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Electrical properties of liquid NiTe alloys with Ni halides
Journal of Non-Crystalline Solids 312–314 (2002) 396–399 www.elsevier.com/locate/jnoncrysol
Electrical properties of liquid NiTe alloys with Ni halides Kanako Ishida a b
a,*
, Satoru Ohno a, Tatsuya Okada
b
Niigata College of Pharmacy, Kamishin’eicho, Niigata 950-2081, Japan Niigata College of Technology, Kamishin’eicho, Niigata 950-2076, Japan
Abstract Liquid NiTe has a large electrical conductivity of 5700 X1 cm1 at the melting point. The decrease in the conductivity on the NiTe side is about 140 and 230 X1 cm1 with the addition of 1 mol% NiCl2 and NiI2 , respectively. Liquid NiTe and molten NiI2 were found to be miscible in all proportions. Molten NiI2 has a conductivity of 35 X1 cm1 at 950 °C. The electrical conductivity on the NiI2 side increases gradually with the addition of NiTe. The composition dependence of the thermoelectric power of molten NiTe–NiI2 mixtures increases gradually from )3 lV/K on the NiTe side to 37.5 lV/K on the NiI2 side. The composition dependence of the conductivity and thermoelectric power for molten NiTe–NiI2 mixtures was analyzed by electronic model of liquid semiconductors. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 72.80.Ph; 72.80.Tm
1. Introduction Liquid NiTe has a large conductivity of 5650 X1 cm1 at 900 °C and a negative temperature coefficient of conductivity [1]. In contrast the ionic conductivities of nickel halides estimated by Tasseven et al. [2] are 4.8, 3.5 and 4.5 X1 cm1 for molten NiCl2 , NiBr2 and NiI2 , respectively. It is not clear that the liquid NiTe and nickel halides are miscible in all proportions. Therefore, we measured the electrical conductivity and the thermoelectric power of molten NiTe–NiX2 (X ¼ I, Cl) mixtures. We present an analysis of the electrical properties of molten NiTe–NiX2 mixtures on
*
Corresponding author. Tel.: +81-25-269-3170; fax: +81-25268-1230. E-mail address: [email protected] (K. Ishida).
the basis of electronic models of liquid semiconductors and molten salts [3]. It is interesting to clarify the contribution to the electrical properties of molten mixtures due to the nickel ions with unoccupied 3d-states.
2. Experimental procedure The electrical conductivity measurements were made using a quartz cell and the four-point-probe method. The four holes of the quartz cell were sealed with four graphite plugs fastened by molybdenum bands. Measurements were carried out under a pressure of about 2.0 MPa helium gas to prevent the evaporation of liquid specimen. The thermoelectric power measurements were made by the DT method. The voltage, DE, between two electrodes was measured by a digital voltmeter.
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 1 7 6 1 - 1
K. Ishida et al. / Journal of Non-Crystalline Solids 312–314 (2002) 396–399
397
The ratio DE=DT gives the thermoelectric power formed by the sample and the molybdenum counter electrode. The absolute thermoelectric power of the liquid sample can be determined by subtracting the thermoelectric power of molybdenum. The NiCl2 and NiI2 are purchased from Aldrich Chemical Company, Inc.
3. Results As shown in Figs. 1 and 2, the temperature dependence of the conductivity for the molten (NiTe)1c (NiI2 )c and (NiTe)1c (NiCl2 )c mixtures is negative for c 6 0:4 and positive for c P 0:5. Molten NiI2 has a conductivity of 35 X1 cm1 , which is larger than that estimated for the molten nickel halide [2]. As shown in Fig. 3, liquid NiTe has a thermoelectric power, S, of )3 lV/K and a positive temperature coefficient of S. The thermoelectric power of the molten NiTe-NiI2 mixtures increases with increasing NiI2 composition and has a positive
Fig. 2. Electrical conductivity as a function of temperature for molten (NiTe)1c (NiI2 )c mixtures with c P 0:58. The arrows indicate the melting point of the mixture. Random errors are about 5%.
Fig. 3. Thermoelectric power as a function of temperature for molten (NITe)1c (NiI2 )c and (NiTe)0:973 (NiCl2 )0:027 mixtures. The arrows indicate the melting point of the mixture. Random errors are about 0.8 lV/K.
Fig. 1. Electrical conductivity as a function of temperature for molten (NiTe)1c (NiI2 )c and (NiTe)1c (NiCl2 )c mixtures for c 6 0:5. The arrows indicate the melting point of the mixture. Random errors are about 3%.
temperature coefficient. The value of S is slightly increased by the addition of 2.7 mol% NiCl2 to liquid NiTe. The thermoelectric power of molten NiI2 is about 37.5 lV/K, which is considerably smaller than that of the molten noble metal halides [3]. Fig. 4 shows the composition dependence of the conductivity and thermoelectric power for molten NiTe–NiX2 (X ¼ I, Cl) mixtures. The conductivity of the liquid mixtures decreases rapidly with the addition of NiX2 to liquid NiTe. The composition
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K. Ishida et al. / Journal of Non-Crystalline Solids 312–314 (2002) 396–399
The electrical conductivity on the NiI2 side increases with the addition of NiTe. The energy gap is a very small value for liquid mixtures in the range 300 6 r 6 3000 X1 cm1 . In this situation, rel in Eq. (1) may be written as [5] rel ¼
Fig. 4. Composition dependence of the conductivity and the thermoelectric power of molten NiTe–NiX2 (X ¼ I, Cl) mixtures. The closed squares and the closed circles indicate the experimental values of r for the molten NiTe–NiI2 and NiTe– NiCl2 mixtures at 950 °C, respectively. The open squares indicate the values of r estimated from the values of ð1 cÞ fNsp ðEF Þ þ Nd ðEF Þg using Eq. (2). The closed triangles indicate the experimental values of S for the molten NiTe–NiI2 mixtures at 950 °C. The open diamonds and closed diamonds indicate the values of ðr =rÞS where S ¼ 500 lV/K, respectively. The lines are a guide for the eye.
dependence of the thermoelectric power of the molten NiTe–NiI2 mixtures increases gradually from )3 lV/K on the NiTe side to 37.5 lV/K on the NiI2 side. 4. Discussion The ionic conductivity estimated by Tasseven et al. [2] is 4.5 X1 cm1 for molten NiI2 . This value is smaller than that obtained experimentally. The conductivity may be given by [3,4] r ¼ rþ þ r þ rel ¼
4nþ e2 Dþ n e2 D þ þ A exp kB T kB T
Ev ; kB T
ð1Þ
where rþ and r are the ionic conductivity due to the Ni2þ ions and I ions, respectively. The values of rþ and r estimated by Tasseven et al. [2] are 3.1 and 1.4 X1 cm1 , respectively. The third term of right hand side in Eq. (1) is the electronic conductivity of molten NiI2 . The other symbols have their usual meaning. The activation energy for conduction electrons, Ev , estimated is about 0.2 eV for molten NiI2 .
p2 e2 h3 L 2 fN ðEF Þg ; 3m2
ð2Þ
where L is the mean free path of conduction electrons and N ðEF Þ is the density of states at EF . We assume that N ðEF Þ in Eq. (2) can be written as ð1 cÞfNsp ðEF Þ þ Nd ðEF Þg for the mixture. The electrical conductivity of the molten mixtures was estimated by using the values of Nsp ðEF Þ and Nd ðEF Þ estimated by Strange and Barnes [6]. It is a reasonable assumption that L is comparable with an interatomic distance, a, in the intermediate range 300 6 r 6 3000 X1 cm1 [5]. As shown in Fig. 4, the composition dependence of conductivity in the intermediate range can be qualitatively explained by this approach. The large difference between rexp and rcal on the NiTe side of the figure may be closely related to the rapid increase in the mean free path of spconduction electrons, Lsp , with decreasing NiI2 composition. It suggests that the electrical conductivity is dominated by the conduction due to the sp-electrons. The thermoelectric power of molten NiI2 is given by [4] þ r r r el S¼ ð3Þ Sþ þ S þ Sel ; r r r where S þ and S are the thermoelectric powers due to the Ni2þ ions and the I ions in molten NiI2 , respectively. The thermoelectric powers for the molten salts suggest that the values of S þ and S in molten NiI2 may be smaller than 500 lV/K [3,4]. The values of fðrþ =rÞS þ þ ðr =rÞS g estimated by putting the values of rþ and r lie in the range of 44 to )20 lV/K for molten NiI2 . The sign of Sel seems to be generally positive because of the d-hole of the Ni ions in molten NiI2 . We examine the composition dependence of the thermoelectric power of molten NiTe–NiI2 mixtures. Assuming that the values of rþ , r and S are 3.1, 1.4 X1 cm1 and 500 lV/K over the whole composition range, we estimated the com-
K. Ishida et al. / Journal of Non-Crystalline Solids 312–314 (2002) 396–399
position dependence of (rþ =rÞS þ and (r =rÞS as shown in Fig. 4. Because of the large values of rel , the composition dependence of S mainly depends on the third term on the right hand side in Eq. (3) in the composition range of c 6 0:8. The thermoelectric power in the intermediate range where 300 6 r 6 3000 X1 cm1 can be written as [5] p2 kB2 T 2 dN ðEF Þ S¼ : ð4Þ 3jej N ðEF Þ dE Eq. (4) can be used for Sel in Eq. (3) under the condition that the mean free paths of the spelectrons and d-electrons are comparable to a. The maximum and minimum values of Sel in Eq. (3) can be estimated from the experimental values of S and the values of (r =rÞS mentioned above. Inserting both values of Sel into S in Eq. (4), we can estimate the maximum and minimum values of dN ðEF Þ=dE. The dN ðEF Þ=dE obtained from this approach lies in the range of )0.10 to )0.15 eV2 atom1 and shows a weak composition dependence. The negative values of dN ðEF Þ=dE obtained experimentally may be closely related to the negative slope in the density of d-like states near EF estimated for liquid NiTe [6]. We briefly consider the change in the sign of S on the NiTe-rich side. As mentioned above, the mean free path of sp-electrons in liquid NiTe is longer than a. The sp-electrons with Lsp a would be scattered into the large density of d-like states at EF . In this process, the mean free path of sp-electrons is given by [7] 1
Lsp LSpd / fNd ðEF Þg :
ð5Þ
According to the sp–d scattering theory [7], the thermoelectric power caused by Eq. (5) can be written as p2 kB2 T 1 dNd ðEF Þ Sspd ¼ : ð6Þ 3jej Nd ðEF Þ dE The negative value of dN ðEF Þ=dE obtained experimentally from Eq. (6) corresponds to the
399
negative slope in the density of d-like states near EF in the NiTe. The change in the sign of S on the NiTe side is caused by the rapid increase in Lsp with decreasing NiI2 composition. This equation may be a major factor for the thermoelectric power of metallic liquids, including the Ni ions with unoccupied 3d-states.
5. Conclusion It was found that the thermoelectric power of molten NiI2 is 37.5 lV/K, which is considerably smaller than that for the silver halides. The smaller value of S in molten NiI2 corresponds to the relatively large electronic conduction in the molten NiI2 . In the intermediate conductivity range, the composition dependence of the conductivity can be explained by the electronic model of liquid semiconductors. The values of dN ðEF Þ=dE obtained from this model lie in the range of )0.10 to )0.15 eV2 atom1 in the composition range 0:3 6 c 6 0:8. The rapid decrease in conductivity on the NiTe-rich side corresponds to the decrease in the mean free path of the sp-conduction electrons. The thermoelectric power of liquid NiTe strongly depends on the sp–d scattering process of the conduction electrons.
References [1] R.J. Newport, R.A. Howe, J.E. Enderby, J. Phys. C 15 (1982) 4635. [2] C. Tasseven, O. Alcaraz, J. Trullas, M. Silbert, High Temp. Mater. Processes 17 (1998) 163. [3] S. Ohno, M. Togashi, A.C. Barnes, J.E. Enderby, J. Phys. Soc. Jpn. 68 (1999) 2338. [4] S. Ohno, K. Ishida, M. Togashi, A.C. Barnes, J.E. Enderby, J. Phys.: Condens. Matter 12 (2000) 1297. [5] N.F. Mott, Philos. Mag. 24 (1971) 1. [6] P. Strange, A.C. Barnes, J. Phys. F 15 (1985) L263. [7] J.M. Ziman, Electrons Phonons, Oxford University, London, 1960 (Chapter 9).
Electrical properties of liquid NiTe alloys with Ni halides Kanako Ishida a b
a,*
, Satoru Ohno a, Tatsuya Okada
b
Niigata College of Pharmacy, Kamishin’eicho, Niigata 950-2081, Japan Niigata College of Technology, Kamishin’eicho, Niigata 950-2076, Japan
Abstract Liquid NiTe has a large electrical conductivity of 5700 X1 cm1 at the melting point. The decrease in the conductivity on the NiTe side is about 140 and 230 X1 cm1 with the addition of 1 mol% NiCl2 and NiI2 , respectively. Liquid NiTe and molten NiI2 were found to be miscible in all proportions. Molten NiI2 has a conductivity of 35 X1 cm1 at 950 °C. The electrical conductivity on the NiI2 side increases gradually with the addition of NiTe. The composition dependence of the thermoelectric power of molten NiTe–NiI2 mixtures increases gradually from )3 lV/K on the NiTe side to 37.5 lV/K on the NiI2 side. The composition dependence of the conductivity and thermoelectric power for molten NiTe–NiI2 mixtures was analyzed by electronic model of liquid semiconductors. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 72.80.Ph; 72.80.Tm
1. Introduction Liquid NiTe has a large conductivity of 5650 X1 cm1 at 900 °C and a negative temperature coefficient of conductivity [1]. In contrast the ionic conductivities of nickel halides estimated by Tasseven et al. [2] are 4.8, 3.5 and 4.5 X1 cm1 for molten NiCl2 , NiBr2 and NiI2 , respectively. It is not clear that the liquid NiTe and nickel halides are miscible in all proportions. Therefore, we measured the electrical conductivity and the thermoelectric power of molten NiTe–NiX2 (X ¼ I, Cl) mixtures. We present an analysis of the electrical properties of molten NiTe–NiX2 mixtures on
*
Corresponding author. Tel.: +81-25-269-3170; fax: +81-25268-1230. E-mail address: [email protected] (K. Ishida).
the basis of electronic models of liquid semiconductors and molten salts [3]. It is interesting to clarify the contribution to the electrical properties of molten mixtures due to the nickel ions with unoccupied 3d-states.
2. Experimental procedure The electrical conductivity measurements were made using a quartz cell and the four-point-probe method. The four holes of the quartz cell were sealed with four graphite plugs fastened by molybdenum bands. Measurements were carried out under a pressure of about 2.0 MPa helium gas to prevent the evaporation of liquid specimen. The thermoelectric power measurements were made by the DT method. The voltage, DE, between two electrodes was measured by a digital voltmeter.
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 1 7 6 1 - 1
K. Ishida et al. / Journal of Non-Crystalline Solids 312–314 (2002) 396–399
397
The ratio DE=DT gives the thermoelectric power formed by the sample and the molybdenum counter electrode. The absolute thermoelectric power of the liquid sample can be determined by subtracting the thermoelectric power of molybdenum. The NiCl2 and NiI2 are purchased from Aldrich Chemical Company, Inc.
3. Results As shown in Figs. 1 and 2, the temperature dependence of the conductivity for the molten (NiTe)1c (NiI2 )c and (NiTe)1c (NiCl2 )c mixtures is negative for c 6 0:4 and positive for c P 0:5. Molten NiI2 has a conductivity of 35 X1 cm1 , which is larger than that estimated for the molten nickel halide [2]. As shown in Fig. 3, liquid NiTe has a thermoelectric power, S, of )3 lV/K and a positive temperature coefficient of S. The thermoelectric power of the molten NiTe-NiI2 mixtures increases with increasing NiI2 composition and has a positive
Fig. 2. Electrical conductivity as a function of temperature for molten (NiTe)1c (NiI2 )c mixtures with c P 0:58. The arrows indicate the melting point of the mixture. Random errors are about 5%.
Fig. 3. Thermoelectric power as a function of temperature for molten (NITe)1c (NiI2 )c and (NiTe)0:973 (NiCl2 )0:027 mixtures. The arrows indicate the melting point of the mixture. Random errors are about 0.8 lV/K.
Fig. 1. Electrical conductivity as a function of temperature for molten (NiTe)1c (NiI2 )c and (NiTe)1c (NiCl2 )c mixtures for c 6 0:5. The arrows indicate the melting point of the mixture. Random errors are about 3%.
temperature coefficient. The value of S is slightly increased by the addition of 2.7 mol% NiCl2 to liquid NiTe. The thermoelectric power of molten NiI2 is about 37.5 lV/K, which is considerably smaller than that of the molten noble metal halides [3]. Fig. 4 shows the composition dependence of the conductivity and thermoelectric power for molten NiTe–NiX2 (X ¼ I, Cl) mixtures. The conductivity of the liquid mixtures decreases rapidly with the addition of NiX2 to liquid NiTe. The composition
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K. Ishida et al. / Journal of Non-Crystalline Solids 312–314 (2002) 396–399
The electrical conductivity on the NiI2 side increases with the addition of NiTe. The energy gap is a very small value for liquid mixtures in the range 300 6 r 6 3000 X1 cm1 . In this situation, rel in Eq. (1) may be written as [5] rel ¼
Fig. 4. Composition dependence of the conductivity and the thermoelectric power of molten NiTe–NiX2 (X ¼ I, Cl) mixtures. The closed squares and the closed circles indicate the experimental values of r for the molten NiTe–NiI2 and NiTe– NiCl2 mixtures at 950 °C, respectively. The open squares indicate the values of r estimated from the values of ð1 cÞ fNsp ðEF Þ þ Nd ðEF Þg using Eq. (2). The closed triangles indicate the experimental values of S for the molten NiTe–NiI2 mixtures at 950 °C. The open diamonds and closed diamonds indicate the values of ðr =rÞS where S ¼ 500 lV/K, respectively. The lines are a guide for the eye.
dependence of the thermoelectric power of the molten NiTe–NiI2 mixtures increases gradually from )3 lV/K on the NiTe side to 37.5 lV/K on the NiI2 side. 4. Discussion The ionic conductivity estimated by Tasseven et al. [2] is 4.5 X1 cm1 for molten NiI2 . This value is smaller than that obtained experimentally. The conductivity may be given by [3,4] r ¼ rþ þ r þ rel ¼
4nþ e2 Dþ n e2 D þ þ A exp kB T kB T
Ev ; kB T
ð1Þ
where rþ and r are the ionic conductivity due to the Ni2þ ions and I ions, respectively. The values of rþ and r estimated by Tasseven et al. [2] are 3.1 and 1.4 X1 cm1 , respectively. The third term of right hand side in Eq. (1) is the electronic conductivity of molten NiI2 . The other symbols have their usual meaning. The activation energy for conduction electrons, Ev , estimated is about 0.2 eV for molten NiI2 .
p2 e2 h3 L 2 fN ðEF Þg ; 3m2
ð2Þ
where L is the mean free path of conduction electrons and N ðEF Þ is the density of states at EF . We assume that N ðEF Þ in Eq. (2) can be written as ð1 cÞfNsp ðEF Þ þ Nd ðEF Þg for the mixture. The electrical conductivity of the molten mixtures was estimated by using the values of Nsp ðEF Þ and Nd ðEF Þ estimated by Strange and Barnes [6]. It is a reasonable assumption that L is comparable with an interatomic distance, a, in the intermediate range 300 6 r 6 3000 X1 cm1 [5]. As shown in Fig. 4, the composition dependence of conductivity in the intermediate range can be qualitatively explained by this approach. The large difference between rexp and rcal on the NiTe side of the figure may be closely related to the rapid increase in the mean free path of spconduction electrons, Lsp , with decreasing NiI2 composition. It suggests that the electrical conductivity is dominated by the conduction due to the sp-electrons. The thermoelectric power of molten NiI2 is given by [4] þ r r r el S¼ ð3Þ Sþ þ S þ Sel ; r r r where S þ and S are the thermoelectric powers due to the Ni2þ ions and the I ions in molten NiI2 , respectively. The thermoelectric powers for the molten salts suggest that the values of S þ and S in molten NiI2 may be smaller than 500 lV/K [3,4]. The values of fðrþ =rÞS þ þ ðr =rÞS g estimated by putting the values of rþ and r lie in the range of 44 to )20 lV/K for molten NiI2 . The sign of Sel seems to be generally positive because of the d-hole of the Ni ions in molten NiI2 . We examine the composition dependence of the thermoelectric power of molten NiTe–NiI2 mixtures. Assuming that the values of rþ , r and S are 3.1, 1.4 X1 cm1 and 500 lV/K over the whole composition range, we estimated the com-
K. Ishida et al. / Journal of Non-Crystalline Solids 312–314 (2002) 396–399
position dependence of (rþ =rÞS þ and (r =rÞS as shown in Fig. 4. Because of the large values of rel , the composition dependence of S mainly depends on the third term on the right hand side in Eq. (3) in the composition range of c 6 0:8. The thermoelectric power in the intermediate range where 300 6 r 6 3000 X1 cm1 can be written as [5] p2 kB2 T 2 dN ðEF Þ S¼ : ð4Þ 3jej N ðEF Þ dE Eq. (4) can be used for Sel in Eq. (3) under the condition that the mean free paths of the spelectrons and d-electrons are comparable to a. The maximum and minimum values of Sel in Eq. (3) can be estimated from the experimental values of S and the values of (r =rÞS mentioned above. Inserting both values of Sel into S in Eq. (4), we can estimate the maximum and minimum values of dN ðEF Þ=dE. The dN ðEF Þ=dE obtained from this approach lies in the range of )0.10 to )0.15 eV2 atom1 and shows a weak composition dependence. The negative values of dN ðEF Þ=dE obtained experimentally may be closely related to the negative slope in the density of d-like states near EF estimated for liquid NiTe [6]. We briefly consider the change in the sign of S on the NiTe-rich side. As mentioned above, the mean free path of sp-electrons in liquid NiTe is longer than a. The sp-electrons with Lsp a would be scattered into the large density of d-like states at EF . In this process, the mean free path of sp-electrons is given by [7] 1
Lsp LSpd / fNd ðEF Þg :
ð5Þ
According to the sp–d scattering theory [7], the thermoelectric power caused by Eq. (5) can be written as p2 kB2 T 1 dNd ðEF Þ Sspd ¼ : ð6Þ 3jej Nd ðEF Þ dE The negative value of dN ðEF Þ=dE obtained experimentally from Eq. (6) corresponds to the
399
negative slope in the density of d-like states near EF in the NiTe. The change in the sign of S on the NiTe side is caused by the rapid increase in Lsp with decreasing NiI2 composition. This equation may be a major factor for the thermoelectric power of metallic liquids, including the Ni ions with unoccupied 3d-states.
5. Conclusion It was found that the thermoelectric power of molten NiI2 is 37.5 lV/K, which is considerably smaller than that for the silver halides. The smaller value of S in molten NiI2 corresponds to the relatively large electronic conduction in the molten NiI2 . In the intermediate conductivity range, the composition dependence of the conductivity can be explained by the electronic model of liquid semiconductors. The values of dN ðEF Þ=dE obtained from this model lie in the range of )0.10 to )0.15 eV2 atom1 in the composition range 0:3 6 c 6 0:8. The rapid decrease in conductivity on the NiTe-rich side corresponds to the decrease in the mean free path of the sp-conduction electrons. The thermoelectric power of liquid NiTe strongly depends on the sp–d scattering process of the conduction electrons.
References [1] R.J. Newport, R.A. Howe, J.E. Enderby, J. Phys. C 15 (1982) 4635. [2] C. Tasseven, O. Alcaraz, J. Trullas, M. Silbert, High Temp. Mater. Processes 17 (1998) 163. [3] S. Ohno, M. Togashi, A.C. Barnes, J.E. Enderby, J. Phys. Soc. Jpn. 68 (1999) 2338. [4] S. Ohno, K. Ishida, M. Togashi, A.C. Barnes, J.E. Enderby, J. Phys.: Condens. Matter 12 (2000) 1297. [5] N.F. Mott, Philos. Mag. 24 (1971) 1. [6] P. Strange, A.C. Barnes, J. Phys. F 15 (1985) L263. [7] J.M. Ziman, Electrons Phonons, Oxford University, London, 1960 (Chapter 9).