Microstructure of binary silver borate glasses and estimation of electronic conductivity by the polarization method

42

Journal of Non-Crystalline Solids 85 (1986) 42 53 North-Holland, Amsterdam

M I C R O S T R U C T U R E OF BINARY SILVER B O R A T E G L A S S E S AND E S T I M A T I O N O F E L E C T R O N I C CONDUCTIVITY BY T H E P O L A R I Z A T I O N M E T H O D Hideyo M O C H I Z U K I Department of Chemistry, Nagoya Industrial Research Institute, Atsuta-ku, Nagoya, Japan

Yoshio M U R A S E Department of Ceramics, Government Industrial Research Institute, Nagoya, Kita-ku, Nagoya, Japan Received 12 July 1985 Revised manuscript received 26 December 1985

Studies pertinent to the total electrical conductivity, ionic and electronic conductivities, microscopic observation and emf measurement were made for the glasses of the system x A g 2 0 ( 1 0 0 - x ) B203 (x = 22, 27 and 38 mol%). The temperature dependence of the total electrical conductivity for all glasses exhibited a linearity against l / T , indicating that the ionic conductivity prevails over electronic conductivity in the present glass system. Electronic conductivity was estimated by a polarization method and was found to be two to three orders of magnitude smaller than the total electrical conductivity. Crystalline diffraction rings were observed in the microstructure of glasses by electron diffraction measurement, which indicated the presence of metallic silver. The higher the Ag20 content in the glass, the larger the diameter of the silver particles. The electronic conduction of these glasses probably depends on the microstructure, which causes deposition of metallic silver particles.

1. Introduction

Nearly complete ionic conductivity in superionic conducting glasses containing a large amount of silver ions as a charge carrier has already been demonstrated by the measurements of transport number using electrolysis and emf methods [1,2]. Silver ions, unlike other monovalent alkali ions, have a covalent character and are expected to be distributed in the glass structure in a somewhat different manner from other alkali ions. Matusita et al. [3] found that the mobility of silver ions in the glass systems AgzO-B203 and A g z O - N a z O - B 2 0 3 with a high concentration of Ag20 is higher than that estimated by assuming their uniform distribution in the glass. It was assumed that the silver ions form a cluster in the glass, so that the jumping distance for ion transfer might be shorter. The formation of pairs and clusters of silver ions was shown by X-ray analyses [4]. It was also shown that the interatomic distances between silver ions were independent of the Ag20 content of the glass, although direct contact between silver ions has not been postulated. 0022-3093/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

H. Mochizuki, Y. Murase / Microstructure of bina~ silver borate glasses

43

Using an electron microscope, the present authors have confirmed that a large number of metallic silver particles precipitated in the glass containing more than 20 mol% of Ag20. The presence of metallic silver suggests that the electron transfer between metallic and ionic silvers might induce electronic conduction. To confirm this, the electronic conduction was examined by the polarization method.

2. Experimental 2.1. Preparation o f glasses

Glasses of nominal composition x A g 2 0 . ( 1 0 0 - x)B203, where x corresponds to 22, 27 and 38 mol%, were prepared. Reagent grade AgNO3 (Supplied by Wako Chemicals Co.) and B203 were used as raw materials. The B203 was prepared by melting reagent grade H3BO 3 at 700 to 800°C followed by grinding under a dry atmosphere. The mixtures were melted in alumina crucibles at 800 to 900°C for 30 to 50 min with frequent stirring. The melt was poured onto a platinum plate to form a circular plate and annealed by cooling from 600°C to room temperature at a rate of 10°C per hour. The samples were stored in black-walled desiccators, The glasses were chemically analyzed for A g 2 0 and the percentage of B203 was obtained by subtracting the percentage of A g 2 0 from 100. Analytical and nominal compositions of the glasses are shown in table 1. 2.2. Electrical measurements

Circular plates of glass of 10 mm diameter with a thickness of 2 - 3 mm were used as a sample. Electrodes of 7 mm in diameter were made on both surfaces of the specimen using silver paste. The total electrical conductivity was obtained from dc and ac measurements. The dc measurements using a vibrating reed electrometer (Takeda Riken, TR-84 M) were applied to conductivities lower than 10 -7 ~2-1 cm -1. The current-voltage curves were linear for all specimens tested. The conductivities higher than 10 7 ~2-1 cm ~ were measured by an ac bridge (Ando Denki, TR-10) at a constant frequency of 1

Table 1 Composition of glasses used in the experiments Glass no. 1 2 3

Nominal x tool%

wt%

Analytical x tool%

wt%

22,0 27.0 38.0

48.4 55.2 67.1

21.9 26.7 35.7

48.3 54.8 64.9

44

H. Mochizuki, Y. Murase / Microstructure of binao' silver borate glasses

kHz. Electronic conductivity was measured by Wagner's polarization method [5], in which the cell consisted of Ag/X/graphite,

(I)

where X denotes the glass. The direct current of 0.2-0.4 V was applied to cell I for about 10 h prior to the measurements. Silver ions migrate initially from the graphite electrode (anode) toward the silver electrode (cathode), while electrons migrate in the opposite direction. Under the steady-state condition, migration of silver ions due to the electric field is balanced by diffusion due to the concentration gradient and the current is carried exclusively by excess electrons or electron holes. As electronic conductivity (oe) for the present glass system is attributed to the electron holes, the following Wagner's equation is used: I = oe [ e x p ( E . ~ / R T ) - 1] R T A / ~ L ,

(1)

where I is the current, E is the applied voltage, A is the cross-sectional area, L is the thickness of the glass plate, ~ is the Faraday constant and R the gas constant. For determining the transport numbers, the emf of the following cell was measured; A g / g l a s s / T e , glass powder.

(II)

The assumed cell reaction was

2Ag(s) + Te(s) =AgzTe(s), where s represents the solid phase. The emf of the cell was measured at different temperatures by a vibrating reed electrometer (Takeda Riken, TR84M) with a pre-amplifier.

2.3. Electron microscopy A few pieces of powdered glass were put onto a resin film supported with copper mesh and examined by a transmission electron microscope (JEM-200 CX). The glass powder was made just before observation under an electron microscope to prevent silver ions from reduction due to exposure to light.

3. Experimental results

3.1. Total electrical conductivity (oT) Plots of the total electrical conductivities versus reciprocal temperature are shown in fig. 1. The curves show a good linearity and are expressed by the Rasch-Hinrichsen relationship; OT = o0 e x p ( - A H / R T ) ,

(2)

-7

£5

31o

1 0 0 0 / T ( K -7)

'

\

o

\

:ig. 1. Total electrical conductivity for glasses Nos. l, 2 and 3 as a unction of reciprocal temperature.

2

'E u c

-6

-5

DC

o AC

•

25

30 Ag20 ( m o [ % )

35

:ig. 2. Variation in total electrical conductivity with A g 2 0 content at arious temperatures.

O~ O -'7

t)

E

2.

:Z::

H. Mochizuki, Y. Murase / Microstructure of binary silver borate glasses

46

where A H is the activation energy for electrical conduction and o0 is a constant. In the temperature range from room temperature to 160 ° C, the total electrical conductivities of glasses Nos. 1 and 2, which contain 21.9 and 26.7 mol% Ag20, are in good agreement with those of glasses of corresponding compositions, 22.3 A g 2 0 . 7 7 . 7 B203 and 25.8 A g 2 0 . 7 4 . 2 B203 respectively

[31.Variation of logo T with the concentration of Ag20 in the glass is shown in

fig. 2 at different temperatures. At temperatures lower than 80°C, the values of logo T for glass No. 3, which contains 35.7 mol% Ag20, are roughly situated on the lines extrapolated from those for glasses of lower Ag20 concentrations. At temperatures higher than 100°C, the values of logo T of glass No. 3 are lower by 0.4 to 1.0 logarithmic units than those extrapolated from the values for glasses of lower concentrations of Ag20. •2. E l e c t r o n i c c o n d u c t i v i t y

The relation between the applied voltage and the current density for cell I is shown in fig. 3. Following theoretical suggestions by Wagner [5], the relation-

-7 o/~

60"C

-8

-9

~ ~ o o ' c

-10

o~~°:~

GI~s s

C~ 0

12 0%

No.~

o

-I 1

~~~oo~ -11

-12

o

0;1

0:2 E (volt)

'

0:3

Fig. 3. Current density versus applied voltages for glasses Nos. 1, 2 and 3 at different temperatures.

-0.5

-9

o

0

0.5

I o g ( e ~ m - 1 ) ART/k~ L

1.0

Fig. 4. Plots of log 1 versus log(e KL~/RT- 1)ART/k.~-L for glass No. 3 at various temperature.

0

v

-7

-11

-10

-9

, 2.5

,

,

o~

o

o

No.2

,

3h0,

~ - ~ ~ N o.1

1000IT ('K')

~

o'~'~ o"

~

o---~_~_ o

'

,

Fig. 5. Electronic conductivity as a function of reciprocal temperature for glasses Nos. 1, 2, and 3.

O

-B

-7

q

48

H. Mochizuki, Y. Murase / Microstructure of binary silver borate glasses

ship between the voltage E and the current density I is represented by I = oe ( RTA/Lf)[ 1 - exp( - E f / R T ) ]

(3)

or

I = o~ ( R T A / L f ) [ e x p ( E f / R T ) - 1], (4) where o s and a s are the electronic conductivities due to electrons and electron holes respectively. Eq. (3) suggests that I approaches a definite value independent of voltage E, if the condition Eft>> ] is satisfied. It is evident from the I - V relations in fig. 3 that eq. (3) is not suitable for the electronic conduction of the present systems. The curves in fig. 3 exhibit essentially a quasi-exponential increase in the range of applied voltages between 0.1 to 0.3 V for all glasses. This indicates that eq. (4) holds in the electronic conduction for the present glasses but the slopes of I - V curves in fig. 3 do not fit the theoretical slopes of the polarization equation (4). Therefore, eq. (5) derived by Takahashi et al. [6] was applied to the present glasses; I = o~ [ e x p ( k E f / R T ) - 1] R T A / k f L , (5) where, k is a positive number smaller than unity, k is estimated from the I - V curves in fig. 3. The plots of log I versus l o g [ e x p ( k E f / R T ) - I]ART/kfL yield virtually straight lines and the points where these lines intersect the ordinate give the I value. Fig. 4 shows the results on typical runs for glass No. 3. Table 2 shows the k values and the electronic conductivities (ae) calculated by eq. (5). It can be seen that the electronic conductivities are two to three orders of magnitude smaller than the total electrical conductivities and the transport numbers of the Ag + ion are close to unity for all glasses. The plots of electronic conductivity versus temperature are shown in fig. 5. Activation energies for the electronic conduction determined from the slopes of the curves are 7.93 kcal/mol (0.34 eV) for glass No. 1, 3.47 kcal/mol (0.15 eV) for glass No. 2 and 12.00 k c a l / m o l (0.52 eV) for glass No. 3. 3.3. E M F m e a s u r e m e n t

The emf values in the temperature range 20 to 70°C are shown in fig. 6. The temperature dependence of the the standard free energy of formation

Table 2 V a l u e s o f the s u p p l e m e n t a l f a c t o r k a n d e l e c t r o n i c c o n d u c t i v i t y (oe) for the glasses N o s . 1, 2 and 3

Temp.

Glass No. I

(°C)

kxl02

oe(~ cm) -1

kxl02

Glass No. 2 o~(12 c m )

40 60 80 100 120

6.74 7.89 5.60 7.24 6.80

7.46 X 1.16× 2.67 X 4.29x 9.97 x

3.26 2.78 3.58 3.80 4.45

8 . 8 7 × 1 0 11 1.65 x 10 10 1 . 8 8 x 10 lo 2.41 x 10 - 1 ° 2.76 X 10 lo

10 - l z 10 - H 10 -11 l 0 -11 10 -11

Glass No. 3 i

k×102

%(12 c m ) - i

8.49 7.67 6.66 8.67 8.06

5 . 6 1 X 10 - 9 1.82 x 10 - 8 6.36×10 -8 1 . 1 7 x 10 - v 2.84×10 -7

H. Mochizuki, Y. Murase / Microstructure of binary sih,er borate g/asses

49

220 Calculated value

j NO.3

[2J

E

210

~

__~_~

LIJ

No.2

No.I

200

2

I

I

30

40

;

5

I

f

60

70

T (*C)

Fig. 6. Values of emf for the cell, Ag/glass/Te, glass powder, for glasses Nos. 1, 2 and 3. derived from the emf of/3-Ag2Te (a lower temperature modification of Ag2Te ) has been reported by Takahashi et al. [7] as follows; A ~ = -- 8.47 -- 0.0048T kcal.

(6)

The emf values calculated from eq. (6) for the glasses are also shown in fig. 6. It can be seen that the observed emf values for all the glasses are about 2 to 10 mV lower than calculated ones in the temperature range of measurement.

3.4. Microstructure of the glasses Fig. 7 shows the electron micrographs of the glasses. Fig. 7(a) shows that a phase separation can be seen even in the glass of the lowest A g 2 0 content (21.9 mol%); the dark particles can be distinguished from the bright matrix in the microstructure. The particles grow into 150 A in diameter with an increase in A g 2 0 content as shown by fig. 7(b). With a further increase in A g 2 0 content, the dark particles aggregate into the lumps of about 500 A in diameter. Selected area electron diffraction pattern of the particle for glass No. 2, shown in fig. 7(d), indicates that these are crystalline, although the crystal was not detectable by X-ray diffraction.

4. Discussion

4.1. Identification of the precipitates in the glass In general, the relation between the reciprocal diameter of the diffraction ring D and the lattice parameter d of the crystal is expressed as d = nXL x 1/D,

(7)

:ig. 7. Electron micrographs of glasses Nos. 1, 2 and 3. (a) The microstructure of glass No. 1 with 21.9 mol% A g 2 0 . (b) The microstructure of glass No. 2 with ~.6.7 mol% Ag20. (c) The microstructure of the glass with the highest A g 2 0 content of 35.7 mol%. (d) Selected area electron diffraction pattern for glass No. !. (e) Electron diffraction pattern for metallic gold as a standard crystal.

-4

H. Moehizuki, Y. Murase / Microstructure of binary silver borate glasses

51

&

oa

zo

E

o Au

¢1.

,~ Ag /

/

*d 1.5 _J

I

1.5

,I

I

~zo

2.5

1 /DxlO0

Fig. 8. Relation between reciprocal diameters of the electron diffraction rings versus lattice parameters of metallic silver with metallic gold as a standard crystal.

where L is the camera length (constant) and X is the wavelength of the electron beam. With metallic gold, a standard crystal, a linear relation has been obtained for the plot of 1 / D against d, as shown in fig. 8. The same relation for the unknown crystal is in a close agreement with the straight line for the metallic gold provided the parameter d is taken for metallic silver. Thus, the crystalline material in the glass has been found to be metallic silver. Fig. 7 indicates, however, that the metallic silver particles are surrounded by a cloudy matrix probably richer in silver ions than the remainder of the bright matrix.

4.2. Applicability of Wagner's equation to glass In the derivation of eq. (1), it has been assumed by Wagner [5] that the chemical potential of metal (/~Me) is equal to that of the electron (/~e), while Takahashi et al. [6] took an equilibrium between the metal and metallic ion into account, as expressed by d/ZMe =dP, Me÷ + d t ~ ,

(8)

where/XM~+ is the chemical potential of the metallic ion. They further assumed that the electron hole concentration varies in proportion to the concentration of the lattice vacancies according to K d # M e ~ = d/.t e.

(9)

Substitution of eq. (9) into eq. (8) yields dbt e = k d/XMe. Integration of I regarding eq. (10) gives eq. (5).

(10)

52

H. MochizukL lq Murase / Microstructure of binary silver borate glasses

It is interesting to examine whether a similar correlation between the electron hole concentration with the concentration of lattice vacancies may be valid in the disordered structure like the present glass system and whether eq. (5) is employed in the calculation of the electronic conductivity. The current density gradually increases with increasing Ag20 content in the glass at a given voltage and temperature as shown in fig. 3. It is reasonable to consider that the electron hole concentration increases with increase in the concentration of Ag20, since the electronic current density versus voltage curves in fig. 3 indicate that the current is carried by electron holes. In nonstoichiometric ionic compounds [6], electron holes are produced from a deficit of metal in a compound. This concept will be applied to the present glasses with the assumption that the glass consists of silver rich regions surrounding metallic silver particles. The defect structure of silver oxide can be expressed by ½ 0 2 = O 0 + 2V~g +

2 ~,

(11)

where • is the electron hole, Vdg the vacancy or the interstitial of the silver ion and O o the oxygen ion in the oxygen site. Application of the mass-action law yields t 2 /.1/2 K = [V,~g] [(~J1 2/t'o2 -

(12)

For the electroneutrality condition,

[v g]

(13)

is given and, to a first approximation, the proportionality between the concentration of electron holes and that of vacancies or the interstitials of silver ions is given below; [ (~ ] o: [V;g].

(14)

It is naturally considered that the structure of Ag20 surrounding the metallic silver particles, shown in fig. 7, can be expressed by eq. (11). Consequently, eq. (14) can also be valid in the present glass system.

4.3. Electronic conductivity The electronic conductivities for glasses Nos. 1 and 2 were much smaller than that for glass No. 3, considering that the difference in the concentration of Ag20 in the glass is small. Much higher conductivity for glass No. 3 may be attributed to its microstructure shown in fig. 7 (c). The metallic silver particles of glass No. 3 are in contact with each other, while those of glasses Nos. 1 and 2, for the most part, are separated by the glass phase. The reason of the highest activation energy for glass No. 3 may be explained by the conducting path model [8].

H. Mochizukg l( Murase / Microstructure of binary silver borate glasses

53

This m o d e l assumes the two d i f f u s i o n processes of the carrier in the oxide glasses. T h e first is c o m m o n in the o x i d e glasses c o n s i s t i n g of the m u l t i c h a n n e l structure for the c o n d u c t i o n with relatively low a c t i v a t i o n energy for the c o n d u c t i o n . T h e s e c o n d is i n h e r e n t in the glasses c o n s i s t i n g of the i n t e r c o n nected s u b m i c r o s t r u c t u r e a n d gives m u c h higher a c t i v a t i o n energy for the c o n d u c t i o n than the former. T h e degree of the i n t e r c o n n e c t i v i t y for the m i c r o s t r u c t u r e of glass No. 3 seems to b e the largest of the three as shown in fig. 7, so that the highest activation energy for the electronic c o n d u c t i o n might result from the s e c o n d diffusion process. A t present, however, a m o r e precise e x p l a n a t i o n a b o u t the relation b e t w e e n the electronic c o n d u c t i o n a n d the m i c r o s t r u c t u r e of the glasses is n o t p o s s i b l e b y the p r e s e n t authors. 4.4. Discussion on e m f values

O b s e r v e d emf values for the p r e s e n t glasses are 2 to 10 mV lower than the c a l c u l a t e d ones d e r i v e d f r o m eq. (6). I n the cell r e a c t i o n of the A g - T e system, it has been r e p o r t e d that an i n t e r m e d i a t e p h a s e Agl.66_~Te ( x = 0.03-0.04) o t h e r than Ag2Te is f o r m e d at r o o m t e m p e r a t u r e [9]. This i n t e r m e d i a t e p h a s e has been f o u n d to give an emf value of 0.207 V at 53°C, a b o u t 10 mV lower than c a l c u l a t e d one [7]. I n the p r e s e n t study, the emf was m e a s u r e d in a low t e m p e r a t u r e range such as 20 to 7 0 ° C , where the i n t e r m e d i a t e p h a s e of Ag2Te will p r o b a b l y be formed. Therefore, the o b s e r v e d emf values for all glasses will give slightly lower values than the c a l c u l a t e d ones.

Acknowledgement T h e a u t h o r s wish to t h a n k D r Y a s u o T a k e d a of M i e U n i v e r s i t y for his h o s p i t a l i t y a n d the facilities p r o v i d e d a n d D r A t s u o I m a i of M a g o y a M u n i cipal I n d u s t r i a l R e s e a r c h I n s t i t u t e for his e n c o u r a g e m e n t a n d s u p p o r t .

References [1] T. Minami, Y. Takuma and M. Tanaka, J. Electrochem. Soc. 124 (1977) 1659. [2] T. Minami, H. Nambu and M. Tanaka, J. Am. Ceram. Soc. 60 (1977) 467. [31 K. Matusita, M. Itoh, K. Kamiya and S. Sakka, Yogyo-Kyokai-Shi (J. Ceram. Soc. Japan) 84 (1976) 496. [4] K. Kamiya, S. Sakka, K. Matusita and Y. Yoshinaga, J. Non-Cryst. Solids 38&39 (1980) 147. [5] C. Wagner, Z. Elektrochem. 60 (1956) 4. [6] T. Takahashi and O. Yamamoto, Denki-Kagaku (Electrochem. Soc. Japan) 31 (1963) 42. [7] T. Takahashi and O. Yamamoto, J. Electrochem. Soc. 117 (1970) 1. [8] H. Namikawa, Proc. Xth Int. Congr. Glass, Kyoto 7 (1974) 7. [9] F.C. Kracek, C.J. Ksanda and L.J. Cabri, Am. Mineral. 51 (1966) 14.