Phase diagram, thermodynamic and transport properties of Ag5−xTe3

Journal of

ALLOY5 AND COMPOUB~D5 ELSEVIER

Journal of Alloys and Compounds 220 (1995) 152-156

Phase diagram, thermodynamic and transport properties of Ag5-xTe3 M. Gobec, W. Sitte * Institut fiir Physikalische und Theoretische Chemie, Technische Universitgit Graz, A-8010 Graz, Austn'a

Abstract

The phase diagram of Ags_xWe3(stiitzite) was established between 120 °C and 320 °C. In addition to results of preliminary thermodynamic investigations, significant transport properties (ionic and electronic conductivity, chemical diffusion coefficient and component diffusion coefficient of silver) were determined between 120 °C and 320 °C as a function of composition in specially designed electrochemical cells. Coulometric titration in the solid state was applied for in situ variation of the silver content. The results indicate that Ags_xTe3 is a structurally cationic-disordered mixed conducting phase with silver deficit and with a high silver ionic conductivity comparable with that of the a modifications of the silver chalcogenides Ag2X (X~-S, Se,Te). In contrast to the latter, no /3 to a transition was observed in Ags-xTe3. Keywords: Stiitzite; Phase diagrams; Structural disorder; Transport properties; Thermodynamics

1. Introduction

Among the various silver tellurides, Ags_xTe3 is a compound which exists at room temperature but, in contrast to the silver chalcogenides Ag2X ( X S, Se,Te), no characteristic/3 to a transition has been reported. Ags_xTe 3 can be found in nature as the mineral stiitzite (or stuetzite). According to Honea [1] the low temperature form of sttitzite is hexagonal, space group C6/mm with a = 13.38 ,~, c=8.45 A. The lowtemperature form undergoes a phase transition into the high-temperature form at 520 K (silver-rich composition) or 568 K (tellurium-rich composition) [2]. The present study was mainly concerned with determination of the range of homogeneity of Ags_xTe3 as a function of temperature using solid state electrochemical methods. Moreover, the ionic and electronic conductivities and the chemical and component diffusion coefficients were determined as a function of composition and temperature in order to obtain information about the transport properties of this compound. The results should answer the question whether there is any analogy between Ags_xTe3 and Ag2Te.

* Corresponding author.

0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(94)06000-2

2. Phase diagram and thermodynamics of Ags_xT% Of the various methods for the simultaneous investigation of phase diagrams and thermodynamic or kinetic properties of solid state systems, electrochemical methods allow the investigation of large temperature ranges, especially if solid electrolytes are applied. Pioneering work regarding the application of solid state electrochemical methods for the investigation of phase diagrams as well as thermodynamic properties was performed by Wagner and coworkers. In an important study, Kiukkola and Wagner [3] investigated the Gibbs energy of formation of various oxides and chalcogenides including the system Ag-Te. They were able to find three silver tellurides Ag2Te, Agl.gTe (designated as the y-phase) and Agl.64Te (designated as the e-phase) at 250 °C and 300 °C. Kracek et al. [2] established the phase diagram of the system Ag-Te including the compounds Ag2Te, Aga.9Te and Ags_xTe 3. Bonnecaze et al. [4] reported a shift of the homogeneity range of Ags_~Te3 towards higher silver contents at elevated temperatures. The existence of the three silver tellurides was also proved by Sitte and Brunner [5] by emf measurements at 200 °C employing solid state coulometric titration. Although no additional phases could be found in these studies, Honea [1] described a mineral with formula AgTe which it has not yet been possible to synthesize in the laboratory

M. Gobec, W. Sitte / Journal of Alloys and Compounds 220 (1995) 152-156

[6]. Sitte and Brunner [5] determined the standard Gibbs energy of formation of the Ag-Te system as well as the activities of silver and tellurium in the twophase regions at 200 °C. The value of AfG°(473 K, Agl.625Te) = -37.7+0.1 kJ mo1-1 from this study may be compared satisfactorily with the results obtained by Bonnecaze et al. [4] of AfG°(435 K, Agl.62Te ) = - 3 6 . 0 kJ mol-t and AfG°(523 K, Aga.64 Te) = - 39.2 kJ mol- 1. The latler value is in agreement with AfG°(523 K, Ag,.64Te)=-39.7 kJ mol -a found by Kiukkola and Wagner [3]. From dissociation pressure measurements by a Kzmdsen effusion method, Mills [7] calculated the standard enthalpy of formation of sttitzite AfH °(298, 15 K, Aga.64Te) = - 29.7 + 5.0 kJ mol- 1. The values differ from a calculation of AfH°(298, 15 K, Agl.667T,~) = - 24.2 kJ mol -~ by Eichler et al. [8] on the basi,; of the Miedema model. Castanet and Laffitte [9] measured the enthalpy of formation of the Ag-Te system at 728 and 745 K by direct calorimetry covering the mole fractions of silver between 0 and 0.70. It should be mentioned that according to Ollitrault-Fichet et al. [10] the formula AgsTe3 should be written Ag~1.67T,~7because the authors observed an isostructural compound Agl~AsTe7 in the quasi-binary system Ag2Te-AszTe3. Nevertheless, in this paper we use Ags_xTe3 as the generally accepted formula for st/itzite.

3. Experimental details

Ags_~Te3 samples were prepared by coulometric titration at 200 °C using commercially available Ag2Te as the starting material (with the stoichiometric point of the latter being determined exactly, details may be found in [11]). At the desired stage of composition the material was ground and pressed to disc-shaped samples or rods for the subsequent conductivity and diffusion experiments. For simultaneous determination of the chemical diffusion coefficient and the partial ionic conductivity of Ags_xTe3, a recently developed transient technique was used [11], employing the symmetric solid state electrochemical cell Ag [AgI[ AgsTe3 IAglI Ag Agre r Pt Agref

(I)

with twc ionic electrodes, two silver reference electrodes and an additional platinum contact on the sample for emf measurements. The composition of the sample was varied by coulometric titration applying a constant current between the silver and the platinum electrodes. The chemical diffusion coefficient and the ionic conductivity were obtained from the time dependence of the transient voltage response of the cell. For temperatures below 160 °C, Ag4RbI5 was used instead of AgI as a solid silver ionic conductor.

153

The electronic conductivity was measured independently using a four-point van der Pauw technique with four platinum wires mounted on one side of the discshaped sample [12]. The sample is part of a solid state galvanic cell with AgI or AgaRbI5 as silver ionic conductor and a silver counter-electrode allowing variation of the silver content by coulometric titrations. All experiments were run in quartz apparatus under a constant helium flow. Combined coulometric titrations and ionic conductivity and diffusion as well as electronic conductivity measurements were performed using a multimeter with scanner (Keithley, model 199) and a precision current source (Knick model J152). During the measurements the temperature was held constant by means of a precise temperature controller (Eurotherm model 818) within 0.2 K, employing chromel-alumel thermocouples. All data were recorded using a self-built data acquisition system monitored by a personal computer.

4. Results and discussion

Examples of coulometric titration curves for temperatures between 160 °C and 280 °C are shown in Fig. 1. At temperatures up to 240 °C, the curvature of the coulometric titration curve is opposite to the curvature at 280 °C and 320 °C. This is a sign of a phase transition between 240 °C and 280 °C. The plateaux with constant emf values represent two-phase regions where Ag5_xTe 3 coexists with Te(Ag) (solid solution of silver in tellurium) and AgtgTe [5].

270

I

'

'

I

'

I

'

I

'

'

I

'

'

250260 ~

'

I

I

I

240°C

220

~-- v--

200°C

210

~\--a

180°C

1.

I

~-320°C 280uC

Ill 230

200

I

. . . . . . . . •.--zx . . . . . . .160°C ... y in AgyTe 1.62

1.64

1.66

1.68

.70

Fig. 1. Coulometric titration curves for Ags-~Te3 at various temperatures.

M. Gobec, W. Sitte / Journal of Alloys and Compounds 220 (1995) 152-156

154

The phase diagram of Ags_~Te3 resulting from the coulometric titration curves is given in Fig. 2. The coulometric titration curves indicate that mgs_.Te 3 mainly exists as a non-stoichiometric compound with silver deficit. Stoichiometric AgsTe 3 (Ag1.667Te) contains 62.5 mol% silver (dashed line in Fig. 2). At temperatures above 200 °C, the homogeneity range is shifted towards higher silver contents. In contrast to the silver chalcogenides Ag2X ( X = S , Se,Te) no /3 to o~ transition could be found. Figs. 3(a) and 3(b) show the chemical diffusion coefficient D as a function of composition between 120 °C and 320 °C. Measurements at temperatures below 250 °C (Fig. 3(a)) revealed increasing values o f / ) with decreasing silver activities, whereas increasing values o f / ) with increasing silver activities could be observed above 250 °C (Fig. 3(b)) in accordance with the shapes of the coulometric titration curves (see below). Moreover, the values of/) increase with temperature between 120 °C and 200 °C, whereas the value o f / ) at 240 °C is considerably smaller. No maximum of 13 as function of composition can be observed as for example in the case of Ag2Te at 160 °C [11]. In contrast to the component diffusion coefficient, the chemical diffusion coefficient usually shows a complex temperature dependence. This originates from the fact that the chemical diffusion coefficient is a function of the concentrations and mobilities of all mobile species (ions, electrons or holes) of the mixed conducting phase [13]. For a detailed discussion of the temperature dependence of the chemical diffusion coefficient, among other parameters the band gap energy of Ags_~Te 3 would be needed [13]. Calculations would be restricted to compositions in the vicinity of the stoichiometric point (where degeneracy of the electrons or holes can be neglected), which in the present case is outside the homogeneity range at tow temperatures (Fig. 2). The ionic conductivity ~r~o, (Fig. 4), which was determined together with the chemical diffusion coefficient

2OO°C S ~ ,

E o

130°C !

:J.20°C

2

ooo

1

1.6

1.6t

.

.

.

,

1.62 y in

.

.

.

,

1.63 AgyTe

•

,

1.64

.

,

.

1.65

.

.

.

.

.

1.65

.

320°C

a7 'In

/

(b)

6

240°C

3

280°C

2 t

.

.

.

1.6

, . . . . . . 1.62 1.64

i . 1.66 y in A g y T e

.

.

, . 1.68

.

. 1.70

Fig. 3. Chemical diffusion coefficient as a function of composition between (a) 120 °C and 200 °C, and (b) 280 °C and 320 °C.

2.5 2.0

320oC.

1.5

?

•

AAA*

" 1.0

E o O3

0.5

c o .r4

1.0

0

g

.t=tla=UOo

~AA

280*C

A

~ 240"C

0220'

30o

i!iiii

(a)

~0°cA\

i

'

' 2 3' 0 '

'

' 2 4' 0 '

,

'

' 25 "0'

,

''

2 6' 0 '

'

' 270

,

200

100

.

1.6

.

1.62

.

1.64

0.5

,~..~,~-,o~o-~~

_,,~ j v l t . - , j ; ~ Z o

160*C

~

13o*c 120*C

.

1.66

' , 1.68

,

,

1.70

y in AgyTe

Fig. 2. Phase diagram of Ags-~Te3 resulting from the coulometric titration curves. The dashed line represents the stoichiometric composition of mgsTe3.

0

180

i 200

i 220

i 240

260

E/mY Fig. 4. Ionic conductivity trio, of Ags-xTe3 as a function of the emf of the galvanic cell AglAgllAgs_~Te3lPt between 120 °C and 320 °C.

M. Gobec, 14. Sitte / Journal of Alloys and Compounds 220 (1995) 152-156

from the transient experiments on the symmetric cell (I), was found to be independent of composition, indicating a structurally cationic-disordered phase. The ionic conductivities are rather high (between 0.20 S cm -1 at 120 °C and 1.4 S cm -1 at 280 °C) and can be compared with those of a-Ag2Te [14]. For better reproduction the ionic conductivities are given as a function of the emf of the galvanic cell AglAgI[ Ags_xTe3JPt. Fig. 5 shows the dependence on composition of the electronic conductivity of Ag5_xTe3 at various temperature:s, determined independently by a modified van der Pauw method. The electronic conductivity is a function of non-stoichiometry below 250 °C (hole conductivity) and almost independent of composition above 250 °C, which again makes a phase transition above 250 °C plausible [2]. For a structurally disordered compound the ionic conductivity is independent of composition at constant temperature, and the chemical diffusion coefficient is given by [13] / ~ =

O'iOre

V

m

d

E

c'~+ ~r~ F dy

(1)

Vm denotes the molar volume of Ags_xTe3 and F the Faraday constant. Because the electronic conductivity prevails over the ionic conductivity, the electronic transference number t e = t r e / ( O ' e W O ' i o n ) is close to unity and we obtain [15]

155

ductivity ~i and the molar volume Vm of the mixed conductor (tri=0.71 S cm -1, Vm=40 cm 3 mo1-1 at 200 °C). The values o f / ) calculated from Eq. (2) concur well with the experimental data at 200 °C (Fig. 6). The component diffusion coefficient D~,g of silver was obtained from /) = W~D~,g

(3)

Wi being the enhancement factor of the silver ions. W~ can be expressed as Wi te =

d In aA~ = tc0i d In CAg

(4)

with 01 being the thermodynamic factor of the silver ions. The thermodynamic factor 01 is related to the first derivative of the coulometric titration curve as d In aA~ 0~= d lncAg = -

Fy(dE~ R-'T~'-~y]

(5)

The component diffusion coefficient of silver was independent of composition within limits of error. Table 1 gives the component diffusion coefficient at temperatures between 120 °C and 280 °C. The values may be 6.5

('kl

E

4.5

CA

oiVm dE F dy The the and the

(2)

o

C) 2.5

chemical diffusion coefficient is proportional to firs! derivative of the coulometric titration curve may alternatively be calculated from the slope of coulometric titration curve the ionic con-

0.5

dE/dy,

,

~62

I

,

~625

,

I

,

~630

.635

y in AgyTe '

•

'

i

.

.

.

,

,

•

t

,

.

en% : _ - . . ~

35

J ~.-_-

r U

t

.

i

,

,

,

Fig. 6. Experimentally determined chemical diffusion coefficients for Ags_xTe3 as a function of composition at 200 °C (O) compared with the values calculated from Eq. (2) at 200 °C ( - - ) .

2800C

:. - . ; - - - -

Table 1 C o m p o n e n t diffusion coefficient of silver D~,g in AgsTe3 compared with those of /3-Ag2Te and a-Ag2Te at various temperatures

2600C

25

(-3

240"C

f_0

T (°C)

200"C

15

1800C

160°C

1.6

t.62

1.64

1,66

1.6fl

1.70

y i n AgyTe Fig. 5. D e p e n d e n c e on composition of the electronic conductivity of Ags-xTe3 at various temperatures.

120 130 160 180 200 240 280 320

/YAg×10 6 (cm 2 s -I) Ag5 _~Te3

Ag2Te

1.7 2.3 3.8 5.7 5.9 9.8 18 41

0.016 (/3) 0.027 (/3) 9.9 (a) 11 (a) 13 (or)

156

M. Gobec, IV.. Sitte / Journal o f Alloys and Compounds 220 (1995) 152-156

compared with those of a-Ag2Te [11] (Table 1). Owing to the enhancement factor, the component diffusion coefficient of silver D~,g is lower by two orders of magnitude than the chemical diffusion coefficient b for

Ag5_xTe3.

affected by changes in the silver content. Therefore, the measured values of the chemical diffusion coefficient agree well with those calculated from the ionic and electronic conductivities as well as the first derivative of the coulometric titration curve.

5. Conclusion

References

In this study the phase diagram of Ags_xTe3 has been determined and significant transport properties have been measured within the homogeneity range of this mixed conducting compound. Ags_xTe3 has been identified as a cationic-disordered compound with high and composition independent ionic conductivity, comparable with those of the silver chalcogenides Ag2X (X=S, Se, Te). A previously reported phase transition at 265 + 15 °C [2] is in agreement with our results, but an order--disorder type transition cannot be confirmed. It must be emphasized that composition dependent measurements of the chemical diffusion coefficient and the ionic conductivity of Ags-~Te3 could be performed successfully owing to a number of simplifications. On the one hand, only silver ions are mobile within a rigid lattice (the latter serves as a frame of reference for the solution of the diffusion equations). On the other hand, Ags_~Te3 is a cationic-disordered compound and neither the ionic disorder nor the lattice constants are

[1] R.M. Honea, Am. Mineral., 49 (1964) 325. [2] F.C. Kracek, C.J. Ksanda and L.J. Kabri, Am. Mineral., 51 (1966) 14. [3] K. Kiukkola and C. Wagner, J. Electrochem. Soc., 104 (1957) 379. [4] G. Bonnecaze, A. Lichanot and S. Gromb, J. Phys. Chem. Solids, 44 (1983) 967. [5] W. Sitte and A. Brunner, Solid State lonics, 28-30 (1988) 1324. [6] E.F. Stumpfl, Am. Mineral., 53 (1968) 1513. [7] K.C. Mills, J. Chem. Thermodyn., 4 (1972) 903. [8] B. Eichler, H. Rossbach and H. G/iggeler, J. Less-Common Met., 163 (1990) 297. [9] R. Castanet and M. Laffitte, Rev. Int. Hautes Temp. Refract., 11 (1974) 103. [10] R. Ollitrault-Fichet, Ch. El Kfouri and J. Rivet, C.R. Acad. Sci. Paris, Ser. II, 313 (1991) 757. [11] W. Sitte, Solid State tonics, 59 (1993) 117. [12] D. Grientschnig and W. Sitte, Z. Phys. Chem. N.F., 168 (1990) 143. [13] D. Grientschnig and W. Sitte, J. Phys. Chem. Solids, 52 (1991) 805. [14] I. Rom and W. Sitte, Solid State lonics, 70/71 (1994) 147. [15] W. Sitte, J. Chim. Phys., 90 (1993) 269.