realized by in~oducing four copper wires of 1 mm diameter into holes drilled on the periphery of pressed copper iodide pellets of 13 mm diameter previously sintered under argon.

231

The impedance spectra were interpreted on the basis of the simple equivalent circuit of Fig. 2b. The electrolyte and the interface electrode-electrolyte were each represented by a parallel resistance-capacitance element [ 13,191. The frequency-independent parameters R, C, Ri and Ci were determined from equations in Fig. 2 by a matrix calculation program in order to obtain the best fit (black squares in Fig. 3a-e) with the experiment. This procedure was tested with known resistance-capacitance elements. Typical values of the phase boundary resistance (Rinl = Ri/2) and capacitance (C,,, = 2Ci) are plotted against reciprocal absolute temperature in Fig. 4. We used the resistance R, measured at 1000 Hz to calculate the electrical conductivity of copper (I) iodide in equilibrium with copper. The values for the commercial product (white dots) and for the product synthesized in our laboratory (black dots) are plotted against the reciprocal absoIute tem~rature and compared with literature data in Fig. 5. 3.2. Four-point de measurements The total conductivity pcan also be calculated from two dc cu~ent/voltage-relations with standard Vander-Pauw switching between current carrying electrodes and voltage probes using E$. ( 1) :

g= I (M&d

+ (Id&d

1 ln2/ (277-L),

(1)

where L is the thickness of the sample pellet and the indices refer to the probes [ 151. Typical experimental data at 420°C are shown in Fig. 6. We obtain a mean slope of 5.7 Q and a conductivity: cr= 0.090 (0 cm)-‘; this value is also reported in Fig. 5 (white square).

3. Results 3; I. Frequency dependence of cell impedance Plots of resistance R, and capacitance C, of the cell Cu 1CuI 1Cu versus ac frequency are shown in Figs. 3ae for the three phases of CuI. One observes a strong increase of the experimental values R, and C, (white squares) for frequencies less than 800 Hz, because of an increasing contribution of the resistance and capacitance of the interface electrode/electrolyte. At frequencies above 800 Hz, R, and C, are approximately constant.

4. Discussion 4. I. Phase boundary copper/~opper (I) iodide

In Fig. 4, we notice approximately exponential temperature dependences of interfacial resistance and capacitance, probably with an exception for the pphase, where the phase boundary resistance is slightly increased and the phase boundary capacitance slightly decreased.

232

S. Villain et al. /Solid State Ionics 76 (1995) 229-235

The interfacial capacitance in the y-phase at 246 and 267 “C is comp~able to the case of liquid electrolytes (10-35 pF/cm’). Very high values are reached at 340°C and in the p- and a-phases (3-16 mF/cm’). The interfacial capacitance is due to the space charge at the interface metal/ionic compound. Qualitatively,

the thickness of the space charge layer, expressed by the Debye length, is inversely proportions to the square root of concentration of mobile charge carriers in the electrolyte [ 20,211. In the CX-and P-phases, the space charge layer is very thin, because the density of ionic charge carriers in the electrolyte is very high.

4220

1820 I

1

q

1600

I

1780

4160 RVlR 4160

I

4140 I 4120 1

I

0

200

400

600

600

1000

1200

1400

0

200

400

600

f/H.

600

1000

1200

1400

f/HZ

30 25 20 CvlnF

'4

Cv/nF 16

3

10 5 0

73

7 13

72 RVlR

0

71 0

G--P

QJ

70 200

(

400

600

600

1000

1200

0

1400

f/HZ

200

400

600

s

800

1000

1200

1400

ioou

1200

1400

f/HI

1600 1400

401 30(

0

1200

s

1000 Cv/nF

CvtnF 21%

600 600 400

101

200

CL

( 0

-u--o-Q-200

400

600

600 fIti2

u

ij

n

1000

,200

1400

0

0

200

400

Fig. 3. Frequency dependence of resistance and capacitance of the cell Cu / Cuf 1Cu at different tern~m~. calculated values. a: T= 246°C; b: T= 267°C; c: T= 34OT; d: T= 383°C.

600

800 t/n2

f ci) Ex~~~nt~

values, f B)

S. Villain et al. /Solid State Ionics 76 (1995) 229-235

constant in the interfacial region, With the tentative value E= 100, we can calculate an interfacial capacitance of 10w9/d,if d is expressed in meters. To obtain a value of 0.1 mF/cm*, the thickness of the space charge layer should be 1 nm. This is the order of magnitude of the thickness of a grain boundary in metals, but appears too small for a contact between a copper iodide pellet and “massive” copper electrodes. The very high interfacial capacitances are certainly also related to the residual roughness of the mechanically polished copper electrodes used in the experiments.

0,3 1

Rvln

.“‘--:.;;c?... % 0

200

400

600

BOO

1000

1200

1400

f/HZ

1400

,

233

I

CvlnF

0

200

400

600

800

1000

1200

1400

f/Hz

Fig. 3. Continued. e: T=420”C.

e-9

0

.

1000

K/T

Fig. 5. Electrical conductivity of CuI plotted against reciprocal temperature: f 1) ac conductivity of the synthesized product, (2) ac conductivity of the commercial product, (3) dc conductivity, (4) Ref. [l], (5) Ref. f12].

II

. .

tf

1.6

1.7 K/T

1.9

1.9

1000

Fig. 4. Resistance and capacitance of the phase boundary Cu 1CuI plotted against reciprocal temperature.

l

0.1

a

0

For high defect concen~ations and an elementary parallel-plate capacitor model of the space charge layer, we expect for the capacitance per area 0

Cint= E 6/d. In this equation, d is the thickness of the boundary layer, 4, is the vacuum ~~ittivity, and E is the dielectric

10

20

30

40

E32

60

60

Fig. 6. DCcu~nt/voI~e relations in four-lint experiments on CuI at 420°C with standard Van-der-Pauw switching of the probes.

234

S. Villain et al. /Solid State Ionics 76 (1995) 22%235

The exponential temperature dependence of the interfacial resistance corresponds to a thermally activated process with an activation energy of 130 kJ/mol. Rintcan be interpreted as the charge transfer resistance, which is described in the theory of liquid electrolytes by the Butler-Volmer equation [ 211. In the case of small overpotentials (linear approximation near equilibrium), the charge transfer resistance is inversely proportional to the exchange current. In this interpretation, the exponential temperature dependence is that of the exchange current density [ 2 11. At temperatures above 300°C the interfacial resistance between copper electrodes and copper iodide is practically negligible. An analogous behaviour was found previously for the yphase of copper bromide [ 161. The apparent anomaly of the phase boundary resistance and capacitance for p-CuI can probably be interpreted by taking into account the electronic charge carriers in the space charge layer at the interface metal/ electrolyte [ 221. 4.2. Conductivity of copper (I) iodide The results of ac and dc experiments are coherent and confirm that the resistance values at 1000 Hz can be used to calculate the conductivity of the solid electrolyte. Comparison with the literature in Fig. 5 reveals that the conductivity reported here is generally somewhat smaller than the literature data; in the a-phase there is good agreement with the results of Wagner and Wagner [ 11. The conductivities calculated by Johansson et al. from tracer diffusion data are at least 0.8 logarithmic units higher than our results in all three phases (Fig. 5). The discrepancy of electrochemical conductivity values with the data of Refs. [ 11,121 is thus confirmed, but our impedance measurements show further that no interfacial resistance is measured at 1000 Hz. This explanation of the discrepancy can thus be ruled out; if we take the correlation factor into account, the difference even increases. One may then ask if a diffusion mechanism by uncharged species (copper atoms or neutral defect complexes) can be predominant in copper iodide. In this case, the ratio of the diffusion coef< 1. However, several arguments ficients D&lDr are in opposition with this hypothesis. Firstly, the difference between electrochemical and diffusion results is particularly important in the a-phase, in which pre-

dominant ionic conduction is recognized. Secondly, a diffusion mechanism by uncharged species should be characterized by different activation parameters, whereas Johansson et al. found activation energies comparable to our results (see below). In our opinion, the most likely explanation of the discrepancy may be found in experimental difficulties to measure diffusion coefficients with radioactive tracers with small period like %u, and to realize an initial activity profile with defined geometry by neutron activation, the technique usedinRefs. [11,12]. We distinguish several temperature domains in Fig. 5, in which the conductivity data can be described by straight lines. The enthalpies of activation Ha are calculated according to Eq. (3) : In u=ln

q,-HaI

.

(3)

Between 405 and 450 “C in the o-phase, the enthalpy of activation amounts to 20 kJ/mol (0.21 eV) in good agreement with Jost (0.20 eV [ 231) and Boyce and Huberman [ 241, who reported an energy of activation for ionic motion of ( 18 + 3) kJ/mol, determined from NMR measurements. Jow and Wagner found a value of 0.09 eV between 402 and 440°C [ 51. Johansson et al. derived an energy of activation for diffusion of copper in cl-CuI of 0.31 eV [ 11,121. In conclusion, the small enthalpy of activation can be attributed to the enthalpy of migration of copper interstitials, which are very mobile in this structure: H,(Cup ) = 20 kJ/mol. Between 370 and 400°C in the B-phase, we find an activation enthalpy of 88 kJ/mol(O.91 eV) . This value is in good agreement with the value reported by Jow and Wagner [ 51 from electrochemical measurements (0.90 eV) and with the energy of activation of copper diffusion in the P-phase (0.91 eV [ 121). We can reasonably assume that the conductivity of the P-phase is intrinsic (like in the y-phase at temperatures above 280°C see below) and that the copper interstitials are mainly responsible for ionic conduction (like in the (Yphase). We can then estimate the enthalpy of formation of Frenkel defects HFr from Eq. (4) : Ha =H,,,(Cu;)

+0.5 HFr .

(4)

We use in a first approximation the enthalpy of migration calculated for the o-phase, because the local symmetry of the anion lattice does not change in the phase transition, it is only a rearrangement of planes to another stacking sequence [ 171. With this assumption,

S. Villain et al. /Solid State Ionics 76 (1995) 229-235

the enthalpy of formation of Frenkel defects in p-CuI can be calculated to 136 kJ/mol, a higher value than for P-AgI ( = 65 kJ/mol [ 25-271)) which has also a wurtzite-type structure. The higher enthalpy of formation can be related to the higher lattice enthalpy of CuI. Herzog et al. [ 281 derived a theoretical value for tetrahedral Frenkel defects in y-Cur, which is lower than 109 kJ/mol with an estimated uncertainty of about 25%. In the y-phase, we distinguish two temperature ranges with different slopes corresponding to “intrinsic” and “extrinsic” conductivity. Between 280 and 35O”C, the enthalpy of activation amounts to 127 kJ/ mol (1.31 eV). This is clearly lower than the value reported by Jow and Wagner (2.03 eV between 330 and 369°C [ 51)) but is similar to the result of Johansson et al. [ 121 for copper tracer diffusion in the yphase between 315 and 369°C (1.30 eV). Ionic transference numbers show that the conduction is essentially ionic in this temperature domain, but the electronic contribution is not negligible [22]. The enthalpy of activation is a complex phenomenological quantity, which contains the enthalpies of formation and migration of the involved defects. Below 27O”C, the ionic transference numbers show that we have mixed conduction. The enthalpy of activation is 49 kJ/mol (0.50 eV), comparable with the activation energy of the copper ion motion between 60 and 120°C deduced from NMR experiments: 0.54 eV [ 241. We estimate that this value is about the enthalpy of migration of copper vacancies: H,,,( V;l, ) = 50 kJ/ mol. In the related silver halides, where silver vacancies are the predominant ionic defects at low temperature, the enthalpy of vacancy migration is in the same order of magnitude (30-50 kJ/mol [ 25,26,29] ).

5. Conclusion By determination of the frequency dependence of the impedance of the cell Cu (CuI (Cu, we show that the phase boundary capacitance increases and the phase boundary resistance decreases exponentially with temperature. This can be related to the space charge layers

235

at the interface. The electrical conductivity of copper iodide confirms previous electrochemical experiments.

References [l] J.B. Wagner and C. Wagner, J. Chem. Phys. 26 (1957) 1597. [2] W. Biermann and H.J. Oel, Z. Phys. Chem. (NF) 17 (1958) 163. [3] K. Funke and R. Hackenberg, Ber. Bunsenges. Physik. Chem. 76 (1972) 885. [4] T. Matsui and J.B. Wagner, J. Electrochem. 300.

Sot. 124 (1977)

[5] T. Jow and J.B. Wagner, J. Electrochem. Sot. 125 (1978) 613. [6] D. Carton, J. Rasneur and H. Le Brusq, C.R. Acad. Sci. Paris II, 309 (1989) 1283.

[ 71 R.A. Montani and J.C. Bazan, J. Phys. Chem. Solids 50 ( 1989) 1207. [8] A. Wojakowska, J. Chim. Phys. 87 ( 1990) 367. [9] R.A. Montani and J.C. Bazan, Solid State Ionics 46 (1991) 211. [lo] S. Crouch-Baker, Solid State Ionics 46 ( 1991) 309. [ 111 R. Dejus, K. Skijld and B. Gram%, Solid State Ionics 1 ( 1980) 327.

[ 121 J.X.M.Z. Johansson, K. Sksld and J.-E. Jorgensen, Solid State Ionics 50 ( 1992) 247.

[ 131 J.E. Bauerle, J. Phys. Chem. Solids 30 (1969) 2657. [ 141 I. Yokota, J. Phys. Sot. Japan 16 (1961) 2213. [ 151 I. Riess and D.S. Tannhauser, Solid State Ionics 7 ( 1982) 307. [ 161 R. Safadi and I. Riess, Solid State Ionics 58 (1992) 139. [ 171 W. Bilhrer and W. Hiilg, Electrochim. Acta 22 ( 1977) 701, 118) N.B.S. Circular N” 539 (1955).

[ 191 J. Maier and G. Schwitzgebel, Mat. Res. Bull. 18 ( 1983) 601. [20] J. Maier, Ionenleitung in Randschichten, Habilitationsschrift (Tilbingen, 1987). [21] J.O.M. Bockris and A.K.N. Reddy, Modem Electrochemistry (Plenum, New York, 1970). [22] S. Villain, J. Caban and P. Knauth, in preparation. [23] W. Jost, Diffusion in Solids, Liquids, Gases (Academic, New York, 1960). [24] J.B. Boyce and B.A. Huberman, Phys. Rep. 51 (1979) 189. [25] G. Cochrane and N.H. Fletcher, J. Phys. Chem. Solids 32 (1971) 2557. [26] P.A. Govindacharyulu, D.N. Bose and S.K. Suri, J. Phys. Chem. Solids 39 ( 1978) 961.

[ 271 L. Smart and E. Moore, Solid State Chemistry (Chapman and Hall, London, 1281 G.W. Herzog, Physik. Chem. [29] U. Lauer and (1992) 111.

1993) p. 103. H. Krischner and M.R. Wabl, Ber. Bunsenges. 75 (1971) 516. J. Maier, Ber. Bunsenges. Physik. Chem. 96