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Ionic conduction of Ag+ and Cu+ ions in vacancy defect spinel compounds (MIn5S8)1 − x(In2S3)x (M = Cu or Ag, x < 1) in microwave regime
SOLID STATE IONICS
ELSEVIER
Solid State Ionics 79 (1995) 53-59
Ionic conduction of Ag+ and Cu+ ions in vacancy defect spine1 compounds (MIn,S,) 1_x(In& x (M = Cu or Ag, x < 1) in microwave regime Y. Ohmuro, T. Ohachi
*, I. Taniguchi
Faculty of Engineering, Doshisha University, Kyo~o 610-03, Japan
Abstract Vacancy defect sulfide spine1 compounds, (MIn,Ss),_,(In,S,), (M = Cu or Ag; x < l), have been studied for ion dynamics by ac conductivity between 26.5 GHZ and 60 GHz using a vector network analyzer. The Cu system has higher plateau frequency than that of Ag system. The increment of the number of vacancy V, leads the increase of the plateau frequency for the Cu system. The plateau frequency for the Ag system is less than 26.5 GHz. Keywords:
Defect type spinel; Microwave
ac conductivity;
Vector network analyzer
1. Introduction Since 1969 [l] our interest in solid state ionics has focused on the mixed conduction of cations and electrons. The mixed conduction can be treated as atomic transport with ambipolar diffusion of cations and electrons, and plays an important role for a solid state reaction such as the growth of ferrite crystals in sintering and the growth of single crystals [2]. The spine1 structure is known as one of structures of ferrite that are formed by high temperature sintering. It is one of the crystal structures of the type AB,X, ternary compounds, where A and B are metallic ions and X is 0, S, Se, Te or CN [3]. The alternative type of sulfide spinels MI@, (M = Cu or Ag) is also
* Author to whom all correspondence should be addressed: Tel. 81-774-65-6329; Fax 81-774-65-6811; e-mail tohachi@ doshisha.ac.jp 0167-2738/95/$09.50 0 1995 Elsevier Science B.V. AII rights reserved SSDI 0167-2738(95)00029-l
known. It is formed by the replacement of two A ions in 2(AB,S,) by M+ (M = Cu or Ag) and In3+ where B is In 3+. Studying sulfide spinels is more advantageous than studying oxide ones in order to obtain a solid of high ionic conductivity. This is because larger lattice constants are expected to give higher ionic conductivity and sulfide spinels have larger lattice constants compared with those of oxide ones. We have found that solid solutions (MIn,S,),_,(In,S,), are vacancy defect spinels [4,5] and are good systems for the study of hopping dynamics of ions in solid state materials. Vacancy defect spinels, which are expected to have larger ionic conductivity, are obtained by introducing vacancies into the stoichiometric spine1 MIn,S,, using In,S,. AgIn,S, and the vacancy defect spinels show the same power law dependance of ac conductivity on angular frequency [6] as do ionically conducting glasses 171.The similar frequency dependence was also observed in a solid
54
Y. Ohmuro et al. /Solid
having a one dimensional tunnel for K+ ions [8]. The dependence is called the “universal behavior” following Jonscher [9]. Ngai’s phenomenological treatment of dielectric relaxation processes [lo], Funke’s jump relaxation equations [11,12] and Monte Carlo calculations by Kniidler et al. [13] attempt to explain the universal behavior and the “highfrequency” plateau. Both new development of technical applications and understanding of the ion dynamics are currently of interest in solid state ionics. The purpose of this report is to investigate of ion hopping dynamics in the microwave regime with relation to the kind of mobile cations and to the vacancy concentration in vacancy defect spinels. The application of a vector network analyzer to measuring material constants from 26.5 GHz to 40 GHz (R band) and 40 GHz to 60 GI-Iz (U band) range is also demonstrated.
2. Experimental 2.1. Vacancy defect spine1 compounds A vacancy defect spine1 is able to form solid solution with In, Clo,ZsS, and MIn,S, (M = Cu or Ag), a stoichiometric spine1 compound, where 0 shows vacancy. M and In are located in the tetrahedral position for MIn,S, stoichiometric spinels. Thus the vacancies are located on the tetrahedral position. (MIn,S,), _x(In,S,), (x 5 1) is rewritten as follows:
(
M32(l-x)In16(2-x) 8-5.x
q
8-5x
8x ~ 8-.5x
1
&6)os32
7
(1)
where t and o represent the tetrahedral and octahedral positions respectively. The number of vacancies in a unit cell V, is given by 8x
v, = 8-5x’ Table 1 shows the relationship between the composition of vacancy defect spinels and the number of vacancies VU. In this report, MIn,S,, MIn,S,,, MIn,,S,, and MIn,,S,, (M = Cu or Ag) have been prepared.
State Ionics 79 (1995) 53-59
2.2. Crystal growth and sample preparation Copper (or silver), indium and sulfur were weighed out to about 5 g in total according to the stoichiometric molar ratio as (MIn,S,), _,(In,S,),. Excess sulfur of 1 wt% of sulfur was added to eliminate the formation of excess metal which would act as a donor for electronic conduction. The elements were sealed in a quartz ampoule of about 8 mm and about 10 cm in diameter and length, respectively, under a vacuum of 5 X 10m3 Pa. The thickness of the ampoule was about 2 mm to prevent explosion. The sealed ampoule was heated slowly to 600°C and kept for 12 h at 600°C in a horizontal furnace. After this reaction the vapour of sulfur was no longer visible. The ampoule was heated to 1150°C and kept there for three hours. Single crystals were grown by cooling the ampoule at a rate of 12.5”C/h with a horizontal Bridgeman technique and annealing at 900°C for 24 h successively. The annealing at 900°C evens out the nonuniform composition which is formed during the solidification of the solid solution. The composition or the number of vacancies in a unit cell was confirmed with the following equation after measuring lattice constants by X-ray powder diffraction using silicon powder as a standard material [14]. a = 1.0685 + 0.0032 VU[ nm] (Cu system), a = 1.0826 - 0.0017 VU[ nm] (Ag system),
(3)
where a is the lattice constant and V, is the number of vacancy in a unit cell. Grown crystals were cut to a rectangular pellet of 7.1 mm X 3.6 mm X about 1 mm and 4.8 mm X 2.4 mm X about 1 mm for ac conductivity measurement in the R and U band respectively.
Table 1 The relationship (MIn,Ss),
between
x and V, for vacancy
_,(In,S,),
Composition
x
V”
MIn,S,
0.000 0.500 0.750 0.889 1.000
0.000 0.727 1.412 2.000 2.667
MIn7Sll MInGI, MInzl% IG3
defect spinels
Y. Ohmuro et al. / Solid State lonics 79 (1995) 53-59
2.3. Measurement of ionic conductivity at microwave regime Complex permittivity was measured to obtain the ionic conductivity in the microwave regime. The transmission/reflection method for complex permittivity and permeability measures the two-port complex scattering parameters (S parameters; Sii, S12, Szl and S,,) of a sample placed in a section of a waveguide by an automatic vector network analyzer WNA, HP85100 The sample is carefully mounted in a waveguide with Ag paste because any air gap or missalignment causes some error. Complex S parameters were measured at stepped 401 frequencies at room temperature between 26.5 GHz and 40 GHz for R band and between 40 GHz and 60 GHz for U band. The scattering equations relate the measured S parameters to the permittivity of the material. From the experimental point of view the calibration reference plane position in the transmission line is important. HP8510C offers a calibration method called the TRL (through, reflection and line) method using a calibrated standard line. The permittivity was calculated with S parameters using the Baker-Jarvis’s
method [15]. As the Baker-Jarvis’s method uses several scattering equations, the position of the sample is a fitting parameter and needs to be specified only as an initial value. A block diagram of the experimental setup is shown in Fig. 1. The VNA is controlled by a computer which is also used to calculate the complex permittivity from the measured S parameters. The conductivity is the real part of complex conductivity calculated from the complex permittivity.
3. Results and discussion Figs. 2 and 3 show conductivity and permittivity-frequency characteristics of (MIn,S,), _#r,S,), between 26.5 GI-Iz and 40 GHz. They indicate that the conductance in the microwave regime is nearly constant and reaches a plateau for the AgIn,S,-In,!& system and increases gradually for the CuIn,S,In,& system. As the number of vacancies, corresponding to x as shown in Table 1, increases, the inclinations of conductivity for Cu systems tend to increase. As shown in Eq. (31, the lattice constant of
HP 382 Work Station with HP85071A software
R-band
55
U-band MUT: material under test Fig. 1. Block diagram of VNA system.
0.008
: $
“‘I
30
,
,
32
,
" 34
,
34
3
[GHz]
” 36
,
36
.
“I’ 38
,
36
,
0
,
40
,
42
42
.>
2 0.014
0.008
0.010
E 8 0.004
fii E 0.006
4 : 0
F z
Fig. 2. Conductivity-frequency
Frequency
characteristics
[GHz]
of (CuIn,S,),
40
_-x-(In,S,J,,
26
20
28
30
30
_._%._
-
V, is the number of vacancies
5 a, 0.000 Gf
26
0.016
'0 x 0.012
2
F
5 0.002 II
’ 26
.
32
Frequency
z
” 26
,
30
% 0.002 P Ti ~0.000 a:
0.004
,
28
b
8
E
?i! E 0.006
0.010
0.012
0.014
5 g
x
b
"
4
yO.016,
26
32
34
[GHz]
[GHz]
34
36
36
-
_
_ _
in a unit cell, Vu = 8x/(8-.5x).
Frequency
32
Frequency
z
38
-
40
40
42
42
0.008
’
26
.
’
28
’
30
’
’
32
’
34
.
’
36
’
’
38
’
0
Q)
’ ’
42
z
28
30
Frequency
32
Fig. 3. Conductivity-frequency
28
34
characteristics
[GHz]
36
38
of (AgIn&),
40
_,-(I~I,S,)~,
42
rif, . , . , , , , , , , , , , ,I
z
0.004
E
, 26
0.012
4 fj 0.008 0
5 'g 0.010
z-.
-b
0.014
B 0.002
, (
28
28
,
30
30
Vu is the number of vacancies
I a, 0.000 [r
% P
28
-c0.016 g
E 8 0.004
[GHz]
0
Frequency
3~0.ooo
of
iJ E 0.006
0.000
0.002
3 0.008
oz
40
5 P
x
B
5 m
0.002
%
E 8 0.004
h: p. 0.006
;
,
,
Frequency
32
Frequency
32
,
34
34
[GHz]
[GHz]
.
I
36
36
in a unit cell, V, = 8x/(8-5x).
,
,
,
36
38
.
,
40
40
.
42
42
58
Y. Ohmuro et al. /Solid
State Ionics 79 (1995) 53-59
l 8a 016~
08b
H16d
Fig. 4. Possible diffusion paths of cations through interstitial vacancies in a spine1 unit cell: (0) and and ( n ) are cations on the tetrahedral and the octahedral positions; (0) and (Cl) are vacancies which connect to the tetrahedral and the octahedral position.
the Cu system becomes large for increasing the number of vacancies in a unit cell Vu. The enlargement of jump distance and the increase of vacancies in a jumping path take place in the Cu system simultaneously. This gives the higher plateau region for larger Vu in the Cu system. The vacancies are located at the tetrahedral positions in which In3+ ions and Cu+ or Ag+ ions are situated as mentioned in Section 2.1. Cations in the spine1 structure have two kind of ion paths as shown in Fig. 4, for the tetrahedral positions and the octahedral positions.
E
5
The scatter of the experimental data of Figs. 1 and 2 originated from the instability of the initial calibration of the reference plane in a waveguide. The contact condition between the wall and the sample is also a possible reason for the scattering even after careful mounting of the sample to the waveguide. Fig. 5 shows conductivity-frequency characteristics of vacancy defect spinels CuIn,,S,, and AgIn,,S,, between 26.5 GHz and 60 GHz of R and U bands. This shows the effect of cations. The conductivity of AgIn,,S,, reaches a plateau in the
0.030 r 0.025
b x * B s z 8
0.020
0.015
u
Frequency Fig. 5. Conductivity-frequency
characteristics
f [GHz]
of MIn,,S,,
(M = Cu or Ag) up to 60 GHz.
Y. Ohmuro et al. /Solid State Ionics 79 (1995) 53-59
frequency regime. This result agrees with the low frequency data (50 MHz-40 GHzl[6]. The conductivity of AgIn,,S,, saturates below 26.5 GHz and that of CuIn,,S,, saturates at 45 GHz. The result, that is the higher plateau frequency of the Cu system than that of the Ag system, indicates that Cu+ ions of the Cu system show frequency dependent conductivity at higher frequency than that of the Ag system due to the lighter mass of Cu+. The permittivities of the above samples were constant with frequency.
4. Conclusion From the conductivity spectrum in the microwave range from 26.5 GHz to 60 GHz the ionic conduction of vacancy defect spinels (MIn,S,),_X(In,S,), (x < 1) shows a conductivity plateau at high frequency. The Cu system has higher plateau frequency than that of the Ag system. This is explained by the difference of the weight of a Cu ion and an Ag ion. The increase of the number of vacancies V,, leads to the increase of the plateau frequency for the Cu system. The plateau frequency for the Ag system is less than 26.5 GHz.
Acknowledgements
Helpful discussion with Dr. S. Yoshikado is gratefully acknowledged. This work was partially supported by a Grant-in Aid of Doshisha University’s research promotion funds, and a Grant in Special
59
Coordination Funds for Promoting Science and Technology of the Science and Technology Agency of Japan.
References [l] T. Ohachi and I. Taniguchi, J. Phys. Sot. Japan 8 (1969) 1062. [2] S. Tanji, S. Matsuzawa, N. Wakatsuki and S. Soejima, IEEE Transact. Magn. MAG-21, 5 (19851 1542. [3] N.N. Greenwood, Ionic Crystals, Lattice Defects and Nonstoichiometry (Butterworths, London, 1968) p. 92. [4] T. Ohachi and B.R. Pamplin, Proc. 3rd Intern. Conf. Ternary Compounds Edinburgh 1977, Inst. Phys. Conf. Ser. 35 (1977) 21. [5] T. Ohachi and B.R. Pamplin, J. Crystal Growth 42 (1977) 598. [6] K. Asahi, S. Yoshikado, T. Ohachi and I. Taniguchi, Ext. Abstr. Intern. Conf. on Ternary and Multinary Compounds92, Japan. J. Apply. Phys., to be published. [7] W.K. Lee, B.S. Lim, J.F. Liu and A.S. Nowick, Solid State Ionics 53-56 (1992) 831. [8] S. Yoshikado, T. Ohachi, I. Tan&hi, Y. Onoda, M. Watanabe and Y. Fujiki, Solid State Ionics 8/9 (1983) 1305. [9] A.K. Jonscher, Nature 267 (1977) 673. [lo] K.L. Ngai and 0. Kane& Solid State Ionics 53-56 (19921 936. [ll] K. Funke, Mat. Res. Sot. Symp. Proc. 210 (1991) 97. [12] K. Funke, T. KIoidt, D. Wilmer and C.J. Carlile, Solid State Ionics 53-56 (1992) 947. [13] D. Knadler, P. Pendzig and W. Dieterich, Solid State Ionics 70-71 (1994) 356. [14] Y. Okano, K. Asahi, T. Ohachi and I. Taniguchi, Sci. Eng. Rev. (Doshisha University) 34 (1993) 83 [in Japanese]. [15] J. Baker-Jarvis, E.J. Vanzura and W.A. I&sick, IEEE Transact. Microwave Theory Tech. 38 (1990) 1096.
ELSEVIER
Solid State Ionics 79 (1995) 53-59
Ionic conduction of Ag+ and Cu+ ions in vacancy defect spine1 compounds (MIn,S,) 1_x(In& x (M = Cu or Ag, x < 1) in microwave regime Y. Ohmuro, T. Ohachi
*, I. Taniguchi
Faculty of Engineering, Doshisha University, Kyo~o 610-03, Japan
Abstract Vacancy defect sulfide spine1 compounds, (MIn,Ss),_,(In,S,), (M = Cu or Ag; x < l), have been studied for ion dynamics by ac conductivity between 26.5 GHZ and 60 GHz using a vector network analyzer. The Cu system has higher plateau frequency than that of Ag system. The increment of the number of vacancy V, leads the increase of the plateau frequency for the Cu system. The plateau frequency for the Ag system is less than 26.5 GHz. Keywords:
Defect type spinel; Microwave
ac conductivity;
Vector network analyzer
1. Introduction Since 1969 [l] our interest in solid state ionics has focused on the mixed conduction of cations and electrons. The mixed conduction can be treated as atomic transport with ambipolar diffusion of cations and electrons, and plays an important role for a solid state reaction such as the growth of ferrite crystals in sintering and the growth of single crystals [2]. The spine1 structure is known as one of structures of ferrite that are formed by high temperature sintering. It is one of the crystal structures of the type AB,X, ternary compounds, where A and B are metallic ions and X is 0, S, Se, Te or CN [3]. The alternative type of sulfide spinels MI@, (M = Cu or Ag) is also
* Author to whom all correspondence should be addressed: Tel. 81-774-65-6329; Fax 81-774-65-6811; e-mail tohachi@ doshisha.ac.jp 0167-2738/95/$09.50 0 1995 Elsevier Science B.V. AII rights reserved SSDI 0167-2738(95)00029-l
known. It is formed by the replacement of two A ions in 2(AB,S,) by M+ (M = Cu or Ag) and In3+ where B is In 3+. Studying sulfide spinels is more advantageous than studying oxide ones in order to obtain a solid of high ionic conductivity. This is because larger lattice constants are expected to give higher ionic conductivity and sulfide spinels have larger lattice constants compared with those of oxide ones. We have found that solid solutions (MIn,S,),_,(In,S,), are vacancy defect spinels [4,5] and are good systems for the study of hopping dynamics of ions in solid state materials. Vacancy defect spinels, which are expected to have larger ionic conductivity, are obtained by introducing vacancies into the stoichiometric spine1 MIn,S,, using In,S,. AgIn,S, and the vacancy defect spinels show the same power law dependance of ac conductivity on angular frequency [6] as do ionically conducting glasses 171.The similar frequency dependence was also observed in a solid
54
Y. Ohmuro et al. /Solid
having a one dimensional tunnel for K+ ions [8]. The dependence is called the “universal behavior” following Jonscher [9]. Ngai’s phenomenological treatment of dielectric relaxation processes [lo], Funke’s jump relaxation equations [11,12] and Monte Carlo calculations by Kniidler et al. [13] attempt to explain the universal behavior and the “highfrequency” plateau. Both new development of technical applications and understanding of the ion dynamics are currently of interest in solid state ionics. The purpose of this report is to investigate of ion hopping dynamics in the microwave regime with relation to the kind of mobile cations and to the vacancy concentration in vacancy defect spinels. The application of a vector network analyzer to measuring material constants from 26.5 GHz to 40 GHz (R band) and 40 GHz to 60 GI-Iz (U band) range is also demonstrated.
2. Experimental 2.1. Vacancy defect spine1 compounds A vacancy defect spine1 is able to form solid solution with In, Clo,ZsS, and MIn,S, (M = Cu or Ag), a stoichiometric spine1 compound, where 0 shows vacancy. M and In are located in the tetrahedral position for MIn,S, stoichiometric spinels. Thus the vacancies are located on the tetrahedral position. (MIn,S,), _x(In,S,), (x 5 1) is rewritten as follows:
(
M32(l-x)In16(2-x) 8-5.x
q
8-5x
8x ~ 8-.5x
1
&6)os32
7
(1)
where t and o represent the tetrahedral and octahedral positions respectively. The number of vacancies in a unit cell V, is given by 8x
v, = 8-5x’ Table 1 shows the relationship between the composition of vacancy defect spinels and the number of vacancies VU. In this report, MIn,S,, MIn,S,,, MIn,,S,, and MIn,,S,, (M = Cu or Ag) have been prepared.
State Ionics 79 (1995) 53-59
2.2. Crystal growth and sample preparation Copper (or silver), indium and sulfur were weighed out to about 5 g in total according to the stoichiometric molar ratio as (MIn,S,), _,(In,S,),. Excess sulfur of 1 wt% of sulfur was added to eliminate the formation of excess metal which would act as a donor for electronic conduction. The elements were sealed in a quartz ampoule of about 8 mm and about 10 cm in diameter and length, respectively, under a vacuum of 5 X 10m3 Pa. The thickness of the ampoule was about 2 mm to prevent explosion. The sealed ampoule was heated slowly to 600°C and kept for 12 h at 600°C in a horizontal furnace. After this reaction the vapour of sulfur was no longer visible. The ampoule was heated to 1150°C and kept there for three hours. Single crystals were grown by cooling the ampoule at a rate of 12.5”C/h with a horizontal Bridgeman technique and annealing at 900°C for 24 h successively. The annealing at 900°C evens out the nonuniform composition which is formed during the solidification of the solid solution. The composition or the number of vacancies in a unit cell was confirmed with the following equation after measuring lattice constants by X-ray powder diffraction using silicon powder as a standard material [14]. a = 1.0685 + 0.0032 VU[ nm] (Cu system), a = 1.0826 - 0.0017 VU[ nm] (Ag system),
(3)
where a is the lattice constant and V, is the number of vacancy in a unit cell. Grown crystals were cut to a rectangular pellet of 7.1 mm X 3.6 mm X about 1 mm and 4.8 mm X 2.4 mm X about 1 mm for ac conductivity measurement in the R and U band respectively.
Table 1 The relationship (MIn,Ss),
between
x and V, for vacancy
_,(In,S,),
Composition
x
V”
MIn,S,
0.000 0.500 0.750 0.889 1.000
0.000 0.727 1.412 2.000 2.667
MIn7Sll MInGI, MInzl% IG3
defect spinels
Y. Ohmuro et al. / Solid State lonics 79 (1995) 53-59
2.3. Measurement of ionic conductivity at microwave regime Complex permittivity was measured to obtain the ionic conductivity in the microwave regime. The transmission/reflection method for complex permittivity and permeability measures the two-port complex scattering parameters (S parameters; Sii, S12, Szl and S,,) of a sample placed in a section of a waveguide by an automatic vector network analyzer WNA, HP85100 The sample is carefully mounted in a waveguide with Ag paste because any air gap or missalignment causes some error. Complex S parameters were measured at stepped 401 frequencies at room temperature between 26.5 GHz and 40 GHz for R band and between 40 GHz and 60 GHz for U band. The scattering equations relate the measured S parameters to the permittivity of the material. From the experimental point of view the calibration reference plane position in the transmission line is important. HP8510C offers a calibration method called the TRL (through, reflection and line) method using a calibrated standard line. The permittivity was calculated with S parameters using the Baker-Jarvis’s
method [15]. As the Baker-Jarvis’s method uses several scattering equations, the position of the sample is a fitting parameter and needs to be specified only as an initial value. A block diagram of the experimental setup is shown in Fig. 1. The VNA is controlled by a computer which is also used to calculate the complex permittivity from the measured S parameters. The conductivity is the real part of complex conductivity calculated from the complex permittivity.
3. Results and discussion Figs. 2 and 3 show conductivity and permittivity-frequency characteristics of (MIn,S,), _#r,S,), between 26.5 GI-Iz and 40 GHz. They indicate that the conductance in the microwave regime is nearly constant and reaches a plateau for the AgIn,S,-In,!& system and increases gradually for the CuIn,S,In,& system. As the number of vacancies, corresponding to x as shown in Table 1, increases, the inclinations of conductivity for Cu systems tend to increase. As shown in Eq. (31, the lattice constant of
HP 382 Work Station with HP85071A software
R-band
55
U-band MUT: material under test Fig. 1. Block diagram of VNA system.
0.008
: $
“‘I
30
,
,
32
,
" 34
,
34
3
[GHz]
” 36
,
36
.
“I’ 38
,
36
,
0
,
40
,
42
42
.>
2 0.014
0.008
0.010
E 8 0.004
fii E 0.006
4 : 0
F z
Fig. 2. Conductivity-frequency
Frequency
characteristics
[GHz]
of (CuIn,S,),
40
_-x-(In,S,J,,
26
20
28
30
30
_._%._
-
V, is the number of vacancies
5 a, 0.000 Gf
26
0.016
'0 x 0.012
2
F
5 0.002 II
’ 26
.
32
Frequency
z
” 26
,
30
% 0.002 P Ti ~0.000 a:
0.004
,
28
b
8
E
?i! E 0.006
0.010
0.012
0.014
5 g
x
b
"
4
yO.016,
26
32
34
[GHz]
[GHz]
34
36
36
-
_
_ _
in a unit cell, Vu = 8x/(8-.5x).
Frequency
32
Frequency
z
38
-
40
40
42
42
0.008
’
26
.
’
28
’
30
’
’
32
’
34
.
’
36
’
’
38
’
0
Q)
’ ’
42
z
28
30
Frequency
32
Fig. 3. Conductivity-frequency
28
34
characteristics
[GHz]
36
38
of (AgIn&),
40
_,-(I~I,S,)~,
42
rif, . , . , , , , , , , , , , ,I
z
0.004
E
, 26
0.012
4 fj 0.008 0
5 'g 0.010
z-.
-b
0.014
B 0.002
, (
28
28
,
30
30
Vu is the number of vacancies
I a, 0.000 [r
% P
28
-c0.016 g
E 8 0.004
[GHz]
0
Frequency
3~0.ooo
of
iJ E 0.006
0.000
0.002
3 0.008
oz
40
5 P
x
B
5 m
0.002
%
E 8 0.004
h: p. 0.006
;
,
,
Frequency
32
Frequency
32
,
34
34
[GHz]
[GHz]
.
I
36
36
in a unit cell, V, = 8x/(8-5x).
,
,
,
36
38
.
,
40
40
.
42
42
58
Y. Ohmuro et al. /Solid
State Ionics 79 (1995) 53-59
l 8a 016~
08b
H16d
Fig. 4. Possible diffusion paths of cations through interstitial vacancies in a spine1 unit cell: (0) and and ( n ) are cations on the tetrahedral and the octahedral positions; (0) and (Cl) are vacancies which connect to the tetrahedral and the octahedral position.
the Cu system becomes large for increasing the number of vacancies in a unit cell Vu. The enlargement of jump distance and the increase of vacancies in a jumping path take place in the Cu system simultaneously. This gives the higher plateau region for larger Vu in the Cu system. The vacancies are located at the tetrahedral positions in which In3+ ions and Cu+ or Ag+ ions are situated as mentioned in Section 2.1. Cations in the spine1 structure have two kind of ion paths as shown in Fig. 4, for the tetrahedral positions and the octahedral positions.
E
5
The scatter of the experimental data of Figs. 1 and 2 originated from the instability of the initial calibration of the reference plane in a waveguide. The contact condition between the wall and the sample is also a possible reason for the scattering even after careful mounting of the sample to the waveguide. Fig. 5 shows conductivity-frequency characteristics of vacancy defect spinels CuIn,,S,, and AgIn,,S,, between 26.5 GHz and 60 GHz of R and U bands. This shows the effect of cations. The conductivity of AgIn,,S,, reaches a plateau in the
0.030 r 0.025
b x * B s z 8
0.020
0.015
u
Frequency Fig. 5. Conductivity-frequency
characteristics
f [GHz]
of MIn,,S,,
(M = Cu or Ag) up to 60 GHz.
Y. Ohmuro et al. /Solid State Ionics 79 (1995) 53-59
frequency regime. This result agrees with the low frequency data (50 MHz-40 GHzl[6]. The conductivity of AgIn,,S,, saturates below 26.5 GHz and that of CuIn,,S,, saturates at 45 GHz. The result, that is the higher plateau frequency of the Cu system than that of the Ag system, indicates that Cu+ ions of the Cu system show frequency dependent conductivity at higher frequency than that of the Ag system due to the lighter mass of Cu+. The permittivities of the above samples were constant with frequency.
4. Conclusion From the conductivity spectrum in the microwave range from 26.5 GHz to 60 GHz the ionic conduction of vacancy defect spinels (MIn,S,),_X(In,S,), (x < 1) shows a conductivity plateau at high frequency. The Cu system has higher plateau frequency than that of the Ag system. This is explained by the difference of the weight of a Cu ion and an Ag ion. The increase of the number of vacancies V,, leads to the increase of the plateau frequency for the Cu system. The plateau frequency for the Ag system is less than 26.5 GHz.
Acknowledgements
Helpful discussion with Dr. S. Yoshikado is gratefully acknowledged. This work was partially supported by a Grant-in Aid of Doshisha University’s research promotion funds, and a Grant in Special
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Coordination Funds for Promoting Science and Technology of the Science and Technology Agency of Japan.
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