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Thermoelectric power of the SnSe liquid alloy
378
Journal of Non-CrystallineSolids 65 (1984) 378-382 North-Holland, Amsterdam
THERMOELECTRIC POWER OF THE Sn-Se LIQUID ALLOY
D. H. KURLAT Facultad de Ingenieria, Paseo Col6n 850, Buenos Aires, ARGENTINA
The Seebeck coefficient of the Snx -Sel-x liquid alloy, was measured as a function of concentration and temperature. For 0.9 ~< x ~< 1.0 the S(T) behaviour is metallic and for x = 0.95 the liquid, which is p-type, presents a maximum around 1150 K. At the composition x = 0.39 (eutectic) and x = 0.33 (Sn-Se2) a transition semiconductor ~ semimetal takes place, when temperature rises. The possibility of ambipolar transport is discussed.
1. INTRODUCTION Unlike other AtV-B Vz liquid binary alloys 1,2, there are few experimental data on the electronic transport properties of the Snx-Sel-x (x = atomic fraction) liquid compounds 3. In this paper, resuits are reported for the thermoelectric power as a function of the temperature and the concentration.
2. EXPERIMENTAL METHOD AND RESULTS The samples were synthesized by fusing the components in quartz ampoules, which were evacuated to 10-6 mm and then filled with Ar, up to a pressure of 200 mmHg. Each samples was kept at temperatures 150 K higher than the liquidus, for at least 60 hours. In order to obtain the Seebeck coefficient we adopted the method described by Bradley 4
A quartz container (80 mm long) was
filled with the sample being investigated. At each end of the container, a hole was made, through which a graphite electrode was passed. A pair of two different metals (Alumel-Molybdenum) was connected to each of the graphite electrodes. With this experimental arrangement the corrosion of Mo or A1 wires was avoided. The voltage drop between either the A1 wires (Uaz) or the Mo leads (UMo) , was measured by a potentiometric method. The change of S at the melting point was registrated with a high impedance digital microvoltmeter. The absolute thermopower (S) of the samples, at the mean temperature, was found from the relation:
S(T) =
UAtSMo(T)- UMoSAt(T) UAI -
UMo
where Sat and SMo are the absolute thermoelectric powers of A1 and Mo respectively. We used the natural gradient of the furnace, which rarely exceeded 10 °C. To prevent evaporation, all the measurements were performed under Ar overpressure (~ 6-7 kg.cm'2), after previous de-gassing under vacuum. To check if the composition changed with time appreciably, we followed the evolution of S as a function of time, for a fixed temperature. The fluctuation in the voltage was less than the experimental error, so it was infered that the homogeneity of the liquid alloy was nearly constant.
0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division
D.H. Kurlat / Thermoelectric power o f the Sn-Se liquid alloy The experimental results are shown in Fig. 1 to Fig. 4 .
379
For the Tin rich side of the phase dia-
gram, (0.90 ~< x ~< 1) these alloys are typically metallic, so the Seebeck coefficient is small. At the composition
x =0.95
the liquid is p-type, and the curve S = S(T) presents a maximum around
1150 K, while for x --- 0.9 the S values are smaller, they decrease with temperature and show a change of sign around 1140 K. As there is a miscibility gap in the concentration range 0.50 ~< x ~< 0.84, no measurements were performed in this zone. For higher Se concentration, we have found that the most interesting are Sno.3p-Seo.61 (eutectic) and Sno.33-Seo.67 (stoichiometric composition). In the case of the chemical compound (Sn-Se2) , S(T) is always positive. Its behaviour as a function of temperature, could be analysed for two different intervals. Between 930 K ~< T ~< 1008 K, S follows a f(T "1) law, while for 1008 K up to 1200 K it remains nearly constant. For the eutectic liquid alloy, S(T) shows, qualitatively, similar results as are seen in Fig. 2a.
Fig. l_a
S(pV/OK)
FJ~ Sno95- Seoo5
kS(pV/OK)
7O
60 5D 40 50 -20 -10
Sno ~) -Seoi 0
*o
30
Tm~
20 lC
lo'oo
- ]0
IOSO
1I00
' ~• ~: ? 1150
~[K)
- 20 Tmelting
- 30 ,
1000
q
1.050
i
I O0
I
1150
J
1200
T(°K)
FIGURE la Thermopower of liquid Sno.ps-Seo.os as a function of temperature
FIGURE lb Thermopower of liquid Sno.9o-Seon o as a function of temperature
Fig 2.0
15o!
S(pV/OK)
hS(pV/*K)
Fig 2 b
250
200
100
150
lO0
melting
50
Trnelting
1 9,50
IO00
1050
]I00
I150
FIGURE 2a Thermopower of liquid Sno.39-Seo.61 as a function o f temperature
II.T{°K)
. 950
lO00
10;0
11100
li50
FIGURE 2b Thermpower of liquid Sno.ss-Seo.67 as a function of temperature
T(°K)
D.H. Kurlat / Thermoelectric power o f the Sn-Se liquid alloy
380
3.
DISCUSSION It is rather difficult to give a quantitative theoretical explanation of the metallic (0.9 % x % 0.1 )
fiquid alloy behaviour. Due to the lack of experimental structure factors data, a direct check with the Faber-Ziman's theory 5 is not possible.
On the other hand, it is evident that the rigid sphere
approximation is meaningless for alloys which contain Se. Empirical rules, like Nordheim-Gorter's 6 are unable to predict the observed experimental values. Now, a simple law of the S = f( Z x/St) type, might at least qualitatively, explain the S(T) values for the x = 0 . 0 5
composition. The liquid is
p-type because Ssn is very small compared with Sse, and a m a x i m u m around 1150 K, is also observed in pure liquid Se 7. For x = 0.1 an unexcepted result was observed, because the addition of Se lowers the t h e r m o p o w e r values. In principle we cannot account for this result. It could be possible that, being this concentration near the miscibility gap, it is very difficult to achieve a good mixing. As we have seen above, for the eutectic and stoichiometric compositions, b o t h curves of S(T) have a similar behaviour. Near the melting point, their absolute values are those typical for a semiconductor. When the temperature rises, a transition semiconductor -+ semimetal seems to take place. If we suppose that the transport is due only to holes, the S(T) function follows the relation 8 :
S
= ke I(Ep- Ev)
___]
k.J
where E F - E v = 1.27 eV,/3/kB = 13.27, for x = 0.39 (938 K <~ T ~ 996 K); and E F - E V = 0.52 eV, /3/k~ = 6 . 1 6 , for x = 0.33 (928 K ~< T ~< 1008 K). It can be noted that /3/kB values are not in agreem e n t with Mott's prediction (2 ~
l S(uV/°K) Sno 39-Seo61(eutectic )
210
125
~ T m
100 75
160 erting 1~0 o.ss
09o
095
16o
l~s
11o
0850;00951]00
105
103 T-I(OK"l)
110 103 T-I(oK-1)
F I G U R E 3a FIGURE 3b ,Variation o f the t h e r m o p o w e r of liquid Sno.39-Seo.61 and Sno.33-Seo.67 with T -t
So, a single band description seems to us an oversimplification.
Even for the pure liquid Se,
Cutler 2 has suggested an ambipolar transport model. According with this autor, for 770 K ~< T ~< 990 K electron transport is dominant, but also holes are generated b y bond breaking. For T > 990 K, a
D.H. Kurlat / Thermoelectric power o f ttle Sn-Se liquid alloy
381
transition to positive S values takes place. Cutler supposes that both types of carriers are present, but due to the larger mobility of holes, S is positive.
In our case, the situation is much more com-
plex. For x >~0.5 we assume that each alloy is a mixture of: the molecular compounds Sn-Se2 and eventually Sn-Se 9 ; Sn-(Se),-Sn chains, where n indicates the degree of polymerisation; pure Se chains, and free Sn atoms. There are three bands of valence electron states (a , 7r and o*) and an excess of Se gives rise to ase bonding and a~e antibonding states. For each fixed composition, these atomic associations are broken under the action of thermal agitation, and this effect generates the majority of charge carriers. The rising of temperature, lowers the influence of holes, because either the relative number of electrons is increased or their mobility is greater. It must be remarked that this hole behaviour with temperature, is opposite to what happens in pure liquid Se. In Fig. 4 the thermoelectric power is represented as a function of concentration. It can be seen that for T > 990 K these curves should present a relative minimum.
S(pV/°K)
• 990°K a i050°K x 1150OK
150 I-~-- MBcibility g a p ~
100
i i i 1 [
50
5n
~ ol
o!2
o'3
o'4
o15
0'.6
0~?'
0~8
019
1'0
, Se
FIGURE 4 Thermopower of liquid Sn-Se as a function of concentration
REFERENCES 1) V.M. Glazov, S.N. Chizhevshaya and N.N. Glagoleva, Liquid Semiconductors (Plenum Press, New York, 1969). 2) M. Cutler, Liquid Semiconductors (Academic Press, New York, 1977). 3) V.M. Glazov and O.V. Situlina, Akad Nauk S.S.S.R. Chem 167 (1976) 587. 4) C.C. Bradley, Phil. Mag. 7 (1962) 1337. 5) T.E. Faber and J.M. Ziman, Phil. Mag. 11 (1965) 153. 6) T. Faber, An Introduction to the theory of liquid metals (Cambridge University Press, 1972). 7) F. Mahdjuri, J. Phys. C8 (1975) 2248.
382
D.H. Kurlat / Thermoelectric power o f the Sn-Se liquid alloy
8) N.F. Mott and E.A. Davis, Electronic processes in non-crystalline materials (Oxford University Press, London, 1971). 9) M. Hansen and K. Anderkov, Constitution of Binary Alloys (Me. Graw Hill, New York, 1958).
Journal of Non-CrystallineSolids 65 (1984) 378-382 North-Holland, Amsterdam
THERMOELECTRIC POWER OF THE Sn-Se LIQUID ALLOY
D. H. KURLAT Facultad de Ingenieria, Paseo Col6n 850, Buenos Aires, ARGENTINA
The Seebeck coefficient of the Snx -Sel-x liquid alloy, was measured as a function of concentration and temperature. For 0.9 ~< x ~< 1.0 the S(T) behaviour is metallic and for x = 0.95 the liquid, which is p-type, presents a maximum around 1150 K. At the composition x = 0.39 (eutectic) and x = 0.33 (Sn-Se2) a transition semiconductor ~ semimetal takes place, when temperature rises. The possibility of ambipolar transport is discussed.
1. INTRODUCTION Unlike other AtV-B Vz liquid binary alloys 1,2, there are few experimental data on the electronic transport properties of the Snx-Sel-x (x = atomic fraction) liquid compounds 3. In this paper, resuits are reported for the thermoelectric power as a function of the temperature and the concentration.
2. EXPERIMENTAL METHOD AND RESULTS The samples were synthesized by fusing the components in quartz ampoules, which were evacuated to 10-6 mm and then filled with Ar, up to a pressure of 200 mmHg. Each samples was kept at temperatures 150 K higher than the liquidus, for at least 60 hours. In order to obtain the Seebeck coefficient we adopted the method described by Bradley 4
A quartz container (80 mm long) was
filled with the sample being investigated. At each end of the container, a hole was made, through which a graphite electrode was passed. A pair of two different metals (Alumel-Molybdenum) was connected to each of the graphite electrodes. With this experimental arrangement the corrosion of Mo or A1 wires was avoided. The voltage drop between either the A1 wires (Uaz) or the Mo leads (UMo) , was measured by a potentiometric method. The change of S at the melting point was registrated with a high impedance digital microvoltmeter. The absolute thermopower (S) of the samples, at the mean temperature, was found from the relation:
S(T) =
UAtSMo(T)- UMoSAt(T) UAI -
UMo
where Sat and SMo are the absolute thermoelectric powers of A1 and Mo respectively. We used the natural gradient of the furnace, which rarely exceeded 10 °C. To prevent evaporation, all the measurements were performed under Ar overpressure (~ 6-7 kg.cm'2), after previous de-gassing under vacuum. To check if the composition changed with time appreciably, we followed the evolution of S as a function of time, for a fixed temperature. The fluctuation in the voltage was less than the experimental error, so it was infered that the homogeneity of the liquid alloy was nearly constant.
0022-3093/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division
D.H. Kurlat / Thermoelectric power o f the Sn-Se liquid alloy The experimental results are shown in Fig. 1 to Fig. 4 .
379
For the Tin rich side of the phase dia-
gram, (0.90 ~< x ~< 1) these alloys are typically metallic, so the Seebeck coefficient is small. At the composition
x =0.95
the liquid is p-type, and the curve S = S(T) presents a maximum around
1150 K, while for x --- 0.9 the S values are smaller, they decrease with temperature and show a change of sign around 1140 K. As there is a miscibility gap in the concentration range 0.50 ~< x ~< 0.84, no measurements were performed in this zone. For higher Se concentration, we have found that the most interesting are Sno.3p-Seo.61 (eutectic) and Sno.33-Seo.67 (stoichiometric composition). In the case of the chemical compound (Sn-Se2) , S(T) is always positive. Its behaviour as a function of temperature, could be analysed for two different intervals. Between 930 K ~< T ~< 1008 K, S follows a f(T "1) law, while for 1008 K up to 1200 K it remains nearly constant. For the eutectic liquid alloy, S(T) shows, qualitatively, similar results as are seen in Fig. 2a.
Fig. l_a
S(pV/OK)
FJ~ Sno95- Seoo5
kS(pV/OK)
7O
60 5D 40 50 -20 -10
Sno ~) -Seoi 0
*o
30
Tm~
20 lC
lo'oo
- ]0
IOSO
1I00
' ~• ~: ? 1150
~[K)
- 20 Tmelting
- 30 ,
1000
q
1.050
i
I O0
I
1150
J
1200
T(°K)
FIGURE la Thermopower of liquid Sno.ps-Seo.os as a function of temperature
FIGURE lb Thermopower of liquid Sno.9o-Seon o as a function of temperature
Fig 2.0
15o!
S(pV/OK)
hS(pV/*K)
Fig 2 b
250
200
100
150
lO0
melting
50
Trnelting
1 9,50
IO00
1050
]I00
I150
FIGURE 2a Thermopower of liquid Sno.39-Seo.61 as a function o f temperature
II.T{°K)
. 950
lO00
10;0
11100
li50
FIGURE 2b Thermpower of liquid Sno.ss-Seo.67 as a function of temperature
T(°K)
D.H. Kurlat / Thermoelectric power o f the Sn-Se liquid alloy
380
3.
DISCUSSION It is rather difficult to give a quantitative theoretical explanation of the metallic (0.9 % x % 0.1 )
fiquid alloy behaviour. Due to the lack of experimental structure factors data, a direct check with the Faber-Ziman's theory 5 is not possible.
On the other hand, it is evident that the rigid sphere
approximation is meaningless for alloys which contain Se. Empirical rules, like Nordheim-Gorter's 6 are unable to predict the observed experimental values. Now, a simple law of the S = f( Z x/St) type, might at least qualitatively, explain the S(T) values for the x = 0 . 0 5
composition. The liquid is
p-type because Ssn is very small compared with Sse, and a m a x i m u m around 1150 K, is also observed in pure liquid Se 7. For x = 0.1 an unexcepted result was observed, because the addition of Se lowers the t h e r m o p o w e r values. In principle we cannot account for this result. It could be possible that, being this concentration near the miscibility gap, it is very difficult to achieve a good mixing. As we have seen above, for the eutectic and stoichiometric compositions, b o t h curves of S(T) have a similar behaviour. Near the melting point, their absolute values are those typical for a semiconductor. When the temperature rises, a transition semiconductor -+ semimetal seems to take place. If we suppose that the transport is due only to holes, the S(T) function follows the relation 8 :
S
= ke I(Ep- Ev)
___]
k.J
where E F - E v = 1.27 eV,/3/kB = 13.27, for x = 0.39 (938 K <~ T ~ 996 K); and E F - E V = 0.52 eV, /3/k~ = 6 . 1 6 , for x = 0.33 (928 K ~< T ~< 1008 K). It can be noted that /3/kB values are not in agreem e n t with Mott's prediction (2 ~
l S(uV/°K) Sno 39-Seo61(eutectic )
210
125
~ T m
100 75
160 erting 1~0 o.ss
09o
095
16o
l~s
11o
0850;00951]00
105
103 T-I(OK"l)
110 103 T-I(oK-1)
F I G U R E 3a FIGURE 3b ,Variation o f the t h e r m o p o w e r of liquid Sno.39-Seo.61 and Sno.33-Seo.67 with T -t
So, a single band description seems to us an oversimplification.
Even for the pure liquid Se,
Cutler 2 has suggested an ambipolar transport model. According with this autor, for 770 K ~< T ~< 990 K electron transport is dominant, but also holes are generated b y bond breaking. For T > 990 K, a
D.H. Kurlat / Thermoelectric power o f ttle Sn-Se liquid alloy
381
transition to positive S values takes place. Cutler supposes that both types of carriers are present, but due to the larger mobility of holes, S is positive.
In our case, the situation is much more com-
plex. For x >~0.5 we assume that each alloy is a mixture of: the molecular compounds Sn-Se2 and eventually Sn-Se 9 ; Sn-(Se),-Sn chains, where n indicates the degree of polymerisation; pure Se chains, and free Sn atoms. There are three bands of valence electron states (a , 7r and o*) and an excess of Se gives rise to ase bonding and a~e antibonding states. For each fixed composition, these atomic associations are broken under the action of thermal agitation, and this effect generates the majority of charge carriers. The rising of temperature, lowers the influence of holes, because either the relative number of electrons is increased or their mobility is greater. It must be remarked that this hole behaviour with temperature, is opposite to what happens in pure liquid Se. In Fig. 4 the thermoelectric power is represented as a function of concentration. It can be seen that for T > 990 K these curves should present a relative minimum.
S(pV/°K)
• 990°K a i050°K x 1150OK
150 I-~-- MBcibility g a p ~
100
i i i 1 [
50
5n
~ ol
o!2
o'3
o'4
o15
0'.6
0~?'
0~8
019
1'0
, Se
FIGURE 4 Thermopower of liquid Sn-Se as a function of concentration
REFERENCES 1) V.M. Glazov, S.N. Chizhevshaya and N.N. Glagoleva, Liquid Semiconductors (Plenum Press, New York, 1969). 2) M. Cutler, Liquid Semiconductors (Academic Press, New York, 1977). 3) V.M. Glazov and O.V. Situlina, Akad Nauk S.S.S.R. Chem 167 (1976) 587. 4) C.C. Bradley, Phil. Mag. 7 (1962) 1337. 5) T.E. Faber and J.M. Ziman, Phil. Mag. 11 (1965) 153. 6) T. Faber, An Introduction to the theory of liquid metals (Cambridge University Press, 1972). 7) F. Mahdjuri, J. Phys. C8 (1975) 2248.
382
D.H. Kurlat / Thermoelectric power o f the Sn-Se liquid alloy
8) N.F. Mott and E.A. Davis, Electronic processes in non-crystalline materials (Oxford University Press, London, 1971). 9) M. Hansen and K. Anderkov, Constitution of Binary Alloys (Me. Graw Hill, New York, 1958).