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The electrical conductivity and thermopower of liquid Ag1 − cSec alloys with 0.4 ≤ c ≤ 1.0
ELSEVIER
Journal of Non-Crystalline
Solids 205-207
(1996)
98-101
The electrical conductivity and thermopower of liquid Ag 1-$3eC alloys with 0.4 5 c 5 1.0 S. Ohno a,*, T. Okada b, A.C. Barnes ‘, J.E. Enderby ’ a Niigata College of Pharmacy, Kamishin’eicho, Niigata, Japan b Niigata Cdllege of Technology, Kamishin’eicho, Niigata, Japan ’ HE?. Wills Physics Laboratory, Royal Fort, Tyndall Avenue, Bristol BS8 ITL,
UK
Abstract Measurements of the electrical conductivity and thermopower of liquid Ag,-,Se, alloys have been extended to the composition range c 2 0.4 by using an argon over pressure of 10 bar to prevent vaporisation of the Se. The composition dependence of the conductivity exhibits a minimum and a broad maximum near the compositions c = 0.4 and 0.65, respectively. The corresponding thennopower data show a p-n transition at c = 0.36. The data have been analysed using equations derived from the Kubo-Greenwood expressions.
1. Introduction Recently our group has reported measurements of the electronic properties of liquid Ag,-,Se, for 0.0 I c I 0.4 [l]. The conductivity on the Ag rich side decreases rapidly with increasing Se content and reaches a minimum at c = 0.32 followed by an unusual sharp peak at c = l/3. It is interesting to extend these measurements to the whole composition range in order to understand more completely the role of chemical bonding, particularly with regard to the effects of Se-Se bonding, in determining its unusual properties. In this paper we present data for the conductivity (5) and thermopower (S) of liquid Ag-Se over the entire composition range. Special care has been taken for the selenium rich compositions to avoid selenium evaporation and to determine the boundary of the
* Corresponding 268 1230.
author.
Tel.:
002%3093/96/$15.00 Copyright Pi1 SOO22-3093(96>00218-9
+81-25
269 3170; fax:
0 1996 Elsevier
Science
4-81-25
two phase region. We attempt to interpret the results in terms of the Kubo-Greenwood transport equations.
2. Experimental
procedure and results
The electrical conductivity and thermopower were measured simultaneously using a quartz cell and a four probe method. The method used has been fully described previously [l-3] except that an argon over pressure of 10 bar was maintained above the sample. This is sufficient to prevent Se evaporating from the surface and ensured a stable sample composition during the course of the measurements. The temperatures where we observe phase separation on cooling are shown in Fig. 1. The phase separation was observed as an abrupt change in L+ as indicated by the arrows in Fig. 2. On the Ag rich side at ambient pressures these were found to be considerably lower than those reported in Massalski [4]. The phase
B.V. All rights reserved.
S. Ohno
1200
/
,
I
,
I
et al./JounzaE
,
I
As-Se
of Non-Crystalline
I
Solids
205-207
(1996)
1
System
I 0.2I Concent
I ---mc-,--,0.4I I 0.6 raton
of
0.8,
#1 I 1.0 to Massal-
As seen in Fig. 2, the conductivity of liquid Ag ,- $ec alloys for c = 0.4 to 0.6 increases approximately linearly with T over a wide temperature range. For c = 0.7 and 0.8, LT decreases rapidly and
boundary on the Se rich side (c > 0.4) was determined from the conductivity data at 10 bar argon pressure.
-I’ F -0 2 200
0’ Fig. 3. The thermopower of liquid Ag,- $ec The lines are shown as a guide to the eye.
’
boys
1
I
Agl +Sec
Liquid
I 800
900 Temperature
as a function
1
Fig. 2. The electrical conductivity as a function of temperature for liquid Ag,- cSec for c 2 0.4. The arrows indicate the temperature at which phase separation occurs. The error in the data is indicated by the scatter of the data points. The lines are shown as a guide to the eye.
Selenium
Fig. 1. The phase diagram for liquid Ag-Se according ski 141 with our new data marked as the points.
(“C
Temperature
EelA 2oo0
99
98-IO1
of temperature
I
i 1000 (“C >
for c 2 0.4. The random
I
1 1100
error in the data is less than 10 p,V K-l.
100
S. Ohno ef al./ Journal
of Non-Crystalline
Solids 205-207
(19961 98-101
gradually decreases with temperature. The largest positive value of S observed is 226 p,V K-r at 817 K for c = 0.55. Fig. 4 and Fig. 5 show the composition dependence of u and S over the entire composition range.
3. Discussion
0.4 0.6 Concentration
&
0.8
1.0 Se
Fig. 4. The composition dependence of u for liquid lines are shown as a guide to the eye.
Ag-Se.
The
The rapid decrease in c7 on approaching stoichiometry indicates a strong tendency for chemical ordering in this system. However, the peak in CT at stoichiometry is in great contrast to the deep minimum observed in the majority of quasi-ionic binary liquid semiconductors 151. This peak may be an indication of an unusually high degree of local order at stoichiometry. The broad maximum and relatively low magnitude of CT on the Se rich side indicate that
da/dT becomes very large as the point of phase separation is approached. For Ag,,,Se,,, the alloy has a conductivity of 90 0-r cm-r at 1193 K. As shown in Fig. 3 the thermopower is positive for all compositions with c 2 0.4 and the magnitude of S 200
1 , 1 Liquid AgImciec
I
1
I
1
I 0.6
I
I 0.8
I
160 c
E 73 3 z
120
-
80
-:
I -"O 4
/
1 0.2
I ' 0.4 ' Concentration
Fig. 5. The composition dependence of S for liquid lines are shown as a guide to the eye.
I 1.0 Se
Ag-Se.
(eV)
The
Fig. 6. (a) The variation of CT as a function of EF and a,. The open circles are the experimental values of u’. (b) The variation of S as a function of I& and a,. The open circles are the experimental data.
5. Ohno et al. / Journal
of Non-Crystalline
there is a strong tendency for Se, pair formation as observed in other selenium based liquid semiconductors such as Tl-Se. The large value of S for c > 0.4 suggests that a gap or a deep pseudogap remains in the electron density of states at these compositions. According to the Kubo-Greenwood transport equations, u and S are given by
k s=-iel
i
o(E) ---dE, o-
E-E,
i3f
k,T
aE
(2)
where f is the Fermi-Dirac function. Assuming simple generic form for a(E) as follows: 0-p)
=a@-E,)
(EZE,),
a(E)
=aV(Ev-E)
(EsE,),
Solids 205-207
(1996)
98-101
101
rigid band model. We believe it is the high carrier mobilities that lead to the large values of a, and a, at stoichiometry. In Fig. 6 we show calculations of CT and S as we allow a, to decrease from 4000 to 1800 s1-’ cm-’ eV-r while holding the ratio a,/a, constant. From the diagram it appears that the region for which this unusually high mobility occurs is in the range 0.31 < c < 0.37. At the current time detailed measurements of the structure of liquid Ag,Se are being carried in order to obtain evidence of strong local order which might give rise to these enhanced mobilities.
a 4. Conclusions (3)
(4) and using Eqs. (1) and (2), we can determine numerically the composition dependence of cr and S for any given conductivity gap AE = EC - E,. Enderby and Barnes [2] showed that the magnitude of AS = s max- Smins where h-,,, and Smin are the maximum and minimum thermopower observed, is a directly related to A E. From our data we find that AS is 180 /.LV K-’ at 1200 K which corresponds to AE N 0.0 eV. The values of a, and a, can be obtained from the value of g at stoichiometry [2] and were found to be 4000 and 2450 0-l cm-’ eV-‘, respectively. The large values of these constants in comparison to other liquid semiconductors suggest that liquid Ag,Se exhibits unusuahy high carrier mobilities. This conclusion is supported by measurements of the Hall mobility by Glazov et al. 161 which were also found to be unusually high compared to other liquid semiconductors. However the sharp peak in CT at the stoichiometric composition cannot be explained in terms of a
We have extended the measurements of the electrical conductivity and thermopower of liquid Ag-Se to the whole composition range. The results support the conclusion that the peak in conductivity observed at stoichiometry is directly related to an enhanced carrier mobility in this region. In the selenium rich compositions the conductivity remains low which is consistent with the formation of Se, chains as observed in other liquid selenide semiconductors.
References [ll [2] [3] 141
[5] [6]
S. Ohno, AC. Barnes and J.E. Enderby, J. Phys.: Condens. Matter 6 (1994) 5335. LE. Enderby and A.C. Barnes, Rep. Prog. Phys. 53 (1990) 85. T. Okada, M. Togashi and S. Ohno, .J. Phys. Sot. Jpn. 64 (1995) 1236. T.B. Massalski, Binary Alloy Phase Diagrams, 2nd Ed. (American Society for Metals International, Metals Park, OH, 1992). J.E. Enderby and E.W. Collings, J. Non-Cryst. Solids 4 (1970) 161. V.M. Glazov, V.B. Koltsov and V.A. Kurbatov, Sov. Phys. 20 (1986) 889.
Journal of Non-Crystalline
Solids 205-207
(1996)
98-101
The electrical conductivity and thermopower of liquid Ag 1-$3eC alloys with 0.4 5 c 5 1.0 S. Ohno a,*, T. Okada b, A.C. Barnes ‘, J.E. Enderby ’ a Niigata College of Pharmacy, Kamishin’eicho, Niigata, Japan b Niigata Cdllege of Technology, Kamishin’eicho, Niigata, Japan ’ HE?. Wills Physics Laboratory, Royal Fort, Tyndall Avenue, Bristol BS8 ITL,
UK
Abstract Measurements of the electrical conductivity and thermopower of liquid Ag,-,Se, alloys have been extended to the composition range c 2 0.4 by using an argon over pressure of 10 bar to prevent vaporisation of the Se. The composition dependence of the conductivity exhibits a minimum and a broad maximum near the compositions c = 0.4 and 0.65, respectively. The corresponding thennopower data show a p-n transition at c = 0.36. The data have been analysed using equations derived from the Kubo-Greenwood expressions.
1. Introduction Recently our group has reported measurements of the electronic properties of liquid Ag,-,Se, for 0.0 I c I 0.4 [l]. The conductivity on the Ag rich side decreases rapidly with increasing Se content and reaches a minimum at c = 0.32 followed by an unusual sharp peak at c = l/3. It is interesting to extend these measurements to the whole composition range in order to understand more completely the role of chemical bonding, particularly with regard to the effects of Se-Se bonding, in determining its unusual properties. In this paper we present data for the conductivity (5) and thermopower (S) of liquid Ag-Se over the entire composition range. Special care has been taken for the selenium rich compositions to avoid selenium evaporation and to determine the boundary of the
* Corresponding 268 1230.
author.
Tel.:
002%3093/96/$15.00 Copyright Pi1 SOO22-3093(96>00218-9
+81-25
269 3170; fax:
0 1996 Elsevier
Science
4-81-25
two phase region. We attempt to interpret the results in terms of the Kubo-Greenwood transport equations.
2. Experimental
procedure and results
The electrical conductivity and thermopower were measured simultaneously using a quartz cell and a four probe method. The method used has been fully described previously [l-3] except that an argon over pressure of 10 bar was maintained above the sample. This is sufficient to prevent Se evaporating from the surface and ensured a stable sample composition during the course of the measurements. The temperatures where we observe phase separation on cooling are shown in Fig. 1. The phase separation was observed as an abrupt change in L+ as indicated by the arrows in Fig. 2. On the Ag rich side at ambient pressures these were found to be considerably lower than those reported in Massalski [4]. The phase
B.V. All rights reserved.
S. Ohno
1200
/
,
I
,
I
et al./JounzaE
,
I
As-Se
of Non-Crystalline
I
Solids
205-207
(1996)
1
System
I 0.2I Concent
I ---mc-,--,0.4I I 0.6 raton
of
0.8,
#1 I 1.0 to Massal-
As seen in Fig. 2, the conductivity of liquid Ag ,- $ec alloys for c = 0.4 to 0.6 increases approximately linearly with T over a wide temperature range. For c = 0.7 and 0.8, LT decreases rapidly and
boundary on the Se rich side (c > 0.4) was determined from the conductivity data at 10 bar argon pressure.
-I’ F -0 2 200
0’ Fig. 3. The thermopower of liquid Ag,- $ec The lines are shown as a guide to the eye.
’
boys
1
I
Agl +Sec
Liquid
I 800
900 Temperature
as a function
1
Fig. 2. The electrical conductivity as a function of temperature for liquid Ag,- cSec for c 2 0.4. The arrows indicate the temperature at which phase separation occurs. The error in the data is indicated by the scatter of the data points. The lines are shown as a guide to the eye.
Selenium
Fig. 1. The phase diagram for liquid Ag-Se according ski 141 with our new data marked as the points.
(“C
Temperature
EelA 2oo0
99
98-IO1
of temperature
I
i 1000 (“C >
for c 2 0.4. The random
I
1 1100
error in the data is less than 10 p,V K-l.
100
S. Ohno ef al./ Journal
of Non-Crystalline
Solids 205-207
(19961 98-101
gradually decreases with temperature. The largest positive value of S observed is 226 p,V K-r at 817 K for c = 0.55. Fig. 4 and Fig. 5 show the composition dependence of u and S over the entire composition range.
3. Discussion
0.4 0.6 Concentration
&
0.8
1.0 Se
Fig. 4. The composition dependence of u for liquid lines are shown as a guide to the eye.
Ag-Se.
The
The rapid decrease in c7 on approaching stoichiometry indicates a strong tendency for chemical ordering in this system. However, the peak in CT at stoichiometry is in great contrast to the deep minimum observed in the majority of quasi-ionic binary liquid semiconductors 151. This peak may be an indication of an unusually high degree of local order at stoichiometry. The broad maximum and relatively low magnitude of CT on the Se rich side indicate that
da/dT becomes very large as the point of phase separation is approached. For Ag,,,Se,,, the alloy has a conductivity of 90 0-r cm-r at 1193 K. As shown in Fig. 3 the thermopower is positive for all compositions with c 2 0.4 and the magnitude of S 200
1 , 1 Liquid AgImciec
I
1
I
1
I 0.6
I
I 0.8
I
160 c
E 73 3 z
120
-
80
-:
I -"O 4
/
1 0.2
I ' 0.4 ' Concentration
Fig. 5. The composition dependence of S for liquid lines are shown as a guide to the eye.
I 1.0 Se
Ag-Se.
(eV)
The
Fig. 6. (a) The variation of CT as a function of EF and a,. The open circles are the experimental values of u’. (b) The variation of S as a function of I& and a,. The open circles are the experimental data.
5. Ohno et al. / Journal
of Non-Crystalline
there is a strong tendency for Se, pair formation as observed in other selenium based liquid semiconductors such as Tl-Se. The large value of S for c > 0.4 suggests that a gap or a deep pseudogap remains in the electron density of states at these compositions. According to the Kubo-Greenwood transport equations, u and S are given by
k s=-iel
i
o(E) ---dE, o-
E-E,
i3f
k,T
aE
(2)
where f is the Fermi-Dirac function. Assuming simple generic form for a(E) as follows: 0-p)
=a@-E,)
(EZE,),
a(E)
=aV(Ev-E)
(EsE,),
Solids 205-207
(1996)
98-101
101
rigid band model. We believe it is the high carrier mobilities that lead to the large values of a, and a, at stoichiometry. In Fig. 6 we show calculations of CT and S as we allow a, to decrease from 4000 to 1800 s1-’ cm-’ eV-r while holding the ratio a,/a, constant. From the diagram it appears that the region for which this unusually high mobility occurs is in the range 0.31 < c < 0.37. At the current time detailed measurements of the structure of liquid Ag,Se are being carried in order to obtain evidence of strong local order which might give rise to these enhanced mobilities.
a 4. Conclusions (3)
(4) and using Eqs. (1) and (2), we can determine numerically the composition dependence of cr and S for any given conductivity gap AE = EC - E,. Enderby and Barnes [2] showed that the magnitude of AS = s max- Smins where h-,,, and Smin are the maximum and minimum thermopower observed, is a directly related to A E. From our data we find that AS is 180 /.LV K-’ at 1200 K which corresponds to AE N 0.0 eV. The values of a, and a, can be obtained from the value of g at stoichiometry [2] and were found to be 4000 and 2450 0-l cm-’ eV-‘, respectively. The large values of these constants in comparison to other liquid semiconductors suggest that liquid Ag,Se exhibits unusuahy high carrier mobilities. This conclusion is supported by measurements of the Hall mobility by Glazov et al. 161 which were also found to be unusually high compared to other liquid semiconductors. However the sharp peak in CT at the stoichiometric composition cannot be explained in terms of a
We have extended the measurements of the electrical conductivity and thermopower of liquid Ag-Se to the whole composition range. The results support the conclusion that the peak in conductivity observed at stoichiometry is directly related to an enhanced carrier mobility in this region. In the selenium rich compositions the conductivity remains low which is consistent with the formation of Se, chains as observed in other liquid selenide semiconductors.
References [ll [2] [3] 141
[5] [6]
S. Ohno, AC. Barnes and J.E. Enderby, J. Phys.: Condens. Matter 6 (1994) 5335. LE. Enderby and A.C. Barnes, Rep. Prog. Phys. 53 (1990) 85. T. Okada, M. Togashi and S. Ohno, .J. Phys. Sot. Jpn. 64 (1995) 1236. T.B. Massalski, Binary Alloy Phase Diagrams, 2nd Ed. (American Society for Metals International, Metals Park, OH, 1992). J.E. Enderby and E.W. Collings, J. Non-Cryst. Solids 4 (1970) 161. V.M. Glazov, V.B. Koltsov and V.A. Kurbatov, Sov. Phys. 20 (1986) 889.