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Electrical measurements on molten TiO2 using a floating zone furnace
Journal of Crystal Growth 237–239 (2002) 1791–1796
Electrical measurements on molten TiO2 using a floating zone furnace T. Katsumata*, T. Shiina, M. Shibasaki, T. Matsuo Faculty of Engineering, Toyo University, 2100 Kujirai Nakanodai, Kawagoe, Saitama 350-8585, Japan
Abstract The electrical properties of high-temperature TiO2 melts were evaluated using a modified floating zone furnace with four ellipsoidal mirrors and Ir electrodes. A droplet of molten TiO2 was suspended with two Ir electrodes. The resistivity of the molten TiO2 decreased in the reducing atmosphere, and with Ta2O5 doping. Thermoelectric power, up to 250 mV, due to the temperature difference at the electrodes, was observed in the specimens with and without Ta2O5 doping in Ar and/or 20% O2–Ar atmospheres. The thermoelectric power of Ta2O5-doped TiO2 is slightly larger than that of non-doped TiO2. This phenomenon is discussed based on the Seebeck effect, the diffusion potential and/or the electrochemical potential. r 2002 Elsevier Science B.V. All rights reserved. Keywords: A1. Floating zone technique; A1. Fluid flows; A1. Growth from melt; A1. Mass transfer; B1. Oxides; B1. Titanium compounds
1. Introduction The electrical evaluations of the molten oxides, from which the crystals were grown, is thought to be a powerful tool to investigate electrochemically the transport phenomenon and interfacial phenomenon between the melt and the electrical conductive crucible material [1,2]. The effects of diffusion potential on the segregation of solute ions have been reported theoretically for the growth of LiNbO3 crystals [3,4]. The electrical potential at the growing interface of LiNbO3 crystal has also been reported [5]. These reports suggest the importance of electrochemical analysis at the growth interface. The interfacial phenom*Corresponding author. Tel.: +81-492-39-1388; fax: +81492-31-1031. E-mail address: [email protected] (T. Katsumata).
enon between the electrical conductive crucible and the molten oxides is also thought to be essential because the crucibles work as the electrodes to the molten oxides during growth. These evaluations were, therefore, important essentially for growing high-quality single crystals. The electrochemical analysis of the molten oxides is also considered to provide useful information for the application of electro-magnetic and/or magnetic stirring techniques for the oxide crystal growth [6,7]. In this paper, the electrical properties of hightemperature TiO2 melts were evaluated using a modified floating zone furnace. Thermoelectric power due to the temperature difference at the electrodes was clearly observed for the molten TiO2 under various conditions of Ta doping and O2 concentrations of atmosphere. The origin of the thermo-electric power is discussed based on the
0022-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 1 ) 0 2 3 4 3 - 0
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T. Katsumata et al. / Journal of Crystal Growth 237–239 (2002) 1791–1796
Seebeck effect, the diffusion potential and/or the difference in the electrochemical potentials at the electrodes.
2. Experiments Fig. 1 shows the equipment for evaluating the electrical properties of molten TiO2. In order to measure the electrical properties of the molten TiO2, a floating zone (FZ) furnace with four ellipsoidal mirrors was modified with two Ir electrodes (Crystal System Co., Japan). The molten TiO2 was suspended with Ir electrodes in the FZ furnace as shown in Fig. 2(a). TiO2 solidified and Ir electrodes are shown in Fig. 2(b). The Ir plates (5 mm 1 mm 40 mm), which are usually used as the crucible material for growing oxide crystals from high-temperature melts, were used as the electrodes. The droplet of molten TiO2 was suspended with two Ir electrodes. The shapes of the droplets were observed using a CCD camera system attached to the FZ furnace. Non-doped and Ta2O5-doped TiO2 were used for the specimens. 4 N TiO2 and 4 N Ta2O5 powders were used as the raw materials. Powders were mixed and sintered at 11501C in air. Sintered
Fig. 2. Droplet of molten TiO2 suspended by the Ir electrodes in the FZ furnace (a). Solidified TiO2 and Ir electrodes after the evaluations are also shown (b).
rods with 8 mm diameter and 40 mm length were used for the measurements. Electrical conductivity was measured using a Kethley 6517A type electrometer with voltage source. The voltage– current (V 2I) curve of the specimen was measured while applying voltage from 1 to +1 V. Resistivity and thermoelectric power were estimated from the V 2I curves of the specimens.
Fig. 1. Equipment for measuring the electrical properties of high-temperature molten TiO2. The floating zone apparatus with four ellipsoidal mirrors was modified with two Ir electrodes.
3. Results and discussion Thermoelectric power due to the temperature difference at the electrodes was clearly observed
T. Katsumata et al. / Journal of Crystal Growth 237–239 (2002) 1791–1796
for the molten TiO2 under various conditions of impurity doping and O2 concentrations of the atmosphere. This phenomenon is explained based on the temperature dependence of the electrochemical potential at the molten TiO2 and Ir electrode interfaces. The V 2I curve of Ta2O5-doped TiO2 melt is shown in Fig. 3. The V 2I curve was measured while applying voltage from 1 to 1 V. Ta2O5doped TiO2 melt shows Ohmic characteristics and a linear correlation between the current and the voltage. The resistivity estimated from the gradient of the fitted lines is 62.5 O in the Ar atmosphere. The resistivity varies with O2 concentration of atmosphere and impurity, Ta2O5, doping into the melt. It increases with O2 concentration, while it decreases with Ta2O5 doping. From Fig. 3, dark current, IV ¼0 ; when applying voltage, V ¼ 0; is estimated to be IV ¼0 ¼ 4:0 mA. Thermo-electric power, VI¼0 ; is estimated from the applying voltage when the current of the circuit is I ¼ 0 mA. Thermo-electric power, VI¼0 ; of Ta2O5-doped molten TiO2 is estimated to be VI¼0 ¼ 250 mV based on Fig. 3.
Fig. 3. V 2I curve of Ta2O5-doped TiO2 melt. The Ta2O5doped TiO2 melt shows Ohmic characteristics, and a linear correlation between the current and the voltage. From the figure, thermoelectric power of 0.25 V is observed at I ¼ 0 mA. Dark current, IV ¼0 ¼ 4:0 mA, is also observed. The resistivity estimated from the gradient of the fitted line is 67 O in the Ar atmosphere.
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V 2I curves of the non-doped TiO2 melt in the pure Ar atmosphere and the Ar atmosphere with 20 vol% of O2 gas are also plotted in Fig. 4. The non-doped TiO2 melt also shows a linear correlation between the current and the voltage both in Ar and 20% O2–Ar atmospheres. The resistivities estimated from the gradient of the fitted lines are 500 and 150 O for 20% O2–Ar and Ar atmospheres, respectively. TiO2 melt is more conductive in the reduced condition as is seen in the TiO2 crystals [8]. Dark currents of non-doped TiO2 are IV ¼0 ¼ 0:029 and 0:16 mA for 20% O2–Ar and Ar atmospheres, respectively. Thermoelectric power of non-doped TiO2 is also estimated to be VI¼0 ¼ 0:031 and 0:018 V for 20% O2–Ar and Ar atmospheres, respectively, from the figure. The thermoelectric power of the molten TiO2 in the reduced atmosphere in Ar is slightly larger than that in 20% O2–Ar atmosphere. The droplet of the molten TiO2 and Ir electrodes in the FZ furnace are illustrated schematically in Fig. 5. Thermoelectric powers of the Ta2O5-doped TiO2 melt were measured at various positions in
Fig. 4. V2I curve of non-doped TiO2 melt in the pure Ar atmosphere and the Ar atmosphere with 20 vol% of O2 gas. The non-doped TiO2 melt shows Ohmic characteristics both in Ar and 20% O2–Ar atmospheres, and a linear correlation between the current and the voltage. From the figure, thermoelectric power of 0.031 and 0.018 V is observed for 20% O2– Ar and Ar, respectively. Dark currents, IV ¼0 ; are 0.029 and 0.16 mA for 20% O2–Ar and Ar, respectively. The resistivities estimated from the gradient of the fitted lines are 500 and 150 O for for 20% O2–Ar and Ar, respectively. The TiO2 melt becomes more conductive in the reduced condition as is seen in the TiO2 crystals.
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Fig. 5. Schematic illustration of molten TiO2 and Ir electrodes in the FZ furnace. The temperatures at the upper and the lower electrodes are represented as T1 and T2 ; respectively. The temperature difference between the upper and the lower electrodes, dT ¼ T1 T2 ; varies with the position in the furnace, L: The condition, dT ¼ T1 T2 ¼ 01C; is obtained at the position, L ¼ 0:
the FZ furnace, L; in Fig. 5. The temperatures, T1 and T2 ; at the interfaces between the melt and the Ir electrodes vary with the position in the furnace, L: When the melt is located at the position, L ¼ 0 mm, the temperature at the upper electrode, T1 ; is the same as that at the lower electrode, T2 : When the melt is located at the position, Lo0 mm, T1 is lower than T2 : The condition, T1 > T2 ; is also achieved when L > 0 mm. Temperature difference between the upper and the lower interfaces, dT ¼ T1 T2 ; varies with the position in the furnace, L: The thermoelectric power of the non-doped TiO2 melt is evaluated at various positions in the FZ furnace in Ar atmosphere. In Fig. 6, thermoelectric power of the molten TiO2 is plotted as the
Fig. 6. Thermoelectric powers of Ta2O5-doped and non-doped TiO2 melts measured at various positions in the FZ furnace, L: Temperature differences, dT ¼ T1 T2 ; vary with the position in the furnace, L: Thermoelectric power decreases linearly as the position, L; increases. In the position, L ¼ 0 mm, where thermoelectric power is 0 V, the upper and the lower electrodes are considered to be at the same temperature, dT ¼ T1 T2 ¼ 01C: The correlations between the position and the thermoelectric power of Ta2O5-doped and non-doped TiO2 melts are quite similar as shown in the figure. The gradients, V=L; of the fitted lines shown in Fig. 6 are 0.038 and 0.042 for the nondoped and Ta2O5-doped specimens, respectively. The Seebeck effects of non-doped TiO2 melt may be slightly smaller than those of the Ta2O5-doped melt.
function of the position in the FZ furnace, L; because the temperature difference of the interfaces, dT ¼ T1 T2 ; varies with the position, L; as shown in Fig. 5. The results for Ta2O5-doped TiO2 and non-doped TiO2 are shown in the figure. The thermoelectric power of the Ta2O5-doped TiO2 melt decreases linearly as the position, L; increases. When the temperature difference between the upper and the lower electrodes, dT ¼ T1 T2 ¼ 01C; at the position, L ¼ 0; thermoelectric power is 0 V. The thermoelectric power varies from 40 to 150 mV with the position, L; from 1 to 4 mm. The thermoelectric power of non-doped TiO2 melt is also measured at various positions, L; in Fig. 6. Thermoelectric power decreases linearly as the position, L; increases. This tendency is similar to that of the Ta2O5-doped TiO2 melt. Thermoelectric power of non-doped TiO2 melt varies from
T. Katsumata et al. / Journal of Crystal Growth 237–239 (2002) 1791–1796
100 to 150 mV with position, L; from 3 to +3 mm. The Seebeck constant of non-doped TiO2 melt may be suggested to be slightly smaller than that in Ta-doped TiO2 melt. The thermo-electric power of the molten TiO2 is considered to be due to the Seebeck effect, liquid potential (in other words, the diffusion current or the diffusion potential) and/or the difference in the electrochemical potential by the difference in the temperatures at Ir molten TiO2 interfaces. According to the Seebeck effect, the electric potential is calculated as follows [8]: dEs ¼ SðT1 T2 Þ:
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thermoelectric power are slightly lower than those in the molten TiO2. This difference may be due to the measuring temperature, the electrode materials, the electrochemical potential and the liquid potential mentioned above. The flow of ions in the droplet of the TiO2 melt suspended with Ir electrodes is schematically shown in Fig. 7(a). The ions in the melt may move
ð1Þ
S means Seebeck constant. dEs is the electrical potential due to the Seebeck effect. T1 and T2 indicate the temperatures at the Ir electrodes. The temperature dependences of the electrochemical potential at the electrodes are also shown by the following equations: 1 Echem ¼ Echem þ RT=nF ln ðkÞ;
ð2Þ
1 þ RðT1 Þ=nF ln k1 dEchem ¼ dEchem
RðT2 Þ=nF ln k2 ;
ð3Þ
where E is the electrochemical potential, T is the temperature at the electrodes, R is the gas constant, n is the number of electrons, F is the Faraday constant, and k is an activity factor. Electrochemical potentials, dEchem ; measured in the experiments are calculated as per Eq. (2). The values of k1 and k2 may vary with the temperature dependences of the ionization of neutral molecules at the electrodes and relative concentration of the oxidation states of Ti ions, Ti3+/Ti4+. The variations in the concentration of ionic species result in the generation of the liquid potential (in other words, diffusion current or diffusion potential) [3–5]. The variations of concentrations may also occur due to the thermal diffusion effect. It is very difficult to evaluate these effects separately because of the high temperature and the melt convections. Based on the Seebeck effect measurements of the solid TiO2 (Rutile), thermoelectric power Q is reported to be from 300 to 700 mV/deg. at temperatures from 3001C to 7001C for partially reduced TiO2 and/or Nb2O5-doped TiO2 using Pt electrodes [8]. These values of the
Fig. 7. Thermoelectric potential and the movements of ions are schematically shown for the molten TiO2 droplet with Ir electrodes, in Fig. 7(a), and the molten oxide in the metal crucible, in Fig. 7(b). A similar phenomenon seen in the droplet of TiO2 may occur in the crucible because the metal crucibles work as the electrodes to the molten oxides. The ions in the melt may move with the electrical potential generated by the thermoelectric power.
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with the electrical potential generated by the thermoelectric power. In the oxide crystal growth using the metal crucibles, similar phenomena may occur generally due to the temperature distribution around the crucible as shown in Fig. 7(b). The transport of ions in the molten oxide may vary with this effect. The thermoelectric effects accelerate the mass transportation in the melt accompanied by the melt convections. It may be clearly detected in m-gravity conditions without convections.
transportation in the melt accompanying the melt convections.
Acknowledgements The authors thank I. Takamura for her help in the experiments. They also thank T. Sato, Y. Shinohara, J. Takahashi and professor S. Komuro for fruitful discussions. This study is carried out as a part of ‘‘Ground Research Announcement for Space Utilization’’ promoted by Japan Space Forum.
4. Conclusions The electrical properties of the high-temperature TiO2 melts were evaluated using a modified floating zone furnace with four ellipsoidal mirrors and the Ir electrodes. The resistivity of the molten TiO2 was measured with and without Ta2O5 doping in Ar and/or 20% O2–Ar atmospheres. Thermoelectric power was also observed in the specimens with and without Ta2O5 doping in Ar and/or 20% O2–Ar atmospheres. The thermoelectric power is considered to be partially due to the Seebeck effect, together with the diffusion potential and/or the temperature dependence of the electrochemical potential. The transport of ions in molten oxide may vary with this effect. The thermoelectric potential accelerates the mass
References [1] T. Katsumata, N. Suzuki, M. Shibasaki, T. Matsuo, in: N. Ramachandran (Ed.), The Proceedings of SPIE, 19–21 July, 1999, Denver, 1999, p. 242. [2] T. Katsumata, N. Suzuki, N. Saito, M. Shibasaki, T. Matsuo, in: The Proceedings of Electrochemical Society, Vol. 99–41, 2000, p. 383. [3] S. Uda, W.A. Tiller, J. Crystal Growth 121 (1992) 155. [4] S. Uda, W.A. Tiller, J. Crystal Growth 121 (1992) 93. [5] V.A. D’yakov, D.P. Shumov, L.N. Rashkovich, A.L. Aleksandrovskii, Bull. Acad. Sci. USSR, Phys. Ser. 49 (1986) 117. [6] M. Watanabe, M. Eguchi, T. Hibiya, Jpn. J. Appl. Phys. 38 (1999) L10. [7] Y. Miyazawa, S. Morita, H. Sekiwa, J. Crystal Growth 166 (1996) 286. [8] H.P.R. Frederikse, J. Appl. Phys. 32 (1961) 2211.
Electrical measurements on molten TiO2 using a floating zone furnace T. Katsumata*, T. Shiina, M. Shibasaki, T. Matsuo Faculty of Engineering, Toyo University, 2100 Kujirai Nakanodai, Kawagoe, Saitama 350-8585, Japan
Abstract The electrical properties of high-temperature TiO2 melts were evaluated using a modified floating zone furnace with four ellipsoidal mirrors and Ir electrodes. A droplet of molten TiO2 was suspended with two Ir electrodes. The resistivity of the molten TiO2 decreased in the reducing atmosphere, and with Ta2O5 doping. Thermoelectric power, up to 250 mV, due to the temperature difference at the electrodes, was observed in the specimens with and without Ta2O5 doping in Ar and/or 20% O2–Ar atmospheres. The thermoelectric power of Ta2O5-doped TiO2 is slightly larger than that of non-doped TiO2. This phenomenon is discussed based on the Seebeck effect, the diffusion potential and/or the electrochemical potential. r 2002 Elsevier Science B.V. All rights reserved. Keywords: A1. Floating zone technique; A1. Fluid flows; A1. Growth from melt; A1. Mass transfer; B1. Oxides; B1. Titanium compounds
1. Introduction The electrical evaluations of the molten oxides, from which the crystals were grown, is thought to be a powerful tool to investigate electrochemically the transport phenomenon and interfacial phenomenon between the melt and the electrical conductive crucible material [1,2]. The effects of diffusion potential on the segregation of solute ions have been reported theoretically for the growth of LiNbO3 crystals [3,4]. The electrical potential at the growing interface of LiNbO3 crystal has also been reported [5]. These reports suggest the importance of electrochemical analysis at the growth interface. The interfacial phenom*Corresponding author. Tel.: +81-492-39-1388; fax: +81492-31-1031. E-mail address: [email protected] (T. Katsumata).
enon between the electrical conductive crucible and the molten oxides is also thought to be essential because the crucibles work as the electrodes to the molten oxides during growth. These evaluations were, therefore, important essentially for growing high-quality single crystals. The electrochemical analysis of the molten oxides is also considered to provide useful information for the application of electro-magnetic and/or magnetic stirring techniques for the oxide crystal growth [6,7]. In this paper, the electrical properties of hightemperature TiO2 melts were evaluated using a modified floating zone furnace. Thermoelectric power due to the temperature difference at the electrodes was clearly observed for the molten TiO2 under various conditions of Ta doping and O2 concentrations of atmosphere. The origin of the thermo-electric power is discussed based on the
0022-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 1 ) 0 2 3 4 3 - 0
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T. Katsumata et al. / Journal of Crystal Growth 237–239 (2002) 1791–1796
Seebeck effect, the diffusion potential and/or the difference in the electrochemical potentials at the electrodes.
2. Experiments Fig. 1 shows the equipment for evaluating the electrical properties of molten TiO2. In order to measure the electrical properties of the molten TiO2, a floating zone (FZ) furnace with four ellipsoidal mirrors was modified with two Ir electrodes (Crystal System Co., Japan). The molten TiO2 was suspended with Ir electrodes in the FZ furnace as shown in Fig. 2(a). TiO2 solidified and Ir electrodes are shown in Fig. 2(b). The Ir plates (5 mm 1 mm 40 mm), which are usually used as the crucible material for growing oxide crystals from high-temperature melts, were used as the electrodes. The droplet of molten TiO2 was suspended with two Ir electrodes. The shapes of the droplets were observed using a CCD camera system attached to the FZ furnace. Non-doped and Ta2O5-doped TiO2 were used for the specimens. 4 N TiO2 and 4 N Ta2O5 powders were used as the raw materials. Powders were mixed and sintered at 11501C in air. Sintered
Fig. 2. Droplet of molten TiO2 suspended by the Ir electrodes in the FZ furnace (a). Solidified TiO2 and Ir electrodes after the evaluations are also shown (b).
rods with 8 mm diameter and 40 mm length were used for the measurements. Electrical conductivity was measured using a Kethley 6517A type electrometer with voltage source. The voltage– current (V 2I) curve of the specimen was measured while applying voltage from 1 to +1 V. Resistivity and thermoelectric power were estimated from the V 2I curves of the specimens.
Fig. 1. Equipment for measuring the electrical properties of high-temperature molten TiO2. The floating zone apparatus with four ellipsoidal mirrors was modified with two Ir electrodes.
3. Results and discussion Thermoelectric power due to the temperature difference at the electrodes was clearly observed
T. Katsumata et al. / Journal of Crystal Growth 237–239 (2002) 1791–1796
for the molten TiO2 under various conditions of impurity doping and O2 concentrations of the atmosphere. This phenomenon is explained based on the temperature dependence of the electrochemical potential at the molten TiO2 and Ir electrode interfaces. The V 2I curve of Ta2O5-doped TiO2 melt is shown in Fig. 3. The V 2I curve was measured while applying voltage from 1 to 1 V. Ta2O5doped TiO2 melt shows Ohmic characteristics and a linear correlation between the current and the voltage. The resistivity estimated from the gradient of the fitted lines is 62.5 O in the Ar atmosphere. The resistivity varies with O2 concentration of atmosphere and impurity, Ta2O5, doping into the melt. It increases with O2 concentration, while it decreases with Ta2O5 doping. From Fig. 3, dark current, IV ¼0 ; when applying voltage, V ¼ 0; is estimated to be IV ¼0 ¼ 4:0 mA. Thermo-electric power, VI¼0 ; is estimated from the applying voltage when the current of the circuit is I ¼ 0 mA. Thermo-electric power, VI¼0 ; of Ta2O5-doped molten TiO2 is estimated to be VI¼0 ¼ 250 mV based on Fig. 3.
Fig. 3. V 2I curve of Ta2O5-doped TiO2 melt. The Ta2O5doped TiO2 melt shows Ohmic characteristics, and a linear correlation between the current and the voltage. From the figure, thermoelectric power of 0.25 V is observed at I ¼ 0 mA. Dark current, IV ¼0 ¼ 4:0 mA, is also observed. The resistivity estimated from the gradient of the fitted line is 67 O in the Ar atmosphere.
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V 2I curves of the non-doped TiO2 melt in the pure Ar atmosphere and the Ar atmosphere with 20 vol% of O2 gas are also plotted in Fig. 4. The non-doped TiO2 melt also shows a linear correlation between the current and the voltage both in Ar and 20% O2–Ar atmospheres. The resistivities estimated from the gradient of the fitted lines are 500 and 150 O for 20% O2–Ar and Ar atmospheres, respectively. TiO2 melt is more conductive in the reduced condition as is seen in the TiO2 crystals [8]. Dark currents of non-doped TiO2 are IV ¼0 ¼ 0:029 and 0:16 mA for 20% O2–Ar and Ar atmospheres, respectively. Thermoelectric power of non-doped TiO2 is also estimated to be VI¼0 ¼ 0:031 and 0:018 V for 20% O2–Ar and Ar atmospheres, respectively, from the figure. The thermoelectric power of the molten TiO2 in the reduced atmosphere in Ar is slightly larger than that in 20% O2–Ar atmosphere. The droplet of the molten TiO2 and Ir electrodes in the FZ furnace are illustrated schematically in Fig. 5. Thermoelectric powers of the Ta2O5-doped TiO2 melt were measured at various positions in
Fig. 4. V2I curve of non-doped TiO2 melt in the pure Ar atmosphere and the Ar atmosphere with 20 vol% of O2 gas. The non-doped TiO2 melt shows Ohmic characteristics both in Ar and 20% O2–Ar atmospheres, and a linear correlation between the current and the voltage. From the figure, thermoelectric power of 0.031 and 0.018 V is observed for 20% O2– Ar and Ar, respectively. Dark currents, IV ¼0 ; are 0.029 and 0.16 mA for 20% O2–Ar and Ar, respectively. The resistivities estimated from the gradient of the fitted lines are 500 and 150 O for for 20% O2–Ar and Ar, respectively. The TiO2 melt becomes more conductive in the reduced condition as is seen in the TiO2 crystals.
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Fig. 5. Schematic illustration of molten TiO2 and Ir electrodes in the FZ furnace. The temperatures at the upper and the lower electrodes are represented as T1 and T2 ; respectively. The temperature difference between the upper and the lower electrodes, dT ¼ T1 T2 ; varies with the position in the furnace, L: The condition, dT ¼ T1 T2 ¼ 01C; is obtained at the position, L ¼ 0:
the FZ furnace, L; in Fig. 5. The temperatures, T1 and T2 ; at the interfaces between the melt and the Ir electrodes vary with the position in the furnace, L: When the melt is located at the position, L ¼ 0 mm, the temperature at the upper electrode, T1 ; is the same as that at the lower electrode, T2 : When the melt is located at the position, Lo0 mm, T1 is lower than T2 : The condition, T1 > T2 ; is also achieved when L > 0 mm. Temperature difference between the upper and the lower interfaces, dT ¼ T1 T2 ; varies with the position in the furnace, L: The thermoelectric power of the non-doped TiO2 melt is evaluated at various positions in the FZ furnace in Ar atmosphere. In Fig. 6, thermoelectric power of the molten TiO2 is plotted as the
Fig. 6. Thermoelectric powers of Ta2O5-doped and non-doped TiO2 melts measured at various positions in the FZ furnace, L: Temperature differences, dT ¼ T1 T2 ; vary with the position in the furnace, L: Thermoelectric power decreases linearly as the position, L; increases. In the position, L ¼ 0 mm, where thermoelectric power is 0 V, the upper and the lower electrodes are considered to be at the same temperature, dT ¼ T1 T2 ¼ 01C: The correlations between the position and the thermoelectric power of Ta2O5-doped and non-doped TiO2 melts are quite similar as shown in the figure. The gradients, V=L; of the fitted lines shown in Fig. 6 are 0.038 and 0.042 for the nondoped and Ta2O5-doped specimens, respectively. The Seebeck effects of non-doped TiO2 melt may be slightly smaller than those of the Ta2O5-doped melt.
function of the position in the FZ furnace, L; because the temperature difference of the interfaces, dT ¼ T1 T2 ; varies with the position, L; as shown in Fig. 5. The results for Ta2O5-doped TiO2 and non-doped TiO2 are shown in the figure. The thermoelectric power of the Ta2O5-doped TiO2 melt decreases linearly as the position, L; increases. When the temperature difference between the upper and the lower electrodes, dT ¼ T1 T2 ¼ 01C; at the position, L ¼ 0; thermoelectric power is 0 V. The thermoelectric power varies from 40 to 150 mV with the position, L; from 1 to 4 mm. The thermoelectric power of non-doped TiO2 melt is also measured at various positions, L; in Fig. 6. Thermoelectric power decreases linearly as the position, L; increases. This tendency is similar to that of the Ta2O5-doped TiO2 melt. Thermoelectric power of non-doped TiO2 melt varies from
T. Katsumata et al. / Journal of Crystal Growth 237–239 (2002) 1791–1796
100 to 150 mV with position, L; from 3 to +3 mm. The Seebeck constant of non-doped TiO2 melt may be suggested to be slightly smaller than that in Ta-doped TiO2 melt. The thermo-electric power of the molten TiO2 is considered to be due to the Seebeck effect, liquid potential (in other words, the diffusion current or the diffusion potential) and/or the difference in the electrochemical potential by the difference in the temperatures at Ir molten TiO2 interfaces. According to the Seebeck effect, the electric potential is calculated as follows [8]: dEs ¼ SðT1 T2 Þ:
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thermoelectric power are slightly lower than those in the molten TiO2. This difference may be due to the measuring temperature, the electrode materials, the electrochemical potential and the liquid potential mentioned above. The flow of ions in the droplet of the TiO2 melt suspended with Ir electrodes is schematically shown in Fig. 7(a). The ions in the melt may move
ð1Þ
S means Seebeck constant. dEs is the electrical potential due to the Seebeck effect. T1 and T2 indicate the temperatures at the Ir electrodes. The temperature dependences of the electrochemical potential at the electrodes are also shown by the following equations: 1 Echem ¼ Echem þ RT=nF ln ðkÞ;
ð2Þ
1 þ RðT1 Þ=nF ln k1 dEchem ¼ dEchem
RðT2 Þ=nF ln k2 ;
ð3Þ
where E is the electrochemical potential, T is the temperature at the electrodes, R is the gas constant, n is the number of electrons, F is the Faraday constant, and k is an activity factor. Electrochemical potentials, dEchem ; measured in the experiments are calculated as per Eq. (2). The values of k1 and k2 may vary with the temperature dependences of the ionization of neutral molecules at the electrodes and relative concentration of the oxidation states of Ti ions, Ti3+/Ti4+. The variations in the concentration of ionic species result in the generation of the liquid potential (in other words, diffusion current or diffusion potential) [3–5]. The variations of concentrations may also occur due to the thermal diffusion effect. It is very difficult to evaluate these effects separately because of the high temperature and the melt convections. Based on the Seebeck effect measurements of the solid TiO2 (Rutile), thermoelectric power Q is reported to be from 300 to 700 mV/deg. at temperatures from 3001C to 7001C for partially reduced TiO2 and/or Nb2O5-doped TiO2 using Pt electrodes [8]. These values of the
Fig. 7. Thermoelectric potential and the movements of ions are schematically shown for the molten TiO2 droplet with Ir electrodes, in Fig. 7(a), and the molten oxide in the metal crucible, in Fig. 7(b). A similar phenomenon seen in the droplet of TiO2 may occur in the crucible because the metal crucibles work as the electrodes to the molten oxides. The ions in the melt may move with the electrical potential generated by the thermoelectric power.
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with the electrical potential generated by the thermoelectric power. In the oxide crystal growth using the metal crucibles, similar phenomena may occur generally due to the temperature distribution around the crucible as shown in Fig. 7(b). The transport of ions in the molten oxide may vary with this effect. The thermoelectric effects accelerate the mass transportation in the melt accompanied by the melt convections. It may be clearly detected in m-gravity conditions without convections.
transportation in the melt accompanying the melt convections.
Acknowledgements The authors thank I. Takamura for her help in the experiments. They also thank T. Sato, Y. Shinohara, J. Takahashi and professor S. Komuro for fruitful discussions. This study is carried out as a part of ‘‘Ground Research Announcement for Space Utilization’’ promoted by Japan Space Forum.
4. Conclusions The electrical properties of the high-temperature TiO2 melts were evaluated using a modified floating zone furnace with four ellipsoidal mirrors and the Ir electrodes. The resistivity of the molten TiO2 was measured with and without Ta2O5 doping in Ar and/or 20% O2–Ar atmospheres. Thermoelectric power was also observed in the specimens with and without Ta2O5 doping in Ar and/or 20% O2–Ar atmospheres. The thermoelectric power is considered to be partially due to the Seebeck effect, together with the diffusion potential and/or the temperature dependence of the electrochemical potential. The transport of ions in molten oxide may vary with this effect. The thermoelectric potential accelerates the mass
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